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Casio ALGEBRA FX 2.0 Plus Calculator User's Guide PDF
Summary of Content for Casio ALGEBRA FX 2.0 Plus Calculator User's Guide PDF
ALGEBRA FX 2.0 PLUS FX 1.0 PLUS
Users Guide
E
CASIO Worldwide Education Website
http://edu.casio.com CASIO EDUCATIONAL FORUM
http://edu.casio.com/forum/
GUIDELINES LAID DOWN BY FCC RULES FOR USE OF THE UNIT IN THE U.S.A. (not appli- cable to other areas).
NOTICE This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protec- tion against harmful interference in a residential installation. This equipment generates, uses and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures:
Reorient or relocate the receiving antenna. Increase the separation between the equipment and receiver. Connect the equipment into an outlet on a circuit different from that to which the receiver is
connected. Consult the dealer or an experienced radio/TV technician for help.
FCC WARNING Changes or modifications not expressly approved by the party responsible for compliance could void the users authority to operate the equipment. Proper connectors must be used for connection to host computer and/or peripherals in order to meet FCC emission limits.
Connector SB-62 Power Graphic Unit to Power Graphic Unit Connector FA-123 Power Graphic Unit to PC for IBM/Macintosh Machine
IBM is a registered trademark of International Business Machines Corporation. Macintosh is a registered trademark of Apple Computer, Inc.
Declaration of Conformity Model Number: ALGEBRA FX 2.0 PLUS / FX 1.0 PLUS Trade Name: CASIO COMPUTER CO., LTD. Responsible party: CASIO AMERICA, INC. Address: 570 MT. PLEASANT AVENUE, DOVER, NEW JERSEY 07801 Telephone number: 973-361-5400
This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) This device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation.
FOR CALIFORNIA USA ONLY Perchlorate Material special handling may apply. See
www.dtsc.ca.gov/hazardouswaste/perchlorate.
BEFORE USING THE CALCULATOR FOR THE FIRST TIME... This calculator does not contain any main batteries when you purchase it. Be sure to perform the following procedure to load batteries, reset the calculator, and adjust the contrast before trying to use the calculator for the first time.
1. Making sure that you do not accidently press the o key, slide the case onto the calculator and then turn the calculator over. Remove the back cover from the calculator by pulling with your finger at the point marked 1.
2. Load the four batteries that come with calculator.
Make sure that the positive (+) and negative () ends of the batteries are facing cor- rectly.
3. Remove the insulating sheet at the location marked BACK UP by pulling in the direc- tion indicated by the arrow.
4. Replace the back cover, making sure that its tabs enter the holes marked 2 and turn the calculator front side up. The calculator should automatically turn on power and perform the memory reset operation.
P
1
BACK UP
BACK UP
2
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P button
5. Press m.
If the Main Menu shown to the right is not on the display, press the P button on the back of the calculator to perform memory reset.
6. Use the cursor keys (f, c, d, e) to select the SYSTEM icon and press w, then press 2( ) to display the contrast adjustment screen.
7. Adjust the contrast.
The e cursor key makes display contrast darker.
The d cursor key makes display contrast lighter.
1(INIT) returns display contrast to its initial default.
8. To exit display contrast adjustment, press m.
* The above shows the ALGEBRA FX 2.0 PLUS screen.
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Turning Power On And Off Using Modes
Basic Calculations
Replay Feature Fraction Calculations
Exponents
Graph Functions
Dual Graph Box Zoom
Dynamic Graph
Table Function
Quick-Start
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Quick-Start Welcome to the world of graphing calculators.
Quick-Start is not a complete tutorial, but it takes you through many of the most common functions, from turning the power on, and on to graphing complex equations. When youre done, youll have mastered the basic operation of this calculator and will be ready to proceed with the rest of this users guide to learn the entire spectrum of functions available.
Each step of the examples in Quick-Start is shown graphically to help you follow along quickly and easily. When you need to enter the number 57, for example, weve indi- cated it as follows:
Press fh Whenever necessary, weve included samples of what your screen should look like. If you find that your screen doesnt match the sample, you can restart from the begin- ning by pressing the All Clear button o.
TURNING POWER ON AND OFF To turn power on, press o.
To turn power off, press !o OFF
.
Calculator power turns off automatically if you do not perform any operation within the Auto Power Off trigger time you specify. You can specify either six minutes or 60 minutes as the trigger time.
USING MODES This calculator makes it easy to perform a wide range of calculations by simply selecting the appropriate mode. Before getting into actual calculations and operation examples, lets take a look at how to navigate around the modes.
To select the RUN MAT Mode 1. Press m to display the Main Menu.
1 Quick-Start
* The above shows the ALGEBRA FX 2.0 PLUS screen.
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2. Use defc to highlight RUN MAT
and then press w.
This is the initial screen of the RUN MAT Mode, where you can perform manual calculations, matrix calculations, and run programs.
BASIC CALCULATIONS With manual calculations, you input formulas from left to right, just as they are written on paper. With formulas that include mixed arithmetic operators and parentheses, the calculator automatically applies true algebraic logic to calculate the result.
Example: 15 3 + 61
1. Press o to clear the calculator.
2. Pressbf*d+gbw.
Parentheses Calculations Example: 15 (3 + 61)
1. Pressbf*(d +gb)w.
Built-In Functions This calculator includes a number of built-in scientific functions, including trigonometric and logarithmic functions.
Example: 25 sin 45
Important!
Be sure that you specify Deg (degrees) as the angle unit before you try this example.
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1. Pressu3 SET UP
to display the SET UP screen.
2. Presscccc1 (Deg) to specify
degrees as the angle unit.
3. Pressi to clear the menu.
4. Presso to clear the unit.
5. Presscf*sefw.
REPLAY FEATURE With the replay feature, simply press d or e to recall the last calculation that was performed so you can make changes or re-execute it as it is.
Example: To change the calculation in the last example from (25 sin 45) to (25 sin 55)
1. Press d to display the last calculation.
2. Press d twice to move the cursor (t) to 4.
3. Press D to delete 4.
4. Press f.
5. Press w to execute the calculation again.
3 Quick-Start
REPLAY
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FRACTION CALCULATIONS You can use the $ key to input fractions into calculations. The symbol { is used to separate the various parts of a fraction.
Example: 1 15/16 + 37/9
1. Presso.
2. Pressb$bf$ bg+dh$ jw.
Converting a Mixed Fraction to an Improper Fraction
While a mixed fraction is shown on the display, press ! d/c
$to convert it to an improper fraction.
Press ! d/c
$again to convert back to a mixed fraction.
Converting a Fraction to Its Decimal Equivalent While a fraction is shown on the display, press $ to convert it to its decimal equivalent.
Press $ again to convert back to a fraction.
Indicates 6 7/144
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EXPONENTS
Example: 1250 2.065
1. Presso.
2. Pressbcfa*c.ag.
3. PressM and the ^ indicator appears on the display.
4. Pressf. The ^5 on the display indicates that 5 is an exponent.
5. Pressw.
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GRAPH FUNCTIONS The graphing capabilities of this calculator makes it possible to draw complex graphs using either rectangular coordinates (horizontal axis: x ; vertical axis: y) or polar coordinates (angle: ; distance from origin: r). All of the following graphing examples are performed starting from the calculator setup in effect immediately following a reset operation.
Example 1: To graph Y = X(X + 1)(X 2)
1. Press m.
2. Use defc to highlight
GRPH TBL, and then press w.
3. Input the formula.
v(v+b) (v-c)w
4. Press 5(DRAW) or w to draw the graph.
Example 2: To determine the roots of Y = X(X + 1)(X 2)
1. Press 4(G-SLV) to display the pull-up menu.
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2. Press b(Root).
Press e for other roots.
Example 3: Determine the area bounded by the origin and the X = 1 root obtained for Y = X(X + 1)(X 2)
1. Press i4(G-SLV)c.
2. Press i(dx).
3. Use d to move the pointer to the location where
X = 1, and then press w. Next, use to
move the pointer to the location where X = 0, and
then press w to input the integration range,
which becomes shaded on the display.
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DUAL GRAPH With this function you can split the display between two areas and display two graphs on the same screen.
Example: To draw the following two graphs and determine the points of intersection
Y1 = X(X + 1)(X 2) Y2 = X + 1.2
1. Press u3 SET UP
ccc2(G+G)
to specify G+G for the Dual Screen setting.
2. Press i, and then input the two functions.
v(v+b) (v-c)w v+b.cw
3. Press 5(DRAW) or w to draw the graphs.
BOX ZOOM Use the Box Zoom function to specify areas of a graph for enlargement.
1. Press 2(ZOOM) b(Box).
2. Use d e f c to move the pointer to one corner of the area you want to specify and then press w.
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3. Use d e f c to move the pointer again. As you do, a box appears on the display. Move the pointer so the box encloses the area you want to enlarge.
4. Press w, and the enlarged area appears in the inactive (right side) screen.
DYNAMIC GRAPH Dynamic Graph lets you see how the shape of a graph is affected as the value assigned to one of the coefficients of its function changes.
Example: To draw graphs as the value of coefficient A in the following function changes from 1 to 3
Y = AX2
1. Press m.
2. Use d e f c to highlight DYNA,
and then press w.
3. Input the formula.
av A
vxw
12356
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4. Press 4(VAR) bw to assign an initial value of 1 to coefficient A.
5. Press 2(RANG) bwdwb wto specify the range and increment of change in coefficient A.
6. Press i.
7. Press 6(DYNA) to start Dynamic Graph drawing. The graphs are drawn 10 times.
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TABLE FUNCTION The Table Function makes it possible to generate a table of solutions as different values are assigned to the variables of a function.
Example: To create a number table for the following function
Y = X (X+1) (X2)
1. Press m.
2. Use defc to highlight
GRPH TBL, and then press w.
3. Input the formula.
v(v+b) (v-c)w
4. Press 6(g)5(TABL) to generate the number table.
To learn all about the many powerful features of this calculator, read on and explore!
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Handling Precautions Your calculator is made up of precision components. Never try to take it apart.
Avoid dropping your calculator and subjecting it to strong impact.
Do not store the calculator or leave it in areas exposed to high temperatures or humidity, or large amounts of dust. When exposed to low temperatures, the calculator may require more time to display results and may even fail to operate. Correct operation will resume once the calculator is brought back to normal temperature.
The display will go blank and keys will not operate during calculations. When you are operating the keyboard, be sure to watch the display to make sure that all your key operations are being performed correctly.
Replace the main batteries once every 2 years regardless of how much the calculator is used during that period. Never leave dead batteries in the battery compartment. They can leak and damage the unit.
Keep batteries out of the reach of small children. If swallowed, consult a physician immediately.
Avoid using volatile liquids such as thinner or benzine to clean the unit. Wipe it with a soft, dry cloth, or with a cloth that has been moistened with a solution of water and a neutral detergent and wrung out.
Always be gentle when wiping dust off the display to avoid scratching it.
In no event will the manufacturer and its suppliers be liable to you or any other person for any damages, expenses, lost profits, lost savings or any other damages arising out of loss of data and/or formulas arising out of malfunction, repairs, or battery replacement. It is up to you to prepare physical records of data to protect against such data loss.
Never dispose of batteries, the liquid crystal panel, or other components by burning them.
When the Low Main Batteries! message or the Low Backup Battery! message appears on the display, replace the main power supply batteries or the back up battery as soon as possible.
Be sure that the power switch is set to OFF when replacing batteries.
If the calculator is exposed to a strong electrostatic charge, its memory contents may be damaged or the keys may stop working. In such a case, perform the Reset operation to clear the memory and restore normal key operation.
If the calculator stops operating correctly for some reason, use a thin, pointed object to press the P button on the back of the calculator. Note, however, that this clears all the data in calculator memory.
Note that strong vibration or impact during program execution can cause execution to stop or can damage the calculators memory contents.
Using the calculator near a television or radio can cause interference with TV or radio reception.
Before assuming malfunction of the unit, be sure to carefully reread this users guide and ensure that the problem is not due to insufficient battery power, programming or operational errors.
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Be sure to keep physical records of all important data! Low battery power or incorrect replacement of the batteries that power the unit can cause the data stored in memory to be corrupted or even lost entirely. Stored data can also be affected by strong electrostatic charge or strong impact. It is up to you to keep back up copies of data to protect against its loss.
In no event shall CASIO Computer Co., Ltd. be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
The contents of this users guide are subject to change without notice.
No part of this users guide may be reproduced in any form without the express written consent of the manufacturer.
The options described in Chapter 10 of this users guide may not be available in certain geographic areas. For full details on availability in your area, contact your nearest CASIO dealer or distributor.
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ALGEBRA FX 2.0 PLUS FX 1.0 PLUS
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Contents
Getting Acquainted Read This First!
Chapter 1 Basic Operation 1-1 Keys ................................................................................................. 1-1-1 1-2 Display .............................................................................................. 1-2-1 1-3 Inputting and Editing Calculations .................................................... 1-3-1 1-4 Option (OPTN) Menu ....................................................................... 1-4-1 1-5 Variable Data (VARS) Menu ............................................................. 1-5-1 1-6 Program (PRGM) Menu ................................................................... 1-6-1 1-7 Using the Set Up Screen .................................................................. 1-7-1 1-8 When you keep having problems ................................................. 1-8-1
Chapter 2 Manual Calculations 2-1 Basic Calculations ............................................................................ 2-1-1 2-2 Special Functions ............................................................................. 2-2-1 2-3 Specifying the Angle Unit and Display Format ................................. 2-3-1 2-4 Function Calculations ....................................................................... 2-4-1 2-5 Numerical Calculations ..................................................................... 2-5-1 2-6 Complex Number Calculations ......................................................... 2-6-1 2-7 Binary, Octal, Decimal, and Hexadecimal Calculations
with Integers ..................................................................................... 2-7-1 2-8 Matrix Calculations ........................................................................... 2-8-1
Chapter 3 List Function 3-1 Inputting and Editing a List ............................................................... 3-1-1 3-2 Manipulating List Data ...................................................................... 3-2-1 3-3 Arithmetic Calculations Using Lists .................................................. 3-3-1 3-4 Switching Between List Files ............................................................ 3-4-1
Chapter 4 Equation Calculations 4-1 Simultaneous Linear Equations ........................................................ 4-1-1 4-2 Higher Degree Equations ................................................................. 4-2-1 4-3 Solve Calculations ............................................................................ 4-3-1 4-4 What to Do When an Error Occurs ................................................... 4-4-1
1 Contents
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Chapter 5 Graphing 5-1 Sample Graphs ................................................................................ 5-1-1 5-2 Controlling What Appears on a Graph Screen ................................. 5-2-1 5-3 Drawing a Graph .............................................................................. 5-3-1 5-4 Storing a Graph in Picture Memory .................................................. 5-4-1 5-5 Drawing Two Graphs on the Same Screen ...................................... 5-5-1 5-6 Manual Graphing .............................................................................. 5-6-1 5-7 Using Tables ..................................................................................... 5-7-1 5-8 Dynamic Graphing ............................................................................ 5-8-1 5-9 Graphing a Recursion Formula ........................................................ 5-9-1
5-10 Changing the Appearance of a Graph ............................................ 5-10-1 5-11 Function Analysis ........................................................................... 5-11-1
Chapter 6 Statistical Graphs and Calculations 6-1 Before Performing Statistical Calculations ....................................... 6-1-1 6-2 Calculating and Graphing Single-Variable Statistical Data ............... 6-2-1 6-3 Calculating and Graphing Paired-Variable Statistical Data .............. 6-3-1 6-4 Performing Statistical Calculations ................................................... 6-4-1
Chapter 7 Computer Algebra System and Tutorial Modes (ALGEBRA FX 2.0 PLUS only)
7-1 Using the CAS (Computer Algebra System) Mode .......................... 7-1-1 7-2 Algebra Mode ................................................................................... 7-2-1 7-3 Tutorial Mode .................................................................................... 7-3-1 7-4 Algebra System Precautions ............................................................ 7-4-1
Chapter 8 Programming 8-1 Basic Programming Steps ................................................................ 8-1-1 8-2 Program Mode Function Keys .......................................................... 8-2-1 8-3 Editing Program Contents ................................................................ 8-3-1 8-4 File Management .............................................................................. 8-4-1 8-5 Command Reference ....................................................................... 8-5-1 8-6 Using Calculator Functions in Programs .......................................... 8-6-1 8-7 Program Mode Command List ......................................................... 8-7-1 8-8 Program Library ................................................................................ 8-8-1
Chapter 9 System Settings Menu 9-1 Using the System Settings Menu ..................................................... 9-1-1 9-2 Memory Operations .......................................................................... 9-2-1 9-3 System Settings ............................................................................... 9-3-1 9-4 Reset ................................................................................................ 9-4-1 9-5 Tutorial Lock (ALGEBRA FX 2.0 PLUS only) ................................... 9-5-1
2 Contents
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3 Contents
Chapter 10 Data Communications 10-1 Connecting Two Units .................................................................. 10-1-1 10-2 Connecting the Unit with a CASIO Label Printer .......................... 10-2-1 10-3 Connecting the Unit to a Personal Computer ............................... 10-3-1 10-4 Performing a Data Communication Operation ............................. 10-4-1 10-5 Data Communications Precautions .............................................. 10-5-1 10-6 Sending a Screen Shot ................................................................ 10-6-1 10-7 Add-ins ......................................................................................... 10-7-1 10-8 MEMORY Mode ........................................................................... 10-8-1
Appendix 1 Error Message Table ........................................................................... -1-1 2 Input Ranges .......................................................................................-2-1 3 Specifications .......................................................................................-3-1 4 Index ....................................................................................................-4-1 5 Key Index .............................................................................................-5-1 6 P Button (In case of hang up) ............................................................. -6-1 7 Power Supply .......................................................................................-7-1
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Additional Functions
Chapter 1 Advanced Statistics Application 1-1 Advanced Statistics (STAT) .............................................................. 1-1-1 1-2 Tests (TEST) .................................................................................... 1-2-1 1-3 Confidence Interval (INTR) ............................................................... 1-3-1 1-4 Distribution (DIST) ............................................................................ 1-4-1
Chapter 2 Financial Calculation (TVM) 2-1 Before Performing Financial Calculations ........................................ 2-1-1 2-2 Simple Interest ................................................................................. 2-2-1 2-3 Compound Interest ........................................................................... 2-3-1 2-4 Cash Flow (Investment Appraisal) .................................................... 2-4-1 2-5 Amortization ..................................................................................... 2-5-1 2-6 Interest Rate Conversion .................................................................. 2-6-1 2-7 Cost, Selling Price, Margin ............................................................... 2-7-1 2-8 Day/Date Calculations ...................................................................... 2-8-1 2-9 Depreciation ..................................................................................... 2-9-1
2-10 Bonds ............................................................................................. 2-10-1 2-11 TVM Graph ..................................................................................... 2-11-1
Chapter 3 Differential Equations 3-1 Using the DIFF EQ Mode ................................................................. 3-1-1 3-2 Differential Equations of the First Order ........................................... 3-2-1 3-3 Linear Differential Equations of the Second Order ........................... 3-3-1 3-4 Differential Equations of the Nth Order ............................................ 3-4-1 3-5 System of First Order Differential Equations .................................... 3-5-1
Chapter 4 E-CON 4-1 E-CON Overview .............................................................................. 4-1-1 4-2 EA-100 Setup ................................................................................... 4-2-1 4-3 Setup Memory .................................................................................. 4-3-1 4-4 Program Converter ........................................................................... 4-4-1 4-5 Starting a Sampling Operation ......................................................... 4-5-1
Index (Additional Functions)
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Getting Acquainted Read This First!
About this Users Guide
u!x( ) The above indicates you should press ! and then x, which will input a symbol. All multiple-key input operations are indicated like this. Key cap markings are shown, followed by the input character or command in parentheses.
uFunction Keys and Menus
Many of the operations performed by this calculator can be executed by pressing function keys 1 through 6. The operation assigned to each function key changes according to the mode the calculator is in, and current operation assignments are indicated by function menus that appear at the bottom of the display.
This users guide shows the current operation assigned to a function key in parentheses following the key cap for that key. 1(Comp), for example, indicates that pressing 1 selects {Comp}, which is also indicated in the function menu.
When (g) is indicated in the function menu for key 6, it means that pressing 6 displays the next page or previous page of menu options.
uMenu Titles
Menu titles in this users guide include the key operation required to display the menu being explained. The key operation for a menu that is displayed by pressing K and then {MAT} would be shown as: [OPTN]-[MAT].
6(g) key operations to change to another menu page are not shown in menu title key operations.
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0-1-1 Getting Acquainted
uGraphs As a general rule, graph operations are shown on facing pages, with actual graph examples on the right hand page. You can produce the same graph on your calculator by performing the steps under the Procedure above the graph. Look for the type of graph you want on the right hand page, and then go to the page indicated for that graph. The steps under Procedure always use initial RESET settings.
The step numbers in the SET UP and Execution sections on the left hand page correspond to the Procedure step numbers on the right hand page.
Example:
Left hand page Right hand page
3. Draw the graph. 3 5(DRAW)(or w)
uCommand List
The Program Mode Command List (page 8-7) provides a graphic flowchart of the various function key menus and shows how to maneuver to the menu of commands you need.
Example: The following operation displays Xfct: [VARS]-[FACT]-[Xfct]
uPage Contents
Three-part page numbers are centered at the top of each page. The page number 1-2-3, for example, indicates Chapter 1, Section 2, page 3.
uSupplementary Information
Supplementary information is shown at the bottom of each page in a (Notes) block.
* indicates a note about a term that appears in the same page as the note.
# indicates a note that provides general information about topic covered in the same section as the note.
1-2-2 Display
1-2-3 Display
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Use this mode for arithmetic calculations and function calculations, and for calculations involving binary, octal, decimal, and hexadecimal values and matrices.
Use this mode to perform single-variable (standard deviation) and paired-variable (regression) statistical calculations, to perform tests, to analyze data and to draw statistical graphs.
Use this mode to store functions, to generate a numeric table of different solutions as the values assigned to variables in a function change, and to draw graphs.
Use this mode to store graph functions and to draw multiple versions of a graph by changing the values assigned to the variables in a function.
Use this mode to store recursion formulas, to generate a numeric table of different solutions as the values assigned to variables in a function change, and to draw graphs.
Use this mode to draw graphs of implicit functions.
Use this mode to solve linear equations with two through six unknowns, quadratic equations, and cubic equations.
Use this mode to store programs in th program area and to run programs.
Use this mode to perform algebraic calculations.
Use this mode for step-by-step solution of expressions.
Use this mode to determine the expression type and solve mode, and for interactive equation solutions.
Use this mode for step-by-step solution of expressions.
Use this mode to manage data stored in memory.
Use this mode to initialize memory, adjust contrast, and to make other system settings.
The following explains the meaning of each icon.
DescriptionIcon Mode Name
RUN
STATistics
GRaPH-TaBLe
DYNAmic graph
RECURsion
CONICS
EQUAtion
PRoGraM
Computer Algebra Syetem
ALGEBRA
TUTORial
LINK
MEMORY
SYSTEM
k About the Function Menu
Use the function keys (1 to 6) to access the menus and commands in the menu bar along the bottom of the display screen. You can tell whether a menu bar item is a menu or a command by its appearance.
Command (Example: )
Pressing a function key that corresponds to a menu bar command executes the command.
Pull-up Menu (Example: )
Pressing a function key that corresponds to a pull-up menu opens the menu.
You can use either of the following two methods to select a command from a pull-up menu.
k About Display Screens
This calculator uses two types of display screens: a text screen and a graphic screen. The text screen can show 21 columns and 8 lines of characters, with the bottom line used for the function key menu. The graph screen uses an area that measures 127 (W) 63 (H) dots.
Input the key to the left of the command on the pull-up menu. Use the f and c cursor keys to move the highlighting to the command you want, and then press w. The symbol ' to the right of a command indicates that executing the command displays a submenu. To cancel the pull-up menu without inputting the command, press i.
Text Screen Graph Screen
The contents of each type of screen are stored in independent memory areas. The contents of each type of screen are stored in independent memory areas.
#The contents of each type of screen are stored in independent memory areas.
#The contents of each type of screen are stored in independent memory
5-1-1 Sample Graphs
5-1-2 Sample Graphs
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
Execution 2. Input the function you want to graph.
Here you would use the V-Window to specify the range and other parameters of the graph. See 5-3-1.
3. Draw the graph.
k How to draw a simple graph (1)
Description
To draw a graph, simply input the applicable function.
Procedure 1 m GRPH-TBL
2 dvxw
35(DRAW) (or w)
Example To graph y = 3x2
Result Screen
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5-1 Sample Graphs
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Basic Operation 1-1 Keys
1-2 Display 1-3 Inputting and Editing Calculations
1-4 Option (OPTN) Menu
1-5 Variable Data (VARS) Menu
1-6 Program (PRGM) Menu 1-7 Using the Set Up Screen
1-8 When you keep having problems
Chapter 1
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1-1 Keys
1-1-1 Keys
REPLAY
COPY PASTE CAT/CAL H-COPY
PRGM
List Mat
i
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Page Page Page Page Page Page
1-3-5
Page Page Page Page Page
1-3-5 1-7-1
1-6-1 2-4-4
1-1-3 1-5-1 2-4-4
1-3-5 5-3-6 10-6-1
5-2-1 1-1-3 1-3-4 1-4-1 1-2-1
2-4-4 2-4-4
2-4-4 2-4-4
2-4-3 2-4-3
2-4-3 2-4-3
1-3-3
1-3-1
2-1-1
2-1-1
2-1-1
2-1-1
2-2-5
2-1-12-1-1
2-4-6
2-1-1
2-4-10
2-4-10
3-1-2 2-8-11
2-4-3
2-4-6 2-4-6
2-1-1
2-4-3
2-4-3
2-2-12-4-6
COPY PASTE CAT/CAL H-COPY
PRGM
List Mat
i
REPLAY
1-1-2 Keys
kKey Table
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1-1-3 Keys
kKey Markings
Many of the calculators keys are used to perform more than one function. The functions marked on the keyboard are color coded to help you find the one you need quickly and easily.
Function Key Operation
1 log l
2 10x !l
3 B al
The following describes the color coding used for key markings.
Color Key Operation
Orange Press ! and then the key to perform the marked function.
Red Press a and then the key to perform the marked function.
# Alpha Lock Normally, once you press a and then a key to input an alphabetic character, the keyboard reverts to its primary functions immediately.
If you press ! and then a, the keyboard locks in alpha input until you press a again.
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1-2-1 Display
1-2 Display
k Selecting Icons
This section describes how to select an icon in the Main Menu to enter the mode you want.
uTo select an icon 1. Press m to display the Main Menu.
2. Use the cursor keys (d, e, f, c) to move the highlighting to the icon you want.
3. Press w to display the initial screen of the mode whose icon you selected. Here we will enter the STAT Mode.
You can also enter a mode without highlighting an icon in the Main Menu by inputting the number or letter marked in the lower right corner of the icon.
Currently selected icon
* The above shows the ALGEBRA FX 2.0 PLUS screen.
Icon Mode Name Description
RUN MATrix Use this mode for arithmetic calculations and function calculations, and for calculations involving binary, octal, decimal, and hexadecimal values and matrices.
STATistics Use this mode to perform single-variable (standard deviation) and paired-variable (regression) statistical calculations, to analyze data and to draw statistical graphs.
The following explains the meaning of each icon.
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1-2-2 Display
Icon Mode Name Description
GRaPH-TaBLe Use this mode to store functions, to generate a numeric table of different solutions as the values assigned to variables in a function change, and to draw graphs.
DYNAmic graph Use this mode to store graph functions and to draw multiple versions of a graph by changing the values assigned to the variables in a function.
RECURsion Use this mode to store recursion formulas, to generate a numeric table of different solutions as the values assigned to variables in a function change, and to draw graphs.
CONICS Use this mode to draw graphs of conic sections.
EQUAtion Use this mode to solve linear equations with 2 to 30 unknowns, and higmh degree (2 to 30) equations.
PRoGraM Use this mode to store programs in th program area and to run programs.
Computer Algebra Use this mode to perform algebraic calculations. System (ALGEBRA FX 2.0 PLUS only)
ALGEBRA Use this mode for step-by-step solution of expressions. (ALGEBRA FX 2.0 PLUS only)
TUTORial Use this mode to determine the expression type and solve mode, and for interactive equation solutions. (ALGEBRA FX 2.0 PLUS only)
TVM Use this mode to perform financial calculations. (Financial) (On the FX 1.0 PLUS menu, the icon has the number 9 in the
lower right corner.) to make other system settings.
DIFFerential Use this mode to solve differential equations. EQuation (On the FX 1.0 PLUS menu, the icon has the letter A in the
lower right corner.)
E-CON Use this mode when you want to control a CASIO EA-100 unit from this calculator. (On the FX 1.0 PLUS menu, the icon has the letter B in the lower right corner.)
LINK Use this mode to transfer memory contents or back-up data to another unit. (On the FX 1.0 PLUS menu, the icon has the letter C in the lower right corner.)
MEMORY Use this mode to manage data stored in memory. (On the FX 1.0 PLUS menu, the icon has the letter D in the lower right corner.)
SYSTEM Use this mode to initialize memory, adjust contrast, and to make other system settings. (On the FX 1.0 PLUS menu, the icon has the letter E in the lower right corner.)
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kAbout the Function Menu
Use the function keys (1 to 6) to access the menus and commands in the menu bar along the bottom of the display screen. You can tell whether a menu bar item is a menu or a command by its appearance.
Command (Example: )
Pressing a function key that corresponds to a menu bar command executes the command.
Pull-up Menu (Example: )
Pressing a function key that corresponds to a pull-up menu opens the menu.
You can use either of the following two methods to select a command from a pull-up menu.
Input the key to the left of the command on the pull-up menu.
Use the f and c cursor keys to move the highlighting to the command you want, and then press w.
The symbol ' to the right of a command indicates that executing the command displays a submenu.
To cancel the pull-up menu without inputting the command, press i.
kAbout Display Screens
This calculator uses two types of display screens: a text screen and a graphic screen. The text screen can show 21 columns and 8 lines of characters, with the bottom line used for the function key menu. The graph screen uses an area that measures 127 (W) 63 (H) dots.
Text Screen Graph Screen
The contents of each type of screen are stored in independent memory areas.
Press u5(GT) to switch between the graphic screen and text screen.
1-2-3 Display
# The symbol in the upper left corner of a pull- up menu indicates that there are more commands running off the top of the menu.
Use the cursor keys to scroll the menu contents to view the commands running off the top.
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kNormal Display
The calculator normally displays values up to 10 digits long. Values that exceed this limit are automatically converted to and displayed in exponential format.
uHow to interpret exponential format
1.2E+12 indicates that the result is equivalent to 1.2 1012. This means that you should move the decimal point in 1.2 twelve places to the right, because the exponent is positive. This results in the value 1,200,000,000,000.
1.2E03 indicates that the result is equivalent to 1.2 103. This means that you should move the decimal point in 1.2 three places to the left, because the exponent is negative. This results in the value 0.0012.
You can specify one of two different ranges for automatic changeover to normal display.
Norm 1 .................. 102 (0.01) > |x|, |x| > 1010
Norm 2 .................. 109 (0.000000001) > |x|, |x| > 1010
All of the examples in this manual show calculation results using Norm 1.
See page 2-3-2 for details on switching between Norm 1 and Norm 2.
1-2-4 Display
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kSpecial Display Formats
This calculator uses special display formats to indicate fractions, hexadecimal values, and degrees/minutes/seconds values.
u Fractions
................. Indicates: 456
u Hexadecimal Values
................. Indicates: ABCDEF12(16), which
equals 1412567278(10)
u Degrees/Minutes/Seconds
................. Indicates: 12 34 56.78
In addition to the above, this calculator also uses other indicators or symbols, which are described in each applicable section of this manual as they come up.
kCalculation Execution Indicator
Whenever the calculator is busy drawing a graph or executing a long, complex calculation or program, a black box k flashes in the upper right corner of the display. This black box tells you that the calculator is performing an internal operation.
1-2-5 Display
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1-3 Inputting and Editing Calculations
k Inputting Calculations
When you are ready to input a calculation, first press A to clear the display. Next, input your calculation formulas exactly as they are written, from left to right, and press w to obtain the result.
Example 1 2 + 3 4 + 10 =
Ac+d-e+baw
Example 2 2(5 + 4) (23 5) =
Ac(f+e)/
(cd*f)w
k Editing Calculations
Use the d and e keys to move the cursor to the position you want to change, and then perform one of the operations described below. After you edit the calculation, you can execute it by pressing w. Or you can use e to move to the end of the calculation and input more.
u To change a step
Example To change cos60 to sin60
Acga
ddd
D
s
1-3-1 Inputting and Editing Calculations
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u To delete a step
Example To change 369 2 to 369 2
Adgj**c
ddD
u To insert a step
Example To change 2.362 to sin2.362
Ac.dgx
ddddd
s
u To change the last step you input
Example To change 396 3 to 396 2
Adgj*d
D
c
1-3-2 Inputting and Editing Calculations
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kUsing Replay Memory
The last calculation performed is always stored into replay memory. You can recall the contents of the replay memory by pressing d or e. If you press e, the calculation appears with the cursor at the beginning. Pressing d causes the calculation to appear with the cursor at the end. You can make changes in the calculation as you wish and then execute it again.
Example 1 To perform the following two calculations 4.12 6.4 = 26.368
4.12 7.1 = 29.252
Ae.bc*g.ew
dddd
!D(INS)
h.b
w
After you press A, you can press f or c to recall previous calculations, in sequence from the newest to the oldest (Multi-Replay Function). Once you recall a calculation, you can use e and d to move the cursor around the calculation and make changes in it to create a new calculation.
Example 2
Abcd+efgw
cde-fghw
A
f (One calculation back)
f (Two calculations back)
1-3-3 Inputting and Editing Calculations
# Pressing !D(INS) changes the cursor to _. The next function or value you input is overwritten at the location of _. To abort this operation, press !D(INS) again.
# A calculation remains stored in replay memory until you perform another calculation or change modes.
# The contents of replay memory are not cleared when you press the A key, so you can recall a calculation and execute it even after performing the all clear operation.
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1-3-4 Inputting and Editing Calculations
kMaking Corrections in the Original Calculation
Example 14 0 2.3 entered by mistake for 14 10 2.3
Abe/a*c.d
w
Press i.
Make necessary changes.
db
Execute again.
w
kCopy and Paste
You can temporarily copy commands, programs, and other text data you input to a memory area called the clipboard, and then paste it to another location on the display.
u To specify the copy range 1. Move the cursor (t) the beginning or end of the range of text you want to copy and
then press u. This changes the cursor to .
2. Use the cursor keys to move the cursor and highlight the range of text you want to copy.
Cursor is positioned automatically at the location of the cause of the error.
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3. Press u1 (COPY) to copy the highlighted text to the clipboard, and exit the copy range specification mode.
To cancel text highlighting without performing a copy operation, press i.
uPasting Text Move the cursor to the location where you want to paste the text, and then press u 2(PASTE). The contents of the clipboard are pasted at the cursor position.
A
u2(PASTE)
kCatalog Function
The Catalog is an alphabetic list of all the commands available on this calculator. You can input a command by calling up the Catalog and then selecting the command you want.
u To use the Catalog to input a command 1. Press u4(CAT/CAL) to display the Catalog at
the bottom of the screen.
2. Press the function key that matches the first letter of the command you want to input.
3. Select the command from the pull-up menu.
Example 1 To use the Catalog to input the ClrGraph command
Au4(CAT/CAL)3(C~)h(CLR)
b(Graph)
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Example 2 To use the Catalog to input the Prog command
Au4(CAT/CAL)6(g)6(g)
5(P)I(Prog)
Pressing i or !i(QUIT) closes the Catalog.
1-3-6 Inputting and Editing Calculations
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1-4 Option (OPTN) Menu The option menu gives you access to scientific functions and features that are not marked on the calculators keyboard. The contents of the option menu differ according to the mode you are in when you press the K key.
See 8-7 Program Mode Command List for details on the option (OPTN) menu.
uOption Menu in the RUN MAT or PRGM Mode
{LIST} ... {list function menu}
{MAT} ... {matrix operation menu}
{CPLX} ... {complex number calculation menu}
{CALC} ... {functional analysis menu}
{NUM} ... {numeric calculation menu}
{PROB} ... {probability/distribution calculation menu}
{HYP} ... {hyperbolic calculation menu}
{ANGL} ... {menu for angle/coordinate conversion, DMS input/conversion}
{STAT} ... {paired-variable statistical estimated value menu}
{FMEM} ... {function memory menu}
{ZOOM} ... {zoom function menu}
{SKTCH} ... {sketch function menu}
{PICT} ... {picture memory menu}
{SYBL} ... {symbol menu}
{ } {DMS}
{ } {DMS conversion}
{ENG}/{ ENG} {ENG conversion}
1-4-1 Option (OPTN) Menu
# The option (OPTN) menu does not appear during binary, octal, decimal, and hexadecimal calculations.
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The following shows the function menus that appear under other conditions.
uOption Menu when a number table value is displayed in the GRPH TBL or RECUR Mode {LMEM} {list memory menu}
{ }/{ENG}/{ ENG}
uOption Menu in the CAS or ALGEBRA or TUTOR Mode (ALGEBRA FX 2.0 PLUS only) t {} {infinity}
{Abs} {absolute value}
{x!} {factorial}
{sign} {signum function}
{HYP}/{FMEM}
The meanings of the option menu items are described in the sections that cover each mode.
1-4-2 Option (OPTN) Menu
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1-5 Variable Data (VARS) Menu To recall variable data, press J to display the variable data menu.
{V-WIN}/{FACT}/{STAT}/{GRPH}/{DYNA}/ {TABL}/{RECR}/{EQUA*1}
See 8-7 Program Mode Command List for details on the variable data (VARS) menu.
u V-WIN Recalling View Window values
{Xmin}/{Xmax}/{Xscale}/{Xdot} X-axis {minimum value}/{maximum value}/{scale}/{dot value*2}
{Ymin}/{Ymax}/{Yscale} Y-axis {minimum value}/{maximum value}/{scale}
{T min}/{T max}/{T ptch} T, {minimum value}/{maximum value}/{pitch}
{R-Xmin}/{R-Xmax}/{R-Xscl}/{R-Xdot} Dual Graph right graph X-axis {minimum value}/{maximum value}/{scale}/
{dot value*2}
{R-Ymin}/{R-Ymax}/{R-Yscl} Dual Graph right graph Y-axis {minimum value}/{maximum value}/{scale}
{R-Tmin}/{R-Tmax}/{R-Tpch} Dual Graph right graph T, {minimum value}/{maximum value}/{pitch}
u FACT Recalling zoom factors
{Xfact}/{Yfact} ... {x-axis factor}/{y-axis factor}
1-5-1 Variable Data (VARS) Menu
*1The EQUA item appears only when you access the variable data menu from the RUN MAT or PRGM Mode.
# The variable data menu does not appear if you press J while binary, octal, decimal, or hexadecimal is set as the default number system.
*2The dot value indicates the display range (Xmax value Xmin value) divided by the screen dot pitch (126). The dot value is normally calculated automati- cally from the minimum and maximum values. Changing the dot value causes the maximum to be calculated automatically.
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u STAT Recalling statistical data
{n} {number of data}
{X} {single-variable, paired-variable x-data}
{o}/{x}/{x2}/{xn}/{xn1}/{minX}/{maxX} {mean}/{sum}/{sum of squares}/{population standard deviation}/{sample
standard deviation}/{minimum value}/{maximum value}
{Y} ... {paired-variable y-data}
{p}/{ y}/{ y2}/{ xy}/{ yn}/{ yn1}/{minY}/{maxY} {mean}/{sum}/{sum of squares}/{sum of products of x-data and y-data}/
{population standard deviation}/{sample standard deviation}/{minimum value}/ {maximum value}
{GRAPH} ... {graph data menu}
{a}/{b}/{c}/{d}/{e}
... {regression coefficient and polynomial coefficients}
{r}/{r2}
... {correlation coefficient}
{Q1}/{Q3} ... {first quartile}/{third quartile}
{Med}/{Mod} ... {median}/{mode} of input data
{H-Strt}/{H-ptch} ... histogram {start division}/{pitch}
{PTS} ... {summary point data menu}
{x1}/{y1}/{x2}/{y2}/{x3}/{y3} ... {coordinates of summary points}
1-5-2 Variable Data (VARS) Menu
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u GRPH Recalling Graph Functions
{Yn}/{rn} ... {rectangular coordinate or inequality function}/{polar coordinate function}
{Xtn}/{Ytn} ... parametric graph function {Xt}/{Yt}
{Xn} ... {X=constant graph function}
(Press these keys before inputting a value to specify a storage area.)
u DYNA Recalling Dynamic Graph Set Up Data
{Start}/{End}/{Pitch} ... {coefficient range start value}/{coefficient range end value}/{coefficient value
increment}
u TABL Recalling Table & Graph Set Up and Content Data
{Start}/{End}/{Pitch} ... {table range start value}/{table range end value}/{table value increment}
{Result*1} ... {matrix of table contents}
1-5-3 Variable Data (VARS) Menu
*1 The Result item appears only when the TABL menu is displayed in the RUN MAT or PRGM Mode.
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u RECR Recalling Recursion Formula*1, Table Range, and Table Content Data
{FORM} ... {recursion formula data menu}
{an}/{an+1}/{an+2}/{bn}/{bn+1}/{bn+2}/{cn}/{cn+1}/{cn+2} ... {an}/{an+1}/{an+2}/{bn}/{bn+1}/{bn+2}/{cn}/{cn+1}/{cn+2} expressions
{RANGE} ... {table range data menu}
{R-Strt}/{R-End} ... table range {start value}/{end value}
{a0}/{a1}/{a2}/{b0}/{b1}/{b2}/{c0}/{c1}/{c2} ... {a0}/{a1}/{a2} {b0}/{b1}/{b2}/{c0}/{c1}/{c2} value
{anStrt}/{bnStrt}/{cnStrt} ... origin of {an }/{bn}/{cn} recursion formula convergence/divergence graph (WEB
graph)
{Result *2} ... {matrix of table contents*3}
u EQUA Recalling Equation Coefficients and Solutions*4 *5
{S-Rslt}/{S-Coef} ... matrix of {solutions}/{coefficients} for linear equations*6
{P-Rslt}/{P-Coef} ... matrix of {solution}/{coefficients} for a high degree equation
1-5-4 Variable Data (VARS) Menu
*1 An error occurs when there is no function or recursion formula numeric table in memory.
*2 Result is available only in the RUN MAT and PRGM Modes.
*3 Table contents are stored automatically in Matrix Answer Memory (MatAns).
*4 Coefficients and solutions are stored automatically in Matrix Answer Memory (MatAns).
*5 The following conditions cause an error. When there are no coefficients input for the
equation When there are no solutions obtained for the
equation *6 Coefficient and solution memory data for a
linear equation cannot be recalled at the same time.
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1-6 Program (PRGM) Menu To display the program (PRGM) menu, first enter the RUN MAT or PRGM Mode from the Main Menu and then press !J(PRGM). The following are the selections available in the program (PRGM) menu.
{Prog } ........ {program recall}
{JUMP} ...... {jump command menu}
{? } .............. {input prompt}
{^} ............. {output command}
{I/O} ............ {I/O control/transfer command menu}
{IF } ............. {conditional jump command menu}
{FOR} ......... {loop control command menu}
{WHLE} ...... {conditional loop control command menu}
{CTRL } ....... {program control command menu}
{LOGIC } ..... {logical operation command menu}
{CLR } ......... {clear command menu}
{DISP } ........ {display command menu}
{:} ............... {multistatement connector}
The following function key menu appears if you press !J(PRGM) in the RUN MAT Mode or the PRGM Mode while binary, octal, decimal, or hexadecimal is set as the default number system.
{Prog}/{JUMP}/{?}/{^}/{:}
{= G <} ....... {relational operator menu}
The functions assigned to the function keys are the same as those in the Comp Mode.
For details on the commands that are available in the various menus you can access from the program menu, see 8. Programming.
1-6-1 Program (PRGM) Menu
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1-7 Using the Set Up Screen The modes set up screen shows the current status of mode settings and lets you make any changes you want. The following procedure shows how to change a set up.
u To change a mode set up 1. Select the icon you want and press w to enter a mode and display its initial screen.
Here we will enter the RUN MAT Mode.
2. Press u3(SET UP) to display the modes SET UP screen.
This SET UP screen is just one possible example. Actual SET UP screen contents will differ according to the mode you are in and that modes current settings.
3. Use the f and c cursor keys to move the highlighting to the item whose setting you want to change.
4. Press the function key (1 to 6) that is marked with the setting you want to make.
5. After you are finished making any changes you want, press i to return to the initial screen of the mode.
k SET UP Screen Function Key Menus
This section details the settings you can make using the function keys in the SET UP display.
indicates default setting.
uMode (calculation/binary, octal, decimal, hexadecimal mode) {Comp} ... {arithmetic calculation mode}
{Dec}/{Hex}/{Bin}/{Oct} ... {decimal}/{hexadecimal}/{binary}/{octal}
1-7-1 Using the Set Up Screen
.. .
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u Func Type (graph function type) Pressing one of the following function keys also switches the function of the v key.
{Y=}/{r=}/{Parm}/{X=c} ... {rectangular coordinate}/{polar coordinate}/{parametric coordinate}/
{X = constant} graph
{Y>}/{Y<}/{Yt}/{Ys} ... {y>f(x)}/{y<f(x)}/{yf(x)}/{yf(x)} inequality graph
uDraw Type (graph drawing method) {Con}/{Plot}
... {connected points}/{unconnected points}
uDerivative (derivative value display) {On}/{Off}
... {display on}/{display off} while Graph-to-Table, Table & Graph, and Trace are being used
uAngle (default angle unit) {Deg}/{Rad}/{Gra}
... {degrees}/{radians}/{grads}
uComplex Mode {Real} ... {calculation in real number range only}
{a + bi}/{r e^i} ... {rectangular format}/{polar format} display of a complex calculation
uCoord (graph pointer coordinate display) {On}/{Off}
... {display on}/{display off}
uGrid (graph gridline display) {On}/{Off}
... {display on}/{display off}
uAxes (graph axis display) {On}/{Off}
... {display on}/{display off}
u Label (graph axis label display) {On}/{Off}
... {display on}/{display off}
1-7-2 Using the Set Up Screen
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uDisplay (display format) {Fix}/{Sci}/{Norm}/{Eng}
... {fixed number of decimal places specification}/{number of significant digits specification}/{normal display setting}/{Engineering Mode}
uStat Wind (statistical graph view window setting method) {Auto}/{Man}
... {automatic}/{manual}
uReside List (residual calculation) {None}/{LIST}
... {no calculation}/{listspecification for the calculated residual data}
u List File (list file display settings) {FILE} ... {settings of list file on the display}
uVariable (table generation and graph draw settings) {Rang}/{LIST}
... {use table range}/{use list data}
uGraph Func (function display during graph drawing and trace) {On}/{Off}
... {display on}/{display off}
uDual Screen (Dual Screen Mode status) {T+G}/{G+G}/{GtoT}/{Off}
... {graph on one side and numeric table on the other side of Dual Screen}/ {graphing on both sides of Dual Screen}/{graph on one side and numeric table on the other side of Dual Screen}/{Dual Screen off}
uSimul Graph (simultaneous graphing mode) {On}/{Off}
... {simultaneous graphing on (all graphs drawn simultaneously)}/{simultaneous graphing off (graphs drawn in area numeric sequence)}
uBackground (graph display background) {None}/{PICT}
... {no background}/{graph background picture specification}
1-7-3 Using the Set Up Screen
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uDynamic Type (Dynamic Graph locus setting) {Cnt}/{Stop}
... {non-stop (continuous)}/{automatic stop after 10 draws}
u Display ( value display in recursion table) {On}/{Off}
... {display on}/{display off}
uSlope (display of derivative at current pointer location in conic section graph) {On}/{Off}
... {display on}/{display off}
uAnswer Type (result range specification) (ALGEBRA FX 2.0 PLUS only) {Real}/{Cplx}
... {real number}/{complex number} range result
uH-Copy (screen shot settings) {Dirct}/{Mem}
... {direct send}/{store in memory}
1-7-4 Using the Set Up Screen
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1-8 When you keep having problems If you keep having problems when you are trying to perform operations, try the following before assuming that there is something wrong with the calculator.
kGetting the Calculator Back to its Original Mode Settings
1. From the Main Menu, enter the SYSTEM Mode.
2. Press 5(Reset).
3. Press 1(S/U), and then press w(Yes).
4. Press m to return to the Main Menu.
Now enter the correct mode and perform your calculation again, monitoring the results on the display.
k In Case of Hang Up
Should the unit hang up and stop responding to input from the keyboard, press the P button on the back of the calculator to reset the calculator to its initial defaults (see page -6-1). Note, however, that this may clear all the data in calculator memory.
1-8-1 When you keep having problems
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k Low Battery Message
If either of the following messages appears on the display, immediately turn off the calculator and replace main batteries or the back up battery as instructed.
If you continue using the calculator without replacing main batteries, power will automatically turn off to protect memory contents. Once this happens, you will not be able to turn power back on, and there is the danger that memory contents will be corrupted or lost entirely.
# You will not be able to perform data communications operations after the low battery message appears.
1-8-2 When you keep having problems
# If main batteries and the back up battery go low at the same time (indicated when both of the messages described above appear), replace the back up battery first and then replace the main batteries.
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Manual Calculations 2-1 Basic Calculations
2-2 Special Functions
2-3 Specifying the Angle Unit and Display Format
2-4 Function Calculations 2-5 Numerical Calculations
2-6 Complex Number Calculations
2-7 Binary, Octal, Decimal, and Hexadecimal Calculations
2-8 Matrix Calculations
Chapter 2
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2-1-1 Basic Calculations
2-1 Basic Calculations
kArithmetic Calculations
Enter arithmetic calculations as they are written, from left to right.
Use the - key to input the minus sign before a negative value.
Calculations are performed internally with a 15-digit mantissa. The result is rounded to a 10-digit mantissa before it is displayed.
For mixed arithmetic calculations, multiplication and division are given priority over addition and subtraction.
Example Operation
23 + 4.5 53 = 25.5 23+4.5-53w
56 (12) (2.5) = 268.8 56*-12/-2.5w
(2 + 3) 102 = 500 (2+3)*1E2w*1
1 + 2 3 4 5 + 6 = 6.6 1+2-3*4/5+6w
100 (2 + 3) 4 = 80 100-(2+3)*4w
2 + 3 (4 + 5) = 29 2+3*(4+5w*2
(7 2) (8 + 5) = 65 (7-2)(8+5)w*3
6 = 0.3 6 /(4*5)w*4
4 5
(1 + 2i) + (2 + 3i) = 3 + 5i (b+c!a(i) +(c+ d!a(i) w
(2 + i) (2 i) = 5 (c+!a(i) *(c-!a(i) )w
*1(2+3)E2 does not produce the correct result. Be sure to enter this calculation as shown.
*2Final closed parentheses (immediately before operation of the w key) may be omitted, no matter how many are required.
*3A multiplication sign immediately before an open parenthesis may be omitted.
*4This is identical to 6 / 4 / 5 w.
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2-1-2 Basic Calculations
*1Displayed values are rounded off to the place you specify.
kNumber of Decimal Places, Number of Significant Digits, Normal Display Range [SET UP]- [Display] -[Fix] / [Sci] / [Norm]
Even after you specify the number of decimal places or the number of significant digits, internal calculations are still performed using a 15-digit mantissa, and displayed values are stored with a 10-digit mantissa. Use Rnd of the Numeric Calculation Menu (NUM) (page 2-4-1) to round the displayed value off to the number of decimal place and significant digit settings.
Number of decimal place (Fix) and significant digit (Sci) settings normally remain in effect until you change them or until you change the normal display range (Norm) setting.
Example 100 6 = 16.66666666...
Condition Operation Display
100/6w 16.66666667
4 decimal places u3(SET UP)cccccccccc *1
1(Fix)ewiw 16.6667
5 significant digits u3(SET UP)cccccccccc *1
2(Sci)fwiw 1.6667E+01
Cancels specification u3(SET UP)cccccccccc 3(Norm)iw 16.66666667
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2-1-3 Basic Calculations
Example 200 7 14 = 400
Condition Operation Display
200/7*14w 400 3 decimal places u3(SET UP)cccccccccc
1(Fix)dwiw 400.000
Calculation continues 200/7w 28.571 using display capacity * Ans of 10 digits 14w 400.000
If the same calculation is performed using the specified number of digits:
200/7w 28.571
The value stored K5(NUM)e(Rnd)w 28.571 internally is rounded * Ans off to the number of 14w 399.994 decimal places you specify.
kCalculation Priority Sequence
This calculator employs true algebraic logic to calculate the parts of a formula in the following order:
1 Coordinate transformation Pol (x, y), Rec (r, )
Differentials, quadratic differentials, integrations, calculations
d/dx, d2/dx2, dx, , Mat, Solve, FMin, FMax, ListMat, Seq, Min, Max, Median, Mean,
Augment, MatList, P(, Q(, R(, t(, List
Composite functions*1 fn, Yn, rn, Xtn, Ytn, Xn
2 Type A functions
With these functions, the value is entered and then the function key is pressed.
x2, x1, x !, , ENG symbols, angle unit o, r, g
*1You can combine the contents of multiple function memory (fn) locations or graph memory (Yn, rn, Xtn, Ytn, Xn) locations into composite functions. Specifying fn1(fn2),
for example, results in the composite function fn1fn2 (see page 5-3-3). A composite function can consist of up to five functions.
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2-1-4 Basic Calculations
3 Power/root ^(xy), x
4 Fractions a b/c
5 Abbreviated multiplication format in front of , memory name, or variable name.
2, 5A, Xmin, F Start, etc.
6 Type B functions
With these functions, the function key is pressed and then the value is entered.
, 3 , log, In, ex, 10x, sin, cos, tan, sin1, cos1, tan1, sinh, cosh, tanh, sinh1, cosh1, tanh1, (), d, h, b, o, Neg, Not, Det, Trn, Dim, Identity, Sum, Prod, Cuml, Percent, AList, Abs, Int, Frac, Intg, Arg, Conjg, ReP, ImP
7 Abbreviated multiplication format in front of Type B functions
2 , A log2, etc.3
8 Permutation, combination nPr, nCr
9 , 0 +,
! Relational operators >, <, , @ Relational operators =, G
# and (bitwise operation)
$ xnor, xor (bitwise operations)
% or (bitwise operation)
^ And (logical operation)
Or (logical operation)
Example 2 + 3 (log sin22 + 6.8) = 22.07101691 (angle unit = Rad) 1
2
3
4
5
6
# When functions with the same priority are used in series, execution is performed from right to left. exIn ex{In( )}120 120
Otherwise, execution is from left to right.
# Compound functions are executed from right to left.
# Anything contained within parentheses receives highest priority.
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2-1-5 Basic Calculations
# Other errors can occur during program execution. Most of the calculators keys are inoperative while an error message is displayed.
Press i to clear the error and display the error position (see page 1-3-4).
# See the Error Message Table on page -1-1 for information on other errors.
kMultiplication Operations without a Multiplication Sign
You can omit the multiplication sign () in any of the following operations.
Before coordinate transformation and Type B functions (1 on page 2-1-3 and 6 on page 2-1-4), except for negative signs
Example 2sin30, 10log1.2, 2 , 2Pol(5, 12), etc.
Before constants, variable names, memory names
Example 2, 2AB, 3Ans, 3Y1, etc.
Before an open parenthesis
Example 3(5 + 6), (A + 1)(B 1), etc.
kOverflow and Errors
Exceeding a specified input or calculation range, or attempting an illegal input causes an error message to appear on the display. Further operation of the calculator is impossible while an error message is displayed. The following events cause an error message to appear on the display.
When any result, whether intermediate or final, or any value in memory exceeds 9.999999999 1099 (Ma ERROR).
When an attempt is made to perform a function calculation that exceeds the input range (Ma ERROR).
When an illegal operation is attempted during statistical calculations (Ma ERROR). For example, attempting to obtain 1VAR without data input.
When an improper data type is specified for the argument of a function calculation (Ma ERROR).
When the capacity of the numeric value stack or command stack is exceeded (Stack ERROR). For example, entering 25 successive ( followed by 2 + 3 * 4 w.
When an attempt is made to perform a calculation using an illegal formula (Syntax ERROR). For example, 5 ** 3 w.
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When you try to perform a calculation that causes memory capacity to be exceeded (Memory ERROR).
When you use a command that requires an argument, without providing a valid argument (Argument ERROR).
When an attempt is made to use an illegal dimension during matrix calculations (Dimension ERROR).
When you are in the real mode and an attempt is made to perform a calculation that produces a complex number solution. Note that Real is selected for the Complex Mode setting on the SET UP Screen (Non-Real ERROR).
kMemory Capacity
Each time you press a key, either one byte or two bytes is used. Some of the functions that require one byte are: b, c, d, sin, cos, tan, log, In, , and . Some of the functions that take up two bytes are d/dx(, Mat, Xmin, If, For, Return, DrawGraph, SortA(, PxIOn, Sum, and an+1.
2-1-6 Basic Calculations
# As you input numeric values or commands, they appear flush left on the display. Calculation results, on the other hand, are displayed flush right.
# The allowable range for both input and output values is 15 digits for the mantissa and two digits for the exponent. Internal calculations are also performed using a 15-digit mantissa and two-digit exponent.
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2-2 Special Functions
kCalculations Using Variables
Example Operation Display
193.2aav(A)w 193.2
193.2 23 = 8.4 av(A)/23w 8.4
193.2 28 = 6.9 av(A)/28w 6.9
kMemory
uVariables This calculator comes with 28 variables as standard. You can use variables to store values you want to use inside of calculations. Variables are identified by single-letter names, which are made up of the 26 letters of the alphabet, plus r and . The maximum size of values that you can assign to variables is 15 digits for the mantissa and 2 digits for the exponent.
u To assign a value to a variable
[value] a [variable name] w
Example To assign 123 to variable A
Abcdaav(A)w
Example To add 456 to variable A and store the result in variable B
Aav(A)+efgaa
l(B)w
2-2-1 Special Functions
# Variable contents are retained even when you turn power off.
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u To display the contents of a variable
Example To display the contents of variable A
Aav(A)w
u To clear a variable
Example To clear variable A
Aaaav(A)w
u To assign the same value to more than one variable [value]a [first variable name*1]K6(g)6(g)4(SYBL)d(~) [last variable name*1]w
Example To assign a value of 10 to variables A through F
Abaaav(A)
K6(g)6(g)4(SYBL)d(~)
at(F)w
uFunction Memory [OPTN]-[FMEM]
Function memory (f1~f20) is convenient for temporary storage of often-used expressions. For longer term storage, we recommend that you use the GRPH TBL Mode for expressions and the PRGM Mode for programs.
{Store}/{Recall}/{fn}/{SEE} ... {function store}/{function recall}/{function area specification as a variable name inside an expression}/{function list}
2-2-2 Special Functions
*1 You cannot use r or as a variable name.
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u To store a function
Example To store the function (A+B) (AB) as function memory number 1
(av(A)+al(B)
(av(A)-al(B)
K6(g)5(FMEM) b(Store)bw
u To recall a function
Example To recall the contents of function memory number 1
K6(g)5(FMEM)
c(Recall)bw
u To display a list of available functions
K6(g)5(FMEM)
e(SEE)
2-2-3 Special Functions
# If the function memory number to which you store a function already contains a function, the previous function is replaced with the new one.
# The recalled function appears at the current location of the cursor on the display.
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2-2-4 Special Functions
u To delete a function
Example To delete the contents of function memory number 1
AK6(g)5(FMEM)
b(Store)bw
Executing the store operation while the display is blank deletes the function in the function memory you specify.
u To use stored functions
Example To store x3 + 1, x2 + x into function memory, and then graph: y = x3 + x2 + x + 1
Use the following View Window settings.
Xmin = 4, Xmax = 4, Xscale = 1
Ymin = 10, Ymax = 10, Yscale = 1
u3(SET UP)c1(Y=)i
AvMd+bK6(g)5(FMEM)b(Store)bw(stores (x3 + 1))
iAvx+v5(FMEM)b(Store)cw(stores (x2 + x))
iAK6(g)6(g)2(SKTCH)b(Cls)w
2(SKTCH)e(GRAPH)b(Y=)
K6(g)5(FMEM)d(fn)b+
5(FMEM)d(fn)cw
For full details about graphing, see 5. Graphing.
# You can also use a to store a function in function memory in a program. In this case, you must enclose the function inside of double quotation marks. The maximum size of the function you can store is 255 bytes.
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kAnswer Function
The Answer Function automatically stores the last result you calculated by pressing w(unless the w key operation results in an error). The result is stored in the answer memory.
u To use the contents of the answer memory in a calculation
Example 123 + 456 = 579 789 579 = 210
Abcd+efgw
hij-!-(Ans)w
kPerforming Continuous Calculations
Answer memory also lets you use the result of one calculation as one of the arguments in the next calculation.
Example 1 1 3 = 1 3 3 =
Ab/dw
(Continuing)*dw
Continuous calculations can also be used with Type A functions (x2, x-1, x!, page 2-1-3), +, , ^(xy), x , , etc.
2-2-5 Special Functions
# The largest value that the answer memory can hold is 15 digits for the mantissa and 2 digits for the exponent.
# Only numeric values and calculation results can be stored in answer memory.
# Answer memory contents are not cleared when you press the A key or when you switch power off.
# Answer memory contents are not changed by an operation that assigns values to value memory (such as: faav(A)w).
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k Stacks
The unit employs memory blocks, called stacks, for storage of low priority values and commands. There is a 10-level numeric value stack, a 26-level command stack, and a 10- level program subroutine stack. An error occurs if you perform a calculation so complex that it exceeds the capacity of available numeric value stack or command stack space, or if execution of a program subroutine exceeds the capacity of the subroutine stack.
Example
2-2-6 Special Functions
1
2
3
4
5
b
c
d
e
f
g
h
2
3
4
5
4
( ( + ( +
...
...
Numeric Value Stack Command Stack
# Calculations are performed according to the pri- ority sequence. Once a calculation is executed, it is cleared from the stack.
# Storing a complex number takes up two numeric value stack levels.
# Storing a two-byte function takes up two command stack levels.
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kUsing Multistatements
Multistatements are formed by connecting a number of individual statements for sequential execution. You can use multistatements in manual calculations and in programmed calcula- tions. There are two different ways that you can use to connect statements to form multistatements.
Colon (:)
Statements that are connected with colons are executed from left to right, without stopping.
Display Result Command (^)
When execution reaches the end of a statement followed by a display result command, execu- tion stops and the result up to that point appears on the display. You can resume execution by pressing the w key.
Example 6.9 123 = 848.7 123 3.2 = 38.4375
Abcdaav(A)
!J(PRGM)6(g)6(g)3(:)g.j
*av(A)!J(PRGM)4(^)
av(A)/d.cw
w
2-2-7 Special Functions
# The final result of a multistatement is always displayed, regardless of whether the calculation ends with a display result command.
Example : 123 456: 5
Invalid
# You cannot construct a multistatement in which one statement directly uses the result of the previous statement.
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2-3 Specifying the Angle Unit and Display Format
Before performing a calculation for the first time, you should use the SET UP screen to specify the angle unit and display format.
kSetting the Angle Unit [SET UP]- [Angle]
1. On the Set Up screen, highlight Angle.
2. Press the function key for the angle unit you want to specify, then press i.
{Deg}/{Rad}/{Gra} ... {degrees}/{radians}{grads}
The relationship between degrees, grads, and radians is shown below.
360 = 2 radians = 400 grads
90 = /2 radians = 100 grads
kSetting the Display Format [SET UP]- [Display]
1. On the Set Up screen, highlight Display.
2. Press the function key for the item you want to set, then press i.
{Fix}/{Sci}/{Norm}/{Eng} ... {fixed number of decimal places specification}/ {number of significant digits specification}/{normal display}/{Engineering Mode}
u To specify the number of decimal places (Fix)
Example To specify two decimal places
1(Fix) cw
Press the function key that corresponds to the number of decimal places you want to specify (n = 0 to 9).
2-3-1 Specifying the Angle Unit and Display Format
# Displayed values are rounded off to the number of decimal places you specify.
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u To specify the number of significant digits (Sci)
Example To specify three significant digits
2(Sci) dw
Press the function key that corresponds to the number of significant digits you want to specify (n = 0 to 9).
u To specify the normal display (Norm 1/Norm 2) Press 3(Norm) to switch between Norm 1 and Norm 2.
Norm 1: 102 (0.01)>|x|, |x| >1010
Norm 2: 109 (0.000000001)>|x|, |x| >1010
Ab/caaw (Norm 1)
(Norm 2)
u To specify the engineering notation display (Eng Mode) Press 4(Eng) to switch between engineering notation and standard notation. The indicator /E is on the display while engineering notation is in effect.
You can use the following symbols to convert values to engineering notation, such as 2,000 (= 2 103) 2k.
E (Exa) 1018 m (milli) 103
P (Peta) 1015 (micro) 106
T (Tera) 1012 n (nano) 109
G (Giga) 109 p (pico) 1012
M (Mega) 106 f (femto) 1015
k (kilo) 103
2-3-2 Specifying the Angle Unit and Display Format
# Displayed values are rounded off to the number of significant digits you specify.
# Specifying 0 makes the number of significant digits 10.
# The engineering symbol that makes the mantissa a value from 1 to 1000 is automatically selected by the calculator when engineering notation is in effect.
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2-4 Function Calculations
k Function Menus
This calculator includes five function menus that give you access to scientific functions not printed on the key panel.
The contents of the function menu differ according to the mode you entered from the Main Menu before you pressed the K key. The following examples show function menus that appear in the RUN MAT Mode.
uNumeric Calculations (NUM) [OPTN]-[NUM]
{Abs} ... {select this item and input a value to obtain the absolute value of the value.}
{Int}/{Frac} ... select the item and input a value to extract the {integer}/{fraction} part.
{Rnd} ... {rounds off the value used for internal calculations to 10 significant digits (to match the value in the Answer Memory), or to the number of decimal places (Fix) and number of significant digits (Sci) specified by you.}
{Intg} ... {select this item and input a value to obtain the largest integer that is not greater than the value.}
{E-SYM} ... {engineering symbol}
{m}/{}/{n}/{p}/{f} ... {milli (103)}/{micro (106)}/{nano (109)}/{pico (1012)}/{femto (1015)}
{k}/{M}/{G}/{T}/{P}/{E} ... {kilo (103)}/{mega (106)}/{giga (109)}/{tera (1012)}/{peta (1015)}/{exa (1018)}
uProbability/Distribution Calculations (PROB) [OPTN]-[PROB]
{x!} ... {press after inputting a value to obtain the factorial of the value.}
{nPr}/{nCr} ... {permutation}/{combination}
{Ran#}... {pseudo random number generation (0 to 1)}
{P(}/{Q(}/{R(} ... normal probability {P(t)}/{Q(t)}/{R(t)}
{t(} ... {value of normalized variate t(x)}
2-4-1 Function Calculations
1
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uHyperbolic Calculations (HYP) [OPTN]-[HYP]
{sinh}/{cosh}/{tanh} ... hyperbolic {sine}/{cosine}/{tangent}
{sinh1}/{cosh1}/{tanh1} ... inverse hyperbolic {sine}/{cosine}/{tangent}
uAngle Units, Coordinate Conversion, Sexagesimal Operations (ANGL) [OPTN]-[ANGL]
{}/{r}/{g} ... {degrees}/{radians}/{grads} for a specific input value
{ }... {specifies degrees (hours), minutes, seconds when inputting a degrees/minutes/ seconds value}
{'DMS} ... {converts decimal value to sexagesimal value}
{Pol(}/{Rec(} ... {rectangular-to-polar}/{polar-to-rectangular} coordinate conversion
u Instant Functions { } ... {converts decimal value to degrees/minutes/seconds value}
{ENG}/{ ENG} ... shifts the decimal place of the displayed value three digits to the {left}/{right} and {decreases}/{increases} the exponent by three. When you are using engineering notation, the engineering symbol is also changed accordingly.
The { }, {ENG} and { ENG} menu operations are available only when there is a calculation result on the display.
kAngle Units
To change the angle unit of an input value, first press K3(ANGL). On the pull-up menu that appears, select , r, or g.
Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
To convert 4.25 rad to degrees: u3(SET UP)cccc1(Deg)i 243.5070629 4.25K6(g)3(ANGL)c(r)w
47.3 + 82.5rad = 4774.20181 47.3+82.5K6(g)3(ANGL)c(r)w
2-4-2 Function Calculations
# Once you specify an angle unit, it remains in effect until you specify a different one.
The specification is retained even if you turn power off.
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k Trigonometric and Inverse Trigonometric Functions
Be sure to set the angle unit before performing trigonometric function and inverse trigonometric function calculations.
Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
sin 63 = 0.8910065242 u3(SET UP)cccc1(Deg)i s63w
cos ( rad) = 0.5 u3(SET UP)cccc2(Rad)i 3
c(!E()/d)w
tan ( 35gra) = 0.6128007881 u3(SET UP)cccc3(Gra)i t-35w
2 sin 45 cos 65 = 0.5976724775 u3(SET UP)cccc1(Deg)i 2*s45*c65w*1
cosec 30 = 1
= 2 1/s30w sin30
sin-10.5 = 30 !s(sin1)0.5*2w
(x when sinx = 0.5)
2-4-3 Function Calculations
*1* can be omitted. *2Input of leading zero is not necessary.
(90 = radians = 100 grads)
2
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k Logarithmic and Exponential Functions
Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
log 1.23 (log101.23) = 8.990511144 102 l1.23w
In 90 (loge90) = 4.49980967 I90w
101.23 = 16.98243652 (To obtain the antilogarithm of common !l(10x)1.23w logarithm 1.23)
e4.5 = 90.0171313 (To obtain the antilogarithm of natural !I(ex)4.5w logarithm 4.5)
(3)4 = (3) (3) (3) (3) = 81 (-3)M4w
34 = (3 3 3 3) = 81 -3M4w
1 7 (= 1237 ) = 1.988647795 7!M(x )123w
2 + 3 3 4 = 10 2+3*3!M(x )64-4w*1
2-4-4 Function Calculations
123
64
*1^ (x y) and x take precedence over multiplication and division.
1
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kHyperbolic and Inverse Hyperbolic Functions
Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
sinh 3.6 = 18.28545536 K6(g)2(HYP)b(sinh)3.6w
cosh 1.5 sinh 1.5 K6(g)2(HYP)c(cosh)1.5- = 0.2231301601 2(HYP)b(sinh)1.5w = e1.5 (Display: 1.5) I!-(Ans)w (Proof of cosh x sinh x = ex)
cosh1 20 = 0.7953654612 K6(g)2(HYP)f(cosh1)(20/15)w 15
Determine the value of x when tanh 4 x = 0.88
x = tanh1 0.88 K6(g)2(HYP)g(tanh1)0.88/4w 4
= 0.3439419141
2-4-5 Function Calculations
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kOther Functions
Be sure to specify Comp for Mode in the SET UP screen.
Example Operation + = 3.65028154 !x( )2+!x( )5w2 5
= 1.755317302 !x( )(d+!a(i) w(3 + i) +0.2848487846i
(3)2 = (3) (3) = 9 (-3)xw
32 = (3 3) = 9 -3xw
(3!)(x1)-4!)(x1) !)(x1)w
8! (= 1 2 3 .... 8) 8K6(g)1(PROB)b(x!)w = 40320
3 = 42 !((3 )(36*42*49)w36 42 49
What is the absolute value of
the common logarithm of
| log | = 0.1249387366 K5(NUM)b(Abs)l(3/4)w
What is the integer part of K5(NUM)c(Int)-3.5w 3.5? 3
What is the decimal part of K5(NUM)d(Frac)-3.5w 3.5? 0.5
What is the nearest integer K5(NUM)f(Intg)-3.5w not exceeding 3.5? 4
2-4-6 Function Calculations
3 4
?
3 4
1 = 12 1 1 3 4
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kRandom Number Generation (Ran#)
This function generates a 10-digit truly random or sequentially random number that is greater than zero and less than 1.
A truly random number is generated if you do not specify anything for the argument.
Example Operation
Ran # (Generates a random number.) K6(g)1(PROB)e(Ran#)w
(Each press of w generates a new random w
number.) w
Specifying an argument from 1 to 9 generates random numbers based on that sequence.
Specifying an argument of 0 initializes the sequence.*1
Example Operation
Ran# 1 (Generates the first random number in sequence 1.) 1(PROB)e(Ran#)bw
(Generates the second random number in sequence 1.) w
Ran# 0 (Initializes the sequence.) 1(PROB)e(Ran#)aw
Ran# 1 (Generates the first random number in sequence 1.) 1(PROB)e(Ran#)bw
2-4-7 Function Calculations
*1Changing to a different sequence or generating a totally random number (without an argument) initializes the sequence.
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2-4-8 Function Calculations
kCoordinate Conversion
u Rectangular Coordinates u Polar Coordinates
With polar coordinates, can be calculated and displayed within a range of 180< < 180 (radians and grads have same range).
Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
Calculate r and when x = 14 and y = 20.7 u3(SET UP)cccc1(Deg)i K6(g)3(ANGL)g(Pol() 14,20.7)w
Calculate x and y when r = 25 and = 56 u3(SET UP)cccc1(Deg)i K6(g)3(ANGL)h(Rec() 25,56)w
1 24.989 24.98979792 (r) 2 55.928 55.92839019 ()
1 13.979 13.97982259 (x) 2 20.725 20.72593931 (y)
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2-4-9 Function Calculations
n! n! nPr = nCr =
(n r)! r! (n r)!
k Permutation and Combination
u Permutation u Combination
Be sure to specify Comp for Mode in the SET UP screen.
Example To calculate the possible number of different arrangements using 4 items selected from among 10 items
Formula Operation
10P4 = 5040 10K6(g)1(PROB)c(nPr)4w
Example To calculate the possible number of different combinations of 4 items that can be selected from among 10 items
Formula Operation
10C4 = 210 10K6(g)1(PROB)d(nCr)4w
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k Fractions Fractional values are displayed with the integer first, followed by the numerator and then
the denominator.
Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
(Display: 3{13{20) 2$5+3$1$4w
= 3.65 $(Conversion to decimal) $(Conversion to fraction)
1$2578+1$4572w
1$2*.5w
$
1.5+2.3!a(i)w $$*3
1$(1$3+1$4)w*4
2-4-10 Function Calculations
2 1 13 + 3 = 3 5 4 20
1 1 + 2578 4572 = 6.066202547 104
1 0.5 = 0.25*2
2
(Display: )6.066202547E04*1
(Norm 1 display format)
1 =
4
(Display: 1{5{7) 1 5
= 1 1 1 7 + 3 4
*1When the total number of characters, including integer, numerator, denominator and delimiter marks exceeds 10, the input fraction is automatically displayed in decimal format.
*2Calculations containing both fractions and decimals are calculated in decimal format.
*3Pressing $ once when converting the decimal part of a complex number to a fraction first displays the real part and imaginary part on separate lines.
*4You can include fractions within the numerator or denominator of a fraction by putting the numerator or denominator in parentheses.
1 3 1.5 + 2.3i = 1 + 2i
2 10 Display: 1{1{2
+2{3{10i
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2-4-11 Function Calculations
k Engineering Notation Calculations
Input engineering symbols using the engineering notation menu.
Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
u3(SET UP)cccccccccc 4(Eng)i
999k (kilo) + 25k (kilo) 999K5(NUM)g(E-SYM)g(k)+255(NUM) = 1.024M (mega) g(E-SYM)g(k)w
9 10 = 0.9 = 900m (milli) 9/10w = 0.9 K6(g)6(g)6(g)3( ENG)*1
= 0.0009k (kilo) 3( ENG)*1
= 0.9 2(ENG)*2
= 900m 2(ENG)*2
*1Converts the displayed value to the next higher engineering unit, by shifting the decimal point three places to the right.
*2Converts the displayed value to the next lower engineering unit, by shifting the decimal point three places to the left.
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2-5 Numerical Calculations The following describes the items that are available in the menus you use when performing differential/ quadratic differential, integration, , maximum/minimum value, and Solve calculations.
When the option menu is on the display, press 4(CALC) to display the function analysis menu. The items of this menu are used when performing specific types of calculations.
{d/dx}/{d2/dx2}/{dx}/{}/{FMin}/{FMax}/{Solve} ... {differential}/{quadratic differential}/ {integration}/{ (sigma)}/{minimum value}/{maximum value}/{solve} calculations
Solve calculations
The following is the syntax for using the Solve function in a program.
Solve( f(x), n, a, b) (a: lower limit, b: upper limit, n: initial estimated value)
There are two different input methods that can be used for Solve calculations: direct assignment and variable table input.
With the direct assignment method (the one described here), you assign values directly to variables. This type of input is identical to that used with the Solve command used in the PRGM Mode.
Variable table input is used with the Solve function in the EQUA Mode. This input method is recommend for most normal Solve function input.
An Error (Iteration ERROR) occurs when there is no convergence of the solution.
2-5-1 Numerical Calculations
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kDifferential Calculations [OPTN]-[CALC]-[d /dx]
To perform differential calculations, first display the function analysis menu, and then input the values shown in the formula below.
K4(CALC)b(d/dx) f(x),a,tol)
The differentiation for this type of calculation is defined as:
In this definition, infinitesimal is replaced by a sufficiently small Ax, with the value in the neighborhood of f ' (a) calculated as:
In order to provide the best precision possible, this unit employs central difference to perform differential calculations.
Using Differential Calculation in a Graph Function Omitting the tolerance (tol) value when using the differential command inside of a graph
function simplifies the calculation for drawing the graph. In such a case, precision is sacrificed for the sake of faster drawing. The tolerance value is specified, the graph is drawn with the same precision obtained when you normally perform a differential calculation.
You can also omit input of the derivative point by using the following format for the differential graph: Y2=d/dx(Y1). In this case, the value of the X variable is used as the derivative point.
2-5-2 Numerical Calculations
d d/dx ( f (x), a) f (a)
dx
f (a + Ax) f (a) f '(a) = lim
AxAx0
f (a + Ax) f (a) f '(a)
Ax
(a: point for which you want to determine the derivative, tol: tolerance)
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Example To determine the derivative at point x = 3 for the function y = x3 + 4x2 + x 6, with a tolerance of tol = 1E 5
Input the function f(x).
AK4(CALC)b(d/dx)vMd+evx+v-g,
Input point x = a for which you want to determine the derivative.
d,
Input the tolerance value.
bE-f)
w
# In the function f(x), only X can be used as a variable in expressions. Other variables (A through Z, r, ) are treated as constants, and the value currently assigned to that variable is applied during the calculation.
# Input of the tolerance (tol) value and the closing parenthesis can be omitted. If you omit tolerance (tol) value, the calculator automati- cally uses a value for tol as 1E-10.
# Specify tolerance (tol) value of 1E-14 or less. An error (Iteration ERROR) occurs whenever no solution that satisfies the tolerance value can be obtained.
# Discontinuous points or sections with drastic fluctuation can adversely affect precision or even cause an error.
2-5-3 Numerical Calculations
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uApplications of Differential Calculations Differentials can be added, subtracted, multiplied or divided with each other.
Therefore:
Differential results can be used in addition, subtraction, multiplication, and division, and in functions.
2 f '(a), log ( f '(a)), etc.
Functions can be used in any of the terms ( f (x), a, tol) of a differential.
2-5-4 Numerical Calculations
# You cannot use a differential, quadratic differential, integration, , maximum/minimum value or solve calculation expression inside a differential calculation term.
# Pressing A during calculation of a differential (while the cursor is not shown on the display) interrupts the calculation.
# Always use radians (Rad Mode) as the angle unit when performing trigonometric differentials.
d d f (a) = f '(a), g (a) = g '(a) dx dx
f '(a) + g '(a), f '(a) g'(a), etc.
d (sinx + cosx, sin0.5, 1E - 8), etc. dx
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kQuadratic Differential Calculations [OPTN]-[CALC]-[d2/dx2]
After displaying the function analysis menu, you can input quadratic differentials using either of the two following formats.
K4(CALC)c(d2/dx2) f(x),a,tol)
Quadratic differential calculations produce an approximate differential value using the following second order differential formula, which is based on Newtons polynomial interpretation.
2 f(a + 3h) 27 f(a + 2h) + 270 f(a + h) 490 f(a)+270 f(a h) 27 f(a 2h) +2 f(a 3h)f ''(a) = 180h2
In this expression, values for sufficiently small increments of h are used to obtain a value that approximates f (a).
Example To determine the quadratic differential coefficient at the point where x = 3 for the function y = x3 + 4x2 + x 6 Here we will use a tolerance tol = 1E 5
Input the function f(x).
AK4(CALC)c(d2/dx2) vMd+
evx+v-g,
Input 3 as point a, which is the differential coefficient point.
d,
Input the tolerance value.
bE-f)
w
2-5-5 Numerical Calculations
# In the function f(x), only X can be used as a variable in expressions. Other variables (A through Z, r, ) are treated as constants, and the value currently assigned to that variable is applied during the calculation.
# Input of the tolerance (tol) value and the closing parenthesis can be omitted.
# Discontinuous points or sections with drastic fluctuation can adversely affect precision or even cause an error.
(a: differential coefficient point , tol: tolerance)
d2 d2
(f (x), a) f (a) dx2 dx2
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uQuadratic Differential Applications Arithmetic operations can be performed using two quadratic differentials.
Therefore:
f ''(a) + g''(a), f ''(a) g''(a), etc.
The result of a quadratic differential calculation can be used in a subsequent arithmetic or function calculation.
2 f ''(a), log ( f ''(a) ), etc.
Functions can be used within the terms ( f(x), a, tol ) of a quadratic differential expression.
2-5-6 Numerical Calculations
d2 d2
f (a) = f ''(a), g (a) = g''(a) dx2 dx2
d2
(sin x + cos x, sin 0.5, 1E - 8), etc. dx2
# You cannot use a differential, quadratic differential, integration, , maximum/minimum value or Solve calculation expression inside of a quadratic differential calculation term.
# Specify tolerance (tol) value of 1E-14 or less. An error (Iteration ERROR) occurs whenever no solution that satisfies the tolerance value can be obtained.
# You can interrupt an ongoing quadratic differential calculation by pressing the A key.
# Always use radians (Rad Mode) as the angle unit when performing trigonometric quadratic differentials.
# Using Quadratic Differential Calculation in a Graph Function (see page 2-5-2)
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k Integration Calculations [OPTN]-[CALC]-[dx]
To perform integration calculations, first display the function analysis menu and then input the values in the formula shown below.
K4(CALC)d (dx) f(x) , a , b , tol )
( f(x), a, b, tol) a b
f(x)dx
As shown in the illustration above, integration calculations are performed by calculating integral values from a through b for the function y = f (x) where a < x < b, and f (x) > 0. This in effect calculates the surface area of the shaded area in the illustration.
2-5-7 Numerical Calculations
Area of a
b f(x)dx is calculated
(a: start point, b: end point, tol: tolerance)
# If f (x) < 0 where a a < x < b, the surface area calculation produces negative values (surface area 1).
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Example To perform the integration calculation for the function shown below, with a tolerance of tol = 1E - 4
1
5 (2x2 + 3x + 4) dx
Input the function f (x).
AK4(CALC)d(dx)cvx+dv+e,
Input the start point and end point.
b,f,
Input the tolerance value.
bE-e)
w
uApplication of Integration Calculation Integrals can be used in addition, subtraction, multiplication or division.
a
b f(x) dx + c
d g (x) dx, etc.
Integration results can be used in addition, subtraction, multiplication or division, in functions.
2 a
b f(x) dx, etc. log (a
b f(x) dx), etc.
Functions can be used in any of the terms ( f (x), a, b, tol) of an integral.
cos 0.5
(sin x + cos x) dx = (sin x + cos x, sin 0.5, cos 0.5, 1E - 4) sin 0.5
2-5-8 Numerical Calculations
# In the function f(x), only X can be used as a variable in expressions. Other variables (A through Z, r, ) are treated as constants, and the value currently assigned to that variable is applied during the calculation.
# Input of tol and closing parenthesis can be omitted. If you omit tol, the calculator automatically uses a default value of 1E-5.
# Integration calculations can take a long time to complete.
# You cannot use a differential, quadratic differential, integration, , maximum/minimum value or Solve calculation expression inside of an integration calculation term.
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Note the following points to ensure correct integration values.
(1) When cyclical functions for integration values become positive or negative for different divisions, perform the calculation for single cycles, or divide between negative and positive, and then add the results together.
a
b f(x)dx = a
c f(x)dx + (c
b f(x)dx)
Positive part (S) Negative part (S)
(2) When minute fluctuations in integration divisions produce large fluctuations in integration values, calculate the integration divisions separately (divide the large fluctuation areas into smaller divisions), and then add the results together.
a
b f(x)dx = a
x1
f(x)dx + x1
x2
f(x)dx +.....+ x4
b f(x)dx
2-5-9 Numerical Calculations
Negative part (S)
Positive part (S)
# Pressing A during calculation of an integral (while the cursor is not shown on the display) interrupts the calculation.
# Always use radians (Rad Mode) as the angle unit when performing trigonometric integrations.
# An error (Iteration ERROR) occurs whenever no solution that satisfies the tolerance value can be obtained.
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k Calculations [OPTN]-[CALC]-[ ]
To perform calculations, first display the function analysis menu, and then input the values shown in the formula below.
K4(CALC)e() ak , k , , , n )
Example To calculate the following:
Use n = 1 as the distance between partitions.
AK4(CALC)e()a,(K)x -da,(K)+f, a,(K),c,g,b)w
2-5-10 Numerical Calculations
6
(k2 3k + 5) k = 2
# You can use only one variable in the function for input sequence ak.
# Input integers only for the initial term () of sequence ak and last term () of sequence ak .
# Input of n and the closing parentheses can be omitted. If you omit n, the calculator automati- cally uses n = 1.
(ak, k, , , n) = ak = a + a+1 +........+ a
k = (n: distance between partitions)
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u Calculation Applications
Arithmetic operations using calculation expressions
Expressions:
Possible operations: Sn + Tn, Sn Tn, etc.
Arithmetic and function operations using calculation results
2 Sn, log (Sn), etc.
Function operations using calculation terms (ak, k)
(sink, k, 1, 5), etc.
2-5-11 Numerical Calculations
n n
Sn = ak, Tn = bk
k = 1 k = 1
# You cannot use a differential, quadratic differential, integration, , maximum/minimum value or Solve calculation expression inside of a calculation term.
# Make sure that the value used as the final term is greater than the value used as the initial term . Otherwise, an error will occur.
# To interrupt an ongoing calculation (indicated when the cursor is not on the display), press the A key.
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2-5-12 Numerical Calculations
kMaximum/Minimum Value Calculations [OPTN]-[CALC]-[FMin]/[FMax]
After displaying the function analysis menu, you can input maximum/minimum calculations using the formats below, and solve for the maximum and minimum of a function within interval a < x < b. (a: start point of interval, b: end point of interval, n: precision (n = 1 to 9))
uMinimum Value
K4(CALC)f(FMin) f(x) , a , b , n )
uMaximum Value
K4(CALC)g(FMax) f(x), a , b , n )
Example 1 To determine the minimum value for the interval defined by start point a = 0 and end point b = 3, with a precision of n = 6 for the function y = x2 4x + 9
Input f(x).
AK4(CALC)f(FMin) vx-ev+j,
Input the interval a = 0, b = 3.
a,d,
Input the precision n = 6.
g)
w
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2-5-13 Numerical Calculations
# In the function f(x), only X can be used as a variable in expressions. Other variables (A through Z, r, ) are treated as constants, and the value currently assigned to that variable is applied during the calculation.
# Input of n and the closing parenthesis can be omitted.
# Discontinuous points or sections with drastic fluctuation can adversely affect precision or even cause an error.
# You cannot use a differential, quadratic differential, integration, , maximum/minimum value or Solve calculation expression inside of a maximum/minimum calculation term.
# Inputting a larger value for n increases the precision of the calculation, but it also increases the amount of time required to perform the calculation.
# The value you input for the end point of the interval (b) must be greater than the value you input for the start point (a). Otherwise an error occurs.
# You can interrupt an ongoing maximum/ minimum calculation by pressing the A key.
# You can input an integer in the range of 1 to 9 for the value of n. Using any value outside this range causes an error.
Example 2 To determine the maximum value for the interval defined by start point a = 0 and end point b = 3, with a precision of n = 6 for the function y = x2 + 2x + 2
Input f(x).
AK4(CALC)g(FMax) -vx+cv+c,
Input the interval a = 0, b = 3.
a,d,
Input the precision n = 6.
g)
w
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2-6 Complex Number Calculations You can perform addition, subtraction, multiplication, division, parentheses calculations, function calculations, and memory calculations with complex numbers just as you do with the manual calculations described on pages 2-1-1 and 2-4-6.
You can select the complex number calculation mode by changing the Complex Mode item on the SET UP screen to one of the following settings.
{Real} ... Calculation in the real number range only*1
{a+bi} ... Performs complex number calculation and displays results in rectangular form
{re^i} ...Performs complex number calculation and displays results in polar form*2
Press K3(CPLX) to display the complex calculation number menu, which contains the following items.
{Abs}/{Arg} ... obtains {absolute value}/{argument}
{Conjg} ... {obtains conjugate}
{ReP}/{ImP} ... {real}/{imaginary} part extraction
{'re^i}/{'a+bi} ... converts the result to {polar}/{linear}
2-6-1 Complex Number Calculations
*1 When there is an imaginary number in the argument, however, complex number calculation is performed and the result is displayed using rectangular form.
Examples: ln 2i = 0.6931471806 + 1.570796327i ln 2i + ln (- 2 ) = (Non-Real ERROR)
*2 The display range of depends on the angle unit set for the Angle item on the SET UP screen.
Deg ... 180 < < 180 Rad ... < < Gra ... 200 < < 200
# Solutions obtained by the Real and a+bi / re^i modes are different for power root (xy) calculations when x < 0 and y = m/n when n is an odd number.
Example: 3x (- 8) = 2 (Real)
= 1 + 1.732050808i(a+bi / re^i)
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2-6-2 Complex Number Calculations
kAbsolute Value and Argument [OPTN]-[CPLX]-[Abs]/[Arg]
The unit regards a complex number in the form a + bi as a coordinate on a Gaussian plane, and calculates absolute value Z and argument (arg).
Example To calculate absolute value (r) and argument () for the complex number 3 + 4i, with the angle unit set for degrees
AK3(CPLX)b(Abs)
(d+e!a(i) w
(Calculation of absolute value)
AK3(CPLX)c(Arg)
(d+e!a(i) w
(Calculation of argument)
# The result of the argument calculation differs in accordance with the current angle unit setting (degrees, radians, grads).
Imaginary axis
Real axis
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kConjugate Complex Numbers [OPTN]-[CPLX]-[Conjg]
A complex number of the form a + bi becomes a conjugate complex number of the form a bi.
Example To calculate the conjugate complex number for the complex number 2 + 4i
AK3(CPLX)d(Conjg)
(c+e!a(i) w
kExtraction of Real and Imaginary Parts [OPTN]-[CPLX]-[ReP]/[lmP]
Use the following procedure to extract the real part a and the imaginary part b from a complex number of the form a + bi.
Example To extract the real and imaginary parts of the complex number 2 + 5i
AK3(CPLX)e(ReP)
(c+f!a(i) w
(Real part extraction)
AK3(CPLX)f(ImP)
(c+f!a(i) w
(Imaginary part extraction)
2-6-3 Complex Number Calculations
# The input/output range of complex numbers is normally 10 digits for the mantissa and two digits for the exponent.
# When a complex number has more than 21 digits, the real part and imaginary part are displayed on separate lines.
# When either the real part or imaginary part of a complex number equals zero, that part is not displayed in rectangular form.
# 18 bytes of memory are used whenever you assign a complex number to a variable.
# The following functions can be used with complex numbers.
, x2, x1, ^(xy), 3 , x , In, log, 10x, ex, sin, cos, tan, sin1, cos1, tan1, sinh, cosh, tanh, sinh1, cosh1, tanh1
Int, Frac, Rnd, Intg, Fix, Sci, ENG, ENG, ,
, a b/c, d/c
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kPolar Form and Rectangular Transformation [OPTN]-[CPLX]-['re^i]
Use the following procedure to transform a complex number displayed in rectangular form to polar form, and vice versa.
Example To transform the rectangular form of complex number 1 + 3 i to its polar form
Ab+(!x( )d)!a(i)
K3(CPLX)g('re^i)w
2-6-4 Complex Number Calculations
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2-7 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
You can use the RUN MAT Mode and binary, octal, decimal, and hexadecimal settings to perform calculations that involve binary, octal, decimal and hexadecimal values. You can also convert between number systems and perform bitwise operations.
You cannot use scientific functions in binary, octal, decimal, and hexadecimal calcula- tions.
You can use only integers in binary, octal, decimal, and hexadecimal calculations, which means that fractional values are not allowed. If you input a value that includes a decimal part, the unit automatically cuts off the decimal part.
If you attempt to enter a value that is invalid for the number system (binary, octal, decimal, hexadecimal) you are using, the calculator displays an error message. The following shows the numerals that can be used in each number system.
Binary: 0, 1
Octal: 0, 1, 2, 3, 4, 5, 6, 7
Decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Negative binary, octal, and hexadecimal values are produced using the twos complement of the original value.
The following are the display capacities for each of the number systems.
Number System Display Capacity
Binary 16 digits
Octal 11 digits
Decimal 10 digits
Hexadecimal 8 digits
2-7-1 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
# The alphabetic characters used in the hexadecimal number appear differently on the display to distinguish them from text characters.
Normal Text
Hexadecimal Values
Keys
A B C D E F
u v w x y z
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The following are the calculation ranges for each of the number systems.
Binary Values
Positive: 0 < x < 111111111111111
Negative: 1000000000000000 < x < 1111111111111111
Octal Values
Positive: 0 < x < 17777777777
Negative: 20000000000 < x < 37777777777
Decimal Values
Positive: 0 < x < 2147483647
Negative: 2147483648 < x < 1
Hexadecimal Values
Positive: 0 < x < 7FFFFFFF
Negative: 80000000 < x < FFFFFFFF
u To perform a binary, octal, decimal, or hexadecimal calculation
1. In the main menu, select RUN MAT. [SET UP]- [Mode] -[Dec]/[Hex]/[Bin]/[Oct]
2. Press u3(SET UP) and then specify the default number system by pressing 2(Dec), 3(Hex), 4(Bin), or 5(Oct).
3. Press i to change to the screen for calculation input. This causes a function menu with the following items to appear.
{d~o}/{LOGIC}/{DISP}/{SYBL} ... {number system specification}/{bitwise operation}/ {decimal/hexadecimal/binary/octal conversion}/{symbol} menu
2-7-2 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
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kSelecting a Number System
You can specify decimal, hexadecimal, binary, or octal as the default number system using the set up screen. After you press the function key that corresponds to the system you want to use, press w.
u To specify a number system for an input value You can specify a number system for each individual value you input. Press 1(d~o) to display a menu of number system symbols. Press the function key that corresponds to the symbol you want to select and then input the value.
{d}/{h}/{b}/{o} ... {decimal}/{hexadecimal}/{binary}/{octal}
u To input values of mixed number systems
Example To input 12310 or 10102, when the default number system is hexadecimal
u3(SET UP)3(Hex)i
A1(d~o)b(d)bcdw
1(d~o)d(b)babaw
kArithmetic Operations
Example 1 To calculate 101112 + 110102
u3(SET UP)4(Bin)i
Ababbb+
bbabaw
2-7-3 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
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Example 2 To input and execute 1238 ABC16, when the default number system is decimal or hexadecimal
u3(SET UP)2(Dec)i
A1(d~o)e(o)bcd*
1(d~o)c(h)ABC*1w
3(DISP)c(Hex)w
kNegative Values and Bitwise Operations
Press 2(LOGIC) to display a menu of negation and bitwise operators.
{Neg} ... {negation}*2
{Not}/{and}/{or}/{xor}/{xnor} ... {NOT}*3/{AND}/{OR}/{XOR}/{XNOR}*4
u Negative Values
Example To determine the negative of 1100102
u3(SET UP)4(Bin)i
A2(LOGIC)b(Neg)
bbaabaw
uBitwise Operations
Example 1 To input and execute 12016 and AD16
u3(SET UP)3(Hex)i
Abca2(LOGIC)
d(and)AD*1w
2-7-4 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
*1 See page 2-7-1. *2 twos complement *3 ones complement (bitwise complement)
1
*4 bitwise AND, bitwise OR, bitwise XOR, bitwise XNOR
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Example 2 To display the result of 368 or 11102 as an octal value
u3(SET UP)5(Oct)i
Adg2(LOGIC)
e(or)1(d~o)d(b)
bbbaw
Example 3 To negate 2FFFED16
u3(SET UP)3(Hex)i
A2(LOGIC)c(Not)
cFFFED*1w
uNumber System Transformation Press 3(DISP) to display a menu of number system transformation functions.
{'Dec}/{'Hex}/{'Bin}/{'Oct} ... transformation of displayed value to its {decimal}/ {hexadecimal}/{binary}/{octal} equivalent
u To convert a displayed value from one number system to another
Example To convert 2210 (default number system) to its binary or octal value
Au3(SET UP)2(Dec)i
1(d~o)b(d)ccw
3(DISP)d('Bin)w
3(DISP)e('Oct)w
2-7-5 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
*1 See page 2-7-1.
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2-8-1 Matrix Calculations
2-8 Matrix Calculations From the Main Menu, enter the RUN MAT Mode, and press 1(MAT) to perform Matrix calculations.
26 matrix memories (Mat A through Mat Z) plus a Matrix Answer Memory (MatAns), make it possible to perform the following matrix operations.
Addition, subtraction, multiplication
Scalar multiplication calculations
Determinant calculations
Matrix transposition
Matrix inversion
Matrix squaring
Raising a matrix to a specific power
Absolute value, integer part extraction, fractional part extraction, maximum integer calculations
Matrix modification using matrix commands
Absolute value, argument, complex conjugate calculation for a matrix with complex number components
Real part and complex number part extraction of a matrix with complex number components
The maximum number of rows that can be specified for a matrix is 255, and the maximum number of columns is 255.
# About Matrix Answer Memory (MatAns) The calculator automatically stores matrix calculation results in Matrix Answer Memory. Note the following points about Matrix Answer Memory.
Whenever you perform a matrix calculation, the current Matrix Answer Memory contents are replaced by the new result. The previous contents are deleted and cannot be recovered.
Inputting values into a matrix does not affect Matrix Answer Memory contents.
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k Inputting and Editing Matrices
Pressing 1(MAT) displays the matrix editor screen. Use the matrix editor to input and edit matrices.
{DIM} ... {specifies the matrix dimensions (number of cells)}
{DEL}/{DELA} ... deletes {a specific matrix}/{all matrices}
u Creating a Matrix To create a matrix, you must first define its dimensions (size) in the Matrix list. Then you can input values into the matrix.
u To specify the dimensions (size) of a matrix
Example To create a 2-row 3-column matrix in the area named Mat B
Highlight Mat B.
c
1(DIM) Specify the number of rows.
cw
Specify the number of columns.
dw
w
All of the cells of a new matrix contain the value 0.
2-8-2 Matrix Calculations
# If Memory ERROR remains next to the matrix area name after you input the dimensions, it
means there is not enough free memory to create the matrix you want.
m n m (row) n (column) matrix
None no matrix preset
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u To input cell values
Example To input the following data into Matrix B : 1 2 3 4 5 6
c (Selects Mat B.)
w
bwcwdw
ewfwgw
(Data is input into the highlighted cell. Each time you press w, the highlighting moves to the next cell to the right.)
# You can input complex numbers into the cell of a matrix.
# Displayed cell values show positive integers up to six digits, and negative integers up to five digits (one digit used for the negative sign). Exponential values are shown with up to two digits for the exponent. Fractional values are not displayed.
# You can see the entire value assigned to a cell by using the cursor keys to move the highlight- ing to the cell whose value you want to view.
# The amount of memory required for a matrix is 9 bytes per cell. This means that a 3 3 matrix requires 81 bytes of memory (3 3 9 = 81).
Inputting complex numbers into a matrix doubles the amount of memory used.
2-8-3 Matrix Calculations
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uDeleting Matrices You can delete either a specific matrix or all matrices in memory.
u To delete a specific matrix 1. While the Matrix list is on the display, use f and c to highlight the matrix you want
to delete.
2. Press 2(DEL).
3. Press w(Yes) to delete the matrix or i(No) to abort the operation without deleting anything.
u To delete all matrices 1. While the Matrix list is on the display, press 3(DELA).
2. Press w(Yes) to delete all matrices in memory or i(No) to abort the operation without deleting anything.
2-8-4 Matrix Calculations
# The indicator None replaces the dimensions of the matrix you delete.
# Inputting the format or changing the dimensions of a matrix deletes its current contents.
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kMatrix Cell Operations
Use the following procedure to prepare a matrix for cell operations.
1. While the Matrix list is on the display, use f and c to highlight the name of the matrix you want to use. You can jump to a specific matrix by inputting the letter that corresponds to the matrix name. Inputting ai(N), for example, jumps to Mat N. Pressing !-(Ans) jumps to the Matrix current Memory.
2. Press w and the function menu with the following items appears.
{EDIT} ... {cell editing screen}
{R-OP} ... {row operation menu}
{R DEL}/{R INS}/{R ADD} ... row {delete}/{insert}/{add}
{C DEL}/{C INS}/{C ADD} ... column {delete}/{insert}/{add}
All of the following examples use Matrix A.
u Row Calculations The following menu appears whenever you press 2(R-OP) while a recalled matrix is on the display.
{Swap} ... {row swap}
{Row} ... {product of specified row and scalar}
{Row+} ... {addition of one row and the product of a specified row with a scalar}
{Row+} ... {addition of specified row to another row}
u To swap two rows
Example To swap rows two and three of the following matrix : 1 2
Matrix A = 3 4
5 6
2(R-OP)b(Swap)
Input the number of the rows you want to swap.
cwdw
6(EXE) (orw)
2-8-5 Matrix Calculations
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u To calculate the scalar multiplication of a row
Example To calculate the product of row 2 of the following matrix and the scalar 4 :
1 2
Matrix A = 3 4
5 6
2(R-OP)c(Row)
Input multiplier value.
ew
Specify row number.
cw
6(EXE) (orw)
u To calculate the scalar multiplication of a row and add the result to another row
Example To calculate the product of row 2 of the following matrix and the scalar 4, then add the result to row 3 :
1 2
Matrix A = 3 4
5 6
2(R-OP)d(Row+)
Input multiplier value.
ew
Specify number of row whose product should be
calculated.
cw
Specify number of row where result should be added.
dw
6(EXE) (orw)
2-8-6 Matrix Calculations
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u To add two rows together
Example To add row 2 to row 3 of the following matrix :
1 2
Matrix A = 3 4
5 6
2(R-OP)e(Row+)
Specify number of row to be added.
cw
Specify number of row to be added to.
dw
6(EXE) (orw)
u Row Operations {R DEL} ... {delete row}
{R INS} ... {insert row}
{R ADD} ... {add row}
u To delete a row
Example To delete row 2 of the following matrix :
1 2
Matrix A = 3 4
5 6
c
3(R DEL)
2-8-7 Matrix Calculations
20010101
u To insert a row
Example To insert a new row between rows one and two of the following matrix :
1 2
Matrix A = 3 4
5 6
c
4(R INS)
u To add a row
Example To add a new row below row 3 of the following matrix :
1 2
Matrix A = 3 4
5 6
cc
5(R ADD)
2-8-8 Matrix Calculations
20010101
2-8-9 Matrix Calculations
uColumn Operations {C DEL} ... {delete column}
{C INS} ... {insert column}
{C ADD} ... {add column}
u To delete a column
Example To delete column 2 of the following matrix :
1 2
Matrix A = 3 4
5 6
e
6(g)1(C DEL)
u To insert a column
Example To insert a new column between columns 1 and 2 of the following matrix :
1 2
Matrix A = 3 4
5 6
e
6(g)2(C INS)
20010101
u To add a column
Example To add a new column to the right of column 2 of the following matrix :
1 2
Matrix A = 3 4
5 6
e
6(g)3(C ADD)
kModifying Matrices Using Matrix Commands [OPTN]-[MAT]
u To display the matrix commands 1. From the Main Menu, enter the RUN MAT Mode.
2. Press K to display the option menu.
3. Press 2(MAT) to display the matrix command menu.
The following describes only the matrix command menu items that are used for creating matrices and inputting matrix data.
{Mat} ... {Mat command (matrix specification)}
{Dim} ... {Dim command (dimension check)}
{Augmnt} ... {Augment command (link two matrices)}
{Ident} ... {Identity command (identity matrix input)}
{Fill} ... {Fill command (identical cell values)}
{MList} ... {MatList command (assign contents of selected column to list file)}
2-8-10 Matrix Calculations
20010101
u Matrix Data Input Format [OPTN]-[MAT]-[Mat]
The following shows the format you should use when inputting data to create a matrix using the Mat command.
a11 a12 a1n
a21 a22 a2n
am1 am2 amn
= [ [a11, a12, ..., a1n] [a21, a22, ..., a2n] .... [am1, am2, ..., amn] ] Mat [letter A through Z]
Example 1 To input the following data as Matrix A :
1 3 5 2 4 6
!+( [ )!+( [ )b,d,f
!-( ] )!+( [ )c,e,g
!-( ] )!-( ] )aK2(MAT)
b(Mat)av(A)
w
2-8-11 Matrix Calculations
# You can also use !c(Mat) in place of K2 (MAT)b(Mat).
# The maximum value of both m and n is 255.
# An error occurs if memory becomes full as you are inputting data.
# You can also use the above format inside a program that inputs matrix data.
Matrix name
20010101
u To input an identity matrix [OPTN]-[MAT]-[Ident]
Use the Identity command to create an identity matrix.
Example 2 To create a 3 3 identity matrix as Matrix A
K2(MAT)g(Ident)
da2(MAT)b(Mat)av(A)w
Number of rows/columns
u To check the dimensions of a matrix [OPTN]-[MAT]-[Dim]
Use the Dim command to check the dimensions of an existing matrix.
Example 3 To check the dimensions of Matrix A, which was input in Example 1
K2(MAT)c(Dim)
2(MAT)b(Mat)av(A)w
The display shows that Matrix A consists of two rows and three columns.
You can also use {Dim} to specify the dimensions of the matrix.
Example 4 To specify dimensions of 2 rows and 3 columns for Matrix B
!*( )c,d!/( )a
K2(MAT)c(Dim)
2(MAT)b(Mat)al(B)w
2-8-12 Matrix Calculations
20010101
uModifying Matrices Using Matrix Commands You can also use matrix commands to assign values to and recall values from an existing matrix, to fill in all cells of an existing matrix with the same value, to combine two matrices into a single matrix, and to assign the contents of a matrix column to a list file.
u To assign values to and recall values from an existing matrix [OPTN]-[MAT]-[Mat]
Use the following format with the Mat command to specify a cell for value assignment and recall.
Mat X [m, n]
X .................................. matrix name (A through Z, or Ans)
m ................................ row number
n ................................. column number
Example 1 Assign 10 to the cell at row 1, column 2 of the following matrix : 1 2
Matrix A = 3 4
5 6
baaK2(MAT)b(Mat)
av(A)!+( )b,c
!-( )w
Example 2 Multiply the value in the cell at row 2, column 2 of the above matrix by 5
K2(MAT)b(Mat)
av(A)!+( )c,c
!-( )*fw
2-8-13 Matrix Calculations
20010101
uTo fill a matrix with identical values and to combine two matrices into a single matrix [OPTN]-[MAT]-[Fill]/[Augmnt]
Use the Fill command to fill all the cells of an existing matrix with an identical value and the Augment command to combine two existing matrices into a single matrix.
Example 1 To fill all of the cells of Matrix A with the value 3
K2(MAT)h(Fill)
d,2(MAT)b(Mat)av(A)w
2(MAT)b(Mat)av(A)w
Example 2 To combine the following two matrices :
A = 1
B = 3
2 4
K2(MAT)f(Augmnt)
2(MAT)b(Mat)av(A),
2(MAT)b(Mat)al(B)w
2-8-14 Matrix Calculations
# The two matrices you combine must have the same number of rows. An error occurs if you try to combine two matrices that have different numbers of rows.
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uTo assign the contents of a matrix column to a list [OPTN]-[MAT]-[MList]
Use the following format with the MatList command to specify a column and a list.
Mat List (Mat X, m) List n
X = matrix name (A through Z, or Ans)
m = column number
n = list number
Example To assign the contents of column 2 of the following matrix to list 1 :
1 2
Matrix A = 3 4
5 6
K2(MAT)i(MList)
2(MAT)b(Mat)av(A),c)
aK1(LIST)b(List)bw
K1(LIST)b(List)bw
# You can also use !b(List) in place of K1(LIST)b(List).
# You can use Matrix Answer Memory to assign the results of the above matrix input and edit operations to a matrix variable. To do so, use the following syntax. Fill (n, Mat ) Mat Augment (Mat , Mat ) Mat
2-8-15 Matrix Calculations
In the above, , , and are any variable names A through Z, and n is any value. The above does not affect the contents of Matrix Answer Memory.
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kMatrix Calculations [OPTN]-[MAT]
Use the matrix command menu to perform matrix calculation operations.
u To display the matrix commands 1. From the Main Menu, enter the RUN MAT Mode.
2. Press K to display the option menu.
3. Press 2(MAT) to display the matrix command menu.
The following describes only the matrix commands that are used for matrix arithmetic operations.
{Mat} ... {Mat command (matrix specification)}
{Det} ... {Det command (determinant command)}
{Trn} ... {Trn command (transpose matrix command)}
{Ident} ... {Identity command (identity matrix input)}
All of the following examples assume that matrix data is already stored in memory.
2-8-16 Matrix Calculations
20010101
uMatrix Arithmetic Operations [OPTN]-[MAT]-[Mat]
Example 1 To add the following two matrices (Matrix A + Matrix B) :
A = 1 1
B = 2 3
2 1 2 1
AK2(MAT)b(Mat)av(A)+
2(MAT)b(Mat)al(B)w
Example 2 Calculate the product to the following matrix using a multiplier value of 5 :
Matrix A = 1 2
3 4
AfK2(MAT)b(Mat)
av(A)w
Example 3 To multiply the two matrices in Example 1 (Matrix A Matrix B)
AK2(MAT)b(Mat)av(A)*
2(MAT)b(Mat)al(B)w
Example 4 To multiply Matrix A (from Example 1) by a 2 2 identity matrix
AK2(MAT)b(Mat)av(A)*
2(MAT)g(Ident)cw
Number of rows and columns
# The two matrices must have the same dimensions in order to be added or subtracted. An error occurs if you try to add or subtract matrices of different dimensions.
# For multiplication (Matrix 1 Matrix 2), the number of columns in Matrix 1 must match the number of rows in Matrix 2. Otherwise, an error occurs.
2-8-17 Matrix Calculations
# When performing matrix arithmetic operations, inputting the Identity command at the location of a matrix command (such as Mat A) makes it possible to perform identity matrix
calculations.
1
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uDeterminant [OPTN]-[MAT]-[Det]
Example Obtain the determinant for the following matrix :
1 2 3
Matrix A = 4 5 6
1 2 0
K2(MAT)d(Det)2(MAT)b(Mat)
av(A)w
uMatrix Transposition [OPTN]-[MAT]-[Trn]
A matrix is transposed when its rows become columns and its columns become rows.
Example To transpose the following matrix :
1 2
Matrix A = 3 4
5 6
K2(MAT)e(Trn)2(MAT)b(Mat)
av(A)w
2-8-18 Matrix Calculations
# Determinants can be obtained only for square matrices (same number of rows and columns). Trying to obtain a determinant for a matrix that is not square produces an error.
# The determinant of a 2 2 matrix is calculated as shown below.
# The determinant of a 3 3 matrix is calculated as shown below.
| A | = a11 a12
= a11a22 a12a21
a21 a22
= a11a22a33 + a12a23a31 + a13a21a32
a11a23a32 a12a21a33 a13a22a31
a11 a12 a13
a21 a22 a23
a31 a32 a33
| A | =
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uMatrix Inversion [OPTN]-[MAT]-[x1]
Example To invert the following matrix :
Matrix A = 1 2
3 4
K2(MAT)b(Mat)
av(A)!) (x1)w
uSquaring a Matrix [OPTN]-[MAT]-[x2]
Example To square the following matrix :
Matrix A = 1 2
3 4
K2(MAT)b(Mat)av(A)xw
2-8-19 Matrix Calculations
# Only square matrices (same number of rows and columns) can be inverted. Trying to invert a matrix that is not square produces an error.
# A matrix with a determinant of zero cannot be inverted. Trying to invert a matrix with determinant of zero produces an error.
# Calculation precision is affected for matrices whose determinant is near zero.
# A matrix being inverted must satisfy the conditions shown below.
The following shows the formula used to invert Matrix A into inverse matrix A1.
A A1 = A1 A = E = 1 0 0 1
A = a b c d
Note that ad bcG 0.
A1= 1 ad bc
d b c a
20010101
uRaising a Matrix to a Power [OPTN]-[MAT]-[ ]
Example To raise the following matrix to the third power :
Matrix A = 1 2
3 4
K2(MAT)b(Mat)av(A)
Mdw
uDetermining the Absolute Value, Integer Part, Fraction Part, and Maximum Integer of a Matrix [OPTN]-[NUM]-[Abs]/[Frac]/[Int]/[Intg]
Example To determine the absolute value of the following matrix :
Matrix A = 1 2
3 4
K5(NUM)b(Abs)
K2(MAT)b(Mat)av(A)w
2-8-20 Matrix Calculations
# Determinants and inverse matrices are subject to error due to dropped digits.
# Matrix operations are performed individually on each cell, so calculations may require considerable time to complete.
# The calculation precision of displayed results for matrix calculations is 1 at the least significant digit.
# If a matrix calculation result is too large to fit into Matrix Answer Memory, an error occurs.
# You can use the following operation to transfer Matrix Answer Memory contents to another matrix (or when Matrix Answer Memory contains a determinant to a variable).
MatAns Mat
In the above, is any variable name A through Z. The above does not affect the contents of Matrix Answer Memory.
19990401
List Function A list is a storage place for multiple data items. This calculator lets you store up to 20 lists in a single file, and you can store up to six files in memory. Stored lists can be used in arithmetic and statistical calculations, and for graphing.
3-1 Inputting and Editing a List
3-2 Manipulating List Data 3-3 Arithmetic Calculations Using Lists
3-4 Switching Between List Files
Chapter 3
List 1 List 2 List 3 List 4 List 5 List 20 1 56 1 107 3.5 4 0 2 37 2 75 6 0 0 3 21 4 122 2.1 0 0 4 69 8 87 4.4 2 0 5 40 16 298 3 0 0 6 48 32 48 6.8 3 0 7 93 64 338 2 9 0 8 30 128 49 8.7 0 0
Element number Display range Cell
Row
List name
Column
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3-1 Inputting and Editing a List Enter the STAT Mode from the Main Menu to input data into a list and to manipulate list data.
u To input values one-by-one Use the cursor keys to move the highlighting to the list name or cell you want to select.
The screen automatically scrolls when the highlighting is located at either edge of the screen.
The following example is performed starting with the highlighting located at Cell 1 of List 1.
1. Input a value and press w to store it in the list.
dw
The highlighting automatically moves down to the next cell for input.
2. Input the value 4 in the second cell, and then input the result of 2 + 3 in the next cell.
ewc+dw
3-1-1 Inputting and Editing a List
# You can also input the result of an expres- sion or a complex number into a cell.
# You can input values up to 255 cells in a single list.
199904012001 1 2
u To batch input a series of values 1. Use the cursor keys to move the highlighting to another list.
2. Press !*( { ), and then input the values you want, pressing , between each one. Press !/( } ) after inputting the final value.
!*( { )g,h,i!/( } )
3. Press w to store all of the values in your list.
w
You can also use list names inside of a mathematical expression to input values into another cell. The following example shows how to add the values in each row in List 1 and List 2, and input the result into List 3.
1. Use the cursor keys to move the highlighting to the name of the list where you want the calculation results to be input.
2. Press K and input the expression.
K1(LIST)b(List)b+
K1(LIST)b(List)cw
3-1-2 Inputting and Editing a List
# You can also use !b(List) in place of K1(LIST)b(List).
# Remember that a comma separates values, so you should not input a comma after the final value of the set you are inputting.
Right: {34, 53, 78}
Wrong: {34, 53, 78,}
199904012001 1 2
kEditing List Values
u To change a cell value Use d or e to move the highlighting to the cell whose value you want to change. Input the new value and press w to replace the old data with the new one.
u To edit the contents of a cell 1. Use the cursor keys to move the highlighting to the cell whose contents you want to
edit.
2. Press 6()2(EDIT) to display the contents of the cell at the bottom of the screen.
3. Make any changes in the data you want.
u To delete a cell 1. Use the cursor keys to move the highlighting to the cell you want to delete.
2. Press 6()3(DEL) to delete the selected cell and cause everything below it to be shifted up.
3-1-3 Inputting and Editing a List
# The cell delete operation does not affect cells in other lists. If the data in the list whose cell you delete is somehow related to the data in
neighboring lists, deleting a cell can cause related values to become misaligned.
199904012001 1 2
u To delete all cells in a list Use the following procedure to delete all the data in a list.
1. Use the cursor key to move the highlighting to any cell of the list whose data you want to delete.
2. Pressing 6()4(DEL A) causes a confirmation message to appear.
3. Press w(Yes) to delete all the cells in the selected list or i(No) to abort the delete operation without deleting anything.
u To insert a new cell 1. Use the cursor keys to move the highlighting to the location where you want to insert
the new cell.
2. Press 6()5(INS) to insert a new cell, which contains a value of 0, causing everything below it to be shifted down.
# The cell insert operation does not affect cells in other lists. If the data in the list where you insert a cell is somehow related to the data in
3-1-4 Inputting and Editing a List
neighboring lists, inserting a cell can cause related values to become misaligned.
19990401
kSorting List Values
You can sort lists into either ascending or descending order. The highlighting can be located in any cell of the list.
u To sort a single list Ascending order
1. While the lists are on the screen, press 6()1(TOOL)b(SortA).
2. The prompt How Many Lists?: appears to ask how many lists you want to sort. Here we will input 1 to indicate we want to sort only one list.
bw
3. In response to the Select List List No: prompt, input the number of the list you want to sort.
bw
Descending order
Use the same procedure as that for the ascending order sort. The only difference is that you should press c(SortD) in place of b(SortA).
3-1-5 Inputting and Editing a List
2001 1 2
19990401
u To sort multiple lists You can link multiple lists together for a sort so that all of their cells are rearranged in accordance with the sorting of a base list. The base list is sorted into either ascending order or descending order, while the cells of the linked lists are arranged so that the relative relationship of all the rows is maintained.
Ascending order
1. While the lists are on the screen, press 6()1(TOOL)b(SortA).
2. The prompt How Many Lists?: appears to ask how many lists you want to sort. Here we will sort one base list linked to one other list, so we should input 2.
cw
3. In response to the Select Base List List No: prompt, input the number of the list you want to sort into ascending order. Here we will specify List 1.
bw
4. In response to the Select Second List List No: prompt, input the number of the list you want to link to the base list. Here we will specify List 2.
cw
3-1-6 Inputting and Editing a List
2001 1 2
19990401
3-1-7 Inputting and Editing a List
Descending order
Use the same procedure as that for the ascending order sort. The only difference is that you should press c(SortD) in place of b(SortA).
# You can specify a value from 1 to 6 as the number of lists for sorting.
# If you specify a list more than once for a single sort operation, an error occurs.
An error also occurs if lists specified for sorting do not have the same number of values (rows).
# Specifying a value of 0 for the number of lists causes all the lists in the file to be sorted. In this case you specify a base list on which all other lists in the file are sorted.
19990401
3-2 Manipulating List Data List data can be used in arithmetic and function calculations. In addition, various list data manipulation functions make manipulation of list data quick and easy.
You can use list data manipulation functions in the RUN MAT, STAT, GRPH TBL, EQUA and PRGM Modes.
k Accessing the List Data Manipulation Function Menu
All of the following examples are performed after entering the RUN MAT Mode.
Press K and then 1(LIST) to display the list data manipulation menu, which contains the following items.
{List}/{Dim}/{Seq}/{Min}/{Max}/{Mean}/{Median}/{Sum}/{Prod}/{Cuml}/{%}/{AList}/ {Augmnt}/{Fill}/{LMat}
Note that all closing parentheses at the end of the following operations can be omitted.
u To count the number of data items in a list [OPTN]-[LIST]-[Dim]
K1(LIST)c(Dim)1(LIST)b(List) w
The number of cells a list contains is its dimension.
Example To count the number of values in List 1 (36, 16, 58, 46, 56)
AK1(LIST)c(Dim)
1(LIST)b(List)bw
u To create a list or matrix by specifying the number of data items
[OPTN]-[LIST]-[Dim]
Use the following procedure to specify the number of data in the assignment statement and create a list.
w
n = 1 ~ 255
3-2-1 Manipulating List Data
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19990401
Example To create five data items (each of which contains 0) in List 1
AfaK1(LIST)c(Dim)
1(LIST)b(List) bw
You can view the newly created list by entering the STAT Mode.
Use the following procedure to specify the number of data rows and columns, and the matrix name in the assignment statement and create a matrix.
!*( { )
K1(LIST)c(Dim)2(MAT)b(Mat)a
m, n = 1 ~ 255, matrix name; A ~ Z
Example To create a 2-row 3-column matrix (each cell of which contains 0) in Matrix A
A!*( { )c,d!/( } )a
K1(LIST)c(Dim)
2(MAT)b(Mat)av(A)w
The following shows the new contents of Mat A.
u To replace all data items with the same value [OPTN]-[LIST]-[Fill]
K1(LIST)c(Fill) )w
Example To replace all data items in List 1 with the number 3
AK1(LIST)c(Fill)
d,1(LIST)b(List)b)w
The following shows the new contents of List 1.
3-2-2 Manipulating List Data
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3-2-3 Manipulating List Data
u To generate a sequence of numbers [OPTN]-[LIST]-[Seq]
K1(LIST)d(Seq)
The result of this operation is stored in ListAns Memory.
Example To input the number sequence 12, 62, 112, into a list, using the function f(x) = X2. Use a starting value of 1, an ending value of 11, and an increment of 5
AK1(LIST)d(Seq)vx,
v,b,bb,f)w
Specifying an ending value of 12, 13, 14, or 15 produces the same result as shown above, because all of them are less than the value produced by the next increment (16).
u To find the minimum value in a list [OPTN]-[LIST]-[Min]
K1(LIST)e(Min)1(LIST)b(List) )w
Example To find the minimum value in List 1 (36, 16, 58, 46, 56)
AK1(LIST)e(Min)
1(LIST)b(List)b)w
u To find the maximum value in a list [OPTN]-[LIST]-[Max]
Use the same procedure as when finding the minimum value (Min), except press f(Max) in place of e(Min).
19990401
3-2-4 Manipulating List Data
u To find which of two lists contains the smallest value [OPTN]-[LIST]-[Min]
K1(LIST)e(Min)1(LIST)b(List)
,1(LIST)b (List) )w
The two lists must contain the same number of data items. If they dont, an error occurs.
The result of this operation is stored in ListAns Memory.
Example To find whether List 1 (75, 16, 98, 46, 56) or List 2 (35, 59, 58, 72, 67) contains the smallest value
K1(LIST)e(Min)
1(LIST)b(List)b,
1(LIST)b(List)c)w
u To find which of two lists contains the greatest value [OPTN]-[LIST]-[Max]
Use the same procedure as that for the smallest value, except press f(Max) in place of e(Min).
The two lists must contain the same number of data items. If they dont, an error occurs.
u To calculate the mean of data items [OPTN]-[LIST]-[Mean]
K1(LIST)g(Mean)1(LIST)b(List) )w
Example To calculate the mean of data items in List 1 (36, 16, 58, 46, 56)
AK1(LIST)g(Mean)
1(LIST)b(List)b)w
u To calculate the mean of data items of specified frequency [OPTN]-[LIST]-[Mean]
This procedure uses two lists: one that contains values and one that indicates the frequency (number of occurrences) of each value. The frequency of the data in Cell 1 of the first list is indicated by the value in Cell 1 of the second list, etc.
The two lists must contain the same number of data items. If they dont, an error occurs.
K1(LIST)g(Mean)1(LIST)b(List)
,1(LIST)b(List) )w
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Example To calculate the mean of data items in List 1 (36, 16, 58, 46, 56), whose frequency is indicated by List 2 (75, 89, 98, 72, 67)
AK1(LIST)g(Mean)
1(LIST)b(List)b,
1(LIST)b(List)c)w
u To calculate the median of data items in a list [OPTN]-[LIST]-[Med]
K1(LIST)h(Median)1(LIST)b(List) )w
Example To calculate the median of data items in List 1 (36, 16, 58, 46, 56)
AK1(LIST)h(Median)
1(LIST)b(List)b)w
u To calculate the median of data items of specified frequency [OPTN]-[LIST]-[Med]
This procedure uses two lists: one that contains values and one that indicates the frequency (number of occurrences) of each value. The frequency of the data in Cell 1 of the first list is indicated by the value in Cell 1 of the second list, etc.
The two lists must contain the same number of data items. If they dont, an error occurs.
K1(LIST)h(Median)1(LIST)b(List) ,1(LIST)b(List)
)w
Example To calculate the median of values in List 1 (36, 16, 58, 46, 56), whose frequency is indicated by List 2 (75, 89, 98, 72, 67)
AK1(LIST)h(Median)
1(LIST)b(List)b,
1(LIST)b(List)c)w
3-2-5 Manipulating List Data
19990401
u To calculate the sum of data items in a list [OPTN]-[LIST]-[Sum]
K1(LIST)i(Sum)1(LIST)b(List) w
Example To calculate the sum of data items in List 1 (36, 16, 58, 46, 56)
AK1(LIST)i(Sum)
1(LIST)b(List)bw
u To calculate the product of values in a list [OPTN]-[LIST]-[Prod]
K1(LIST)j(Prod)1(LIST)b(List) w
Example To calculate the product of values in List 1 (2, 3, 6, 5, 4)
AK1(LIST)j(Prod)
1(LIST)b(List)bw
u To calculate the cumulative frequency of each data item [OPTN]-[LIST]-[Cuml]
K1(LIST)v(Cuml)1(LIST)b(List) w
The result of this operation is stored in ListAns Memory.
Example To calculate the cumulative frequency of each data item in List 1 (2, 3, 6, 5, 4)
AK1(LIST)v(Cuml)
1(LIST)b(List)bw
3-2-6 Manipulating List Data
2+3= 2+3+6= 2+3+6+5= 2+3+6+5+4=
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u To calculate the percentage represented by each data item [OPTN]-[LIST]-[%]
K1(LIST)l(%)1(LIST)b(List) w
The above operation calculates what percentage of the list total is represented by each data item.
The result of this operation is stored in ListAns Memory.
Example To calculate the percentage represented by each data item in List 1 (2, 3, 6, 5, 4)
AK1(LIST)l(%)
1(LIST)b(List)bw
u To calculate the differences between neighboring data inside a list [OPTN]-[LIST]-[AList]
K1(LIST)I(AList) w
The result of this operation is stored in ListAns memory.
Example To calculate the difference between the data items in List 1 (1, 3, 8, 5, 4)
AK1(LIST)I(AList)
bw
3-2-7 Manipulating List Data
# You can specify the location of the new list (List 1 through List 20) with a statement like: A List 1 List 2. You cannot specify another memory or ListAns as the destination of the A List operation. An error also occurs if you specify a A List as the destination of the results of another A List operation.
# The number of cells in the new A List is one less than the number of cells in the original list.
# An error occurs if you execute A List for a list that has no data or only one data item.
2/(2+3+6+5+4) 100 = 3/(2+3+6+5+4) 100 = 6/(2+3+6+5+4) 100 = 5/(2+3+6+5+4) 100 = 4/(2+3+6+5+4) 100 =
3 1 = 8 3 = 5 8 = 4 5 =
19990401
u To combine lists [OPTN]-[LIST]-[Augmnt]
You can combine two different lists into a single list. The result of a list combination operation is stored in ListAns memory.
K1(LIST)s(Augmnt)1(LIST)b(List) < list number 1-20 > ,1(LIST)b(List) < list number 1-20 >)w
Example To combine the List 1 (3, 2) and List 2 (1, 9, 10)
AK1(LIST)s(Augmnt) 1(LIST)b(List)b,
1(LIST)b(List)c)w
u To transfer list contents to Matrix Answer Memory [OPTN]-[LIST]-[LMat]
K1(LIST)t(LMat)1(LIST)b(List)
,1(LIST)b(List) )w
You can skip input 1(LIST)b(List) in the part of the above operation.
Example: List Mat (1, 2)w
Example To transfer the contents of List 1 (2, 3, 6, 5, 4) to column 1, and the contents of List 2 (11, 12, 13, 14, 15) to column 2 of Matrix Answer Memory
AK1(LIST)t(LMat) 1(LIST)b(List)b, 1(LIST)b(List)c)w
3-2-8 Manipulating List Data
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3-3 Arithmetic Calculations Using Lists You can perform arithmetic calculations using two lists or one list and a numeric value.
Calculation results are stored in ListAns Memory.
k Error Messages
A calculation involving two lists performs the operation between corresponding cells. Because of this, an error occurs if the two lists do not have the same number of values (which means they have different dimensions).
An error occurs whenever an operation involving any two cells generates a mathematical error.
k Inputting a List into a Calculation
There are two methods you can use to input a list into a calculation.
u To input a specific list by name 1. Press K to display the first Operation Menu.
This is the function key menu that appears in the RUN MAT Mode when you press K.
2. Press 1(LIST) to display the List Data Manipulation Menu.
3. Press b(List) to display the List command and input the number of the list you want to specify.
3-3-1 Arithmetic Calculations Using Lists
List Numeric Value
List Numeric Value
+
= List
ListAns Memory
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u To directly input a list of values You can also directly input a list of values using {, }, and ,.
Example 1 To input the list: 56, 82, 64
!*( { )fg,ic,
ge!/( } )
41 6
Example 2 To multiply List 3 ( = 65 ) by the list 0
22 4
K1(LIST)b(List)d*!*( { )g,a,e!/( } )w
246 The resulting list 0 is stored in ListAns Memory.
88
u To assign the contents of one list to another list Use a to assign the contents of one list to another list.
Example 1 To assign the contents of List 3 to List 1
K1(LIST)b(List)da1(LIST)b(List)bw
In place of K1(LIST)b(List)d operation in the above procedure, you could input
!*( { )eb,gf,cc!/( } ).
Example 2 To assign the list in ListAns Memory to List 1
K1(LIST)b(List)!-(Ans)a1(LIST)b(List)bw
3-3-2 Arithmetic Calculations Using Lists
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u To recall the value in a specific list cell You can recall the value in a specific list cell and use it in a calculation. Specify the cell number by enclosing it inside square brackets.
Example To calculate the sine of the value stored in Cell 3 of List 2
sK1(LIST)b(List)c!+( [ )d!-( ] )w
u To input a value into a specific list cell You can input a value into a specific list cell inside a list. When you do, the value that was previously stored in the cell is replaced with the new value you input.
Example To input the value 25 into Cell 2 of List 3
cfaK1(LIST)b(List)d!+( [ )c!-( ] )w
kRecalling List Contents
Example To recall the contents of List 1
K1(LIST)b(List)bw
The above operation displays the contents of the list you specify and also stores them in ListAns Memory. You can then use the ListAns Memory contents in a calculation.
u To use list contents in ListAns Memory in a calculation
Example To multiply the list contents in ListAns Memory by 36
K1(LIST)b(List)!-(Ans)*dgw
The operation K1(LIST)b(List)!-(Ans) recalls ListAns Memory contents.
This operation replaces current ListAns Memory contents with the result of the above calculation.
3-3-3 Arithmetic Calculations Using Lists
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kGraphing a Function Using a List
When using the graphing functions of this calculator, you can input a function such as Y1 = List 1 X. If List 1 contains the values 1, 2, 3, this function will produces three graphs: Y = X, Y = 2X, Y = 3X.
There are certain limitations on using lists with graphing functions.
k Inputting Scientific Calculations into a List
You can use the numeric table generation functions in the Table & Graph Menu to input values that result from certain scientific function calculations into a list. To do this, first generate a table and then use the list copy function to copy the values from the table to the list.
k Performing Scientific Function Calculations Using a List
Lists can be used just as numeric values are in scientific function calculations. When the calculation produces a list as a result, the list is stored in ListAns Memory.
41
Example To use List 3 65 to perform sin (List 3)
22
Use radians as the angle unit.
sK1(LIST)b(List)dw
0.158
The resulting list 0.8268 is stored in ListAns Memory.
8E3
In place of the K1(LIST)b(List)d operation in the above procedure, you could input !*( { ) eb,gf,cc!/( } ).
3-3-4 Arithmetic Calculations Using Lists
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1 4
Example To use List 1 2 and List 2 5 to perform List 1List 2
3 6
This creates a list with the results of 14, 25, 36.
K1(LIST)b(List)bM1(LIST)b(List)cw
1 The resulting list 32 is stored in ListAns Memory.
729
3-3-5 Arithmetic Calculations Using Lists
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3-4-1 Switching Between List Files
3-4 Switching Between List Files You can store up to 20 lists (List 1 to List 20) in each file (File 1 to File 6). A simple operation lets you switch between list files.
u To switch between list files 1. From the Main Menu, enter the STAT Mode.
Press u3(SET UP) to display the STAT Mode SET UP screen.
2. Press 1(FILE) and then input the number of the list file you want to use.
Example To select File 3
1(FILE)d
w
All subsequent list operations are applied to the lists contained in the file you select (List File 3 in the above example).
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Chapter
Equation Calculations Your graphic calculator can perform the following three types of calculations:
Simultaneous linear equations Higher degree equations Solve calculations
From the Main Menu, enter the EQUA Mode.
{SIML} ... {linear equation with 2 to 30 unknowns}
{POLY} ... {degree 2 to 30 equations}
{SOLV} ... {solve calculation}
4-1 Simultaneous Linear Equations
4-2 Higher Degree Equations
4-3 Solve Calculations
4-4 What to Do When an Error Occurs
4
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4-1-1 Simultaneous Linear Equations
4-1 Simultaneous Linear Equations Description You can solve simultaneous linear equations with two to thirty unknowns.
Simultaneous Linear Equation with Two Unknowns:
a1x1 + b1x2 = c1
a2x1 + b2x2 = c2
Simultaneous Linear Equation with Three Unknowns:
a1x1 + b1x2 + c1x3 = d1
a2x1 + b2x2 + c2x3 = d2
a3x1 + b3x2 + c3x3 = d3
Set Up 1. From the Main Menu, enter the EQUA Mode.
Execution 2. Select the SIML (simultaneous equation) Mode, and specify the number of unknowns
(variables). You can specify from 2 to 30 unknowns. To specify more than six unknowns, press 6(n) and then input a value.
3. Sequentially input the coefficients.
The cell that is currently selected for input is highlighted. Each time you input a coefficient, the highlighting shifts in the sequence:
a1 b1 c1 an bn cn (n = 2 to 30)
You can also input fractions, complex numbers, and values assigned to variables as coefficients.
You can cancel the value you are inputting for the current coefficient by pressing i at any time before you press w to store the coefficient value. This returns to the coefficient to what it was before you input anything. You can then input another value if you want. To change the value of a coefficient that you already stored by pressing w, move the cursor to the coefficient you want to edit. Next, input the value you want to change to or press 1(EDIT).
Pressing 3(CLR) clears all coefficients to zero.
4. Solve the equations.
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4-1-2 Simultaneous Linear Equations
Example To solve the following simultaneous linear equations for x, y, and z
4x + y 2z = 1 x + 6y + 3z = 1
5x + 4y + z = 7
Procedure 1m EQUA
21(SIML)
2(3)
3 ewbw-cw-bw
bwgwdwbw
-fwewbw-hw
46(SOLV)
Result Screen
# Internal calculations are performed using a 15- digit mantissa, but results are displayed using a 10-digit mantissa and a 2-digit exponent.
# Simultaneous linear equations are solved by inverting the matrix containing the coefficients of the equations. For example, the following shows the solution (x1, x2, x3) of a simultane- ous linear equation with three unknowns.
x1 a1 b1 c1 1 d1
x2 = a2 b2 c2 d2
x3 a3 b3 c3 d3
Because of this, precision is reduced as the value of the determinant approaches zero. Also, simultaneous equations with three or more unknowns may take a very long time to solve.
# An error occurs if the calculator is unable to find a solution.
# After calculation is complete, you can press 1 (REPT), change coefficient values, and then
re-calculate.
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4-2-1 Higher Degree Equations
# Internal calculations are performed using a 15-digit mantissa, but results are displayed using a 10-digit mantissa and a 2-digit exponent.
# High degree equations of third degree or higher may take a very long time to solve.
# An error occurs if the calculator is unable to find a solution.
# After calculation is complete, you can press 1(REPT), change coefficient values, and then re-calculate.
4-2 Higher Degree Equations Description You can use this calculator to solve higher degree equations such as quadratic equations and cubic equations.
Quadratic Equation: ax2 + bx + c = 0 (a 0)
Cubic Equation: ax3 + bx2 + cx + d = 0(a 0)
Set Up 1. From the Main Menu, enter the EQUA Mode.
Execution 2. Select the POLY (higher degree equation) Mode, and specify the degree of the
equation. You can specify a degree from 2 to 30. To specify a degree greater than three, press 3(n) and then input a value.
3. Sequentially input the coefficients.
The cell that is currently selected for input is highlighted. Each time you input a coefficient, the highlighting shifts in the sequence:
a b c
You can also input fractions, complex numbers, and values assigned to variables as coefficients.
You can cancel the value you are inputting for the current coefficient by pressing i at any time before you press w to store the coefficient value. This returns to the coefficient to what it was before you input anything. You can then input another value if you want. To change the value of a coefficient that you already stored by pressing w, move the cursor to the coefficient you want to edit. Next, input the value you want to change to or press 1(EDIT).
Pressing 3(CLR) clears all coefficients to zero.
4. Solve the equations.
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4-2-2 Higher Degree Equations
Example To solve the cubic equation
x3 2x2 x + 2 = 0
Procedure 1m EQUA
22(POLY)
2(3)
3 bw-cw-bwcw
46(SOLV)
Result Screen
(Multiple Solutions) (Complex Number Solution)
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4-3-1 Solve Calculations
4-3 Solve Calculations Description The Solve Calculation Mode lets you determine the value of any variable in a formula without having to solve the equation.
Set Up 1. From the Main Menu, enter the EQUA Mode.
Execution 2. Select the SOLV (Solver) Mode, and input the equation as it is written.
If you do not input an equals sign, the calculator assumes that the expression is to the left of the equals sign, and there is a zero to the right. *1
3. In the table of variables that appears on the display, input values for each variable. You can also specify values for Upper and Lower to define the upper and lower limits of the range of solutions. *2
4. Select the variable for which you want to solve to obtain the solution. Lft and Rgt indicate the left and right sides that are calculated using the solution.*3
*1An error occurs if you input more than one equals sign.
*2An error occurs if the solution falls outside the range you specify.
*3Solutions are approximated using Newtons method. Lft and Rgt values are displayed for confirmation, because Newtons method may produce results that are the real solution.
The closer the difference between the Lft and Rgt values is to zero, the lower degree of error in the result.
# The message Retry appears on the display when the calculator judges that convergence is not sufficient for the displayed results.
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4-3-2 Solve Calculations
Example An object thrown into the air at initial velocity V takes time T to reach height H. Use the following formula to solve for initial velocity V when H = 14 (meters), T = 2 (seconds) and gravitational acceleration is G = 9.8 (m/s2).
H = VT 1/2 GT2
Procedure 1m EQUA
23(SOLV)
ax(H)!.(=)ac(V)a/(T)-(b/c)
a$(G)a/(T)xw
3 bew(H = 14)
aw(V = 0)
cw(T = 2)
j.iw(G = 9.8)
4 Press f to highlight V = 0, and then press 6(SOLV).
Result Screen
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4-4 What to Do When an Error Occurs
uError during coefficient value input Press the i key to clear the error and return to the value that was registered for the coefficient before you input the value that generated the error. Try inputting a new value again.
uError during calculation Press the i key to clear the error and display the coefficient. Try inputting values for the coefficients again.
4-4-1 What to Do When an Error Occurs
kClearing Equation Memories
1. Enter the equation calculation mode (SIML or POLY) you want to use and perform the function key operation required for that mode.
In the case of the SIML Mode (1), use number keys to specify the number of unknowns.
In the case of the POLY Mode (2), use number keys to specify the degree of the polynomial.
If you pressed 3(SOLV), advance directly to step 2.
2. Press 2(DEL A).
3. Press w(Yes) to delete the applicable equation memories or i(No) to abort the operation without deleting anything.
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Graphing Sections 5-1 and 5-2 of this chapter provide basic information you need to know in order to draw a graph. The remaining sections describe more advanced graphing features and functions.
Select the icon in the Main Menu that suits the type of graph you want to draw or the type of table you want to generate. GRPH TBL General function graphing or number table generation CONICS Conic section graphing
(5-1-5 ~ 5-1-6, 5-11-17~5-11-21) RUN MAT Manual graphing (5-6-1 ~ 5-6-4) DYNA Dynamic Graph (5-8-1 ~ 5-8-6) RECUR Recursion graphing or number table generation
(5-9-1 ~ 5-9-8)
5-1 Sample Graphs 5-2 Controlling What Appears on a Graph Screen
5-3 Drawing a Graph
5-4 Storing a Graph in Picture Memory
5-5 Drawing Two Graphs on the Same Screen 5-6 Manual Graphing
5-7 Using Tables
5-8 Dynamic Graphing
5-9 Graphing a Recursion Formula 5-10 Changing the Appearance of a Graph
5-11 Function Analysis
Chapter
5
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5-1-1 Sample Graphs
5-1 Sample Graphs
kHow to draw a simple graph (1)
Description To draw a graph, simply input the applicable function.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
Execution 2. Input the function you want to graph.
Here you would use the V-Window to specify the range and other parameters of the graph. See 5-2-1.
3. Draw the graph.
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5-1-2 Sample Graphs
Example To graph y = 3x2
Procedure 1m GRPH TBL
2 dvxw
35(DRAW) (or w)
Result Screen
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5-1-3 Sample Graphs
kHow to draw a simple graph (2)
Description You can store up to 20 functions in memory and then select the one you want for graphing.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
Execution 2. Specify the function type and input the function whose graph you want to draw.
You can use the GRPH TBL Mode to draw a graph for the following types of expres- sions: rectangular coordinate expression, polar coordinate expression, parametric function, X = constant expression, inequality.
3(TYPE)b(Y =) ... rectangular coordinates
c(r =) ... polar coordinates
d(Param) ... parametric function
e(X = c) ... X = constant function
f(INEQUA)b(Y>)~e(Y<) ... inequality
g(CONV)b('Y=)~f('Y<) ... changes the function type
Repeat this step as many times as required to input all of the functions you want.
Next you should specify which of the functions among those that are stored in memory you want to graph (see 5-3-6). If you do not select specific functions here, the graph operation will draw graphs of all the functions currently stored in memory.
3. Draw the graph.
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5-1-4 Sample Graphs
Example Input the functions shown below and draw their graphs Y1 = 2x2 3, r2 = 3sin2
Procedure 1m GRPH TBL
23(TYPE)b(Y=)cvx-dw
3(TYPE)c(r=)dscvw
35(DRAW)
Result Screen
(Param) (INEQUA) (Plot)
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5-1-5 Sample Graphs
kHow to draw a simple graph (3)
Description Use the following procedure to graph the function of a parabola, circle, ellipse, or hyperbola.
Set Up 1. From the Main Menu, enter the CONICS Mode.
Execution 2. Use the cursor fc keys to specify one of the function type as follows.
3. Input values for the required variables.
4. Graph the function.
Graph Type Function
Parabola X = A (Y K)2 + H X = AY2 + BY + C Y = A (X H)2 + K Y = AX2 + BX + C
Circle (X H)2 + (Y K)2 = R2
AX2 + AY2 + BX + CY + D = 0
Ellipse (X H)2 (Y K)2
+ = 1 A2 B2
Hyperbola (X H)2 (Y K)2
= 1 A2 B2
(Y K)2 (X H)2
= 1 A2 B2
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5-1-6 Sample Graphs
Example Graph the circle (X1)2 + (Y1)2 = 22
Procedure 1m CONICS
2ccccw
3 bwbwcw
46(DRAW)
Result Screen
(Parabola) (Ellipse) (Hyperbola)
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5-2 Controlling What Appears on a Graph Screen
kV-Window (View Window) Settings
Use the View Window to specify the range of the x- and y-axes, and to set the spacing between the increments on each axis. You should always set the V-Window parameters you want to use before graphing.
u To make V-Window settings 1. From the Main Menu, enter the GRPH TBL Mode.
2. Press !K(V-Window) to display the V-Window setting screen.
Rectangular coordinate parameter
Xmin Minimum x-axis value
Xmax Maximum x-axis value
Xscale Spacing of x-axis increments
Xdot Value that corresponds to one x-axis dot
Ymin Minimum y-axis value
Ymax Maximum y-axis value
Yscale Spacing of y-axis increments
Polar coordinate parameter
T min ... T, minimum values
T max ... T, maximum values
T ptch ... T, pitch
3. Press c to move the highlighting and input an appropriate value for each parameter, pressing w after each.
{INIT}/{TRIG}/{STD} V-Window {initial settings}/{initial settings using specified angle unit}/{standardized settings}
{STO}/{RCL} V-Window setting {store}/{recall}
After settings are the way you want them, press i or !i(QUIT) to exit the V-Window setting screen.*1
5-2-1 Controlling What Appears on a Graph Screen
*1Pressing w without inputting anything while k is displayed exits the View Window setting screen.
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5-2-2 Controlling What Appears on a Graph Screen
uV-Window Setting Precautions Inputting zero for T ptch causes an error.
Any illegal input (out of range value, negative sign without a value, etc.) causes an error.
An error occurs when Xmax is less than Xmin, or Ymax is less than Ymin. When T max is less than T min, T ptch becomes negative.
You can input expressions (such as 2) as V-Window parameters.
When the V-Window setting produces an axis that does not fit on the display, the scale of the axis is indicated on the edge of the display closest to the origin.
Changing the V-Window settings clears the graph currently on the display and replaces it with the new axes only.
Changing the Xmin or Xmax value causes the Xdot value to be adjusted automatically. Changing the Xdot value causes the Xmax value to be adjusted automatically.
A polar coordinate (r =) or parametric graph will appear coarse if the settings you make in the V-Window cause the T, pitch value to be too large, relative to the differential between the T, min and T, max settings. If the settings you make cause the T, pitch value to be too small relative to the differential between the T, min and T, max settings, on the other hand, the graph will take a very long time to draw.
The following is the input range for V-Window parameters.
9.999999999E 97 to 9.999999999E 97
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k Initializing and Standardizing the V-Window
u To initialize the V-Window 1. From the Main Menu, enter the GRPH TBL Mode.
2. Press !K(V-Window).
This displays the V-Window setting screen.
3. Press 1(INIT) to initialize the V-Window.
Xmin = 6.3, Xmax = 6.3, Xscale = 1 Xdot = 0.1
Ymin = 3.1, Ymax = 3.1, Yscale = 1
T min = 0, T max = 2 (rad), T ptch = 2 /60 (rad)
u To initialize the V-Window in accordance with an angle unit In step 3 of the procedure under To initialize the V-Window above, press 2(TRIG) to initialize the V-Window in accordance with an angle unit.
Xmin = 3 (rad), Xmax = 3 (rad), Xscale = /2 (rad), Xdot = /21 (rad),
Ymin = 1.6, Ymax = 1.6, Yscale = 0.5
u To standardize the V-Window The following are the standard V-Window settings of this calculator.
Xmin = 10, Xmax = 10, Xscale = 1, Xdot = 0.15873015,
Ymin = 10, Ymax = 10, Yscale = 1,
T min = 0, T max = 2 (rad), T ptch = 2 /60 (rad)
In step 3 of the procedure under To initialize the V-Window above, press 3(STD) to standardize V-Window settings in accordance with the above.
5-2-3 Controlling What Appears on a Graph Screen
# Initialization and standardization cause T min, T max, T ptch values to change automatically in accordance with the current angle unit setting as shown below.
Deg Mode: T min = 0, T max = 360, T ptch = 6
Gra Mode: T min = 0, T max = 400, T ptch = 400/60
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kV-Window Memory
You can store up to six sets of V-Window settings in V-Window memory for recall when you need them.
u To store V-Window settings 1. From the Main Menu, enter the GRPH TBL Mode.
2. Press !K(V-Window) to display the V-Window setting screen, and input the values you want.
3. Press 4(STO) to display the pop-up window.
4. Press a number key to specify the V-Window memory where you want to save the settings, and then press w. Pressing bw stores the settings in V-Window Memory 1 (V-Win1).
u To recall V-Window memory settings 1. From the Main Menu, enter the GRPH TBL Mode.
2. Press !K(V-Window) to display the V-Window setting screen.
3. Press 5(RCL) to display the pop-up window.
4. Press a number key to specify the V-Window memory number for the settings you want to recall, and then press w. Pressing bw recalls the settings in V-Window Memory 1 (V-Win1).
5-2-4 Controlling What Appears on a Graph Screen
# Storing V-Window settings to a memory that already contains setting data replaces the previous data with the new settings.
# Recalling settings causes the current V-Window settings to be replaced with those recalled from memory.
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kSpecifying the Graph Range
Description You can define a range (start point, end point) for a function before graphing it.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
2. Make V-Window settings.
Execution 3. Specify the function type and input the function. The following is the syntax for function
input.
Function ,!+( [ )Start Point , End Point !-( ] )
4. Draw the graph.
5-2-5 Controlling What Appears on a Graph Screen
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5-2-6 Controlling What Appears on a Graph Screen
Example Graph y = x2 + 3x 2 within the range 2 < x < 4
Use the following V-Window settings.
Xmin = 3, Xmax = 5, Xscale = 1
Ymin = 10, Ymax = 30, Yscale = 5
Procedure 1m GRPH TBL
2!K(V-Window)-dwfwbwc
-bawdawfwi
33(TYPE)b(Y=)vx+dv-c,
!+( [ )-c,e!-( ] )w
45(DRAW)
Result Screen
# You can specify a range when graphing rectangular expressions, polar expressions, parametric functions, and inequalities.
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5-2-7 Controlling What Appears on a Graph Screen
k Zoom
Description This function lets you enlarge and reduce the graph on the screen.
Set Up 1. Draw the graph.
Execution 2. Specify the zoom type.
2(ZOOM)b(Box) ... Box zoom Draw a box around a display area, and that area is enlarged to fill the entire screen.
c(Factor)
d(In)/e(Out) ... Factor zoom The graph is enlarged or reduced in accordance with the factor you specify, centered on the current pointer location.
f(Auto) ...Auto zoom V-Window y-axis settings are automatically adjusted so the graph fills the screen along the y-axis.
g(Orig) ...Original size Returns the graph to its original size following a zoom opera- tion.
h(Square) ... Graph correction V-Window x-axis values are corrected so they are identical to the y-axis values.
i(Rnd) ... Coordinate rounding Rounds the coordinate values at the current pointer location.
j(Intg) ... Integer Each dot is given a width of 1, which makes coordinate values integers.
v(Pre) ...Previous V-Window parameters are returned to what they were prior to the last zoom operation.
l(QUICK) ... Quick zoom Redraws the graph in accordance with the settings stored in a selected V-Window memory.
Box zoom range specification
3. Use the cursor keys to move the pointer ( ) in the center of the screen to the location where you want one corner of the box to be, and then press w.
4. Use the cursor keys to move the pointer. This causes a box to appear on the screen. Move the cursor until the area you want to enlarge is enclosed in the box, and then press w to enlarge it.
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5-2-8 Controlling What Appears on a Graph Screen
# You must specify two different points for box zoom, and the two points cannot be on a straight line vertically or horizontally from each other.
Example Graph y = (x + 5)(x + 4)(x + 3), and then perform a box zoom.
Use the following V-Window settings.
Xmin = 8, Xmax = 8, Xscale = 2
Ymin = 4, Ymax = 2, Yscale = 1
Procedure 1m GRPH TBL
!K(V-Window)-iwiwcwc
-ewcwbwi
3(TYPE)b(Y=)(v+f)(v+e)
(v+d)w
5(DRAW)
22(ZOOM)b(Box)
3d~dw
4d~d,f~fw
Result Screen
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5-2-9 Controlling What Appears on a Graph Screen
k Factor Zoom
Description With factor zoom, you can zoom in or out, centered on the current cursor position.
Set Up 1. Draw the graph.
Execution 2. Press 2(ZOOM)c(Factor) to open a pop-up window for specifying the x-axis and
y-axis zoom factor. Input the values you want and then press i.
3. Press 2(ZOOM)d(In) to enlarge the graph, or 2(ZOOM)e(Out) to reduce it. The graph is enlarged or reduced centered on the current pointer location.
4. Use the cursor keys to move the cursor to the point upon which you want the zoom operation to be centered, and then press w to zoom.
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5-2-10 Controlling What Appears on a Graph Screen
Example Enlarge the graphs of the two expressions shown below five times on both the x-and y-axis to see if they are tangent. Y1 = (x + 4)(x + 1)( x 3), Y2 = 3x + 22
Use the following V-Window settings.
Xmin = 8, Xmax = 8, Xscale = 1
Ymin = 30, Ymax = 30, Yscale = 5
Procedure 1m GRPH TBL
!K(V-Window)-iwiwbwc
-dawdawfwi
3(TYPE)b(Y=)(v+e)(v+b)
(v-d)w
dv+ccw
5(DRAW)
22(ZOOM)c(Factor)fwfwi
32(ZOOM)d(In)
4f~f,d~dw
Result Screen
# You can repeat factor zoom to enlarge or reduce a graph even further.
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k Turning Function Menu Display On and Off
Press ua to toggle display of the menu at the bottom of the screen on and off.
Turning off the function menu display makes it possible to view part of a graph hidden behind it. When you are using the trace function or other functions during which the function menu is normally not displayed, you can turn on the menu display to execute a menu command.
5-2-11 Controlling What Appears on a Graph Screen
# If a pull-up menu is open when you press u a to turn off menu display, the pull-up menu remains on the screen.
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kAbout the Calc Window
Pressing u4(CAT/CAL) while a graph or number table is on the display opens the Calc Window. You can use the Calc Window to perform calculations with values obtained from graph analysis, or to change the value assigned to variable A in Y = AX and other expressions and then redraw the graph.
Press i to close the Calc Window.
5-2-12 Controlling What Appears on a Graph Screen
# After using the Calc Window to change the value of a variable connected with a graph or table, be sure to always execute Re-G (re- graph) or Re-T (re-calculate table). Doing so ensures that the displayed graph or table is current.
# Calc Window cannot be used in the RUN MAT Mode while a program is running, or in combination with Dynamic Graph.
# Calc Window cannot be used in combination with V-Window or the table range setting screen.
# Complex number calculations cannot be performed on the Calc Window.
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5-3-1 Drawing a Graph
5-3 Drawing a Graph You can store up to 20 functions in memory. Functions in memory can be edited, recalled, and graphed.
kSpecifying the Graph Type
Before you can store a graph function in memory, you must first specify its graph type.
1. While the Graph function list is on the display, press 6(g)3(TYPE) to display the graph type menu, which contains the following items.
{Y=}/{r=}/{Param}/{X=c} ... {rectangular coordinate}/{polar coordinate}/{parametric}/ {X=constant}*1 graph
{INEQUA}
{Y>}/{Y<}/{Yt}/{Ys} ... {Y>f(x)}/{Y<f(x)}/{Y>f(x)}/{Y<f(x)} inequality graph
{CONV}
{'Y=}/{'Y>}/{'Y<}/{'Yt}/{'Ys} ... changes the function type
2. Press the number key that corresponds to the graph type you want to specify.
kStoring Graph Functions
u To store a rectangular coordinate function (Y =) *2
Example To store the following expression in memory area Y1 : y = 2x2 5
3(TYPE)b(Y =) (Specifies rectangular coordinate expression.)
cvx-f(Inputs expression.)
w (Stores expression.)
u To store a polar coordinate function (r =) *2
Example To store the following expression in memory area r2 : r = 5 sin3
3(TYPE)c(r =) (Specifies polar coordinate expression.)
fsdv(Inputs expression.)
w(Stores expression.)
*1 Attempting to draw a graph for an expression in which X is input for an X = constant expression results in an error.
*2A function cannot be stored into a memory area that already contains a function of a different type from the one you are trying to store. Select a memory area that contains a function that is the same type as the one you are storing, or delete the function in the memory area to which you are trying to store.
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5-3-2 Drawing a Graph
u To store a parametric function *1
Example To store the following functions in memory areas Xt3 and Yt3 : x = 3 sin T y = 3 cos T
3(TYPE)d(Param) (Specifies parametric expression.)
dsvw(Inputs and stores x expression.)
dcvw(Inputs and stores y expression.)
u To store an X = constant expression *2
Example To store the following expression in memory area X4 : X = 3
3(TYPE)e(X = c) (Specifies X = constant expression.)
d(Inputs expression.)
w(Stores expression.)
Inputting X, Y, T, r, or for the constant in the above procedures causes an error.
u To store an inequality *2
Example To store the following inequality in memory area Y5 : y > x2 2x 6
3(TYPE)f(INEQUA)b(Y>) (Specifies an inequality.)
vx-cv-g(Inputs expression.)
w(Stores expression.)
*1You will not be able to store the expression in an area that already contains a rectangular coordinate expression, polar coordinate expression, X = constant expression or inequality. Select another area to store your expression or delete the existing expression first.
*2A function cannot be stored into a memory area that already contains a function of a different type from the one you are trying to store. Select a memory area that contains a function that is the same type as the one you are storing, or delete the function in the memory area to which you are trying to store.
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5-3-3 Drawing a Graph
u To create a composite function
Example To register the following functions as a composite function:
Y1= (X + 1), Y2 = X2 + 3
Assign Y1Y2 to Y3, and Y2Y1 to Y4.
(Y1Y2 = ((x2 + 3) +1) = (x2 + 4) Y2Y1 = ( (X + 1)) 2
+ 3 = X + 4 (X 1))
3(TYPE)b(Y=)
J4(GRPH)b(Yn)b
(1(Yn)c)w
4(GRPH)b(Yn)c
(1(Yn)b)w
A composite function can consist of up to five functions.
u To assign values to the coefficients and variables of a graph function After you combine functions or equations into a composite function, you can assign values to the coefficients and variables of the expression and draw a graph.
Example Assign the values 1, 0, and 1 to the expression Y = AX2 1, which is in memory area A
3(TYPE)b(Y=)
av(A)vx-bw
J4(GRPH)b(Yn)b
(av(A)!.(=)-b)w
4(GRPH)b(Yn)b
(av(A)!.(=)a)w
4(GRPH)b(Yn)b
(av(A)!.(=)b)w
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ffffi1(SEL)5(DRAW)
The above three screens are produced using the Trace function. See 5-11 Function Analysis for more information.
If you do not specify a variable name (variable A in the above key operation), the calculator automatically uses one of the default variables listed below. Note that the default variable used depends on the memory area type where you are storing the graph function.
Memory Area Type Default Variable
Yn X
rn Xtn T
Ytn T
fn X
Example Y1 (3) and Y1 (X = 3) are identical values.
You can also use Dynamic Graph for a look at how changes in coefficients alter the appearance of a graph. See 5-8 Dynamic Graphing for more information.
5-3-4 Drawing a Graph
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kEditing and Deleting Functions
u To edit a function in memory
Example To change the expression in memory area Y1 from y = 2x2 5 to y = 2x2 3
e (Displays cursor.)
eeeeDd(Changes contents.)
w(Stores new graph function.)
u To change the type of a function*1
1. While the Graph function list is on the display, press f or c to move the highlighting to the area that contains the function whose type you want to change.
2. Press 3(TYPE)g(CONV).
3. Select the function type you want to change to.
Example To change the function in memory area Y1 from y = 2x2 3 to y < 2x2 3
3(TYPE)g(CONV)d('Y<) (Changes the function type to Y<.)
u To delete a function 1. While the Graph function list is on the display, press f or c to move the highlighting
to the area that contains the function you want to delete.
2. Press 2(DEL) or D.
3. Press w(Yes) to delete the function or i(No) to abort the procedure without deleting anything.
*1The function type can be changed for rectangular coordinate functions and inequalities only.
# Parametric functions come in pairs (Xt and Yt). When editing a parametric function, clear the graph functions and re-input from the beginning.
5-3-5 Drawing a Graph
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kSelecting Functions for Graphing
u To specify the draw/non-draw status of a graph
Example To select the following functions for drawing : Y1 = 2x2 5, r2 = 5 sin3 Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
T min = 0, T max = , T ptch = 2 / 60
cc (Select a memory area that contains a function for which you want to specify non-draw.)
1(SEL) (Specifies non-draw.) 5(DRAW) or w (Draws the graphs.)
Each press of 1(SEL) toggles a graph between draw and non-draw.
Pressing u5(GT) or i returns to the Graph function list.
You can use the SET UP screen settings to alter the appearance of the graph screen as shown below.
Grid: On (Axes: On Label: Off)
This setting causes dots to appear at the grid intersects on the display.
Axes: Off (Label: Off Grid: Off)
This setting clears the axis lines from the display.
Label: On (Axes: On Grid: Off)
This setting displays labels for the x- and y-axes.
5-3-6 Drawing a Graph
199904012001 1 2
kGraph Memory
Graph memory lets you store up to 20 sets of graph function data and recall it later when you need it.
A single save operation saves the following data in graph memory.
All graph functions in the currently displayed Graph function list (up to 20)
Graph types
Draw/non-draw status
View Window settings (1 set)
u To store graph functions in graph memory 1. Press 4(GMEM)b(Store) to display the pop-up window.
2. Press a number key to specify the Graph memory where you want to save the graph function, and then press w. Pressing bw stores the graph function to Graph Memory 1 (G-Mem1).
There are 20 graph memories numbered G-Mem1 to G-Mem20.
u To recall a graph function 1. Press 4(GMEM)c(Recall) to display the pop-up window.
2. Press a number key to specify the Graph memory for the function you want to recall, and then press w. Pressing bw recalls the graph function in Graph Memory 1 (G-Mem1).
5-3-7 Drawing a Graph
# Storing a function in a memory area that already contains a function replaces the existing function with the new one.
# If the data exceeds the calculators remaining memory capacity, an error occurs.
# Recalling data from graph memory causes any data currently on the Graph function list to be deleted.
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5-4 Storing a Graph in Picture Memory You can save up to 20 graphic images in picture memory for later recall. You can overdraw the graph on the screen with another graph stored in picture memory.
u To store a graph in picture memory 1. After graphing in GRPH TBL Mode, press 6(g)1(PICT)b(Store) to display the
pop-up window.
2. Press a number key to specify the Picture memory where you want to save the picture, and then press w. Pressing bw stores the picture function to Picture Memory 1 (Pict 1).
There are 20 picture memories numbered Pict 1 to Pict 20.
u To recall a stored graph 1. After graphing in GRPH TBL Mode, press 6(g)1(PICT)c(Recall) to display the
pop-up window.
2. Press a number key to specify the Picture memory for the picture you want to recall, and then press w. Pressing bw recalls the picture function in Picture Memory 1 (Pict 1).
5-4-1 Storing a Graph in Picture Memory
# Storing a graphic image in a memory area that already contains a graphic image replaces the existing graphic image with the new one.
# A dual Graph screen or any other type of graph that uses a split screen cannot be saved in picture memory.
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5-5 Drawing Two Graphs on the Same Screen
kCopying the Graph to the Sub-screen
Description Dual Graph lets you split the screen into two parts. Then you can graph two different functions in each for comparison, or draw a normal size graph on one side and its enlarged version on the other side. This makes Dual Graph a powerful graph analysis tool.
With Dual Graph, the left side of the screen is called the main screen, while the right side is called the sub-screen.
u Main Screen The graph in the main screen is actually drawn from a function.
u Sub-screen The graph on the sub-screen is produced by copying or zooming the main screen graph. You can even make different V-Window settings for the sub-screen and main screen.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
2. On the SET UP screen, select G+G for Dual Screen.
3. Make V-Window settings for the main screen.
Press 6(RIGHT) to display the sub-graph settings screen. Pressing 6(LEFT) returns to the main screen setting screen.
Execution 4. Store the function, and draw the graph in the main screen.
5. Perform the Dual Graph operation you want.
4(COPY) ... Duplicates the main screen graph in the sub-screen
5(SWAP) ... Swaps the main screen contents and sub-screen contents
5-5-1 Drawing Two Graphs on the Same Screen
19990401
Example Graph y = x(x + 1)(x 1) in the main screen and sub-screen.
Use the following V-Window settings.
(Main Screen)
Xmin = 2, Xmax = 2, Xscale = 0.5
Ymin = 2, Ymax = 2, Yscale = 1
(Sub-screen)
Xmin = 4, Xmax = 4, Xscale = 1
Ymin = 3, Ymax = 3, Yscale = 1
Procedure 1m GRPH TBL
2u3(SET UP)ccc2(G+G)i
3!K(V-Window)-cwcwa.fwc
-cwcwbw
6(RIGHT)-ewewbwc
-dwdwbwi
43(TYPE)b(Y=)v(v+b)(v-b)w
5(DRAW)
56(g)4(COPY)
Result Screen
5-5-2 Drawing Two Graphs on the Same Screen
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kGraphing Two Different Functions
Description Use the following procedure to graph different functions in the main screen and sub-screen.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
2. On the SET UP screen, select G+G for Dual Screen.
3. Make V-Window settings for the main screen.
Press 6(RIGHT) to display the sub-graph settings screen. Pressing 6(LEFT) returns to the main screen setting screen.
Execution 4. Store the functions for the main screen and sub-screen.
5. Select the function of the graph that you want to eventually have in the sub-screen.
6. Draw the graph in the main screen.
7. Swap the main screen and sub-screen contents.
8. Return to the function screen.
9. Select the function of the next graph you want in the main screen.
10. Draw the graph in the main screen.
5-5-3 Drawing Two Graphs on the Same Screen
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Example Graph y = x(x + 1)(x 1) in the main screen, and y = 2x2 3 in the sub- screen.
Use the following V-Window settings.
(Main Screen)
Xmin = 4, Xmax = 4, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
(Sub-screen)
Xmin = 2, Xmax = 2, Xscale = 0.5
Ymin = 2, Ymax = 2, Yscale = 1
Procedure 1m GRPH TBL
2u3(SET UP)ccc2(G+G)i
3!K(V-Window)-ewewbwc
-fwfwbw
6(RIGHT)-cwcwa.fwc
-cwcwbwi
43(TYPE)b(Y=)v(v+b)(v-b)w
cvx-dw
5ff1(SEL)
65(DRAW)
76(g)5(SWAP)
8i
91(SEL)
05(DRAW)
Result Screen
5-5-4 Drawing Two Graphs on the Same Screen
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kUsing Zoom to Enlarge the Sub-screen
Description Use the following procedure to enlarge the main screen graph and then move it to the sub- screen.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
2. On the SET UP screen, select G+G for Dual Screen.
3. Make V-Window settings for the main screen.
Execution 4. Input the function and draw the graph in the main screen.
5. Use Zoom to enlarge the graph, and then move it to the sub-screen.
5-5-5 Drawing Two Graphs on the Same Screen
19990401
Example Draw the graph y = x(x + 1)(x 1) in the main screen, and then use Box Zoom to enlarge it.
Use the following V-Window settings.
(Main Screen)
Xmin = 2, Xmax = 2, Xscale = 0.5
Ymin = 2, Ymax = 2, Yscale = 1
Procedure 1m GRPH TBL
2u3(SET UP)ccc2(G+G)i
3!K(V-Window)-cwcwa.fwc
-cwcwbwi
43(TYPE)b(Y=)v(v+b)(v-b)w
5(DRAW)
52(ZOOM)b(BOX)
c~ce~ew
f~fd~dw
Result Screen
5-5-6 Drawing Two Graphs on the Same Screen
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5-6-1 Manual Graphing
5-6 Manual Graphing
kRectangular Coordinate Graph
Description Inputting the Graph command in the RUN MAT Mode enables drawing of rectangular coordinate graphs.
Set Up 1. From the Main Menu, enter the RUN MAT Mode.
2. Make V-Window settings.
Execution 3. Input the commands for drawing the rectangular coordinate graph.
4. Input the function.
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5-6-2 Manual Graphing
Example Graph y = 2x2 + 3x 4
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 2
Ymin = 10, Ymax = 10, Yscale = 5
Procedure 1m RUN MAT
2!K(V-Window)-fwfwcwc
-bawbawfwi
3K6(g)6(g)2(SKTCH)b(Cls)w
2(SKTCH)e(GRAPH)b(Y=)
4 cvx+dv-ew
Result Screen
12
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5-6-3 Manual Graphing
k Integration Graph
Description Inputting the Graph command in the RUN MAT Mode enables graphing of functions produced by an integration calculation. The calculation result is shown in the lower left of the display, and the calculation range is blackened in the graph.
Set Up 1. From the Main Menu, enter the RUN MAT Mode.
2. Make V-Window settings.
Execution 3. Input graph commands for the integration graph.
4. Input the function.
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5-6-4 Manual Graphing
Example Graph the integration (x + 2)(x 1)(x 3) dx.
Use the following V-Window settings.
Xmin = 4, Xmax = 4, Xscale = 1
Ymin = 8, Ymax = 12, Yscale = 5
Procedure 1m RUN MAT
2!K(V-Window)-ewewbwc
-iwbcwfwi
3K6(g)6(g)2(SKTCH)b(Cls)w
2(SKTCH)e(GRAPH)c( dx)
4 (v+c)(v-b)(v-d),
-c,bw
Result Screen
1
2
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5-6-5 Manual Graphing
kDrawing Multiple Graphs on the Same Screen
Description Use the following procedure to assign various values to a variable contained in an expres- sion and overwrite the resulting graphs on the screen.
Set Up 1. From the Main Menu, Enter GRPH TBL Mode.
2. Make V-Window settings.
Execution 3. Specify the function type and input the function. The following is the syntax for function
input.
Expression containing one variable ,!+( [ ) variable !.(=)
value , value , ... , value !-( ] )
4. Draw the graph.
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5-6-6 Manual Graphing
Example To graph y = Ax2 3 as the value of A changes in the sequence 3, 1, 1.
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 10, Ymax = 10, Yscale = 2
Procedure 1m GRPH TBL
2!K(V-Window)-fwfwbwc
-bawbawcwi
33(TYPE)b(Y=)av(A)vx-d,
!+( [ )av(A)!.(=)d,b,-b!-( ] )w
45(DRAW)
Result Screen
# The value of only one of the variables in the expression can change.
# Any of the following cannot be used for the variable name: X, Y, r, , T.
# You cannot assign a variable to the variable inside the function.
# When Simul Graph is turned on, all of the graphs for the specified variable values are drawn simultaneously.
# Overwrite can be used when graphing rectangular expressions, polar expressions, parametric functions, X = constant functions, and inequalities.
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5-7 Using Tables
kStoring a Function and Generating a Number Table
u To store a function
Example To store the function y = 3x2 2 in memory area Y1
Use f and c to move the highlighting in the Graph function list to the memory area where you want to store the function. Next, input the function and press w to store it.
uVariable Specifications There are two methods you can use to specify value for the variable x when generating a numeric table.
Table range method
With this method, you specify the conditions for the change in value of the variable.
List
With this method, the data in the list you specify is substituted for the x-variable to generate a number table.
u To generate a table using a table range
Example To generate a table as the value of variable x changes from 3 to 3, in increments of 1
6(g)2(RANG)
-dwdwbw
The numeric table range defines the conditions under which the value of variable x changes during function calculation.
Start ........... Variable x start value
End ............. Variable x end value
pitch ............ Variable x value change (interval)
After specifying the table range, press i to return to the Graph function list.
5-7-1 Using Tables
19990401
u To generate a table using a list 1. While the Graph function list is on the screen, display the SET UP screen.
2. Highlight Variable and then press 2(LIST) to display the pop-up window.
3. Select the list whose values you want to assign for the x-variable. To select List 6, for example, press gw. This causes the setting of the Variable item
of the SET UP screen to change to List 6.
4. After specifying the list you want to use, press i to return to the previous screen.
Note that the {RANG} item does not appear when a list name is specified for the Variable item of the SET UP screen.
uGenerating a Table
Example To generate a table of values for the functions stored in memory areas Y1 and Y3 of the Graph function list
Use f and c to move the highlighting to the function you want to select for table genera- tion and press 1(SEL) to select it.
The = sign of selected functions is highlighted on the screen. To deselect a function, move the cursor to it and press 1(SEL) again.
Press 5(TABL) to generate a number table using the functions you selected. The value of variable x changes according to the range or the contents of the list you specified.
The example screen shown here shows the results based on the contents of List 6 ( 3, 2, 1, 0, 1, 2, 3).
Each cell can contain up to six digits, including negative sign.
5-7-2 Using Tables
19990401
You can use cursor keys to move the highlighting around the table for the following purposes.
To display the selected cells value at the bottom of the screen, using the calculators current number of decimal place, number of significant digit, and exponential display range settings
To scroll the display and view parts of the table that do not fit in the display
To display at the top of the screen the scientific function that produced the value in the selected cell (in columns Y1, Y2, etc.)
To change x variable values by replacing values in column X
Press i to return to the Graph function list.
u To generate a differential number table *1
Changing the setting of SET UP screens Derivative item to On causes a number table that includes the derivative to be displayed whenever you generate a number table.
uSpecifying the function type You can specify a function as being one of three types.*2
Rectangular coordinate (Y=)
Polar coordinate (r =)
Parametric (Param)
1. Press 3(TYPE) while the function list is on the screen.
2. Press the number key that corresponds to the function type you want to specify.
5-7-3 Using Tables
Locating the cursor at a differential coefficient displays dy/dx in the top line, which indicates differential.
*1An error occurs if a graph for which a range is specified or an overwrite graph is included among the graph expressions.
*2The number table is generated only for the function type specified on the function list (Graph Func). You cannot generate a number table for a mixture of different function types.
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kEditing and Deleting Functions
u To edit a function
Example To change the function in memory area Y1 from y = 3x2 2 to y = 3x2 5
Use f and c to move the highlighting to the function you want to edit.
Use d and e to move the cursor to the location of the change.
eeeeeDf
w
6(g)5(TABL)
The Function Link Feature automatically reflects any changes you make to functions in the GRPH TBL Mode list, and DYNA Mode list.
u To delete a function 1. Use f and c to move the highlighting to the function you want to delete and then
press 2(DEL) or D.
2. Press w(Yes) to delete the function or i(No) to abort the operation without deleting anything.
5-7-4 Using Tables
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5-7-5 Using Tables
kEditing Tables
You can use the table menu to perform any of the following operations once you generate a table.
Change the values of variable x
Edit (delete, insert, and append) rows
Delete a table and regenerate table
Draw a connect type graph
Draw a plot type graph
While the Table & Graph menu is on the display, press 5(TABL) to display the table menu.
{EDIT } ... {edit value of x-variable}
{DELA} ... {delete table}
{Re-T} ... {regenerate table from function}
{GCON}/{GPLT } ... {connected type}/{draw plot type} graph draw
{RDEL}/{RINS} /{RADD} ... {delete}/{insert}/{add} row
u To change variable values in a table
Example To change the value in Column x, Row 3 of the table generated on page 5-7-2 from 1 to 2.5
cc -c.fw
When you change a variable value in Column x, all values in the columns to the right are recalculated and displayed.
# If you try to replace a value with an illegal operation (such as division by zero), an error occurs and the original value remains unchanged.
# You cannot directly change any values in the other (non-x) columns of the table.
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5-7-6 Using Tables
uRow Operations
u To delete a row
Example To delete Row 2 of the table generated on page 5-7-2
c 6(g)1(RDEL)
u To insert a row
Example To insert a new row between Rows 1 and 2 in the table generated on page 5-7-2
c 6(g)2(RINS)
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5-7-7 Using Tables
u To add a row
Example To add a new row below Row 7 in the table generated on page 5-7-2
cccccc 6(g)3(RADD)
uDeleting a Table 1. Display the table and then press 2(DELA).
2. Press w(Yes) to delete the table or i(No) to abort the operation without deleting anything.
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kCopying a Table Column to a List
A simple operation lets you copy the contents of a numeric table column into a list.
u To copy a table to a list
Example To copy the contents of Column x into List 1
K1(LMEM)
You can select any row of the column you want to copy.
Input the number of the list you want to copy and then press w.
bw
5-7-8 Using Tables
19990401
kDrawing a Graph from a Number Table
Description Use the following procedure to generate a number table and then draw a graph based on the values in the table.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
2. Make V-Window settings.
Execution 3. Store the functions.
4. Specify the table range.
5. Generate the table.
6. Select the graph type and draw it.
4(G CON) ... line graph*1
5(G PLT) ... plot type graph*1*2
5-7-9 Using Tables
*1After drawing the graph, pressing u 5(G T) or i returns to the function storage screen. To return to the number table screen, press 5(TABL).
*2Pressing 6(g) 4(G PLT) on the function storage screen generates the number table and plots the graph simultaneously.
19990401
Example Store the two functions below, generate a number table, and then draw a line graph. Specify a range of 3 to 3, and an increment of 1. Y1 = 3x2 2, Y2 = x2
Use the following V-Window settings.
Xmin = 0, Xmax = 6, Xscale = 1
Ymin = 2, Ymax = 10, Yscale = 2
Procedure 1m GRPH TBL
2!K(V-Window)awgwbwc
-cwbawcwi
33(TYPE)b(Y=)dvx-cw
vxw
46(g)2(RANG)-dwdwbwi
55(TABL)
64(G CON)
Result Screen
5-7-10 Using Tables
# You can use Trace, Zoom, or Sketch after drawing a graph.
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kSpecifying a Range for Number Table Generation
Description Use the following procedure to specify a number table range when calculating scatter data from a function.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
Execution 2. Store the functions.
3. Specify the table range.
4. Select the functions for which you want to generate a table.
The = sign of selected functions is highlighted on the screen.
5. Generate the table.
5-7-11 Using Tables
19990401
Example Store the three functions shown below, and then generate a table for functions Y1 and Y3. Specify a range of 3 to 3, and an increment of 1.
Y1 = 3x2 2, Y2 = x + 4, Y3 = x2
Procedure 1m GRPH TBL
23(TYPE)b(Y=)dvx-cw
v+ew
vxw
36(g)2(RANG)-dwdwbwi
4ff1(SEL)
55(TABL)
Result Screen
5-7-12 Using Tables
# You can generate number tables from rectangular coordinate, polar coordinate, and parametric functions.
# You can include derivatives in generated number tables by specifying On for the Derivative item on the SET UP screen.
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kSimultaneously Displaying a Number Table and Graph
Description Specifying T+G for Dual Screen on the SET UP makes it possible to display a number table and graph at the same time.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
2. Make V-Window settings.
3. On the SET UP screen, select T+G for Dual Screen.
Execution 4. Input the function.
5. Specify the table range.
6. The number table is displayed in the sub-screen on the right.
7. Specify the graph type and draw the graph.
4(G CON) ... line graph
5(G PLT) ... plot type graph*1
5-7-13 Using Tables
*1Pressing 6(g) 4(G PLT) on the function storage screen generates the number table and plots the graph simultaneously.
19990401
Example Store the function Y1 = 3x2 2 and simultaneously display its number table and line graph. Use a table range of 3 to 3 with an increment of 1.
Use the following V-Window settings.
Xmin = 0, Xmax = 6, Xscale = 1
Ymin = 2, Ymax = 10, Yscale = 2
Procedure 1m GRPH TBL
2!K(V-Window)awgwbwc
-cwbawcwi
3u3(SET UP)ccc1(T+G)i
43(TYPE)b(Y=)dvx-cw
56(g)2(RANG)
-dwdwbwi
65(TABL)
74(G CON)
Result Screen
5-7-14 Using Tables
200111
19990401
5-7-15 Using Tables
kUsing Graph-Table Linking
Description With Dual Graph, you can use the following procedure to link the graph and table screens so the pointer on the graph screen jumps to the location of the currently selected table value.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
2. Make the required V-Window settings.
Display the SET UP screen, select the Dual Screen item, and change its setting to T+G.
Execution 3. Input the function of the graph and make the required table range settings.
4. With the number table on the right side of the display, draw the graph on the left side.
4(G CON) ... connect type graph
5(G PLT) ... plot type graph
5. Turn on G Link.
6. Now when you use c and f to move the highlighting among the cells in the table, the pointer jumps to the corresponding point on the graph screen. If there are multiple graphs, pressing d and e causes the pointer to jump between them.
To turn off G Link, press i or !i(QUIT).
19990401
5-7-16 Using Tables
Example Store the function Y1 = 3logx and simultaneously display its number table and plot-type graph. Use a table range of 2 through 9, with an increment of 1.
Use the following V-Window settings.
Xmin = 1, Xmax = 10, Xscale = 1
Ymin = 1, Ymax = 4, Yscale = 1
Procedure 1m GRPH TBL
2!K(V-Window)-bwbawbwc
-bwewbwi
u3(SET UP)ccc1(T+G)i
33(TYPE)b(Y=)dlvw
6(g)2(RANG)
cwjwbwi
45(TABL)
5(G PLT)
56(g)4(G Link)
6c ~ c, f ~ f
Result Screen
19990401
5-8 Dynamic Graphing
kUsing Dynamic Graph
Description Dynamic Graph lets you define a range of values for the coefficients in a function, and then observe how a graph is affected by changes in the value of a coefficient. It helps to see how the coefficients and terms that make up a function influence the shape and position of a graph.
Set Up 1. From the Main Menu, enter the DYNA Mode.
2. Make V-Window settings.
Execution 3. On the SET UP screen, specify the Dynamic Type.
1(Cont) ... Continuous
2(Stop) ... Automatic stop after 10 draws
4. Use the cursor keys to select the function type on the built-in function type list.*1
5. Input values for coefficients, and specify which coefficient will be the dynamic vari- able.*2
6. Specify the start value, end value, and increment.
7. Specify the drawing speed.
3(SPEED)1( ) ..... Pause after each draw (Stop & Go)
2( ) ....... Half normal speed (Slow)
3( ) ....... Normal speed (Normal)
4( ) ......Twice normal speed (Fast)
8. Draw the Dynamic Graph.
5-8-1 Dynamic Graphing
*1The following are the seven built-in function types.
Y=AX+B Y=A(XB)2+C Y=AX2+BX+C Y=AX^3+BX2+CX+D Y=Asin(BX+C) Y=Acos(BX+C) Y=Atan(BX+C)
After you press 3(TYPE) and select the function type you want, you can then input the actual function.
b ... rectangular coordinate expression c ... polar coordinate expression d ... parametric function
*2You could also press w here and display the parameter setting menu.
# The message Too Many Functions appears when more than one function is selected for Dynamic Graphing.
19990401
Example Use Dynamic Graph to graph y = A (x 1)2 1, in which the value of coefficient A changes from 2 through 5 in increments of 1. The Graph is drawn 10 times.
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1 (initial defaults)
Procedure 1m DYNA
2!K(V-Window)1(INIT)i
3u3(SET UP)2(Stop)i
46(g)3(B-IN)c1(SEL)
56(g)4(VAR)cwbw-bw
62(RANG)cwfwbwi
73(SPEED)3( ) i
86(DYNA)
Result Screen
5-8-2 Dynamic Graphing
1
4
2
3
Repeats from 1 through 4.
19990401
kDynamic Graph Application Examples
Description You can also use Dynamic Graph to simulate simple physical phenomena.
Set Up 1. From the Main Menu, enter the DYNA Mode.
2. Make V-Window settings.
Execution 3. On the SET UP screen, specify Stop for Dynamic Type and Deg for Angle.
4. Specify Param (parametric function) as the function type, and input a function that contains a dynamic variable.
5. Specify the dynamic coefficient.
6. Specify the start value, end value, and increment.
7. Specify Normal for the draw speed.
8. Start the Dynamic Graph operation.
5-8-3 Dynamic Graphing
19990401
Example The path over time T of a ball thrown in the air at initial velocity V and an angle of degrees from horizontal can be calculated as follows. X = (Vcos )T, Y = (Vsin )T (1/2)gT2 (g = 9.8m/s2)
Use Dynamic Graph to plot the path of a ball thrown at an initial velocity of 20 meters per second, at horizontal angles of 30, 45, and 60 degrees (Angle: Deg).
Use the following V-Window settings.
Xmin = 1, Xmax = 42, Xscale = 5
Ymin = 1, Ymax = 16, Yscale = 2
Tmin = 0, Tmax = 6, T ptch = 0.1
Procedure 1m DYNA
2!K(V-Window)-bwecwfwc
-bwbgwcw
awgwa.bwi
3u3(SET UP)2(Stop)
cccc1(Deg)i
43(TYPE)d(Param)
(cacav(A) vw
(casav(A) v-e.jvxw
54(VAR)
62(RANG)dawgawbfwi
73(SPEED)3( ) i
86(DYNA)
Result Screen
5-8-4 Dynamic Graphing
2001101
19990401
kAdjusting the Dynamic Graph Speed
You can use the following procedure to adjust the Dynamic Graph speed while the draw operation is taking place.
1. While a Dynamic Graph draw operation is being performed, press A to change to the speed adjustment menu.
{ } ... {Each step of the Dynamic Graph draw operation is performed each time you press w.}
{ }/{ }/{ } ... {slow (1/2 speed)}/{normal (default speed)}/{fast (double speed)}
{STO} ... {stores graph conditions and screen data in Dynamic Graph memory}
2. Press the function key (1 to 4) that corresponds to the speed you want to change to.
5-8-5 Dynamic Graphing
# To clear the speed adjustment menu without changing anything, press w.
# Press u5 (GT) to return to the graph screen.
19990401
kUsing Dynamic Graph Memory
You can store Dynamic Graph conditions and screen data in Dynamic Graph memory for later recall when you need it. This lets you save time, because you can recall the data and immediately begin a Dynamic Graph draw operation. Note that you can store one set of data in memory at any one time.
The following is all of the data that makes up a set.
Graph functions (up to 20)
Dynamic Graph conditions
SET UP screen settings
V-Window contents
Dynamic Graph screen
uTo save data in Dynamic Graph memory 1. While a Dynamic Graph draw operation is being performed, press A to change to the
speed adjustment menu.
2. Press 6(STO). In response to the confirmation dialog that appears, press w(Yes) to save the data.
uTo recall data from Dynamic Graph memory 1. Display the Dynamic Graph function list.
2. Press 6(RCL) to recall all the data stored in Dynamic Graph memory.
5-8-6 Dynamic Graphing
# If there is already data stored in Dynamic Graph memory, the data save operation replaces it with the new data.
# Data recalled from Dynamic Graph memory replaces the calculators current graph functions, draw conditions, and screen data. The previous data is lost when it is replaced.
2004 9
19990401
5-9 Graphing a Recursion Formula
kGenerating a Number Table from a Recursion Formula
Description You can input up to three of the following types of recursion formulas and generate a number table.
General term of sequence {an}, composed of an, n
Linear two-term recursion composed of an+1, an, n
Linear three-term recursion composed of an+2, an+1, an, n
Set Up 1. From the Main Menu, enter the RECUR Mode.
Execution 2. Specify the recursion type.
3(TYPE)b(an=) ... {general term of sequence an}
c(an+1=) ... {linear two-term recursion}
d(an+2=) ... {linear three-term recursion}
3. Input the recursion formula.
4. Specify the table range. Specify a start point and end point for n. If necessary, specify a value for the initial term, and a pointer start point value if you plan to graph the formula.
5. Display the recursion formula number table.
5-9-1 Graphing a Recursion Formula
19990401
Example Generate a number table from recursion between three terms as expressed by an+2 = an+1 + an, with initial terms of a1 = 1, a2 = 1 (Fibonacci sequence), as n changes in value from 1 to 6.
Procedure 1m RECUR
23(TYPE)d(an+2=)
34(n. an )d(an+1)+2(an)w
45(RANG)2(a1)bwgwbwbwi
56(TABL)
Result Screen
5-9-2 Graphing a Recursion Formula
# Specifying On for the Display of the SET UP screen causes the sum of each term to be included in the table.
* The first two values correspond to a1 = 1 and a2 = 1.
200111
19990401
kGraphing a Recursion Formula (1)
Description After generating a number table from a recursion formula, you can graph the values on a line graph or plot type graph.
Set Up 1. From the Main Menu, enter the RECUR Mode.
2. Make V-Window settings.
Execution 3. Specify the recursion formula type and input the formula.
4. Specify the table range, and start and ending values for n. If necessary, specify the initial term value and pointer start point.
5. Display the recursion formula number table.
6. Specify the graph type and draw the graph.
5(G CON) ... line graph
6(G PLT) ... plot type graph
5-9-3 Graphing a Recursion Formula
19990401
Example Generate a number table from recursion between two terms as expressed by an+1 = 2an+1, with an initial term of a1 = 1, as n changes in value from 1 to 6. Use the table values to draw a line graph.
Use the following V-Window settings.
Xmin = 0, Xmax = 6, Xscale = 1
Ymin = 15, Ymax = 65, Yscale = 5
Procedure 1m RECUR
2!K(V-Window)awgwbwc
-bfwgfwfwi
33(TYPE)c(an+1=)c2(an)+bw
45(RANG)2(a1)bwgwbwi
56(TABL)
65(G CON)
Result Screen
5-9-4 Graphing a Recursion Formula
19990401
kGraphing a Recursion Formula (2)
Description The following describes how to generate a number table from a recursion formula and graph the values while Display is On.
Set Up 1. From the Main Menu, enter the RECUR Mode.
2. On the SET UP screen, specify On for Display.
3. Make V-Window settings.
Execution 4. Specify the recursion formula type and input the recursion formula.
5. Specify the table range, and start and ending values for n. If necessary, specify the initial term value and pointer start point.
6. Display the recursion formula number table.
7. Specify the graph type and draw the graph.
5(G CON)b(an) ... Line graph with ordinate an, abscissa n
c(an) ... Line graph with ordinate an, abscissa n
6(G PLT) b(an) ... Plot type graph with ordinate an, abscissa n
c(an) ... Plot type graph with ordinate an, abscissa n
5-9-5 Graphing a Recursion Formula
19990401
Example Generate a number table from recursion between two terms as expressed by an+1 = 2an+1, with an initial term of a1 = 1, as n changes in value from 1 to 6. Use the table values to draw a plot line graph with ordinate an, abscissa n.
Use the following V-Window settings.
Xmin = 0, Xmax = 6, Xscale = 1
Ymin = 15, Ymax = 65, Yscale = 5
Procedure 1m RECUR
2u3(SET UP)1(On)i
3!K(V-Window)awgwbwc
-bfwgfwfwi
43(TYPE)c(an+1=)c2(an)+bw
55(RANG)2(a1)bwgwbwi
66(TABL)
76(G PLT)c(an)
Result Screen
5-9-6 Graphing a Recursion Formula
19990401
kWEB Graph (Convergence, Divergence)
Description y = f(x) is graphed by presuming an+1 = y, an = x for linear two-term regression an+1 = f(an) composed of an+1, an. Next, it can be determined whether the function is convergent or divergent.
Set Up 1. From the Main Menu, enter the RECUR Mode.
2. Make V-Window settings.
Execution 3. Select 2-term recursion as the recursion formula type, and input the formula.
4. Specify the table range, n start and end points, initial term value, and pointer start point.
5. Display the recursion formula number table.
6. Draw the graph.
7. Press w, and the pointer appears at the start point you specified. Press w several times.
If convergence exists, lines that resemble a spider web are drawn on the display. Failure of the web lines to appear indicates either divergence or that the graph is outside the boundaries of the display screen. When this happens, change to larger View Window values and try again.
You can use fc to select the graph.
5-9-7 Graphing a Recursion Formula
19990401
Example To draw the WEB graph for the recursion formula an+1 = 3(an)2 + 3an, bn+1 = 3bn + 0.2, and check for divergence or convergence. Use the following table range and V-Window Settings.
Table Range
Start = 0, End = 6, a0 = 0.01, anStr = 0.01, b0 = 0.11, bnStr = 0.11
V-Window Settings
Xmin = 0, Xmax = 1, Xscale = 1
Ymin = 0, Ymax = 1, Yscale = 1
Procedure 1m RECUR
2!K(V-Window)awbwbwc
awbwbwi
33(TYPE)c(an+1=)-d2(an)x+d2(an)w
d3(bn)+a.cw
45(RANG)1(a0)
awgwa.abwa.bbwc
a.abwa.bbwi
56(TABL)
64(WEB)
71(TRACE)w~w(an is convergence)
cw~w(bn is divergence)
Result Screen
5-9-8 Graphing a Recursion Formula
19990401
5-10-1 Changing the Appearance of a Graph
5-10 Changing the Appearance of a Graph
kDrawing a Line
Description The sketch function lets you draw points and lines inside of graphs.
Set Up 1. Draw the graph.
Execution 2. Select the sketch function you want to use.*1
3(SKTCH)b(Cls) ... Screen clear
c(PLOT) {On}/{Off}/{Change}/{Plot} ... Point {On}/{Off}/{Change}/{Plot}
d(LINE) {F-Line}/{Line} ... {Freehand line}/{Line}
e(Text) ... Text input
f(Pen) ... Freehand
g(Tangnt) ... Tangent line
h(Normal) ... Line normal to a curve
i(Invrse) ... Inverse function*2
j(Circle) ... Circle
v(Vert) ... Vertical line
l(Horz) ... Horizontal line
3. Use the cursor keys to move the pointer ( ) to the location where you want to draw, and press w.*3
*1The above shows the function menu that appears in the GRPH TBL Mode. Menu items may differ somewhat in other modes.
*2In the case of an inverse function graph, drawing starts immediately after you select this option.
*3Some sketch functions require specification of two points. After you press w to specify the first point, use the cursor keys to move the pointer to the location of the second point and press w.
19990401
Example Draw a line that is tangent to point (2, 0) on the graph for y = x (x + 2)(x 2).
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
Procedure 1m GRPH TBL
!K(V-Window)-fwfwbwc
-fwfwbwi
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
23(SKTCH)g(Tangnt)
3e~ew*1
Result Screen
5-10-2 Changing the Appearance of a Graph
*1You can draw a tangent line in succession by moving the pointer and pressing w.
19990401
k Inserting Comments
Description You can insert comments anywhere you want in a graph.
Set Up 1. Draw the graph.
Execution 2. Press 3(SKTCH)e(Text), and a pointer appears in the center of the display.
3. Use the cursor keys to move the pointer to the location where you want the text to be, and input the text.
5-10-3 Changing the Appearance of a Graph
# You can input any of the following characters as comment text: A~Z, r, , space, 0~9, ., +, , , , (), EXP, , Ans, (, ), [, ], {, }, comma, ,
x2, ^, log, In, , x , 10x, ex, 3 , x1, sin, cos, tan, sin1, cos1, tan1, i, List, Mat
19990401
Example Insert text into the graph y = x (x + 2)(x 2).
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
Procedure 1m GRPH TBL
!K(V-Window)-fwfwbwc
-fwfwbwi
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
23(SKTCH)e(Text)
3f~f d~d
a-(Y)!.(=)v(v+c)(v-c)
i
Result Screen
5-10-4 Changing the Appearance of a Graph
12
19990401
k Freehand Drawing
Description You can use the pen option for freehand drawing in a graph.
Set Up 1. Draw the graph.
Execution 2. Press 3(SKTCH)f(Pen), and a pointer appears in the center of the screen.
3. Use the cursor keys to move the pointer to the point from which you want to start drawing, and then press w.
4. Use the cursor keys to move the pointer. A line is drawn wherever you move the pointer. To stop the line, press w.
Repeat step 3 and 4 to draw other lines.
After you are finished drawing, press i.
5-10-5 Changing the Appearance of a Graph
19990401
Example Use the pen to draw on the graph y = x (x + 2)(x 2).
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
Procedure 1m GRPH TBL
!K(V-Window)-fwfwbwc
-fwfwbwi
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
23(SKTCH)f(Pen)
3f~f d~dw
4cd, e~e, ef, d~dw
Result Screen
5-10-6 Changing the Appearance of a Graph
12
19990401
5-10-7 Changing the Appearance of a Graph
kChanging the Graph Background
You can use the set up screen to specify the memory contents of any picture memory area (Pict 1 through Pict 20) as the Background item. When you do, the contents of the corresponding memory area is used as the background of the graph screen.
Example 1 With the circle graph X2 + Y2 = 1 as the background, use Dynamic Graph to graph Y = X2 + A as variable A changes value from 1 to 1 in increments of 1.
Recall the background graph.
(X2 + Y2 = 1)
19990401
5-10-8 Changing the Appearance of a Graph
Draw the dynamic graph.
(Y = X2 1)
(Y = X2)
(Y = X2 + 1)
See 5-8-1 Dynamic Graphing for details on using the Dynamic Graph feature.
19990401
5-11 Function Analysis
kReading Coordinates on a Graph Line
Description Trace lets you move a pointer along a graph and read out coordinates on the display.
Set Up 1. Draw the graph.
Execution 2. Press 1(TRACE), and a pointer appears in the center of the graph.*1
3. Use d and e to move the pointer along the graph to the point at which you want to display the derivative.
When there are multiple graphs on the display, press f and c to move between them along the x-axis of the current pointer location.
4. You can also move the pointer by pressing v to display the pop-up window, and then inputting coordinates.
The pop-up window appears even when you input coordinates directly.
To exit a trace operation, press i.
*1The pointer is not visible on the graph when it is located at a point outside the graph display area or when an error of no value occurs.
# You can turn off display of the coordinates at the pointer location by specifying Off for the Coord item on the SET UP screen.
12
5-11-1 Function Analysis
2001 1
19990401
Example Read coordinates along the graph of the function shown below. Y1 = x2 3
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 10, Ymax = 10, Yscale = 2
Procedure 1m GRPH TBL
!K(V-Window)-fwfwbwc
-bawbawcwi
3(TYPE)b(Y=)vx-dw
5(DRAW)
21(TRACE)
3d~d
4-bw
Result Screen
5-11-2 Function Analysis
# The following shows how coordinates are displayed for each function type.
Polar Coordinate Graph
Parametric Graph
Inequality Graph
12
19990401
kDisplaying the Derivative
Description In addition to using Trace to display coordinates, you can also display the derivative at the current pointer location.
Set Up 1. On the SET UP screen, specify On for Derivative.
2. Draw the graph.
Execution 3. Press 1(TRACE), and the pointer appears at the center of the graph. The current
coordinates and the derivative also appear on the display at this time.
4. Use d and e to move the pointer along the graph to the point at which you want to display the derivative.
When there are multiple graphs on the display, press f and c to move between them along the x-axis of the current pointer location.
5. You can also move the pointer by pressing v to display the pop-up window, and then inputting coordinates.
The pop-up window appears even when you input coordinates directly.
5-11-3 Function Analysis
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19990401
Example Read coordinates and derivatives along the graph of the function shown below. Y1 = x2 3
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 10, Ymax = 10, Yscale = 2
Procedure 1m GRPH TBL
u3(SET UP)ccccc1(On)i
2!K(V-Window)-fwfwbwc
-bawbawcwi
3(TYPE)b(Y=)vx-dw
5(DRAW)
31(TRACE)
4d~d
5-bw
Result Screen
5-11-4 Function Analysis
12
19990401
kGraph to Table
Description You can use trace to read the coordinates of a graph and store them in a number table. You can also use Dual Graph to simultaneously store the graph and number table, making this an important graph analysis tool.
Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
2. On the SET UP screen, specify GtoT for Dual Screen.
3. Make V-Window settings.
Execution 4. Save the function and draw the graph on the active (left) screen.
5. Activate Trace. When there are multiple graphs on the display, press f and c to select the graph you want.
6. Use d to move the pointer and press w to store coordinates into the number table. Repeat this step to store as many values as you want.
7. Press 6(CHNG) to switch the number table side.
8. From the pop-up window, input the list number you want to save.
5-11-5 Function Analysis
19990401
Example Save, in a table, the coordinates in the vicinity of the points of intersection at X = 0 for the two graphs shown below, and store the table contents in List 1.
Y1 = x2 3, Y2 = x + 2
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 10, Ymax = 10, Yscale = 2
Procedure 1m GRPH TBL
2u3(SET UP)ccc3(GtoT)i
3!K(V-Window)-fwfwbwc
-bawbawcwi
43(TYPE)b(Y=)vx-dw
-v+cw
5(DRAW)
51(TRACE)
6d~dwe~ewi
76(CHNG)
8K1(LMEM)bw
Result Screen
5-11-6 Function Analysis
200111
19990401
kCoordinate Rounding
Description This function rounds off coordinate values displayed by Trace.
Set Up 1. Draw the graph.
Execution 2. Press 2(ZOOM)i(Rnd). This causes the V-Window settings to be changed
automatically in accordance with the Rnd value.
3. Press 1(TRACE), and then use the cursor keys to move the pointer along the graph. The coordinates that now appear are rounded.
5-11-7 Function Analysis
19990401
Example Use coordinate rounding and display the coordinates in the vicinity of the points of intersection for the two graphs produced by the functions shown below. Y1 = x2 3, Y2 = x + 2
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 10, Ymax = 10, Yscale = 2
Procedure 1m GRPH TBL
!K(V-Window)-fwfwbwc
-bawbawcwi
3(TYPE)b(Y=)vx-dw
-v+cw
5(DRAW)
22(ZOOM)i(Rnd)
31(TRACE)
d~d
Result Screen
5-11-8 Function Analysis
19990401
kCalculating the Root
Description This feature provides a number of different methods for analyzing graphs.
Set Up 1. Draw the graphs.
Execution 2. Select the analysis function.
4(G-SLV)b(Root) ... Calculation of root
c(Max) ... Local maximum value
d(Min) ... Local minimum value
e(Y-lcpt) ... y-intercept
f(Isect) ... Intersection of two graphs
g(Y-Cal) ... y-coordinate for given x-coordinate
h(X-Cal) ... x-coordinate for given y-coordinate
i(dx) ... Integral value for a given range
3. When there are multiple graphs on the screen, the selection cursor (k) is located at the lowest numbered graph. Use the cursor keys to move the cursor to the graph you want to select.
4. Press w to select the graph where the cursor is located and display the value produced by the analysis. When an analysis produces multiple values, press e to calculate the next value. Pressing d returns to the previous value.
5-11-9 Function Analysis
200111
19990401
Example Draw the graph shown below and calculate the root for Y1. Y1 = x(x + 2)(x 2)
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1 (initial defaults)
Procedure 1m GRPH TBL
!K(V-Window)1(INIT)i
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
24(G-SLV)b(Root)
4e
e
Result Screen
5-11-10 Function Analysis
# When analyzing a single graph, results appear as soon as you select an analysis function in step 2, so step 3 is not necessary.
# Root, local maximum value, local minimum value, and y-intercept can be calculated for rectangular coordinate graphs and inequality graphs only.
# The y-intercept is the point where the graph crosses the y-axis.
200111
19990401
kCalculating the Point of Intersection of Two Graphs
Description Use the following procedure to calculate the point of intersection of two graphs.
Set Up 1. Draw the graphs.
Execution 2. Press 4(G-SLV)5(Isect). When there are three or more graphs, the selection cursor
(k) appears at the lowest numbered graph.
3. Use the cursor keys to move the cursor to the graph you want to select.
4. Press w to select the first graph, which changes the shape of the cursor from k to .
5. Use the cursor keys to move the cursor to the second graph.
6. Press w to calculate the point of intersection for the two graphs. When an analysis produces multiple values, press e to calculate the next value. Pressing d returns to the previous value.
5-11-11 Function Analysis
19990401
Example Graph the two functions shown below, and determine the point of intersection between Y1 and Y2. Y1 = x + 1, Y2 = x2
Use the following V-Window settings.
Xmin = 5, Xmax = 5, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
Procedure 1m GRPH TBL
!K(V-Window)-fwfwbwc
-fwfwbwi
3(TYPE)b(Y=)v+bw
vxw
5(DRAW)
24(G-SLV)f(Isect)
6e
Result Screen
5-11-12 Function Analysis
# In the case of two graphs, the point of intersection is calculated immediately after you press 4f in step 2.
# You can calculate the point of intersection for rectangular coordinate graphs and inequality graphs only.
19990401
kDetermining the Coordinates for Given Points
Description The following procedure describes how to determine the y-coordinate for a given x, and the x-coordinate for a given y.
Set Up 1. Draw the graph.
Execution 2. Select the function you want to perform. When there are multiple graphs, the selection
cursor (k) appears at the lowest numbered graph.
4(G-SLV)g(Y-Cal) ... y-coordinate for given x
h(X-Cal) ... x-coordinate for given y
3. Use fc to move the cursor (k) to the graph you want, and then press w to select it.
4. Input the given x-coordinate value or y-coordinate value. Press w to calculate the corresponding y-coordinate value or x-coordinate value.
5-11-13 Function Analysis
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Example Graph the two functions shown below and then determine the y- coordinate for x = 0.5 and the x-coordinate for y = 2.2 on graph Y2. Y1 = x + 1, Y2 = x(x + 2)(x 2)
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1 (initial defaults)
Procedure 1m GRPH TBL
!K(V-Window)1(INIT)i
3(TYPE)b(Y=)v+bw
v(v+c)(v-c)w
5(DRAW)
24(G-SLV)g(Y-Cal) 2 4(G-SLV)h(X-Cal)
3cw 3 cw
4 a.fw 4 c.cw
Result Screen
5-11-14 Function Analysis
# When there are multiple results for the above procedure, press e to calculate the next value. Pressing d returns to the previous value.
# Step 3 of the above procedure is skipped when there is only one graph on the display.
# The X-Cal value cannot be obtained for a parametric function graph.
# After obtaining coordinates with the above procedure, you can input different coordinates by first pressing v.
19990401
kCalculating the lntegral Value for a Given Range
Description Use the following procedure to obtain integration values for a given range.
Set Up 1. Draw the graph.
Execution 2. Press 4(G-SLV)i(dx). When there are multiple graphs, this causes the selection
cursor (k) to appear at the lowest numbered graph.
3. Use fc to move the cursor (k) to the graph you want, and then press w to select it.
4. Use d to move the lower limit pointer to the location you want, and then press w.
You can also move the pointer by pressing v to display the pop-up window, and then inputting coordinates.
5. Use e to move the upper limit pointer to the location you want.
You can also move the pointer by pressing v to display the pop-up window, and then inputting the upper limit and lower limit values for the integration range.
6. Press w to calculate the integral value.
5-11-15 Function Analysis
# You can also specify the lower limit and upper limit by inputting them on the 10-key pad.
# When setting the range, make sure that the lower limit is less than the upper limit.
# Integral values can be calculated for rectangular coordinate graphs only.
12
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Example Graph the function shown below, and then determine the integral value at (2, 0). Y1 = x(x + 2)(x 2)
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 4, Ymax = 4, Yscale = 1
Procedure 1m GRPH TBL
!K(V-Window)-g.dwg.dwbwc
-ewewbwi
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
24(G-SLV)i(dx)
4d~dw
5e~e(Upper limit; x= 0)
6w
Result Screen
5-11-16 Function Analysis
19990401
kConic Section Graph Analysis
You can determine approximations of the following analytical results using conic section graphs.
Focus/vertex/eccentricity
Latus rectum
Center/radius
x-/y-intercept
Directrix/axis of symmetry drawing and analysis
Asymptote drawing and analysis
After graphing a conic section, press 4(G-SLV) to display the following graph analysis menus.
uParabolic Graph Analysis {Focus}/{Vertex}/{Length}/{e} ... {focus}/{vertex}/{latus rectum}/{eccentricity}
{Dirtrx}/{Sym} ... {directrix}/{axis of symmetry}
{X-Icpt}/{Y-Icpt} ... {x-intercept}/{y-intercept}
uCircular Graph Analysis {Center}/{Radius} ... {center}/{radius}
{X-Icpt}/{Y-Icpt} ... {x-intercept}/{y-intercept}
uElliptical Graph Analysis {Focus}/{Vertex}/{Center}/{e} ... {focus}/{vertex}/{center}/{eccentricity}
{X-Icpt}/{Y-Icpt} ... {x-intercept}/{y-intercept}
uHyperbolic Graph Analysis {Focus}/{Vertex}/{Center}/{e} ... {focus}/{vertex}/{center}/{eccentricity}
{Asympt} ... {asymptote}
{X-Icpt}/{Y-Icpt} ... {x-intercept}/{y-intercept}
The following examples show how to use the above menus with various types of conic section graphs.
5-11-17 Function Analysis
200111
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u To calculate the focus, vertex and latus rectum [G-SLV]-[Focus]/[Vertex]/[Length]
Example To determine the focus, vertex and latus rectum for the parabola X = (Y 2)2 + 3
Use the following V-Window settings.
Xmin = 1, Xmax = 10, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
4(G-SLV)
b(Focus)
(Calculates the focus.)
i
4(G-SLV)
d(Vertex)
(Calculates the vertex.)
i
4(G-SLV)
f(Length)
(Calculates the latus rectum.)
When calculating two foci for an ellipse or hyperbolic graph, press e to calculate the second focus. Pressing d returns to the first focus.
When calculating two vertexes for an ellipse or hyperbolic graph, press e to calculate the second vertex. Pressing d returns to the first vertex.
5-11-18 Function Analysis
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u To calculate the center and radius [G-SLV]-[Center]/[Radius]
Example To determine the center and radius for the circle (X + 2)2 + (Y + 1)2 = 22
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1
4(G-SLV)
b(Center)
(Calculates the center.)
i
4(G-SLV)
c(Radius)
(Calculates the radius.)
u To calculate the x- and y-intercepts [G-SLV]-[X-Icpt]/[Y-Icpt]
Example To determine the x- and y-intercepts for the hyperbola
(X 3)2 (Y 1)2
= 1 22 22
Use the following V-Window settings.
Xmin = 4, Xmax = 8, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
4(G-SLV)
g(X-Icpt)
(Calculates the x-intercept.)
5-11-19 Function Analysis
19990401
i
4(G-SLV)
h(Y-Icpt)
(Calculates the y-intercept.)
Press e to calculate the second set of x-/y-intercepts. Pressing d returns to the first set of intercepts.
u To draw and analyze the axis of symmetry and directrix [G-SLV]-[Sym]/[Dirtrx]
Example To draw the axis of symmetry and directrix for the parabola X = 2(Y 1)2 + 1
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1
4(G-SLV)
e(Sym)
(Draws the axis of symmetry.)
i
4(G-SLV)
c(Dirtrx)
(Draws the directrix.)
5-11-20 Function Analysis
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uTo draw and analyze the asymptotes [G-SLV]-[Asympt]
Example To draw the asymptotes for the hyperbola
(X 1)2 (Y 1)2
= 1 22 22
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 5, Ymax = 5, Yscale = 1
4(G-SLV)
e(Asympt)
(Draws the asymptotes.)
uTo calculate eccentricity [G-SLV]-[e]
Example To determine the eccentricity of the graph for ellipse
(X 2)2 +
(Y 2)2 = 1
42 22
Use the following V-Window settings.
Xmin = 3, Xmax = 7, Xscale = 1
Ymin = 1, Ymax = 5, Yscale = 1
4(G-SLV)
e(e)
(Calculates eccentricity.)
5-11-21 Function Analysis
# Certain V-Window parameters can produce errors in values produced as graph analysis results.
# The message Not Found appears on the display when graph analysis is unable to produce a result.
# The following can result in inaccurate analysis results or may even make it impossible to obtain a solution at all. When the solution is tangent to the x-axis. When the solution is a point of tangency
between two graphs.
19990401
Chapter
Statistical Graphs and Calculations This chapter describes how to input statistical data into lists, and how to calculate the mean, maximum and other statistical values. It also tells you how to perform regression calculations.
6-1 Before Performing Statistical Calculations
6-2 Calculating and Graphing Single-Variable Statistical Data
6-3 Calculating and Graphing Paired-Variable Statistical Data
6-4 Performing Statistical Calculations 6-5 Distribution
Important! This chapter contains a number of graph screen shots. In each case, new
data values were input in order to highlight the particular characteristics of the graph being drawn. Note that when you try to draw a similar graph, the unit uses data values that you have input using the List function. Because of this, the graphs that appear on the screen when you perform a graphing operation will probably differ somewhat from those shown in this manual.
6
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6-1 Before Performing Statistical Calculations From the Main Menu, enter the STAT Mode and display the statistical data lists.
Use the statistical data lists to input data and to perform statistical calculations.
Use f, c, d and e to move
the highlighting around the lists.
Once you input data, you can use it to produce a graph and check for tendencies. You can also use a variety of different regression calculations to analyze the data.
k Inputting Data into Lists
Example To input the following two data groups
0.5, 1.2, 2.4, 4.0, 5.2 2.1, 0.3, 1.5, 2.0, 2.4
a.fwb.cw
c.ewewf.cw
e
-c.bwa.dw
b.fwcwc.ew
Once data is input, you can use it for graphing and statistical calculations.
6-1-1 Before Performing Statistical Calculations
# Except for complex numbers, calculation results can be input as statistical data.
# You can use the f, c, d and e keys to move the highlighting to any cell in the lists for data input.
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kChanging Graph Parameters
Use the following procedures to specify the graph draw/non-draw status, the graph type, and other general settings for each of the graphs in the graph menu (GPH1, GPH2, GPH3).
While the statistical data list is on the display, press 1(GRPH) to display the graph menu, which contains the following items.
{S-Gph1}/{S-Gph2}/{S-Gph3} ... graph {1}/{2}/{3} drawing*1
{Select} ... {simultaneous graph (GPH1, GPH2, GPH3) selection} (You can specify the multiple graphs.)
{Set} ... {graph settings (graph type, list assignments)}
1. General graph settings [GRPH]-[Set]
This section describes how to use the general graph settings screen to make the following settings for each graph (GPH1, GPH2, GPH3).
Graph Type
The initial default graph type setting for all the graphs is scatter graph. You can select one of a variety of other statistical graph types for each graph.
List
The initial default statistical data is List 1 for single-variable data, and List 1 and List 2 for paired-variable data. You can specify which statistical data list you want to use for x-data and y-data.
Frequency
Normally, each data item or data pair in the statistical data list is represented on a graph as a point. When you are working with a large number of data items however, this can cause problems because of the number of plot points on the graph. When this happens, you can specify a frequency list that contains values indicating the number of instances (the frequency) of the data items in the corresponding cells of the lists you are using for x-data and y-data. Once you do this, only one point is plotted for the multiple data items, which makes the graph easier to read.
6-1-2 Before Performing Statistical Calculations
*1 The initial default graph type setting for all the graphs (Graph 1 through Graph 3) is scatter diagram, but you can change to one of a number of other graph types.
# You can specify the graph draw/non-draw status, the graph type, and other general
settings for each of the graphs in the graph menu (GPH1, GPH2, GPH3).
19990401
Mark Type
This setting lets you specify the shape of the plot points on the graph.
u To display the general graph settings screen [GRPH]-[Set]
Pressing 1(GRPH)f(Set) displays the general graph settings screen.
The settings shown here are examples only. The settings on your general graph settings screen may differ.
StatGraph (statistical graph specification)
{GPH1}/{GPH2}/{GPH3} ... graph {1}/{2}/{3}
Graph Type (graph type specification)
{Scat}/{xy}/{NPP} ... {scatter diagram}/{xy line graph}/{normal probability plot}
{Hist}/{Box}/{ModB}/{NDis}/{Brkn} ... {histogram}/{med-box graph}/{modified-box graph}/{normal distribution curve}/{broken line graph}
{X}/{Med}/{X^2}/{X^3}/{X^4} ... {linear regression graph}/{Med-Med graph}/{quadratic regression graph}/{cubic regression graph}/{quartic regression graph}
{Log}/{Exp}/{Pwr}/{Sin}/{Lgst} ... {logarithmic regression graph}/{exponential regression graph}/{power regression graph}/{sinusoidal regression graph}/{logistic regression graph}
XList (x-axis data list)
{LIST} ... {List 1 to 20}
YList (y-axis data list)
{LIST} ... {List 1 to 20}
Frequency (number of times a value occurs)
{1} ... {1-to-1 plot}
{LIST} ... contents of this list indicates the frequency of XList and YList data
Mark Type (plot mark type)
{ }/{}/{} ... scatter diagram plot points
6-1-3 Before Performing Statistical Calculations
19990401
2. Graph draw/non-draw status [GRPH]-[Select]
The following procedure can be used to specify the draw (On)/non-draw (Off) status of each of the graphs in the graph menu.
u To specify the draw/non-draw status of a graph 1. Pressing 1(GRPH) e(Select) displays the graph On/Off screen.
Note that the StatGraph1 setting is for Graph 1 (GPH1 of the graph menu), StatGraph2 is for Graph 2, and StatGraph3 is for Graph 3.
2. Use the cursor keys to move the highlighting to the graph whose status you want to change, and press the applicable function key to change the status.
{On}/{Off} ... {On (draw)}/{Off (non-draw)} {DRAW} ... {draws all On graphs}
3. To return to the graph menu, press i.
6-1-4 Before Performing Statistical Calculations
# View Window parameters are normally set automatically for statistical graphing. If you want to set View Window parameters manually, you must change the Stat Wind item to Manual. While the statistical data list is on the display, perform the following procedure.
u3(SET UP)2(Man)
i(Returns to previous menu.)
# The default setting automatically uses List 1 data as x-axis (horizontal) values and List 2 data as y-axis (vertical) values. Each set of x/y data is a point on the scatter diagram.
# Pressinguadoes not hide the menu while a statistical graph is on the display.
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6-2 Calculating and Graphing Single-Variable Statistical Data
Single-variable data is data with only a single variable. If you are calculating the average height of the members of a class for example, there is only one variable (height).
Single-variable statistics include distribution and sum. The following types of graphs are available for single-variable statistics.
You can also use the procedures under Changing Graph Parameters on page 6-1-2 to make the settings you want before drawing each graph.
kNormal Probability Plot (NPP)
This plot compares the data accumulated ratio with a normal distribution accumulated ratio. XList specifies the list where data is input, and Mark Type is used to select from among the marks { / / }you want to plot.
Press i or !i(QUIT) to return to the statistical data list.
kHistogram (Bar Graph) (Hist)
XList specifies the list where the data is input, while Freq specifies the list where the data frequency is input. 1 is specified for Freq when frequency is not specified.
6-2-1 Calculating and Graphing Single-Variable Statistical Data
w(Draw)
The display screen appears as shown above before the graph is drawn. At this point, you can change the Start and pitch values.
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kMed-box or Box and Whisker Graph (Box)
This type of graph lets you see how a large number of data items are grouped within specific ranges. A box encloses all the data in an area from the first quartile (Q1) to the third quartile (Q3), with a line drawn at the median (Med). Lines (called whiskers) extend from either end of the box up to the minimum (minX) and maximum (maxX) of the data.
XList specifies the list where the data is input, while Freq specifies the list where the data frequency is input. 1 is specified for Freq when frequency is not specified.
kModified Box Graph (ModB)
The modified box graph omits everything in the range past 1.5 IQR (IQR = Q3 Q1, Q3: 3rd quartile, Q1: 1st quartile) from the med-box 4th quartile and draws whiskers.
Outliers are displayed as plot points.
XList specifies the list where the data is input, while Freq specifies the list where the data frequency is input. 1 is specified for Freq when frequency is not specified.
6-2-2 Calculating and Graphing Single-Variable Statistical Data
# Input a positive integer for frequency data. Other types of values (decimals, etc.) cause an error.
minX Q1 Med Q3 maxX
# Dimension ERROR usually occurs when two lists contain a different number of elements.
19990401
kNormal Distribution Curve (N Dis)
The normal distribution curve is graphed using the following normal distribution function.
y = 1
(2 ) xn
e
2xn 2
(xx) 2
XList specifies the list where the data is input, while Freq specifies the list where the data frequency is input. 1 is specified for Freq when frequency is not specified.
kBroken Line Graph (Brkn)
Lines connect center points of a histogram bar.
XList specifies the list where the data is input, while Freq specifies the list where the data frequency is input. 1 is specified for Freq when frequency is not specified.
6-2-3 Calculating and Graphing Single-Variable Statistical Data
w(Draw)
The display screen appears as shown above before the graph is drawn. At this point, you can change the Start and pitch values.
19990401
kDisplaying the Calculation Results of a Drawn Single-Variable Graph
Single-variable statistics can be expressed as both graphs and parameter values. When these graphs are displayed, the single-variable calculation results appear as shown below when you press 4(CALC)b(1VAR).
Use c to scroll the list so you can view the items that run off the bottom of the screen.
The following describes the meaning of each of the parameters.
o ............. mean
x ........... sum
x2 .......... sum of squares
xn .......... population standard deviation
xn1 ........ sample standard deviation
n ............. number of data items
minX ....... minimum
Q1 .......... first quartile
Med ........ median
Q3 .......... third quartile
maxX ...... maximum
Mod ........ mode
Mod : n ... number of data mode items
Mod : F ... data mode frequency
Press 6(DRAW) to return to the original single-variable statistical graph.
6-2-4 Calculating and Graphing Single-Variable Statistical Data
# When Mod has multiple solutions, they are all displayed.
19990401
6-3-1 Calculating and Graphing Paired-Variable Statistical Data
6-3 Calculating and Graphing Paired-Variable Statistical Data
k Drawing a Scatter Diagram and xy Line Graph
Description The following procedure plots a scatter diagram and connects the dots to produce an xy line graph.
Set Up 1. From the Main Menu, enter the STAT Mode.
Execution 2. Input the data into a list.
3. Specify Scat (scatter diagram) or xy (xy line graph) as the graph type, and then execute the graph operation.
Press i or !i(QUIT) to return to the statistical data list.
19990401
Example Input the two sets of data shown below. Next, plot the data on a scatter diagram and connect the dots to produce an xy line graph.
0.5, 1.2, 2.4, 4.0, 5.2, (xList)
2.1, 0.3, 1.5, 2.0, 2.4 (yList)
Procedure 1m STAT
2 a.fwb.cw
c.ewewf.cw
e
-c.bwa.dw
b.fwcwc.ew
3 (Scatter diagram)1(GRPH)f(Set)c1(Scat)i
1(GRPH)b(S-Gph1)
3 (xy line graph)1(GRPH)f(Set)c2(xy)i
1(GRPH)b(S-Gph1)
Result Screen
(Scatter diagram)
(xy line graph)
6-3-2 Calculating and Graphing Paired-Variable Statistical Data
19990401
k Drawing a Regression Graph
Description Use the following procedure to input paired-variable statistical data, perform a regression calculation using the data, and then graph the results.
Set Up 1. From the Main Menu, enter the STAT Mode.
Execution 2. Input the data into a list, and plot the scatter diagram.
3. Select the regression type, execute the calculation, and display the regression parameters.
4. Draw the regression graph.
6-3-3 Calculating and Graphing Paired-Variable Statistical Data
# You can perform trace on a regression graph. You cannot perform trace scroll.
19990401
Example Input the two sets of data shown below and plot the data on a scatter diagram. Next, perform logarithmic regression on the data to display the regression parameters, and then draw the corresponding regression graph.
0.5, 1.2, 2.4, 4.0, 5.2, (xList)
2.1, 0.3, 1.5, 2.0, 2.4 (yList)
Procedure 1m STAT
2 a.fwb.cw
c.ewewf.cw
e
-c.bwa.dw
b.fwcwc.ew
1(GRPH)f(Set)c1(Scat)i
1(GRPH)b(S-Gph1)
34(CALC)h(Log)
46(DRAW)
Result Screen
6-3-4 Calculating and Graphing Paired-Variable Statistical Data
2001 1 220 1 101
19990401
kSelecting the Regression Type
After you graph paired-variable statistical data, press 4(CALC). Then you can use the function menu at the bottom of the display to select from a variety of different types of regression.
{2VAR} ... {paired-variable statistical results}
{Linear}/{MedMed}/{Quad}/{Cubic}/{Quart}/{Log}/{Exp}/{Power}/{Sin}/{Lgstic} ... {linear regression}/{Med-Med}/{quadratic regression}/{cubic regression}/{quartic regression}/{logarithmic regression}/{exponential regression}/{power regression}/ {sinusoidal regression}/{logistic regression} calculation and graphing
kDisplaying Statistical Calculation Results
Whenever you perform a regression calculation, the regression formula parameter (such as a and b in the linear regression y = ax + b) calculation results appear on the display. You can use these to obtain statistical calculation results.
Regression parameters are calculated as soon as you press a function key to select a regression type, while a graph is on the display.
kGraphing Statistical Calculation Results
While the parameter calculation result is on the display, you can graph the displayed regression formula by pressing 6(DRAW).
6-3-5 Calculating and Graphing Paired-Variable Statistical Data
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k Linear Regression Graph
Linear regression uses the method of least squares to plot a straight line that passes close to as many data points as possible, and returns values for the slope and y-intercept (y-coordinate when x = 0) of the line.
The graphic representation of this relationship is a linear regression graph.
4(CALC)c(Linear)
6(DRAW)
The following is the linear regression model formula.
y = ax + b
a ............. regression coefficient (slope)
b ............. regression constant term (y-intercept)
r ............. correlation coefficient
r2 ............ coefficient of determination
MSe ........ mean square error
kMed-Med Graph
When it is suspected that there are a number of extreme values, a Med-Med graph can be used in place of the least squares method. This is similar to linear regression, but it minimizes the effects of extreme values.
4(CALC)d(MedMed)
6(DRAW)
The following is the Med-Med graph model formula.
y = ax + b
a ............. Med-Med graph slope
b ............. Med-Med graph y-intercept
6-3-6 Calculating and Graphing Paired-Variable Statistical Data
# Input a positive integer for frequency data. Other types of values (decimals, etc.) cause an error.
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kQuadratic/Cubic/Quartic Regression Graph
A quadratic/cubic/quartic regression graph represents connection of the data points of a scatter diagram. It uses the method of least squares to draw a curve that passes close to as many data points as possible. The formula that represents this is quadratic/cubic/quartic regression.
Ex. Quadratic regression
4(CALC)e(Quad)
6(DRAW)
Quadratic regression
Model formula ..... y = ax2 + bx + c
a ............. regression second coefficient
b ............. regression first coefficient
c ............. regression constant term (y-intercept)
r2 ............ coefficient of determination
MSe ........ mean square error
Cubic regression
Model formula ..... y = ax3 + bx2 + cx + d
a ............. regression third coefficient
b ............. regression second coefficient
c ............. regression first coefficient
d ............. regression constant term (y-intercept)
r2 ............ coefficient of determination
MSe ........ mean square error
Quartic regression
Model formula ..... y = ax4 + bx3 + cx2 + dx + e
a ............. regression fourth coefficient
b ............. regression third coefficient
c ............. regression second coefficient
d ............. regression first coefficient
e ............. regression constant term (y-intercept)
r2 ............ coefficient of determination
MSe ........ mean square error
6-3-7 Calculating and Graphing Paired-Variable Statistical Data
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k Logarithmic Regression Graph
Logarithmic regression expresses y as a logarithmic function of x. The standard logarithmic regression formula is y = a + b In x, so if we say that X = In x, the formula corresponds to linear regression formula y = a + bX.
4(CALC)h(Log)
6(DRAW)
The following is the logarithmic regression model formula.
y = a + b ln x
a ............. regression constant term
b ............. regression coefficient
r .............. correlation coefficient
r2 ............ coefficient of determination
MSe ........ mean square error
k Exponential Regression Graph
Exponential regression expresses y as a proportion of the exponential function of x. The standard exponential regression formula is y = a ebx, so if we take the logarithms of both sides we get In y = In a + bx. Next, if we say Y = In y, and A = In a, the formula corresponds to linear regression formula Y = A + bx.
4(CALC)i(Exp)
6(DRAW)
The following is the exponential regression model formula.
y = a ebx
a ............. regression coefficient
b ............. regression constant term
r .............. correlation coefficient
r2 ............ coefficient of determination
MSe ........ mean square error
6-3-8 Calculating and Graphing Paired-Variable Statistical Data
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kPower Regression Graph
Power regression expresses y as a proportion of the power of x. The standard power regression formula is y = a xb, so if we take the logarithm of both sides we get In y = In a + b In x. Next, if we say X = In x, Y = In y, and A = In a, the formula corresponds to linear regression formula Y = A + bX.
4(CALC)j(Power)
6(DRAW)
The following is the power regression model formula.
y = a xb
a ............. regression coefficient
b ............. regression power
r .............. correlation coefficient
r2 ............. coefficient of determination
MSe ........ mean square error
kSinusoidal Regression Graph
Sinusoidal regression is best applied for cyclical data.
The following is the sinusoidal regression model formula.
y = asin(bx + c) + d
While the statistical data list is on the display, perform the following key operation.
4(CALC)v(Sin)
6(DRAW)
Drawing a sinusoidal regression graph causes the angle unit setting of the calculator to automatically change to Rad (radians). The angle unit does not change when you perform a sinusoidal regression calculation without drawing a graph.
Certain types of data may take a long time to calculate. This does not indicate malfunction.
6-3-9 Calculating and Graphing Paired-Variable Statistical Data
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k Logistic Regression Graph
Logistic regression is best applied for time-based phenomena in which there is a continual increase until a saturation point is reached.
The following is the logistic regression model formula.
y = c 1 + aebx
4(CALC)l(Lgstic)
6(DRAW)
Certain types of data may take a long time to calculate. This does not indicate malfunction.
kResidual Calculation
Actual plot points (y-coordinates) and regression model distance can be calculated during regression calculations.
While the statistical data list is on the display, recall the SET UP screen to specify a LIST (List 1 through List 20) for Resid List. Calculated residual data is stored in the specified list.
The vertical distance from the plots to the regression model will be stored in the list.
Plots that are higher than the regression model are positive, while those that are lower are negative.
Residual calculation can be performed and saved for all regression models.
6-3-10 Calculating and Graphing Paired-Variable Statistical Data
# Any data already existing in the selected list is cleared. The residual of each plot is stored in the same precedence as the data used as the model.
19990401
kDisplaying the Calculation Results of a Drawn Paired-Variable Graph
Paired-variable statistics can be expressed as both graphs and parameter values. When these graphs are displayed, the paired-variable calculation results appear as shown below when you press 4(CALC)b(2VAR).
Use c to scroll the list so you can view the items that run off the bottom of the screen.
o ............... mean of data stored in xList x ............. sum of data stored in xList x2 ........... sum of squares of data
stored in xList xn ............ population standard
deviation of data stored in xList
xn-1 .......... sample standard deviation of data stored in xList
n ............... number of data p ............... mean of data stored in yList y ............. sum of data stored in yList
kCopying a Regression Graph Formula to the GRPH TBL Mode
You can copy regression formula calculation results to the GRPH TBL Mode graph formula area, and store and compare.
1. Press 5(COPY) to copy the regression formula that produced the displayed data to the GRPH TBLMode graph formula area*1.
2. Press w to save the copied graph formula and return to the previous regression calculation result display.
6-3-11 Calculating and Graphing Paired-Variable Statistical Data
y2 ...... sum of squares of data stored in yList yn ...... population standard deviation of data
stored in yList yn-1 .... sample standard deviation of data
stored in yList xy ..... sum of the product of data stored in
xList and yList minX ... minimum of data stored in xList maxX .. maximum of data stored in xList minY ... minimum of data stored in yList maxY .. maximum of data stored in yList
*1You cannot edit regression formulas for graph formulas in the GRPH TBLMode.
19990401
kMultiple Graphs
You can draw more than one graph on the same display by using the procedure under Changing Graph Parameters to set the graph draw (On)/non-draw (Off) status of two or all three of the graphs to draw On, and then pressing 6(DRAW)(see page 6-1-4). After drawing the graphs, you can select which graph formula to use when performing single- variable statistic or regression calculations.
4(CALC)
c(Linear)
The text at the top of the screen indicates the currently selected graph (StatGraph1 = Graph 1, StatGraph2 = Graph 2, StatGraph3 = Graph 3).
1. Press c. The graph name at the top of the screen changes when you do.
2. When the graph you want to use is selected, press w.
Now you can use the procedure under Displaying the Calculation Results of a Drawn Paired-Variable Graph on page 6-3-11 to perform statistical calculations.
6-3-12 Calculating and Graphing Paired-Variable Statistical Data
19990401
k Overlaying a Function Graph on a Statistical Graph
Description You can overlay a paired-variable statistical graph with any type of function graph you want.
Set Up 1. From the Main Menu, enter the STAT Mode.
Execution 2. Input the data into a list, and draw the statistical graph.
3. Display the Graph Function menu, and input the function you want to overlay on the statistical graph.
4. Graph the function.
6-3-13 Calculating and Graphing Paired-Variable Statistical Data
19990401
Example Input the two sets of data shown below. Next, plot the data on a scatter diagram and overlay a function graph y = 2ln x.
0.5, 1.2, 2.4, 4.0, 5.2,
2.1, 0.3, 1.5, 2.0, 2.4
Procedure 1m STAT
2 a.fwb.cw
c.ewewf.cw
e
-c.bwa.dw
b.fwcwc.ew
1(GRPH)b(S-Gph1)
35(DefG)
cIvw(Register Y1 = 2In x)
46(DRAW)
Result Screen
6-3-14 Calculating and Graphing Paired-Variable Statistical Data
# You can also perform trace, etc. for drawn function graphs.
# Graphs of types other than rectangular coordinate graphs cannot be drawn.
# Pressing i while inputting a function returns the expression to what it was prior to input.
Pressing !i(QUIT) clears the input expression and returns to the statistical data list.
19990401
6-4 Performing Statistical Calculations All of the statistical calculations up to this point were performed after displaying a graph. The following procedures can be used to perform statistical calculations alone.
uTo specify statistical calculation data lists You have to input the statistical data for the calculation you want to perform and specify where it is located before you start a calculation. Display the statistical data and then press 2(CALC)e(Set).
The following is the meaning for each item.
1Var XList ............ location of single-variable statistic x values (XList)
1Var Freq ............ location of single-variable frequency values (Frequency)
2Var XList ............ location of paired-variable statistic x values (XList)
2Var YList ............ location of paired-variable statistic y values (YList)
2Var Freq ............ location of paired-variable frequency values (Frequency)
Calculations in this section are performed based on the above specifications.
6-4-1 Performing Statistical Calculations
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kSingle-Variable Statistical Calculations
In the previous examples from Normal Probability Plot and Histogram (Bar Graph) to Line Graph, statistical calculation results were displayed after the graph was drawn. These were numeric expressions of the characteristics of variables used in the graphic display.
These values can also be directly obtained by displaying the statistical data list and pressing 2(CALC)b(1VAR).
After this, pressing f or c scrolls the statistical calculation result display so you can view variable characteristics.
For details on the meanings of these statistical values, see Displaying the Calculation Results of a Drawn Single-Variable Graph (page 6-2-4).
kPaired-Variable Statistical Calculations
In the previous examples from Linear Regression Graph to Logistic Regression Graph, statistical calculation results were displayed after the graph was drawn. These were numeric expressions of the characteristics of variables used in the graphic display.
These values can also be directly obtained by displaying the statistical data list and pressing 2(CALC)c(2VAR).
After this, pressing f or c scrolls the statistical calculation result display so you can view variable characteristics.
For details on the meanings of these statistical values, see Displaying the Calculation Results of a Drawn Paired-Variable Graph (page 6-3-11).
6-4-2 Performing Statistical Calculations
19990401
kRegression Calculation
In the explanations from Linear Regression Graph to Logistic Regression Graph, regression calculation results were displayed after the graph was drawn. Here, each coefficient value of the regression line and regression curve is expressed as a number.
You can directly determine the same expression from the data input screen.
Pressing 2(CALC)d(REG) displays the pull-up menu, which contains the following items.
{Linear}/{MedMed}/{Quad}/{Cubic}/{Quart}/{Log}/{Exp}/{Power}/{Sin}/{Lgstic} ... {linear regression}/{Med-Med}/{quadratic regression}/{cubic regression}/ {quartic regression}/{logarithmic regression}/{exponential regression}/ {power regression}/{sinusoidal regression}/{logistic regression} parameters
Example To display single-variable regression parameters
2(CALC)d(REG)b(Linear)
The meanings of the parameters that appear on this screen are the same as those for Linear Regression Graph to Logistic Regression Graph.
6-4-3 Performing Statistical Calculations
19990401
k Estimated Value Calculation ( , )
After drawing a regression graph with the STAT Mode, you can use the RUN MAT Mode to calculate estimated values for the regression graph's x and y parameters.
Example To perform a linear regression using the nearby data and estimate the values of and when xi = 20 and yi = 1000
1. From the Main Menu, enter the STAT Mode.
2. Input data into the list and draw the linear regression graph.
3. From the Main Menu, enter the RUN MAT Mode.
4. Press the keys as follows.
ca(value of xi)
K6(g)4(STAT)c( )w
The estimated value is displayed for xi = 20.
baaa(value of yi)
4(STAT)b( )w
The estimated value is displayed for yi = 1000.
6-4-4 Performing Statistical Calculations
xi yi 10 1003
15 1005 20 1010
25 1011
30 1014
# You cannot obtain estimated values for a Med- Med, quadratic regression, cubic regression,
quartic regression, sinusoidal regression, or logistic regression graph.
19990401
kNormal Probability Distribution Calculation
You can calculate normal probability distributions for single-variable statistics with the RUN MAT Mode.
Press K6(g)1(PROB) to display a function menu, which contains the following items.
{P(}/{Q(}/{R(} ... obtains normal probability {P(t)}/{Q(t)}/{R(t)} value
{t(} ... {obtains normalized variate t(x) value}
Normal probability P(t), Q(t), and R(t), and normalized variate t(x) are calculated using the following formulas.
P (t) Q (t) R (t)
Example The following table shows the results of measurements of the height of 20 college students. Determine what percentage of the students fall in the range 160.5 cm to 175.5 cm. Also, in what percentile does the 175.5 cm tall student fall?
Class no. Height (cm) Frequency
1 158.5 1
2 160.5 1
3 163.3 2
4 167.5 2
5 170.2 3
6 173.3 4
7 175.5 2
8 178.6 2
9 180.4 2
10 186.7 1
6-4-5 Performing Statistical Calculations
19990401
1. Input the height data into List 1 and the frequency data into List 2.
2. Perform the single-variable statistical calculations.*1
2(CALC)e(Set)
1(LIST)bw
c2(LIST)cwi
2(CALC)b(1VAR)
3. Press m, select the RUN MAT Mode, press K6(g)1(PROB) to recall the probability calculation (PROB) menu.
1(PROB)i(t() bga.f)w
(Normalized variate t for 160.5cm) Result: 1.633855948
( 1.634)
1(PROB)i(t() bhf.f)w
(Normalized variate t for 175.5cm) Result: 0.4963343361
( 0.496)
1(PROB)f(P()a.ejg)-
1(PROB)f(P()-b.gde)w
(Percentage of total) Result: 0.638921
(63.9% of total)
1(PROB)h(R()a.ejg)w
(Percentile) Result: 0.30995
(31.0 percentile)
6-4-6 Performing Statistical Calculations
*1 You can obtain the normalized variate immediately after performing single-variable statistical calculations only.
19990401
k Drawing a Normal Probability Distribution Graph
Description You can draw a normal probability distribution graph using manual graphing with the RUN MAT Mode.
Set Up 1. From the Main Menu, enter the RUN MAT Mode.
Execution 2. Input the commands to draw a rectangular coordinate graph.
3. Input the probability value.
6-4-7 Performing Statistical Calculations
19990401
Example To draw a normal probability P (0.5) graph.
Procedure 1m RUN MAT
2K6(g)6(g)2(SKTCH)b(Cls)w
2(SKTCH)e(GRPH)b(Y=)
3K6(g)1(PROB)f(P()a.fw
Result Screen
6-4-8 Performing Statistical Calculations
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Computer Algebra System and Tutorial Modes (ALGEBRA FX 2.0 PLUS only)
7-1 Using the CAS (Computer Algebra System) Mode
7-2 Algebra Mode 7-3 Tutorial Mode
7-4 Algebra System Precautions
Chapter
7
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7-1-1 Using the CAS (Computer Algebra System) Mode
7-1 Using the CAS (Computer Algebra System) Mode
On the Main Menu, select the CAS icon to enter the CAS Mode.
The following table shows the keys that can be used in the CAS Mode.
k Inputting and Displaying Data
Input in the Algebra Mode is performed in the upper part of the display, which is called the input area. You can input commands and expressions at the current cursor location.
Calculation results appear in the lower part of the display, which is called the output area. When a calculation produces an equation or inequality, the lower part of the display is divided between a natural result display area for the result, and a formula number area for the formula number as shown below.
REPLAY
COPY PASTE H-COPY
i
20010102
If all the result does not fit on the display, use the cursor keys to scroll it.
k Inputting List Data
List: {element, element, ..., element}
Elements should be separated by commas, and the entire set of elements should be enclosed within {curly braces}.
You can input numeric values and expressions, equations, and inequalities as list elements.
Example To input List {1, 2, 3}
!*( { )b,c,d
!/( } )w
k Inputting Matrix Data
Matrix (m n): [[(1,1) entry, (1,2) entry, ..., (1,m) entry] [(2,1) entry, ......, (2,n) entry]... [(m, n) entry, ..., (m, n) entry]]
The above input is arranged to show the relative positions of entries in the matrix. Actual input is an unbroken line, from left to right.
Entries should be separated by commas, and the entire set of elements should be enclosed within [square brackets]. And each line also should be enclosed within [square brackets].
You can input numeric values and expressions as matrix entries.
Example To input the matrix shown below 1 2 3 4 5 6 7 8 9
!+( [ )!+( [ )b,c,d
!-( ] )!+( [ )e,f,g
!-( ] )!+( [ )h,i,j
!-( ] )!-( ] )w
7-1-2 Using the CAS (Computer Algebra System) Mode
1 1
20010102
7-1-3 Using the CAS (Computer Algebra System) Mode
k Inputting Vector Data
Vector: [component, component, ..., component]
Components should be separated by commas, and the entire set of components should be enclosed within [square brackets].
You can input numeric values and expressions as vector component entries.
Example To input Vector (1 2 3)
!+( [ )b,c,d
!-( ] )w
k Performing an Algebra Mode Operation
There are two methods that you can use for input in the Algebra Mode.
Function menu command input
Manual formula and parameter input
k Menu Command Input
Press a function menu key to display the menu of functions for the type of operation you are trying to perform.
TRNS ... {formula transformation menu}
CALC ... {formula calculation menu}
EQUA ... {equation, inequality menu}
eqn ... {calls up an equation stored in Equation Memory in accordance with a specified input value}
CLR ... {variable/formula delete menu}
Pressing the K key displays the menu shown below.
LIST ... {list calculation menu}
MAT ... {matrix calculation menu}
VECT ... {vector calculation menu}
For details on commands and their formats, see the Algebra Command Reference on page 7-1-11.
1 1
20010102
k Manual Formula and Parameter Input
You can use the function menus, K key, and J key in combination to input formulas and parameters as described below.
3(EQUA)b(INEQUA)
{>}/{<}/{t}/{s} ... {inequality}
Kkey
{}/{Abs}/{x!}/{sign} ... {infinity}/{absolute value}/{factorial}/{signum function*1}
{HYP} ... {hyperbolic}/{inverse hyperbolic} functions
{sinh}/{cosh}/{tanh}/{sinh1}/{cosh1}/{tanh1}
Jkey
{Yn}/{rn}/{Xtn}/{Ytn}/{Xn}... input of graph memory {Yn}/{rn}/{Xtn}/{Ytn}/{Xn}
k Formula Memory
The CAS Mode has 28 formula variables. Variable names are the letters A through Z, plus r, and . CAS Mode formula variables are independent of standard value variables.
Example To assign a formula that differentiates sin(X) at X (cos(X)) to variable A
2(CALC)b(diff)sv,
v)aav(A)w
7-1-4 Using the CAS (Computer Algebra System) Mode
1 (real number, A > 0) 1 (real number, A < 0)
*1signum (A) A (A= imaginary number)
|A|
Undefined (A = 0)
1 1
20010102
Example To assign M to row 1 column 2 of variable A when the matrix is assigned to it
ah(M)aav(A)
!+( [ )b,c!-( ] )w
Example To recall the value of variable A when the list {X, Y, Z} is assigned to it
av(A)w
Example To recall the first component (A [1]) of variable A when vector (X Y Z) is assigned to it
av(A)!+( [ )b
!-( ] )w
7-1-5 Using the CAS (Computer Algebra System) Mode
1 2 3 X Y Z
20010102
k Function Memory and Graph Memory
Function memory lets you store functions for later recall when you need them.
With graph memory, you can store graphs in memory. Press the J key and then input the name of the graph.
Example To differentiate f1 = cos(X), which is assigned to function memory f1, at X
2(CALC)b(diff)K6(g)4(FMEM)
d(fn)b,v)w
Example To differentiate Y1 = cos(X), which is assigned to graph memory Y1, at X
2(CALC)b(diff)
J1(Yn) b,v)w
k Eqn Memory
When a calculation result is an equation or inequality, its formula number is displayed in the formula number area, and the equation is stored in Eqn memory.*1 Stored equations can be recalled with the eqn command, rclEqn command or rclAllEqn command.
7-1-6 Using the CAS (Computer Algebra System) Mode
*1Up to 99 formulas can be stored in Eqn memory. The error message Memory ERROR when you try to store an equation when there are already 99 equations in Eqn memory. When this happens, execute the ALLEQU (Delete All Equations) from the CLR menu.
1 1
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k Answer (Ans) Memory and Continuous Calculation
Answer (Ans) memory and continuous calculation can be used just as with standard calculations. In the Algebra Mode, you can even store formulas in Ans memory.
Example To expand (X+1)2 and add the result to 2X
1(TRNS)b(expand)
(v+b)x)w
Continuing:
+cvw
k Replay Contents
Replay memory can be used in the input area. After a calculation is complete, pressing d or e in the input area recalls the formula of the last calculation performed. After a calculation or after pressing A, you can press f or c to recall previous formulas.
k Moving the Cursor Between Display Areas
When ] ' ` $ indicates a calculation result that does not fit on the display, the cursor keys perform output area scrolling. To use the Replay Function from this condition, press 6(g)2(SW). ] ' ` $ change to a dotted line display to indicate that cursor key operations control the input area.
Pressing 2(SW) again moves the cursor back to the output area.
7-1-7 Using the CAS (Computer Algebra System) Mode
# Pressing 6(g)1(CLR)d(ALLEQU) deletes Eqn memory, Ans memory, and Replay memory contents.
# You can input up to 255 bytes of data into the input area.
20010102
SET UP Items uAngle ... Unit of angular measurement specification
{Deg}/{Rad} ... {degrees}/{radians}
uAnswer Type ... Result range specification
{Real}/{Cplx}... {real number}/{complex number}
uDisplay ... Display format specification (for approx only)
{Fix}/{Sci}/{Norm}... {number of decimal places}/{number of significant digits}/ {normal display format}
k Graph Function
Pressing 5(GRPH) displays the graph formula screen, which you can use to input a graph formula. Press 4(G VAR) if you want to input a graph memory. You can also use the 1(SEL), 2(DEL), and 3(TYPE) functions while the graph formula screen is on the display.
Press 6(DRAW) to draw a graph.
k RECALL ANS Function
Pressing 6(g)3(R ANS) recalls Ans Memory contents.
k Solution Memory
In the CAS Mode or ALGEBRA Mode, you can save the history of a calculation you perform (replay memory contents) into solution memory. This section describes how you can access and work with the contents of solution memory. Pressing 6(g)4(MEM) on the CAS Mode or ALGEBRA Mode main menu display the initial solution memory screen shown below.
7-1-8 Using the CAS (Computer Algebra System) Mode
{SAVE} ... {saves the calculation history to solution memory}
{DEL A}... {deletes solution memory contents}
{OPT} ... {optimizes solution memory}
{DISP} ... {displays solution memory contents}
20010102
7-1-9 Using the CAS (Computer Algebra System) Mode
u To save a calculation history to solution memory (Save) On the initial solution memory screen, press 1(SAVE).
Press 1(YES) to save the calculation history to solution memory.
Pressing i returns to the solution memory initial screen.
Pressing 6(NO) in place of 1(YES) returns to the solution memory initial screen without saving anything.
u To clear solution memory contents (Clear Memory) On the initial solution memory screen, press 2(DEL A).
Press 1(YES) to clear solution memory contents.
Pressing i returns to the solution memory initial screen.
Pressing 6(NO) in place of 1(YES) returns to the solution memory initial screen without clearing anything.
This clears both CAS Mode and ALGEBRA Mode memory contents. You cannot select the mode shows memory contents you want to delete.
20010102
6(DISP) is disabled when there is no data in Solution memory.
To display the next record
Press 6(NEXT).
To display the previous record
Press 1(BACK).
Pressing 1(BACK) while the oldest record is on the display returns to the solution memory initial screen.
To display a particular record
Press 5(SEL) and then input the number of the record you want to display.
Pressing w displays the record whose number you input.
To delete a single solution memory record
Display the record you want to delete, and then press 2(DEL).
In response to the confirmation message that appears, press w(Yes) to delete the record you displayed.
To clear the above screen without deleting anything, press i(No).
To toggle record number display on and off
Press 4(NUM) to toggle display of the record number on and off.
u To optimize solution memory (Optimization) On the initial solution memory screen, press 3(OPT).
Pressing i returns to the solution memory initial screen.
Optimizing solution memory rearranges data and can free up more storage space. Perform the above procedure when solution memory capacity starts running low.
7-1-10 Using the CAS (Computer Algebra System) Mode
u To display solution memory contents (Display Memory) On the initial solution memory screen, press 6(DISP).
This displays the oldest expression and result in solution memory. The bottom line shows the record number.
20010102
7-1-11 Using the CAS (Computer Algebra System) Mode
Algebra Command Reference
The following are the abbreviations used in this section.
Exp ... Expression (value, formula, variable, etc.)
Eq ... Equation
Ineq ... Inequality
List ... List
Mat ... Matrix
Vect ... Vector
Anything enclosed within square brackets can be omitted.
u expand Function: Expands an expression.
Syntax: expand ( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
Example To expand (X+2)2
1(TRNS)b(expand)(v+c)xw X2 + 4X + 4
u rFactor (rFctor) Function: Factors an expression up to its root.
Syntax: rFactor ( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
Example To factor the X2 3
1(TRNS)c(rFctor)vx-dw (X 3) (X + 3)
u factor Function: Factors an expression.
Syntax: factor ( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
Example To factor X2 4X + 4
1(TRNS)d(factor)vx-ev+ew (X 2)2
20010102
u solve Function: Solves an equation.
Syntax: solve( Eq [,variable] [ ) ]
solve( {Eq-1,..., Eq-n}, {variable-1,...,variable-n} [ ) ]
Example To solve AX + B = 0 for X
1(TRNS)e(solve)av(A)v+
al(B)!.(=)aw
Example To solve simultaneous linear equation 3X + 4Y = 5, 2X 3Y = 8
1(TRNS)e(solve)!*( { )
da+(X)+ea-(Y)!.(=)f,
ca+(X)-da-(Y)!.(=)-i
!/( } ),!*( { )a+(X), X = 1
a-(Y)!/( } )w Y = 2
X is the default when no variable is specified.
u tExpand (tExpnd) Function: Employs the addition theorem to expand a trigonometric function.
Syntax: tExpand( {Exp/List/Mat/Vect} [ ) ]
Example To employ the addition theorem to expand sin(A+B)
1(TRNS)f(TRIG)b(tExpnd)
s(av(A)+al(B)w cos(B) sin(A) + sin(B) cos(A)
u tCollect (tCollc) Function: Employs the addition theorem to transform the product of a trigonometric
function to a sum.
Syntax: tCollect( {Exp/List/Mat/Vect} [ ) ]
Example To employ the addition theorem to transform sin(A)cos(B) to trigonometric sum
1(TRNS)f(TRIG)c(tCollc)
sav(A)cal(B)w
7-1-12 Using the CAS (Computer Algebra System) Mode
sin (A + B) 2
sin (A B) 2+
B A
X =
1 1
20010102
7-1-13 Using the CAS (Computer Algebra System) Mode
u trigToExp (trigToE) Function: Transforms a trigonometric or hyperbolic function to an exponential function.
Syntax: trigToExp( {Exp/List/Mat/Vect} [ ) ]
Example To convert cos(iX) to an exponential function
1(TRNS)f(TRIG)d(trigToE)c!a(i)vw
u expToTrig (expToT) Function: Converts an exponential function to a trigonometric or hyperbolic function.
Syntax: expToTrig( {Exp/List/Mat/Vect} [ ) ]
Example To convert eix to a trigonometric function
1(TRNS)f(TRIG)e(expToT)
!I(ex)(!a(i)vw cos(X) + sin(X) i
u simplify (smplfy) Function: Simplifies an expression.
Syntax: simplify( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
Example To simplify 2X + 3Y X + 3 = Y + X 3Y + 3 X
1(TRNS)g(smplfy)ca+(X)+da-(Y)
-a+(X)+d!.(=)a-(Y)
+a+(X)-da-(Y)+d-
a+(X)w X + 3Y + 3 = 2Y + 3
ex+ ex 2
20010102
u combine (combin) Function: Adds and reduces rational expressions.
Syntax: combine( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
Example To reduce the fraction (X + 1) / (X + 2) + X (X + 3)
1(TRNS)h(combin)(v+b)/
(v+c)+v(v+dw
u collect (collct) Function: Rearranges an expression, focusing on a particular variable.
Syntax: collect( {Exp/Eq/Ineq/List/Mat/Vect} [,{Exp/variable}] [ ) ]
Example To rearrange X2 + AX + BX, focusing on the variable X
1(TRNS)i(collct)vx+av(A)v+
al(B)vw X2 + (A + B)X
X is the default when nothing is specified for [,{Exp/variable}].
u substitute (sbstit) Function: Assigns an expression to a variable.
Syntax: substitute( {Exp/Eq/Ineq/List/Mat/Vect}, variable=expression [,..., variable=expression] [ ) ]
Example To assign 5 to X in 2X 1
1(TRNS)j(sbstit)cv-b,
v!.(=)fw 9
7-1-14 Using the CAS (Computer Algebra System) Mode
X3 + 5X2 + 7X + 1 X + 2
1 1
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u cExpand (cExpnd) Function: Expands xth root of imaginary number.
Syntax: cExpand( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
Example To expand 2 i
1(TRNS)v(cExpnd)!x( )c!a(i)w 1 + i
u approx Function: Produces a numerical approximation for an expression.
Syntax: approx( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
Example To obtain a numerical value for 2
1(TRNS)l(approx)!x( )cw 1.414213562
Example 920
Normal:jMcaw 12157665459056928801
approx:1(TRNS)l(approx)jMcaw 1. 215766546E+19 (Display: Norm1)
7-1-15 Using the CAS (Computer Algebra System) Mode
# About approx With normal calculations (when approx is not used) in the CAS Mode, calculation results are displayed in full, without using exponents. When you use approx in the CAS Mode, however, results are displayed using the
exponential format range specified by the Display item of the SET UP screen.
This means approx displays results in the CAS Mode the same way they are displayed in the RUN MAT Mode.
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u diff Function: Differentiates an expression.
Syntax: diff( {Exp/List} [, variable, order, derivative] [ ) ]
diff( {Exp/List}, variable [, order, derivative] [ ) ]
diff( {Exp/List}, variable, order [, derivative] [ ) ]
Example To differentiate X6 with respect to X
2(CALC)b(diff)vMgw 6X5
X is the default when no variable is specified.
1 is the default when no order is specified.
u Function: Integrates an expression.
Syntax: ( {Exp/List} [, variable, integration constant] [ ) ]
( {Exp/List}, variable [, integration constant] [ ) ]
( {Exp/List}, variable, lower limit, upper limit [ ) ]
Example To integrate X2 with respect to X
2(CALC)c( )vxw
X is the default when no variable is specified.
u lim Function: Determines the limits of a function expression.
Syntax: lim( {Exp/List}, variable, point [, direction] [ ) ]
Example To determine the limits of sin(X)/X when X = 0
2(CALC)d(lim)sv/v,v,aw 1
Direction can be positive (from right) or negative (from left).
7-1-16 Using the CAS (Computer Algebra System) Mode
X3
3
20010102
u Function: Calculates a sum.
Syntax: ( {Exp/List}, variable, start value, end value [ ) ]
Example To calculate the sum as the value of X in X2 changes from X = 1 through X = 10
2(CALC)e()vx,v,b,baw 385
u Function: Calculates a product.
Syntax: ( {Exp/List}, variable, start value, end value [ ) ]
Example To calculate the product as the value of X in X2 changes from X = 1 through X = 5
2(CALC)f()vx,v,b,fw 14400
u taylor Function: Finds a Taylor polynomial.
Syntax: taylor( {Exp/List}, variable, order [, center point] [ ) ]
Example To find a 5th order Taylor polynomial for sin(X) with respect to X = 0
2(CALC)g(taylor)sv,v,f,aw
The default center point is zero.
u arcLen Function: Returns the arc length.
Syntax: arcLen( {Exp/List}, variable, start value, end value [ ) ]
Example To determine the arc length for X2 from X = 0 to X = 1
2(CALC)h(arcLen)
vx,v,a,bw
7-1-17 Using the CAS (Computer Algebra System) Mode
X5
X3 +
X
120 6
In (4 5 + 8)
In(2) +
5 4 2 2
20010102
u tanLine (tanLin) Function: Returns the expression for a tangent line.
Syntax: tanLine( {Exp/List}, variable, variable value at point of tangency [ ) ]
Example To determine the expression for a line tangent with X3 when X = 2
2(CALC)i(tanLin)vMd,v,cw 12X 16
u denominator (den) Function: Extracts the denominator of a fraction.
Syntax: denominator( {Exp/List} [ ) ]
Example To extract the denominator of the fraction (X + 2)/(Y 1)
2(CALC)j(EXTRCT)b(den)
(a+(X)+c)/(a-(Y)-bw Y 1
u numerator (num) Function: Extracts the numerator of a fraction.
Syntax: numerator( {Exp/List} [ ) ]
Example To extract the numerator of the fraction (X + 2)/(Y 1)
2(CALC)j(EXTRCT)c(num)
(a+(X)+c)/(a-(Y)-bw X + 2
u gcd Function: Returns the greatest common divisor.
Syntax: gcd( {Exp/List}, {Exp/List} [ ) ]
Example To determine the greatest common divisor of X + 1 and X2 3X 4
2(CALC)v(gcd)v+b,vx-
dv-ew X + 1
7-1-18 Using the CAS (Computer Algebra System) Mode
1 1
20010102
u lcm Function: Obtains the least common multiple of two expressions
Syntax: lcm( {Exp/List}, {Exp/List} [ ) ]
Example To obtain the least common multiple of X2 1 and X2 + 2X 3
2(CALC)l(lcm)vx-b,
vx+cv-dw X3 + 3X2 X 3
u rclEqn Function: Recalls multiple eqn memory contents.
Syntax: rclEqn( memory number [, ..., memory number] [ ) ]
Example To recall the contents of equation memory 2 and equation memory 3
3(EQUA)c(rclEqn)c,dw 3X Y = 7
3X + 6Y = 63
The memory numbers of equations produced as the result of a recall are not updated.
u rclAllEqn (rclAll) Function: Recall all eqn memory contents.
Syntax: rclAllEqn
The memory numbers of equations produced as the result of a recall are not updated.
u rewrite (rewrit) Function: Moves the right side expression to the left side.
Syntax: rewrite( {Eq/Ineq/List} [ ) ]
Example To move the right side expression of X + 3 = 5X X2 to the left side
3(EQUA)e(rewrit)v+d!.(=)
fv-vxw X2 4X + 3 = 0
7-1-19 Using the CAS (Computer Algebra System) Mode
1 1
20010102
u exchange (exchng) Function: Exchanges the right-side and left-side expressions.
Syntax: exchange( {Eq/Ineq/List} [ ) ]
Example To exchange the left-side and right-side expressions of 3 > 5X 2Y
3(EQUA)f(exchng)d3(EQUA)b(INEQUA)b(>)
fa+(X)-ca-(Y)w 5X 2Y < 3
u eliminate (elim) Function: Assigns an expression to a variable.
Syntax: eliminate( {Eq/Ineq/List} -1, variable, Eq-2 [ ) ]
Example To transform Y = 2X + 3 to X= and then substitute into 2X + 3Y = 5
3(EQUA)g(elim)ca+(X)+da-(Y)!.(=)
f,a+(X),a-(Y)!.(=)
ca+(X)+dw 4Y 3 = 5
u getRight (getRgt) Function: Gets the right-side element.
Syntax: getRight( {Eq/Ineq/List} [ ) ]
Example To extract the right side element of Y = 2X2 + 3X + 5
3(EQUA)h(getRgt)a-(Y)!.(=)
ca+(X)x+da+(X)+fw 2X2 + 3X + 5
u invert Function: Inverts two variables.
Syntax: invert( {Exp/Eq/Ineq/List} [,variable name 1, variable name 2] [ ) ]
If you omit the variable names, variables X and Y are inverted.
Example To invert X and Y in the expression 2X = Y
3(EQUA)i(invert)cv!.(=)a-(Y)w 2Y = X
7-1-20 Using the CAS (Computer Algebra System) Mode
1 1
20010102
u absExpand (absExp) Function: Divides an expression that contains an absolute value into two expressions.
Syntax: absExpand( {Eq/Ineq} [ ) ]
Example To strip the absolute value from | 2X 3 | = 9
3(EQUA)j(absExp)K5(Abs)(
cv-d)!.(=)jw
u andConnect (andCon) Function: Connects two inequalities into a single expression.
Syntax: andConnect( Ineq-1, Ineq-2 [ ) ]
Example To combine X > 1 and X < 3 into a single inequality
3(EQUA)v(andCon)v3(EQUA)b(INEQUA)b(>)
-b,v3(EQUA)b(INEQUA)c(<)dw 1 < X < 3
u eqn Function: Recalls eqn memory contents.
Syntax: eqn( memory number [ ) ]
Example To add 15 to both sides of the equation 6X 15 = X 7, which is stored in equation memory 3
4(eqn)d)+bfw 6X = X + 8
2X 3 = 9
or 2X 3 = 9 2
1
7-1-21 Using the CAS (Computer Algebra System) Mode
20010102
u clear (clrVar) Function: Clears the contents of specific equation (A to Z, r, ).*1
Syntax: clear( variable [ ) ]
clear( {variable list} [ ) ]
Example To clear the contents of variable A
6(g)1(CLR)b(clrVar)av(A)w { }
Example To clear the contents of variables X, Y, and Z
6(g)1(CLR)b(clrVar)!*( { )a+(X),
a-(Y),aa(Z)!/( } )w { }
u clearVarAll (VarAll) Function:Clears the contents of all 28 variables (A to Z, r, ).
Syntax: clearVarAll { }
7-1-22 Using the CAS (Computer Algebra System) Mode
*1When you start out with memories A, B, C, and D, for example, and delete memories A and B, the display shows only C,D because they are the only memories remaining.
20010102
k List Calculation Commands [OPTN]-[LIST]
uDim Function: Returns the dimension of a list.
Syntax: Dim List
Example To determine the dimension of list {1, 2, 3}
K1(LIST)b(CALC)b(Dim)!*( { )b,c,d
!/( } )w 3
uMin Function: Returns the minimum value of an expression or the elements in a list.
Syntax: Min( {List/Exp} [ ) ]
Min( {List/Exp}, {List/Exp} [ ) ]
Example To determine the minimum value of the elements in list {1, 2, 3}
K1(LIST)b(CALC)c(Min)!*( { )b,c,d
!/( } )w 1
Example To compare each element of list {1, 2, 3} with the value 2, and produce a list whose elements are the minimum value resulting from each comparison
K1(LIST)b(CALC)c(Min)!*( { )b,c,d
!/( } ),cw { 1, 2, 2 }
Example To compare the elements of list {1, 2, 3} and list {3, 1, 2}, and produce a list whose elements are the minimum value resulting from each comparison
K1(LIST)b(CALC)c(Min)!*( { )b,c,d
!/( } ),!*( { )d,b,c!/( } )w {1, 1, 2 }
7-1-23 Using the CAS (Computer Algebra System) Mode
20010102
7-1-24 Using the CAS (Computer Algebra System) Mode
uMax Function: Returns the maximum value of an expression or the elements of a list.
Syntax: Max( {List/Exp} [ ) ]
Max( {List/Exp}, {List/Exp} [ ) ]
Example To determine the maximum value of the elements in list {1, 2, 3}
K1(LIST)b(CALC)d(Max)!*( { )b,c,d
!/( } )w 3
Example To compare each element of list {1, 2, 3} with the value 2, and produce a list whose elements are the maximum value resulting from each comparison
K1(LIST)b(CALC)d(Max)!*( { )b,c,d
!/( } ),cw { 2, 2, 3 }
Example To compare the elements of list {1, 2, 3} and list {3, 1, 2}, and produce a list whose elements are the maximum value resulting from each comparison
K1(LIST)b(CALC)d(Max)!*( { )b,c,d
!/( } ),!*( { )d,b,c!/( } )w { 3, 2, 3 }
u Mean Function: Returns the mean of the elements in a list.
Syntax: Mean( List [ ) ]
Mean( List, List [ ) ]
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To determine the mean of the elements in list {1, 2, 3}
K1(LIST)b(CALC)e(Mean)!*( { )b,c,d
!/( } )w 2
20010102
Example To determine the mean of the elements in list {1, 2, 3} when their frequencies are {3, 2, 1}
K1(LIST)b(CALC)e(Mean)!*( { )b,c,d
!/( } ),!*( { )d,c,b!/( } )w
uMedian Function: Returns the median of the elements in a list.
Syntax: Median( List [ ) ]
Median( List, List [ ) ]
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To determine the median of the elements in list {1, 2, 3}
K1(LIST)b(CALC)f(Median)!*( { )b,c,d
!/( } )w 2
Example To determine the median of the elements in list {1, 2, 3} when their frequencies are {3, 2, 1}
K1(LIST)b(CALC)f(Median)!*( { )b,c,d
!/( } ),!*( { )d,c,b!/( } )w
u Sum Function: Returns the sum of the elements in a list.
Syntax: Sum List
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To determine the sum of the elements in list {1, 2, 3}
K1(LIST)b(CALC)g(Sum)!*( { )b,c,d
!/( } )w 6
7-1-25 Using the CAS (Computer Algebra System) Mode
5 3
3 2
20010102
u Prod Function: Returns the product of the elements in a list.
Syntax: Prod List
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To determine the product of the elements in list {2, 3, 4}
K1(LIST)b(CALC)h(Prod)!*( { )c,d,e
!/( } )w 24
uCuml Function: Returns the cumulative frequency of the elements in a list.
Syntax: Cuml List
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To determine the cumulative frequency of the elements in list {1, 2, 3}
K1(LIST)b(CALC)i(Cuml)!*( { )b,c,d
!/( } )w { 1, 3, 6 }
u Percent (%) Function: Returns the percentage of each element in a list, the sum of which is assumed
to be 100.
Syntax: Percent List
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To determine the percentage of each element in the list {1, 2, 3}
K1(LIST)b(CALC)j(%)!*( { )b,c,d
!/( } )w
7-1-26 Using the CAS (Computer Algebra System) Mode
3 50
3 100
50 ,,{ {
20010102
uA List Function: Returns a list whose elements are the differences between the elements of
another list.
Syntax: A List List
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To generate a list whose elements are the differences between the elements of list {1, 2, 4}
K1(LIST)b(CALC)v(AList)!*( { )b,c,e
!/( } )w { 1, 2 }
uStdDev Function: Returns the sample standard deviation of the elements in a list.
Syntax: StdDev List
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To determine the sample standard deviation of the elements in list {1, 2, 4}
K1(LIST)b(CALC)l(StdDev)!*( { )b,c,e
!/( } )w
u Variance (Vari) Function: Returns the variance of the elements in a list.
Syntax: Variance List
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To determine the variance of the elements in list {1, 2, 4}
K1(LIST)b(CALC)I(Vari)!*( { )b,c,e
!/( } )w
7-1-27 Using the CAS (Computer Algebra System) Mode
7 3
3 21
1 1
20010102
uSeq Function: Generates a list in accordance with a numeric sequence expression.
Syntax: Seq( Exp, variable, start value, end value, [increment] [ ) ]
If you do not specify an increment, an increment of 1 is used.
Example To generate a list in accordance with the expression: value A, end value 3A, increment A
K1(LIST)c(CREATE)b(Seq)v,v,av(A),d
av(A),av(A)w { A, 2A, 3A }
u Augment (Augmnt) Function: Returns a new list that appends List 2 to List 1.
Syntax: Augment( List, List [ ) ]
Example To combine list {1, 2} and list {3, 4}
K1(LIST)c(CREATE)c(Augmnt)!*( { )b,c
!/( } ),!*( { )d,e!/( } )w { 1, 2, 3, 4 }
u Fill Function: Replaces the elements of a list with a specified value or expression.
This command can also be used to create a new list whose elements all contain the same value or expression.
Syntax: Fill( {Exp/Eq/Ineq}, List [ ) ]
Fill( Exp, numeric value [ ) ]
Example To replace the elements of list {3, 4} with X
K1(LIST)c(CREATE)d(Fill)v,!*( { )
d,e!/( } )w { X, X }
Example To create a list with eight elements, all of which are X
K1(LIST)c(CREATE)d(Fill)v,iw { X, X, X, X, X, X, X, X }
7-1-28 Using the CAS (Computer Algebra System) Mode
1 1
20010102
uSortA Function: Sorts the elements of a list into ascending order.
Syntax: SortA( List [ ) ]
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To sort the elements of list {1, 5, 3} into ascending order
K1(LIST)c(CREATE)e(SortA)!*( { )b,f,d
!/( } )w { 1, 3, 5 }
u SortD Function: Sorts the elements of a list into descending order.
Syntax: SortD( List [ ) ]
The list must contain values or mathematical expressions only. Equations and inequalities are not allowed.
Example To sort the elements of list {1, 5, 3} into descending order
K1(LIST)c(CREATE)f(SortD)!*( { )b,f,d
!/( } )w { 5, 3, 1 }
u SubList (SubLst) Function: Extracts a specific section of a list into a new list.
Syntax: SubList( List, start number [, end number] [ ) ]
Example To extract element 2 through element 3 from list {1, 2, 3, 4}
K1(LIST)c(CREATE)g(SubLst)!*( { )b,c,d
,e!/( } ),c,dw { 2, 3 }
If you do not specify an end number, all the elements from the start number to the end of the list are extracted.
7-1-29 Using the CAS (Computer Algebra System) Mode
20010102
u ListMat (LMat) Function: Converts lists into a matrix.
Syntax: ListMat( List [ , ... ,List ] [ ) ]
Example To convert list {3, 5} and list {2, 4} into a matrix
K1(LIST)d(LIST)b(LMat)!*( { )d,f 3 2
!/( } ),!*( { )c,e!/( } )w 5 4
u ListVect (LVect) Function: Converts a list into a vector.
Syntax: ListVect List
Example To convert list {3, 2} into a vector
K1(LIST)d(LIST)c(LVect)!*( { )d,c
!/( } )w [ 3, 2 ]
7-1-30 Using the CAS (Computer Algebra System) Mode
20010102
kMatrix Calculation Commands [OPTN]-[MAT]
uDim Function: Returns the dimensions of a matrix.
Syntax: Dim Mat
Example To determine the dimensions of the matrix below
1 2 3 4 5 6
K2(MAT)b(CALC)b(Dim)!+( [ )!+( [ )
b,c,d!-( ] )!+( [ )e,f,g
!-( ] )!-( ] )w { 2, 3 }
u Det Function: Returns the determinant of a matrix.
Syntax: Det Mat
Example To determine the determinant of the matrix below
1 2 4 5
K2(MAT)b(CALC)c(Det)!+( [ )!+( [ )
b,c!-( ] )!+( [ )e,f
!-( ] )!-( ] )w 3
u Norm Function: Returns the norm of a matrix.
Syntax: Norm Mat
Example To determine the norm of the matrix below
1 2 4 5
K2(MAT)b(CALC)d(Norm)!+( [ )!+( [ )
b,c!-( ] )!+( [ )e,f
!-( ] )!-( ] )w 46
7-1-31 Using the CAS (Computer Algebra System) Mode
1 1
20010102
u EigVc Function: Returns the eigenvector of a matrix.
Syntax: EigVc Mat
Example To determine the eigenvector of the matrix below
3 4 1 3
K2(MAT)b(CALC)e(EigVc)
!+( [ )!+( [ )d,e
!-( ] )!+( [ ) [ 0.894427191 0.894427191 ]
b,d!-( ] )!-( ] )w [ 0.4472135955 0.4472135955 ]
Eigenvectors are stacked vertically on the display.
In this example, (0.8944271910.4472135955) are the eigenvectors that correspond to 5, while (0.8944271910.4472135955) are the eigenvectors that correspond to 1.
An eigenvector has an infinite number of solutions. The eigenvector displayed by this command is the one with a size of 1.
u EigVl Function: Returns the eigenvalue of a matrix.
Syntax: EigVl Mat
Example To determine the eigenvalue of the matrix below
3 4 1 3
K2(MAT)b(CALC)f(EigVl)!+( [ )!+( [ )
d,e!-( ] )!+( [ )b,d
!-( ] )!-( ] )w { 5, 1 }
7-1-32 Using the CAS (Computer Algebra System) Mode
1 1
20010102
u Rref Function: Returns the reduced row echelon form of a matrix.
Syntax: Rref Mat
Example To determine the reduced row echelon form of the matrix below
2 2 0 6
1 1 9 9
5 2 4 4
K2(MAT)b(CALC)g(Rref)!+( [ )!+( [ )
-c,-c,a,-g!-( ] )!+( [ )
b,-b,j,-j!-( ] )
!+( [ )-f,c,e,-e
!-( ] )!-( ] )w
u Ref Function: Returns the row echelon form of a matrix.
Syntax: Ref Mat
Example To determine the row echelon form of the matrix below
2 2 0 6
1 1 9 9
5 2 4 4
K2(MAT)b(CALC)h(Ref)!+( [ )!+( [ )
-c,-c,a,-g!-( ] )!+( [ )
b,-b,j,-j!-( ] )
!+( [ )-f,c,e,-e
!-( ] )!-( ] )w
7-1-33 Using the CAS (Computer Algebra System) Mode
71 66
71 147
71 62
1 0 0
0 1 0
0 0 1
71 62
1 1 0
0 1
3
6
0 0 1
2 9
20010102
u LU Function: Returns the LU resolution of a matrix.
Syntax: LU( Mat, lower memory, upper memory)
Example To determine the LU resolution of the matrix below
6 12 18
5 14 31
3 8 18
The lower matrix is assigned to variable A, while the upper matrix is assigned to variable B.
K2(MAT)b(CALC)i(LU)!+( [ )!+( [ )
g,bc,bi!-( ] )!+( [ )
f,be,db!-( ] )!+( [ ) 6 12 18
d,i,bi!-( ] )!-( ] ), 0 4 16
av(A),al(B)w 0 0 1
The upper matrix is displayed as the calculation result.
To display the lower matrix, recall the lower matrix variable (A in this example) specified by the command.
av(A)w
To display the upper matrix, recall the upper matrix variable (B in this example) specified by the command.
u Trn Function: Transposes a matrix.
Syntax: Trn Mat
Example To transpose the matrix below
1 2 3 4
K2(MAT)c(CREATE)b(Trn)!+( [ )!+( [ )
b,c!-( ] )!+( [ )d,e 1 3
!-( ] )!-( ] )w 2 4
7-1-34 Using the CAS (Computer Algebra System) Mode
1 0 0
01
1
6 5
2 1
2 1
20010102
u Augment (Augmnt) Function: Combines two matrices.
Syntax: Augment( Mat, Mat [ ) ]
Example To combine the two matrices below
1 2 5 6 3 4 7 8
K2(MAT)c(CREATE)c(Augmnt)!+( [ )!+( [ )
b,c!-( ] )!+( [ )d,e
!-( ] )!-( ] ),!+( [ )!+( [ )
f,g!-( ] )!+( [ )h,i 1 2 5 6
!-( ] )!-( ] )w 3 4 7 8
u Identify (Ident) Function: Creates an identity matrix
Syntax: Ident numeric value
Example To create a 2 2 identity matrix
K2(MAT)c(CREATE)d(Ident)cw 1 0
0 1
u Fill Function: Replaces the elements of a matrix with a specified value or expression.
This command can also be used to create a new matrix whose elements all contain the same value or expression.
Syntax: Fill( Exp, Mat [ ) ]
Fill( Exp, number of lines, number of rows [ ) ]
Example To replace the elements of the matrix below with X
3 4 1 2
K2(MAT)c(CREATE)e(Fill)v,!+( [ )
!+( [ )d,e!-( ] )!+( [ ) X X
b,c!-( ] )!-( ] )w X X
7-1-35 Using the CAS (Computer Algebra System) Mode
20010102
Example To create a 2 3 matrix, all of whose entries are X
K2(MAT)c(CREATE)e(Fill)v,c,dw X X X
X X X
u SubMat Function: Extracts a specific section of a matrix into a new matrix.
Syntax: SubMat( Mat [, start row] [, start column] [, end row] [, end column] [ ) ]
Example To extract the section from row 2, column 2 to row 3, column 3 from the following matrix
1 2 3
4 5 6
7 8 9
K2(MAT)c(CREATE)f(SubMat)!+( [ )!+( [ )
b,c,d!-( ] )!+( [ )e,f,g
!-( ] )!+( [ )h,i,j!-( ] ) 5 6
!-( ] ),c,c,d,dw 8 9
If you do not specify an end row and column, all the entries from the start row/column to the end of the matrix are extracted.
7-1-36 Using the CAS (Computer Algebra System) Mode
20010102
uDiag Function: Extracts the diagonal elements of a matrix.
Syntax: Diag Mat
Example To extract the diagonal elements of the matrix below
1 2 3 4
K2(MAT)c(CREATE)g(Diag)!+( [ )!+( [ )
b,c!-( ] )!+( [ )d,e
!-( ] )!-( ] )w [ 1, 4 ]
uMatList (MList) Function: Converts a specific column of a matrix into a list.
Syntax: MatList( Mat, column number [ ) ]
Example To convert column 2 of the matrix below to a list
1 2 3 4
K2(MAT)d(MAT)b(MList)!+( [ )!+( [ )
b,c!-( ] )!+( [ )d,e
!-( ] )!-( ] ),cw { 2, 4 }
uMatVect (MVect) Function: Converts a specific column of a matrix into a vector.
Syntax: MatVect( Mat, column number [ ) ]
Example To convert column 2 of the matrix below to a vector
1 2 3 4
K2(MAT)d(MAT)c(MVect)!+( [ )!+( [ )
b,c!-( ] )!+( [ )d,e
!-( ] )!-( ] ),cw [ 2, 4 ]
7-1-37 Using the CAS (Computer Algebra System) Mode
1 1
20010102
uSwap Function: Swaps two rows of a matrix.
Syntax: Swap Mat, row number 1, row number 2
Example To swap row 1 with row 2 of the following matrix
1 2 3 4
K2(MAT)e(ROW)b(Swap)!+( [ )!+( [ )
b,c!-( ] )!+( [ )d,e 3 4
!-( ] )!-( ] ),b,cw 1 2
u`Row Function: Returns the scalar product of a row of a matrix.
Syntax: `Row( Exp, Mat, row number [ ) ]
Example To multiply row 1 of the matrix below by X
1 2 3 4
K2(MAT)e(ROW)c(`Row)v,!+( [ )
!+( [ )b,c!-( ] )!+( [ ) X 2X
d,e!-( ] )!-( ] ),bw 3 4
u`Row+ Function: Calculates the scalar product of one row of a matrix and adds the result to
another row.
Syntax: `Row+( Exp, Mat, line number 1, line number 2 [ ) ]
Example To multiply row 1 of the matrix below by X, and add the result to row 2
1 2 3 4
K2(MAT)e(ROW)d(`Row+)v,!+( [ )
!+( [ )b,c!-( ] )!+( [ ) 1 2
d,e!-( ] )!-( ] ),b,cw X + 3 2X + 4
7-1-38 Using the CAS (Computer Algebra System) Mode
20010102
uRow+ Function: Adds one row of a matrix and to another row.
Syntax: Row+( Mat, row number 1, row number 2 [ ) ]
Example To add row 1 of the matrix below to row 2
1 2 3 4
K2(MAT)e(ROW)e(Row+)!+( [ )
!+( [ )b,c!-( ] )!+( [ ) 1 2
d,e!-( ] )!-( ] ),b,cw 4 6
7-1-39 Using the CAS (Computer Algebra System) Mode
20010102
k Vector Calculation Commands [OPTN]-[VECT]
uDim Function: Returns the dimension of a vector.
Syntax: Dim Vect
Example To determine the dimension of the vector (1 2 3)
K3(VECT)b(CALC)b(Dim)!+( [ )b,c,d
!-( ] )w 3
uCrossP Function: Returns the cross product of two vectors.
Syntax: CrossP( Vect, Vect [ ) ]
Example To determine the cross product of vector (1 2 3) and vector (4 5 6)
K3(VECT)b(CALC)c(CrossP)!+( [ )b,c,d
!-( ] ),!+( [ )e,f,g!-( ] )w [ 3, 6, 3 ]
uDotP Function: Returns the dot product of two vectors.
Syntax: DotP( Vect, Vect [ ) ]
Example To determine the dot product of vector (1 2 3) and vector (4 5 6)
K3(VECT)b(CALC)d(DotP)!+( [ )b,c,d
!-( ] ),!+( [ )e,f,g!-( ] )w 32
uNorm Function: Returns the norm of a vector.
Syntax: Norm Vect
Example To determine the norm of the vector (1 2 3)
K3(VECT)b(CALC)e(Norm)!+( [ )b,c,d
!-( ] )w 14
7-1-40 Using the CAS (Computer Algebra System) Mode
1 1
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uUnitV Function: Normalizes a vector.
Syntax: UnitV Vect
Example To normalize a vector (1 2 3)
K3(VECT)b(CALC)f(UnitV)
!+( [ )b,c,d
!-( ] )w
uAngle Function: Returns the angle formed by two vectors.
Syntax: Angle( Vect, Vect [ ) ]
Example To determine the angle formed by vector (1 2) and vector (3 4) (Unit Angle: Rad)
K3(VECT)b(CALC)g(Angle)!+( [ )b,c
!-( ] ),!+( [ )d,e!-( ] )w
uAugment (Augmnt) Function: Combines two vectors.
Syntax: Angle( Vect, Vect [ ) ]
Example To combine vector (1 2) and vector (3 4)
K3(VECT)c(CREATE)b(Augmnt)!+( [ )b,c
!-( ] ),!+( [ )d,e!-( ] )w [ 1, 2, 3, 4 ]
u Fill Function: Replaces the elements of a vector with a specified value or expression.
Syntax: Fill( Exp, Vect [ ) ]
Example To replace the components of the vector below with X
K3(VECT)c(CREATE)c(Fill)v,!+( [ )
d,e!-( ] )w [ X, X ]
7-1-41 Using the CAS (Computer Algebra System) Mode
,, 14 3 14
14 14
7 14
25 11 5cos1
1 1
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uVectList (VList) Function: Converts a vector into a list.
Syntax: VectList Vect
Example To convert vector (3 2) into a list
K3(VECT)d(VECT)b(VList)!+( [ )d,c
!-( ] )w { 3, 2 }
uVectMat (VMat) Function: Converts vectors into a matrix.
Syntax: VectMat( Vect [, ... ,Vect ] ( ] )
Example To convert vector (3 5) and (2 4) into a matrix
K3(VECT)d(VECT)c(VMat)!+( [ )d,f 3 2
!-( ] ),!+( [ )c,e!-( ] )w 5 4
7-1-42 Using the CAS (Computer Algebra System) Mode
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7-2 Algebra Mode The CAS Mode automatically provides you with the final result only. The Algebra Mode, on the other hand, lets you obtain intermediate results at a number of steps along the way.
On the Main Menu, select the ALGEBRA icon to enter the Algebra Mode. The screens in this mode are the same as those in the CAS Mode.
Operations in the Algebra Mode are identical to those in the CAS Mode, except for a number of limitations. Also, the following commands are available in the Algebra Mode only.
u arrange (arrang) Function: Collects like terms and arranges them in order, starting with the term that
contains the smallest coefficient.
Syntax: arrange( {Exp/Eq/Ineq} [ ) ]
Example To arrange 2X + 3 5X + 8Y in sequence of its variables
1(TRNS)j(arrang)ca+(X)+d-
fa+(X)+ia-(Y)w 5X + 2X + 8Y + 3
u replace (replac) Function: Replaces a variable with the expression assigned to the corresponding
expression variable.
Syntax: replace( {Exp/Eq/Ineq} [ ) ]
Example To replace S in the expression 3X + 2S, when the expression 2X + 1 is assigned to S
1(TRNS)v(replac)dv+ca*(S)w 3X + 2 (2X + 1)
7-2-1 Algebra Mode
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7-3 Tutorial Mode On the Main Menu, select the TUTOR icon to enter the Tutorial Mode.
k Tutorial Mode Flow
1. Specify the expression type.
2. Define the expression.
3. Specify the solve mode.
k Specifying the Expression Type
Entering the Tutorial Mode displays a menu of the following expression types.
Linear Equation
Linear Inequality
Quadratic Equation
Simul (Simultaneous) Equation
Use the cursor keys to highlight the expression type you want to specify, and then press w.
This displays a list of formulas for the expression type you select. Move the cursor to the formula you want to use.
In the case of Linear Inequality, press 4(TYPE) to select the inequality type.
7-3-1 Tutorial Mode
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The following shows the formulas available for each type of expression.
Linear Equation 6 Types
AX = B X + A = B AX + B = C AX + B = CX + D A(BX + C) = D(EX + F) AX + B= C
Linear Inequality 6 4 Types
AX { > < > < } B X + A { > < > < } B AX + B { > < > < } C AX + B { > < > < } CX + D A(BX + C) { > < > < } D(EX + F) AX + B{ > < > < } C
Quadratic Equation 5 Types
AX2 = B (AX + B)2 = C AX2 + BX + C = 0 AX2 + BX + C = D AX2 + BX + C = DX2 + EX + F
Simul Equation 10 Types
AX + BY = C Y = AX + B DX + EY = F Y = CX + D
AX + BY + C = 0 AX + BY + C = DX + EY + F DX + EY + F = 0 GX + HY + I = JX + KY + L
AX + BY = C AX + BY = C Y = DX + E DX + EY + F = 0
AX + BY = C AX + BY + C = 0 DX + EY + F = GX + HY + I Y = DX + E
AX + BY + C = DX + EY + F AX + BY + C = 0 Y = GX + H DX + EY + F = GX + HY + I
Pressing 6(EXCH) reverses the left side and right side elements of the expression.
7-3-2 Tutorial Mode
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kDefining the Expression
In this step, you specify coefficients and define the expression. You can select any of the three following methods for specifying coefficients.
{RAND} ... {random generation of coefficients}
{INPUT} ... {key input of coefficients}
{SMPL} ... {selection of coefficients from samples}
{SEED} ... {selection of a number from 1 to 99 (specification of the same number displays the same expression)}
1(RAND) or w generates random coefficients and defines the expression.
2(INPUT) displays the coefficient input screen. Input coefficients, pressing w after each. After you finish inputting all the coefficients, press 6(EXE) to define the coefficient.
3(SMPL) displays a number of preset sample expressions. Highlight the one you want to use and then press w to define it.
Pressing4(SEED) displays a number selection screen. When you want to create the same problem on another calculator, specify an appropriate matching number and press w.
No matter what method you use, the expression you define is displayed in the output area.
You can copy an expression to the Graph Mode as a graph function*1.
{LCOP}/{RCOP} ... copy {left side element}/{right side element} as a graph function
(Simultaneous Equation Mode*2)
{1COP}/{2COP} ... copy {first}/{second} expression as a graph function
7-3-3 Tutorial Mode
*1In the case of an inequality, the inequality symbols are also copied.
*2Simultaneous equations are transformed to the format Y = AX + B when copied.
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k Specifying the Solve Mode
You can select one of the following three solve modes for the displayed expression.
{VRFY}... {Verify Mode}
In this mode, you input a solution for verification of whether or not it is correct. It provides a good way to check solutions you arrive at manually.
{MANU} ... {Manual Mode}
In this mode, you manually input algebra commands, transform the expression, and calculate a result.
{AUTO}... {Auto Mode}
In this mode, the solution is produced automatically, one step at a time.
k Verify Mode
Press 4(VRFY) to enter the Verify Mode.
The expression is shown in the top line of the display. Input the solution underneath it, and then press6(JUDG) to determine whether the solution is correct.
The verification result screen shows the left side and right side verification result (except for a linear equation).
However, in the case where a linear equation or quadratic equation has two solutions, the left side and right side are obtained for the value where the pointer is located.
In the case of simultaneous equations where the left side and right side of the second equation are dissimilar even though the left side and right side of the first equation match, the left side and right side of the second equation only are obtained. In other cases, the left side and right side of the first equation are obtained.
The type of solution input screen that appears is selected according to the expression type. To input a different type, press 1(TYPE) and then select the solution type you want to want to use. Available solution types depend on the mode.
{X = a} ... X has one solution (X = a) (linear equation default)
{X = a, b} ... X has two solutions (X = a, X = b) (quadratic equation default)
{X = a, Y=}... X and Y have one solution each (X = a, Y = b) (simultaneous equation default)
{X > a} ... X { > < > < } a (linear inequality default)
{X < a, b <} ... X < a, b < X or X < a, b < X
{a < X < b} ... a < X< b, a < X < b or X = a
{Identi} (Identity) ... identity of left side and right side
{Many} (Many Solutions) ... many solutions
{No sol} (No Solution) ... no solution
7-3-4 Tutorial Mode
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7-3-5 Tutorial Mode
You can press 4(MANU) to change to the Manual Mode or 5(AUTO) to change to the Auto Mode.
Example To solve 4X = 8 in the Verify Mode
(Linear Equation)(AX = B)
2(INPUT)ewiw6(EXE)
4(VRFY)cw
6(JUDG)
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7-3-6 Tutorial Mode
k Manual Mode
Press 5(MANU) to enter the Manual Mode.
As with the Algebra Mode, the screen is divided between an input area and a display area. This means you can select Algebra Mode commands from the function menu, transform the expression, and solve it.
Operation is the same as that in the Algebra Mode.
After you obtain a result, you can press 5(JUDG) to determine whether or not it is correct.
{DISP} ... Determines whether the expression in the display area is a correct solution.
{Identi} ... identity of left side and right side
{Many}... many solutions
{No sol} ... no solution
You can press 6(AUTO) to change to the Auto Mode.
Example Solve 4X = 8 in the Manual Mode
(Linear Equation)(AX=B)
2(INPUT)ewiw6(EXE)
5(MANU)
4(eqn)b)/e
w
1(TRNS)b(smplfy)
4(eqn)c
w
5(JUDG)b(DISP)
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7-3-7 Tutorial Mode
Example 4X2 = 16 True (X = 2, X = 2)
Besides TRUE the messages shown below can also appear as the result of verification. CAN NOT JUDGE appears in the Manual Mode, while the other messages appear in both the Verify Mode and Manual Mode.
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7-3-8 Tutorial Mode
k Auto Mode
Press 6(AUTO) to enter the Auto Mode.
In the Simultaneous Equation Mode, you must also select SBSTIT (Substitution Method) or ADD-SU (Addition/Subtraction Method).
The Substitution Method first transforms the equation to the format Y = aX + b, and substitutes aX + b for Y*1 in the other equation.
The Addition/Subtraction Method multiplies both sides of the expression by the same value to isolate the coefficient X (or Y).
As with the Algebra Mode, the screen is divided between an input area and a display area.
Each press of 6(NEXT) advances to the next step. 6(NEXT) is not shown on the display when the solution is obtained.
You can scroll back through the steps by pressing 1(BACK).
Example To solve 4X = 8 in the Auto Mode
(Linear Equation)(AX = B)
2(INPUT)ewiw6(EXE)
6(AUTO)
6(NEXT)
6(NEXT)
*1You can press 5(ADD SU) at any time to switch from Substitution Method to Addition / Subtraction Method.
# See 7-1-8 for information about graph functions.
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a b f(x)dx = F(b) F(a)
7-4-1 Algebra System Precautions
7-4 Algebra System Precautions If an algebraic operation cannot be performed for some reason, the original expression
remains on the display.
It may take considerable time to perform an algebraic operation. Failure of a result to appear immediately does not indicate malfunction of the computer.
Any expression can be displayed in various different formats. Because of this, you should not assume that an expression is wrong just because it does not appear as you expected.
This calculator performs integration calculations under the assumption that integrals are always positive, even when the integrals switch between positive and negative.
f(x)
F(x): primitive function of f(x)
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Programming 8-1 Basic Programming Steps
8-2 Program Mode Function Keys 8-3 Editing Program Contents
8-4 File Management
8-5 Command Reference
8-6 Using Calculator Functions in Programs 8-7 Program Mode Command List
8-8 Program Library
Chapter
This unit comes with approximately 144 kbytes of memory.
You can check how much memory has been used and how much remains by entering the SYSTEM Mode from the Main Menu, and then pressing 1(Mem). See 9-2 Memory Operations for details.
8
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8-1 Basic Programming Steps Description Commands and calculations are executed sequentially, just like manual calculation multistatements.
Set Up 1. From the Main Menu, enter the PRGM Mode. When you do, a program list appears on
the display.
Selected program area
(use f and c to move)
Files are listed in the alphabetic sequence of their names.
Execution 2. Register a file name.
3. Input the program.
4. Run the program.
8-1-1 Basic Programming Steps
# If there are no programs stored in memory when you enter the PRGM Mode, the message No Programs appears on the display and only the NEW item (3) is shown in the function menu.
# The values to the right of the program list indicate the number of bytes used by each program.
# A file name can be up to eight characters long.
# The following are the characters you can use in a file name: A through Z, r, , spaces, [, ], {, }, , , ~, 0 through 9, ., +, , ,
# Registering a file name uses 24 bytes of memory.
# The file name input screen remains on the display if you press w without inputting a file name.
# To exit the file name input screen and return to the program list without registering a file name, press i.
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Example 1 To calculate the surface area (cm2) and volume (cm3) of three regular octahedrons when the length of one side is 7, 10, and 15 cm, respectively.
Store the calculation formula under the file name OCTA.
A
The following are the formulas used for calculating surface area S and volume V of a regular octahedron for which the length of one side A is known.
Procedure 1m PRGM
23(NEW)OCTAw*1
3!J(PRGM)3(?)aav(A)6(g)6(g)3(:)*2
c*!x( )d*av(A)x6(g)4(^)
!x( )c/d*av(A)Md
ii
41(EXE) or w
hw(Value of A)
w
w
wbaw
w
w
wbfw
w*3
8-1-2 Basic Programming Steps
2 S = 2 3 A2, V = A3
3
*1Press 3(NEW) and the cursor changes form to indicate alpha character input.
*2The following shows how the calculation of the surface area and volume of a regular octahedron would be calculated using a manual calculation.
Surface Area S ...c*!x( )d*
Volume V ............!x( )c/d*
*3Pressing w while the final result of a program is on the display changes to the program list.
# You can also run a program while in the RUN
MAT Mode by inputting: Prog
# Pressing w while the final result of a program executed using this method is on the display
re-executes the program.
# An error occurs if the program specified by Prog
S when A = 7 V when A = 7
S when A = 10 V when A = 10
S when A = 15 V when A = 15
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8-2 Program Mode Function Keys {NEW} ... {new program}
u When you are registering a file name
{RUN}/{BASE} ... {general calculation}/{number base} program input
{Q} ... {password registration}
{SYBL} ... {symbol menu}
u When you are inputting a program 1(RUN) default
{JUMP} ... {top}/{bottom} of program
{SRC} ... {search}
{MAT}/ {STAT}/{LIST}/{GRPH}/{DYNA}/{RECR} ... {matrix}/{statistic}/{list}/{graph}/ {Dynamic Graph}/{recursion} menu
Pressing !J(PRGM) displays the following PRGM (PROGRAM) menu.
{Prog} ... {program recall}
{JUMP} ... {jump command menu}
{?}/{^} ... {input}/{output} command
{I/O} ... {I/O control/transfer command menu}
{IF}/{FOR}/{WHLE}/{CTRL}/{LOGIC}
... {conditional jump}/{loop control}/{conditional loop control}/{program control}/ {logical operation} command menu
{CLR}/{DISP} ... {clear}/{display} command menu
{:} ......... {separator for expressions and commands}
See 8-5 Command Reference for full details on each of these commands.
Pressing u3(SET UP) displays the mode command menu shown below.
{ANGL}/{DISP}/{CPLX}/{GRPH}/{STAT}/{DERIV}/{T-VAR}/{ DSP}
See SET UP Screen Function Key Menus on page 1-7-1 for details about each of these commands.
8-2-1 Program Mode Function Keys
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u When you are inputting a program 2(BASE)*1
{JUMP}/{SRC}
{d~o} ... {decimal}/{hexadecimal}/{binary}/{octal} value input
{LOG} ... {logical operators}
{DISP}... conversion of displayed value to {decimal}/{hexadecimal}/{binary}/{octal}
{SYBL}... {symbol menu}
Pressing !J(PRGM) displays the following PRGM (PROGRAM) menu.
{Prog}/{JUMP}/{?}/{^}
{= <} ... {logical operator menu}
{:} ......... {separator for expressions and commands}
Pressing u3(SET UP) displays the mode command menu shown below.
{Dec}/{Hex}/{Bin}/{Oct}
{EXE}/{EDIT} ... program {execute}/{edit}
{NEW} ... {new program}
{DEL}/{DELA} ... {specific program}/{all program} delete
{SRC}/{REN} ... file name {search}/{change}
8-2-2 Program Mode Function Keys
*1Programs input after pressing 2(BASE) are indicated by B to the right of the file name.
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8-3-1 Editing Program Contents
8-3 Editing Program Contents
kDebugging a Program
A problem in a program that keeps the program from running correctly is called a bug, and the process of eliminating such problems is called debugging. Either of the following symptoms indicates that your program contains bugs that require debugging.
Error messages appearing when the program is run
Results that are not within your expectations
uTo eliminate bugs that cause error messages An error message, like the one shown below, appears whenever something illegal occurs during program execution.
When such a message appears, press i to display the place in the program where the error was caused. The cursor will be flashing at the location of the problem. Check the Error Message Table (page -1-1) for steps you should take to correct the situation.
Note that pressing i does not display the location of the error if the program is password protected. Instead, it returns to the program list screen.
uTo eliminate bugs that cause bad results If your program produces results that are not what you normally expect, check the contents of the program and make necessary changes. The 1(JUMP) key is also useful when editing program contents.
1(JUMP)b(Top) ....... Moves the cursor to the top of the program
1(JUMP)c(Bottom)Moves the cursor to the bottom of the program
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kUsing an Existing Program to Create a New Program
Sometimes you can input a new program by using a program already in memory as a base. Simply recall the existing program, make the changes you need, and then execute it.
Example 2 To use the OCTA program (page 8-1-2) to create a program that calculates the surface area (cm2) and volume (cm3) of regular tetrahedrons when the length of one side is 7, 10, and 15 cm Use TETRA as the file name.
The following are the formulas used for calculating surface area S and volume V of a regular tetrahedron for which the length of one side A is known.
Use the following key operations when inputting the program.
Length of One Side A ..!J(PRGM)3(?)aav(A)6(g)6(g)3(:)
Surface Area S ............!x( )d*av(A)x6(g)4(^)
Volume V .....................!x( )c/bc*av(A)Md
Compare this with the program for calculating the surface area and volume of a regular octahedron.
Length of One Side A ..!J(PRGM)3(?)aav(A)6(g)6(g)3(:)
Surface Area S ............c*!x( )d*av(A)x6(g)4(^)
Volume V .....................!x( )c/d*av(A)Md
As you can see, you can produce the TETRA program by making the following changes in the OCTA program.
Deleting c * (underlined using a wavy line above)
Changing d to b c (underlined using a solid line above)
A
8-3-2 Editing Program Contents
2 S = 3 A2, V = A3
12
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8-3-3 Editing Program Contents
Now edit OCTA to produce the TETRA program.
1. Edit the program name.
6(g)2(REN)ATETRAw
2. Edit the program contents.
2(EDIT)
eeeeDD
cdDbc
i
3. Try running the program.
1(EXE) or w
hw(Value of A)
w
w
wbaw
w
w
wbfw
w
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8-3-4 Editing Program Contents
k Searching for Data Inside a Program
Example To search for the letter A inside the program named OCTA
1. Recall the program.
2. Press 2(SRC) or w and input the data you want to find.
2(SRC)
av(A)
3. Press w to begin the search. The contents of the program appear on the screen with the cursor located at the first instance of the data you specified.*1
4. Each press of w or 1(SRC) causes the cursor to jump to the next instance of the data you specified.*2
*1The message Not Found appears when the search data you specify cannot be found in the program.
*2If there are no more instances of the data you specified, the search operation ends and the cursor returns to the point from which you started your search.
# You cannot specify the newline symbol (_) or display command (^) for the search data.
# Once the contents of the program are on the screen, you can use the cursor keys to move the cursor to another location before searching for the next instance of the data. Only the part of the program starting from the current cursor location is searched when you press w.
# Once the search finds an instance of your data, inputting characters or moving the cursor causes the search operation to be cancelled.
# If you make a mistake while inputting characters to search for, press A to clear your input and re-input from the beginning.
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8-4-1 File Management
8-4 File Management
k Searching for a File
u To find a file using initial character search
Example To use initial character search to recall the program named OCTA
1. While the program list is on the display, press 6(g)1(SRC) and input the initial characters of the file you want to find.
6(g)1(SRC)
OCT
2. Press w to search.
The name that starts with the characters you input highlights.
# If there is no program whose file name starts with the characters you input, the message
Not Found appears on the display. If this happens, press i to clear the error message.
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8-4-2 File Management
kEditing a file name
Example To change the name of a file from TRIANGLE to ANGLE
1. While the program list is on the display, use f and c to move the highlighting to the file whose name you want to edit and then press 6(g)2(REN).
2. Make any changes you want.
DDD
3. Press w to register the new name and return to the program list.
The program list is resorted according to the changes you made in the file name.
kDeleting a Program
u To delete a specific program 1. While the program list is on the display, use f and c to move the highlighting to the
name of the program you want to delete.
2. Press 4(DEL).
3. Press w(Yes) to delete the selected program or i(No) to abort the operation without deleting anything.
# If the modifications you make result in a file name that is identical to the name of a program already stored in memory, the message Already Exists appears. When this happens, you can perform either of the following two operations to correct the situation.
Press i to clear the error and return to the file name editing screen.
Press A to clear the input file name and input a new one.
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8-4-3 File Management
u To delete all programs 1. While the program list is on the display, press 5(DELA).
2. Press w(Yes) to delete all the programs in the list or i(No) to abort the operation without deleting anything.
You also can delete all programs by entering the SYSTEMMode from the Main Menu, and then pressing 1(Mem) to display the memory management screen. See 9-2 Memory Operations for details.
kRegistering a password
When inputting a program, you can protect it with a password that limits access to the program contents to those who know the password.
You do not need to input the password to run a program.
Example To create a program file under the name AREA and protect it with the password CASIO
1. While the program list is on the display, press 3(NEW) and input the file name of the new program file.
3(NEW)
AREA
2. Press 5(Q) and then input the password.
5(Q)
CASIO
# The password input procedure is identical to that used for file name input.
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8-4-4 File Management
3. Press w to register the file name and password. Now you can input the contents of the program file.
4. After inputting the program, press !i(QUIT) to exit the program file and return to the program list. Files that are password protected are indicated by an asterisk to the right of the file name.
kRecalling a Password Protected Program
Example To recall the file named AREA which is protected by the password CASIO
1. In the program list, use f and c to move the highlighting to the name of the program you want to recall.
2. Press 2(EDIT).
3. Input the password and press w to recall the program.
# Pressing w without inputting a password while saving a new program causes the file to be saved without a password. Pressing w without inputting a password registers the file name only, without a password.
# Inputting the wrong password when recalling a password protected program causes the message "Mismatch" to appear. Press i to return to the password input screen.
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8-5-1 Command Reference
8-5 Command Reference
kCommand Index
Break ...............................................................................................................8-5-6
ClrGraph ....................................................................................................... 8-5-11
ClrList ............................................................................................................8-5-11
ClrText ...........................................................................................................8-5-12
ClrMat ............................................................................................................8-5-12
DispF-Tbl, DispR-Tbl .....................................................................................8-5-12
Do~LpWhile .....................................................................................................8-5-5
DrawDyna ..................................................................................................... 8-5-12
DrawFTG-Con, DrawFTG-Plt ........................................................................8-5-13
DrawGraph ................................................................................................... 8-5-13
DrawR-Con, DrawR-Plt .................................................................................8-5-13
DrawR-Con, DrawR-Plt .............................................................................8-5-14
DrawStat ....................................................................................................... 8-5-14
DrawWeb .......................................................................................................8-5-14
Dsz ..................................................................................................................8-5-9
For~To~(Step~)Next ........................................................................................8-5-4
Getkey ...........................................................................................................8-5-15
Goto~Lbl ....................................................................................................... 8-5-10
If~Then~(Else~)IfEnd ......................................................................................8-5-4
Isz ..................................................................................................................8-5-11
Locate ............................................................................................................8-5-16
Prog ................................................................................................................ 8-5-7
Receive ( / Send ( ..........................................................................................8-5-17
Return .............................................................................................................8-5-8
Stop ................................................................................................................ 8-5-8
While~WhileEnd ..............................................................................................8-5-6
? (Input Command) .........................................................................................8-5-2
^ (Output Command) .....................................................................................8-5-3
: (Multi-statement Command) ..........................................................................8-5-3
_ (Carriage Return) .......................................................................................8-5-3
(Comment Text Delimiter) ..............................................................................8-5-3
=, G, >, <, , (Relational Operators) ........................................................... 8-5-18
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8-5-2 Command Reference
The following are conventions that are used in this section when describing the various commands.
Boldface Text ............... Actual commands and other items that always must be input are shown in boldface.
{Curly Brackets} ........... Curly brackets are used to enclose a number of items, one of which must be selected when using a command. Do not input the curly brackets when inputting a com- mand.
[Square Brackets] ........ Square brackets are used to enclose items that are optional. Do not input the square brackets when inputting a command.
Numeric Expressions ... Numeric expressions (such as 10, 10 + 20, A) indicate constants, calculations, numeric constants, etc.
Alpha Characters ......... Alpha characters indicate literal strings (such as AB).
kBasic Operation Commands
? (Input Command)
Function: Prompts for input of values for assignment to variables during program execution.
Syntax: ?
Example: ? A
Description:
This command momentarily interrupts program execution and prompts for input of a value or expression for assignment to a variable. If you do not specify a prompt, execution of this command causes ? to appear indicating the calculator is standing by for input. If a prompt is specified,
Input in response to the input command must be a value or an expression, and the expression cannot be a multi-statement.
You can specify a list name, matrix name, function memory (fn), graph (Yn), etc. as a variable name.
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8-5-3 Command Reference
^ (Output Command)
Function: Displays an intermediate result during program execution.
Description:
This command momentarily interrupts program execution and displays alpha character text or the result of the calculation immediately before the command.
The output command should be used at locations where you would normally press the w key during a manual calculation.
: (Multi-statement Command)
Function: Connects two statements for sequential execution without stopping.
Description:
Unlike the output command (^), statements connected with the multi-statement command are executed non-stop.
The multi-statement command can be used to link two calculation expressions or two commands.
You can also use a carriage return indicated by _ in place of the multi-statement command.
_ (Carriage Return)
Function: Connects two statements for sequential execution without stopping.
Description:
Operation of the carriage return is identical to that of the multi-statement command.
You can create a blank line in a program by inputting a carriage return only. Using a carriage return in place of the multi-statement command makes the displayed program easier to read.
(Comment Text Delimiter)
Function: Indicates comment text inserted inside a program.
Description: Anything following the apostrophe is treated as non-executable comment text.
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k Program Commands (COM)
If~Then~(Else~)IfEnd
Function: The Then-statement is executed only when the If-condition is true (non-zero). The Else-statement is executed when the If-condition is false (0). The IfEnd- statement is always executed following either the Then-statement or Else-statement.
Syntax:
Parameters: condition, numeric expression
Description:
(1) If ~ Then ~ IfEnd When the condition is true, execution proceeds with the Then-statement and then
continues with the statement following IfEnd. When the condition is false, execution jumps to the statement following IfEnd.
(2) If ~ Then ~ Else ~ IfEnd When the condition is true, execution proceeds with the Then-statement and then jumps
to the statement following IfEnd. When the condition is false, execution jumps to the Else-statement and then continues
with the statement following IfEnd.
For~To~(Step~)Next
Function: This command repeats everything between the For-statement and the Next- statement. The starting value is assigned to the control variable with the first execution, and the value of the control variable is changed according to the step value with each execution. Execution continues until the value of the control variable exceeds the ending value.
Syntax:
Parameters:
control variable name: A to Z starting value: value or expression that produces a value (i.e. sin x, A, etc.) ending value: value or expression that produces a value (i.e. sin x, A, etc.) step value: numeric value (default: 1)
8-5-4 Command Reference
If
Then
_ : ^
Else
IfEnd
_
For
Next
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8-5-5 Command Reference
Description:
The default step value is 1.
Making the starting value less than the ending value and specifying a positive step value causes the control variable to be incremented with each execution. Making the starting value greater than the ending value and specifying a negative step value causes the control variable to be decremented with each execution.
Do~LpWhile
Function: This command repeats specific commands as long as its condition is true (non- zero).
Syntax:
Parameters: expression
Description:
This command repeats the commands contained in the loop as long as its condition is true (non-zero). When the condition becomes false (0), execution proceeds from the statement following the LpWhile-statement.
Since the condition comes after the LpWhile-statement, the condition is tested (checked) after all of the commands inside the loop are executed.
_ _
Do :
19990401
8-5-6 Command Reference
While~WhileEnd
Function: This command repeats specific commands as long as its condition is true (non- zero).
Syntax:
Parameters: expression
Description:
This command repeats the commands contained in the loop as long as its condition is true (non-zero). When the condition becomes false (0), execution proceeds from the statement following the WhileEnd-statement.
Since the condition comes after the While-statement, the condition is tested (checked) before the commands inside the loop are executed.
kProgram Control Commands (CTL)
Break
Function: This command breaks execution of a loop and continues from the next command following the loop.
Syntax: Break
Description:
This command breaks execution of a loop and continues from the next command following the loop.
This command can be used to break execution of a For-statement, Do-statement, and While-statement.
_
: ^
_
: ^
While
19990401
8-5-7 Command Reference
Prog
Function: This command specifies execution of another program as a subroutine. In the RUN MAT Mode, this command executes a new program.
Syntax: Prog file name
Example: Prog ABC
Description:
Even when this command is located inside of a loop, its execution immediately breaks the loop and launches the subroutine.
This command can be used as many times as necessary inside of a main routine to call up independent subroutines to perform specific tasks.
A subroutine can be used in multiple locations in the same main routine, or it can be called up by any number of main routines.
Main Routine Subroutines
D
C E I J
Prog E Prog I Prog J
A
Prog D
Prog C
Level 1 Level 2 Level 3 Level 4
Calling up a subroutine causes it to be executed from the beginning. After execution of the subroutine is complete, execution returns to the main routine, continuing from the state- ment following the Prog command.
A Goto~Lbl command inside of a subroutine is valid inside of that subroutine only. It cannot be used to jump to a label outside of the subroutine.
If a subroutine with the file name specified by the Prog command does not exist, an error occurs.
In the RUN MAT Mode, inputting the Prog command and pressing w launches the program specified by the command.
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8-5-8 Command Reference
Return
Function: This command returns from a subroutine.
Syntax: Return
Description:
Execution of the Return command inside a main routine causes execution of the program to stop. Execution of the Return command within a subroutine terminates the subroutine and returns to the program from which the subroutine was jumped to.
Stop
Function: This command terminates execution of a program.
Syntax: Stop
Description:
This command terminates program execution.
Execution of this command inside of a loop terminates program execution without an error being generated.
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8-5-9 Command Reference
k Jump Commands (JUMP)
Dsz
Function: This command is a count jump that decrements the value of a control variable by 1, and then jumps if the current value of the variable is zero.
Syntax:
Parameters: variable name: A to Z, r, [Example] Dsz B : Decrements the value assigned to variable B by 1.
Description:
This command decrements the value of a control variable by 1, and then tests (checks) it. If the current value is non-zero, execution continues with the next statement. If the current value is zero, execution jumps to the statement following the multi-statement command (:), display command (^), or carriage return (_).
Variable Value G 0 _
Dsz
^ Variable Value = 0
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8-5-10 Command Reference
Goto~Lbl
Function: This command performs an unconditional jump to a specified location.
Syntax: Goto
Parameters: label name: value (0 to 9), variable (A to Z, r, )
Description:
This command consists of two parts: Goto n (where n is a parameter as described above) and Lbl n (where n is the parameter referenced by Goto n). This command causes program execution to jump to the Lbl-statement whose n parameter matches that specified by the Goto-statement.
This command can be used to loop back to the beginning of a program or to jump to any location within the program.
This command can be used in combination with conditional jumps and count jumps.
If there is no Lbl-statement whose value matches that specified by the Goto-statement, an error occurs.
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Isz
Function: This command is a count jump that increments the value of a control variable by 1, and then jumps if the current value of the variable is zero.
Syntax:
Parameters: variable name: A to Z, r, [Example] Isz A : Increments the value assigned to variable A by 1.
Description:
This command increments the value of a control variable by 1, and then tests (checks) it. If the current value is non-zero, execution continues with the next statement. If the current value is zero, execution jumps to the statement following the multi-statement command (:), display command (^), or carriage return (_).
kClear Commands (CLR)
ClrGraph
Function: This command clears the graph screen and returns View Window settings to their INIT values.
Syntax: ClrGraph
Description: This command clears the graph screen during program execution.
ClrList
Function: This command deletes list data.
Syntax: ClrList
ClrList
Parameters: list name: 1 to 20, Ans
Description: This command deletes the data in the list specified by list name. All list data is deleted if nothing is specified for list name.
8-5-11 Command Reference
Variable Value G 0 _
Isz
^ Variable Value = 0
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8-5-12 Command Reference
ClrText
Function: This command clears the text screen.
Syntax: ClrText
Description: This command clears text from the screen during program execution.
ClrMat
Function: This command deletes matrix data.
Syntax: ClrMat
ClrMat
Parameters: matrix name: A to Z, Ans
Description: This command deletes the data in the matrix specified by matrix name. All matrix data is deleted if nothing is specified for matrix name.
kDisplay Commands (DISP)
DispF-Tbl, DispR-Tbl No parameters
Function: These commands display numeric tables.
Description:
These commands generate numeric tables during program execution in accordance with conditions defined within the program.
DispF-Tbl generates a function table, while DispR-Tbl generates a recursion table.
DrawDyna No parameters
Function: This command executes a Dynamic Graph draw operation.
Description: This command draws a Dynamic Graph during program execution in accordance with current Dynamic Graph parameters.
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8-5-13 Command Reference
DrawFTG-Con, DrawFTG-Plt No parameters
Function: This command uses values in a generated table to graph a function.
Description:
This command draws a function graph in accordance with current conditions. DrawFTG-Con produces a connect type graph, while DrawFTG-Plt produces a plot type
graph.
DrawGraph No parameters
Function: This command draws a graph.
Description: This command draws a graph in accordance with current conditions.
DrawR-Con, DrawR-Plt No parameters
Function: These commands use values in a generated table to graph a recursion expression with an(bn or cn) as the vertical axis and n as the horizontal axis.
Description:
These commands graph recursion expressions in accordance with current conditions, with an(bn or cn) as the vertical axis and n as the horizontal axis.
DrawR-Con produces a connect type graph, while DrawR-Plt produces a plot type graph.
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8-5-14 Command Reference
DrawR-Con, DrawR-Plt No parameters
Function: These commands use values in a generated table to graph a recursion expression with an(bn or cn) as the vertical axis and n as the horizontal axis.
Description:
These commands graph recursion expressions in accordance with current conditions, with an(bn or cn) as the vertical axis and n as the horizontal axis.
DrawR-Con produces a connect type graph, while DrawR-Plt produces a plot type graph.
DrawStat
Function: This draws a statistical graph.
Syntax: See 8-6-9 Using Statistical Calculations and Graphs in a Program.
Description:
This command draws a statistical graph in accordance with current statistical graph conditions.
DrawWeb
Function: This command graphs convergence/divergence of a recursion expression (WEB graph).
Syntax: DrawWeb
Example: DrawWeb an+1 (bn+1 or cn+1), 5
Description:
This command graphs convergence/divergence of a recursion expression (WEB graph).
Omitting the number of lines specification automatically specifies the default value 30.
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8-5-15 Command Reference
k Input/Output Commands (I/O)
Getkey
Function: This command returns the code that corresponds to the last key pressed.
Syntax: Getkey
Description:
This command returns the code that corresponds to the last key pressed.
64
79
78 68 58 48
77 67 57 47
76 66 56 46
75
74 54 44
6373 53 43 33
6272 52 42 32
6171 51 41 31
65 55 45
36
35
26
25
69 59 49 39 29
28 38 27
37
A value of zero is returned if no key was pressed previous to executing this command.
This command can be used inside of a loop.
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8-5-16 Command Reference
Locate
Function: This command displays alpha-numeric characters at a specific location on the text screen.
Syntax: Locate
Locate
Locate
[Example] Locate 1, 1, AB_
Parameters:
line number: number from 1 to 7 column number: number from 1 to 21 value and numeric expression string: character string
Description:
This command displays values (including variable contents) or text at a specific location on the text screen. If there is a calculation input, that calculation result is displayed.
The line is designated by a value from 1 to 7, while the column is designated by a value from 1 to 21.
(1, 1) (21, 1)
(1, 7) (21, 7)
Example: Cls_ Locate 7, 1, CASIO FX This program displays the text CASIO FX in the center of the screen.
In some cases, the ClrText command should be executed before running the above program.
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8-5-17 Command Reference
Receive ( / Send (
Function: This command receives data from and sends data to a connected device.
Syntax: Receive () / Send ()
Description:
This command receives data from and sends data to a connected device.
The following types of data can be received (sent) by this command.
Individual values assigned to variables
Matrix data (all values - individual values cannot be specified)
List data (all values - individual values cannot be specified)
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8-5-18 Command Reference
kConditional Jump Relational Operators (REL)
=, G, >, <, ,
Function: These relational operators are used in combination with the conditional jump command.
Syntax:
Parameters:
left side/right side: variable (A to Z, r, ), numeric constant, variable expression (such as: A 2)
relational operator: =, G, >, <, ,
19990401
8-6 Using Calculator Functions in Programs
k Text Display
You can include text in a program by simply enclosing it between double quotation marks. Such text appears on the display during program execution, which means you can add labels to input prompts and results.
Program Display
CASIO CASIO
? X ?
X = ? X X = ?
If the text is followed by a calculation formula, be sure to insert a display command (^) between the text and calculation.
Inputting more than 21 characters causes the text to move down to the next line. The screen scrolls automatically if the text exceeds 21 characters.
You can specify up to 255 bytes of text for a comment.
kUsing Matrix Row Operations in a Program
These commands let you manipulate the rows of a matrix in a program.
For this program, enter the RUN MAT Mode and then use the MAT Editor to input the matrix, and then enter the PRGM Mode to input the program.
u To swap the contents of two rows (Swap)
Example 1 To swap the values of Row 2 and Row 3 in the following matrix: 1 2
Matrix A = 3 4
5 6
The following is the syntax to use for this program.
Swap A, 2, 3_
Mat A
Executing this program produces the following result.
8-6-1 Using Calculator Functions in Programs
Rows to be swapped Matrix name
122001 1
19990401
u To calculate a scalar multiplication (`Row)
Example 2 To calculate the product of Row 2 of the matrix in Example 1 and the scalar 4
The following is the syntax to use for this program.
`Row 4, A, 2_
Mat A
Executing this program produces the following result.
u To calculate a scalar multiplication and add the results to another row (`Row+)
Example 3 To calculate the product of Row 2 of the matrix in Example 1 and the scalar 4, then add the result to row 3
The following is the syntax to use for this program.
`Row+ 4, A, 2, 3_
Mat A
Executing this program produces the following result.
8-6-2 Using Calculator Functions in Programs
Row Matrix name Multiplier
Matrix name Multiplier
Rows to be added Row for which scalar multiplication is to be calculated.
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u To add two rows (Row+)
Example 4 To add Row 2 to Row 3 of the matrix in Example 1
The following is the syntax to use for this program.
Row+ A, 2, 3_
Mat A
Executing this program produces the following result.
kUsing Graph Functions in a Program
You can incorporate graph functions into a program to draw complex graphs and to overlay graphs on top of each other. The following shows various types of syntax you need to use when programming with graph functions.
View Window
View Window 5, 5, 1, 5, 5, 1_
Graph function input
Y = Type_ ..................... Specifies graph type.
X2 3 Y1_
Graph draw operation
DrawGraph_
Example Program 1ClrGraph_ 1 !J661ci
2View Window 10, 10, 2, 120, 150, 50_ 2 !K1i
3Y = Type_ 3 61db
X^4X^324X2 + 4X + 80 @ Y1_ 4 J4bi 4
5G SelOn 1_ 5 61b
6DrawGraph 6 !J662c
Executing this program produces the result shown here.
8-6-3 Using Calculator Functions in Programs
200111
Matrix name
the row number to be added to the row number to be added
19990401
8-6-4 Using Calculator Functions in Programs
uSyntax of other graphing functions V-Window
View Window
StoV-Win .............. area: 1 to 6
RclV-Win .............. area: 1 to 6
Zoom
Factor
ZoomAuto ........... Non-parameter
Pict
StoPict ................ area: 1 to 20
RclPict ................ area: 1 to 20
Sketch
PlotOn
PlotOff
PlotChg
PxlOn
PxlOff
PxlChg
PxlTest(
F-Line
Text
Text
Tangent
Normal
Inverse
Circle
Vertical
Horizontal
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kUsing Dynamic Graph Functions in a Program
Using Dynamic Graph functions in a program makes it possible to perform repeated Dynamic Graph operations. The following shows how to specify the Dynamic Graph range inside a program.
Dynamic Graph range
1 D Start_
5 D End_
1 D pitch_
Example Program
ClrGraph_
View Window 5, 5, 1, 5, 5, 1_
Y = Type_
AX + 1 Y1_ 1 J4bi 1
2D SelOn 1_ 2 62b
3D Var A_ 3 2d
1 4 D Start_ 4 J5b
5 5 D End_ 5 5c
1 6 D pitch_ 6 5d
7DrawDyna 7 !J662d
Executing this program produces the result shown here.
8-6-5 Using Calculator Functions in Programs
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kUsing Table & Graph Functions in a Program
Table & Graph functions in a program can generate numeric tables and perform graphing operations. The following shows various types of syntax you need to use when programming with Table & Graph functions.
Table range setting
1 F Start_
5 F End_
1 F pitch_
Numeric table generation
DispF-Tbl_
Graph draw operation
Connect type: DrawFTG-Con_
Plot type: DrawFTG-Plt_
Example Program
ClrGraph_
ClrText_
View Window 0, 6, 1, 20, 106, 10_
Y = Type_
3X2 2 Y1_ 1G SelOn 1_ 1 61b
0 2 F Start_ 2 J61b
6 3 F End_ 3 1c
1 4 F pitch_ 4 1d
5DispF-Tbl^ 5 !J662eb
6DrawFTG-Con 6 !J662ec
Executing this program produces the results shown here.
Numeric Table Graph
8-6-6 Using Calculator Functions in Programs
19990401
kUsing Recursion Table & Graph Functions in a Program
Incorporating Recursion Table & Graph functions in a program lets you generate numeric tables and perform graphing operations. The following shows various types of syntax you need to use when programming with Recursion Table & Graph functions.
Recursion formula input
an+1 Type_ ..... Specifies recursion type.
3an + 2 an+1_
4bn + 6 bn+1_
Table range setting
1 R Start_
5 R End_
1 a0_
2 b0_
1 an Start_
3 bn Start_
Numeric table generation
DispR-Tbl_
Graph draw operation
Connect type: DrawR-Con_, DrawR-Con_
Plot type: DrawR-Plt_, DrawR-Plt_
Statistical convergence/divergence graph (WEB graph)
DrawWeb an+1, 10_
8-6-7 Using Calculator Functions in Programs
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8-6-8 Using Calculator Functions in Programs
Example Program
View Window 0, 1, 1, 0.2, 1, 1_ 1an+1 Type_
2 3
3an2 + 3an an+1_
0 R Start_
6 R End_
0.01 a0_
0.01 an Start_
8DispR-Tbl^ 0
9DrawWeb an+1, 30
Executing this program produces the results shown here.
Numeric Table Recursion graph
kUsing List Sort Functions in a Program
These functions let you sort data in lists into ascending or descending order.
Ascending order 1 2
SortA (List 1, List 2, List 3)
Lists to be sorted (up to six can be specified)
1 5b 2 4e
Descending order 3
SortD (List 1, List 2, List 3)
Lists to be sorted (up to six can be specified)
3 5c
4
5
6
1 63gc 2 3bc 3 3bd 4 J62cb 5 2cc 6 2cd 7 2cC 8 !J662fb 9 2fci 0 63bd
7
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kUsing Solve Calculation Function in a Program
The following is the syntax for using the Solve function in a program.
Solve( f(x), n, a, b)
Upper limit Lower limit Initial estimated value
Example Program
1Solve( 2X2 + 7X 9, 1, 0, 1) 1K4h
In the function f(x), only X can be used as a variable in the expression. Other variables (A through Z, r, ) are treated as constants, and the value currently assigned to that variable is applied during the calculation.
Input of the closing parenthesis, lower limit a and upper limit b can be omitted.
kUsing Statistical Calculations and Graphs in a Program
Including statistical calculations and graphing operations in a program lets you calculate and graph statistical data.
u To set conditions and draw a statistical graph Following StatGraph, you must specify the following graph conditions:
Graph draw/non-draw status (DrawOn/DrawOff)
Graph Type
x-axis data location (list name)
y-axis data location (list name)
Frequency data location (list name)
Mark Type
8-6-9 Using Calculator Functions in Programs
# Solutions obtained using Solve may include errors.
# You cannot use a differential, quadratic differential, integration, , maximum/ minimum value or Solve calculation expressions inside of a Solve calculation term.
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The graph conditions that are required depends on the graph type. See Changing Graph Parameters (page 6-1-2).
The following is a typical graph condition specification for a scatter diagram or xyLine graph.
S-Gph1 DrawOn, Scatter, List 1, List 2, 1, Square _
In the case of an xy line graph, replace Scatter in the above specification with xyLine.
The following is a typical graph condition specification for a normal probability plot.
S-Gph1 DrawOn, NPPlot, List 1, Square _
The following is a typical graph condition specification for a single-variable graph.
S-Gph1 DrawOn, Hist, List 1, List 2 _
The same format can be used for the following types of graphs, by simply replacing Hist in the above specification with the applicable graph type.
Histogram: ..................................... Hist
Median Box: ................................... MedBox
Modified Box: ................................. Modified
Normal Distribution: ....................... N-Dist
Broken Line: .................................. Broken
The following is a typical graph condition specification for a regression graph.
S-Gph1 DrawOn, Linear, List 1, List 2, List 3 _
The same format can be used for the following types of graphs, by simply replacing Linear in the above specification with the applicable graph type.
Linear Regression: ........................ Linear
Med-Med: ...................................... Med-Med
Quadratic Regression: ................... Quad
Cubic Regression: ......................... Cubic
Quartic Regression: ....................... Quart
Logarithmic Regression: ................. Log
Exponential Regression: ................ Exp
Power Regression: ........................ Power
8-6-10 Using Calculator Functions in Programs
19990401
The following is a typical graph condition specification for a sinusoidal regression graph.
S-Gph1 DrawOn, Sinusoidal, List 1, List 2 _
The following is a typical graph condition specification for a logistic regression graph.
S-Gph1 DrawOn, Logistic, List 1, List 2 _
Example Program
ClrGraph_ 1
S-Wind Auto_
{1, 2, 3} List 1_
{1, 2, 3} List 2_ 2 3 4 5
S-Gph1 DrawOn, Scatter, List 1, List 2, 1, Square _ 6
DrawStat
Executing this program produces the scatter diagram shown here.
k Performing Statistical Calculations
Single-variable statistical calculation 11-Variable List 1, List 2
Frequency data (Frequency)
x-axis data (XList)
14gb
8-6-11 Using Calculator Functions in Programs
1u35bbi
24bb
34cb
44db
54fb
6!J662b
19990401
Paired-variable statistical calculation 12-Variable List 1, List 2, List 3
Frequency data (Frequency)
y-axis data (YList)
x-axis data (XList)
14gc
Regression statistical calculation 1LinearReg List 1, List 2, List 3
Calculation Frequency data (Frequency) type*
y-axis data (YList)
x-axis data (XList)
14gd
* Any one of the following can be specified as the calculation type.
LinearReg .......... linear regression Med-MedLine .... Med-Med calculation QuadReg ........... quadratic regression CubicReg ........... cubic regression QuartReg ........... quartic regression LogReg .............. logarithmic regression ExpReg ............. exponential regression PowerReg .......... power regression
8-6-12 Using Calculator Functions in Programs
Sinusoidal regression statistical calculation
SinReg List 1, List 2
Logistic regression statistical calculation
LogisticReg List 1, List 2
y-axis data (YList)
x-axis data (XList)
y-axis data (YList)
x-axis data (XList)
19990401
8-7-1 Program Mode Command List
8-7 Program Mode Command List G_SelOn_ G_SelOff_ Y=TYPE r=TYPE ParamTYPE X=cTYPE Y>Type Y
bn bn+1
cn cn+1
R_SelOn_ R_SelOff_ Sel_a0
Sel_a1
anType an+1Type an+2Type
SelOn SelOff TYPE
GMEM
SelOn SelOff Var TYPE
n,an..
SelOn SelOff Sel a0
Sel a1
TYPE
Y= r= Param X=c Y> Y< Y> Y< Store Recall
Y= r= Param n an an+1
bn bn+1
cn cn+1
an an+1
an+2
Level 1
Level 2 Level 3 Command
MAT
STAT
LIST
Swap *Row *Row+ Row+ S-GPH
DRAW
GRAPH
List MARK
CALC
SortA SortD
Swap_ *Row_ *Row+_ Row+_ S-Gph1_ S-Gph2_ S-Gph3_ DrawOn DrawOff Scatter xyLine NPPlot Hist MedBox ModifiedBox N-Dist Broken Linear Med-Med Quad Cubic Quart Log Exp Power Sinusoidal Logistic List_ Square Cross Dot 1-Variable_ 2-Variable_ LinearReg_ Med-MedLine_ QuadReg_ CubicReg_ QuartReg_ LogReg_ ExpReg_ PowerReg_ SinReg_ LogisticReg_ SortA( SortD(
S-Gph1 S-Gph2 S-Gph3 On Off Scat xyLine NPPlot Hist Box ModBox N-Dist Broken Linear MedMed Quad Cubic Quart Log Exp Power Sin Lgstic
1VAR 2VAR Linear MedMed Quad Cubic Quart Log Exp Power Sin Lgstic
x! nPr nCr Ran# P( Q( R( t( sinh cosh tanh sinh1
cosh1
tanh1
r g 'DMS Pol( Rec( m
n
fn Factor Auto Cls PLOT
LINE
GRAPH
Text PIXEL
Tangnt Normal Invrse Circle Vert Horz Store Recall
~ * #
On Off Change Plot F-Line Line Y= dx
On Off Change Test
! P C Ran#_ P( Q( R( t( sinh_ cosh_ tanh_ sinh1_ cosh1_ tanh1_ r g
'DMS Pol( Rec( m
n
fn Factor_ ZoomAuto Cls PlotOn_ PlotOff_ PlotChg_ Plot_ F-Line_ Line Graph_Y= Graph_ Text_ PxlOn_ PxlOff_ PxlChg_ PxlTest( Tangent_ Normal_ Inverse_ Circle_ Vertical_ Horizontal_ StoPict_
RclPict_
~ * #
Level 1
Level 2 Level 3 Command [OPTN] key PROB
HYP
ANGL
STAT
FMEM ZOOM
SKTCH
PICT
SYBL
LIST
MAT
CPLX
CALC
NUM
List Dim Seq Min Max Mean Median Sum Prod Cuml % AList Augmnt Fill LMat Mat Dim Det Trn Augmnt Ident Fill MList Abs Arg Conjg ReP ImP 're^ i 'a+bi
d/dx d2/dx2
dx FMin FMax Solve Abs Int Frac Rnd Intg E-SYM
List_ Dim_ Seq( Min( Max( Mean( Median( Sum_ Prod_ Cuml_ Percent_ AList_ Augment( Fill( ListMat( Mat_ Dim_ Det_ Trn_ Augment( Identity_ Fill( MatList( Abs_ Arg_ Conjg_ ReP_ ImP_ 're^ i 'a+bi
d/dx( d2/dx2( ( ( FMin( FMax( Solve( Abs_ Int_ Frac_ Rnd Intg_ m n p f k M G T P
E
m
n p f k M G T P
E
RUN Program
GRPH
DYNA
RECR
19990401
Level 1 V-WIN
FACT
STAT
Level 2 Xmin Xmax Xscale Xdot Ymin Ymax Yscale T min T max T ptch R-Xmin R-Xmax R-Xscl R-Xdot R-Ymin R-Ymax R-Yscl R-Tmin R-Tmax R-Tpch Xfact Yfact n X
Y
GRAPH
Level 3
x x x2
xn xn1
minX maxX y y y2
xy yn yn1
minY maxY a b c d e r r2
Q1 Med Q3 Mod H-Strt H-ptch
Command [VARS] key
GRPH
DYNA
TABL
RECR
EQUA
PTS
Yn rn Xtn Ytn Xn Start End Pitch Start End Pitch Result FORM
RANGE
Result S-Rslt S-Coef P-Rslt P-Coef
x1 y1 x2 y2 x3 y3
an an+1
an+2
bn bn+1
bn+2
cn cn+1
cn+2
R-Strt R-End a0 a1 a2 b0 b1 b2 c0 c1 c2 anStrt bnstrt cnStrt
x1 y1 x2 y2 x3 y3 Y r Xt Yt X D_Start D_End D_pitch F_Start F_End F_pitch F_Result an an+1
an+2
bn bn+1
bn+2
cn cn+1
cn+2
R_Start R_End a0 a1 a2 b0 b1 b2 c0 c1 c2 anStart bnStart cnStart R_Result Sim_Result Sim_Coef Ply_Result Ply_Coef
Level 1 Prog JUMP
? ^
I/O
IF
FOR
WHLE
CTRL
LOGIC
CLR
DISP
:
Level 2
Lbl Goto lsz Dsz
Locate Getkey Send Receiv If Then Else IfEnd For To Step Next While WhlEnd Do LpWhle Prog Return Break Stop = G <
And Or Not Text Graph List Matrix Stat Graph Dyna F-TBL
R-TBL
Level 3
= G
> < >
<
Table G-Con G-Plot Table Web R-Con R-Con R-Plot R-Plt
Command Prog_ Lbl_ Goto_ lsz_ Dsz_ ? ^
Locate_ Getkey Send( Receive( If_ Then_ Else_ IfEnd For_ _To_ _Step_ Next While_ WhileEnd Do LpWhile_ Prog_ Return Break Stop = G
> < >
<
_And_ _Or_ Not_ ClrText ClrGraph ClrList_ ClrMat_ DrawStat DrawGraph DrawDyna DispF-Tbl DrawFTG-Con DrawFTG-Plt DispR-Tbl DrawWeb_ DrawR-Con DrawR-Con DrawR-Plt DrawR-Plt :
[SHIFT][VARS](PRGM) key
Xmin Xmax Xscl Xdot Ymin Ymax Yscl T min T max T ptch RightXmin RightXmax RightXscl RightXdot RightYmin RightYmax RightYscl RightT min RightT max RightT ptch Xfct Yfct n x x x2
xn xn1
minX maxX y y y2
xy yn yn1
minY maxY a b c d e r r2
Q1 Med Q3 Mod H_Start H_pitch
Level 1 ANGL
DISP
CPLX
GRPH
STAT
DERIV
T-VAR
DSP
Level 2 Deg Rad Gra Fix Sci Norm EngOn EngOff Real a+bi re^ i
G-FUNC
D-TYPE
BG
SIMUL
COORD
GRID
AXES
LABEL
S-WIN
File RESID
On Off Range List On Off
Level 3
On Off G-Con G-Plot None Pict On Off On Off On Off On Off On Off Auto Manual
None
List
Command Deg Rad Gra Fix_ Sci_ Norm EngOn EngOff Real a+bi re^ i
FuncOn FuncOff G-Connect G-Plot BG-None BG-Pict_ SimulOn SimulOff CoordOn CoordOff GridOn GridOff AxesOn AxesOff LabelOn LabelOff S-WindAuto S-WindMan File_ Resid-None Resid-List_ DerivOn DerivOff VarRange VarList_ dispOn dispOff
[CTRL][F3](SET UP) key
8-7-2 Program Mode Command List
19990401
Level 1 d~o
LOG
DISP
Level 2 d h b o Neg Not and or xor xnor 'Dec 'Hex 'Bin 'Oct
Level 3 Command d h b o Neg_ Not_ and or xor xnor 'Dec 'Hex 'Bin 'Oct
Level 1 Dec Hex Bin
Oct
Level 2 Level 3
Command Dec Hex Bin
Oct
[CTRL][F3](SETUP) key Level 1 V-Win Sto Rcl
Level 2 Level 3
Command ViewWindow_ StoV-Win_ RclV-Win_
[SHIFT][OPTN](V-Window)key BASE Program
Level 1 Prog JUMP
?
^
= G <
:
Level 2
Lbl Goto lsz Dsz
= G
> < >
<
Level 3 Command Prog_ Lbl_ Goto_ lsz_ Dsz_ ?
^
= G
> < >
<
:
[SHIFT][VARS](PRGM) key
8-7-3 Program Mode Command List
19990401
8-8-1 Program Library
Description
This program continually divides a natural number by factors until all its prime factors are produced.
Purpose
This program accepts input of natural number A, and divides it by B (2, 3, 5, 7....) to find the prime factors of A.
If a division operation does not produce a remainder, the result of the operation is assigned to A.
The above procedure is repeated until B > A.
Example 440730 = 2 3 3 5 59 83
Program Name Prime Factorization
8-8 Program Library Be sure to check how many bytes of unused memory are remaining before attempting to
perform any programming.
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8-8-2 Program Library
egcw
w
ww
w
19990401
Description
After inputting sequence terms 1, 2, and 3, this program determines whether it is an arithmetic sequence or geometric sequence based on the differences and ratios of the terms.
Purpose
This program determines whether a specific sequence is an arithmetic sequence or geometric sequence.
Example 1 5, 10, 15, ... Arithmetic sequence
Example 2 5, 10, 20, ... Geometric sequence
Program Name Arithmetic-Geometric Sequence Differentiation
8-8-3 Program Library
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8-8-4 Program Library
Example 1 Example 2
fw
baw
bf
w
fw
baw
ca
w
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8-8-5 Program Library
Description
This program displays a number table of the following values based on input of the foci of an ellipse, the sum of the distance between the loci and foci, and the pitch (step size) of X.
Y1: Coordinate values of upper half of ellipse
Y2: Coordinate values of lower half of ellipse
Y3: Distances between right focus and loci
Y4: Distances between left focus and loci
Y5: Sum of Y3 and Y4
Next, the program plots the foci and values in Y1 and Y2.
Purpose
This program shows that the sums of the distances between the loci and two foci of an ellipse are equal.
Program Name Ellipse
19990401
8-8-6 Program Library
wba
wb
w
wua
d
12
19990401
Description
This program draws an angle at the coordinate defined by an input vertex, and then rotates it to a specified angle around the vertex.
Purpose
This program demonstrates coordinate transformation using a matrix.
Important!
Deg must be set as the angle unit for this program.
Program Name Rotation
8-8-7 Program Library
19990401
8-8-8 Program Library
dw
fcde
wwfcde
wwfcde
fcde
ww
daw
ww
12
19990401
Description
This program calculates the interior angles and surface area of a triangle defined by input coordinates for angles A, B, and C.
Purpose
This program calculates the interior angles and surface area of a triangle defined by coordinates for angles A, B, and C.
Important!
Inputting the same coordinates for any two angles (A, B, C) causes an error.
Program Name Interior Angles and Surface Area of a Triangle
8-8-9 Program Library
19990401
8-8-10 Program Library
b
awaw
bwaw
aw9d
w
19990401
Chapter
System Settings Menu Use the system settings menu to view system information and make system settings. The system settings menu lets you do the following.
View memory usage information Make contrast settings Make Auto Power Off settings Specify the system language Reset the calculator Tutorial Lock (ALGEBRA FX 2.0 PLUS only)
9-1 Using the System Settings Menu
9-2 Memory Operations
9-3 System Settings 9-4 Reset
9-5 Tutorial Lock (ALGEBRA FX 2.0 PLUS only)
9
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9-1-1 Using the System Settings Menu
9-1 Using the System Settings Menu From the Main Menu, enter the SYSTEM Mode and display the following menu items.
1(Mem) ... {display current memory status and delete data stored in memory}
2( ) ... {display contrast adjustment}
3(APO) ... {Auto Power Off time setting}
4(Lang) ... {system language}
5(Reset) ... {system reset operations}
6(T-Lock) ... {Tutorial Lock}
The T-Lock menu does not appear on the FX 1.0 PLUS.
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9-2 Memory Operations Use the Mem (Memory Usage) item to view current memory status and to delete certain data stored in memory.
While the initial System Settings Mode screen is displayed, press 1(Mem) to display the Memory Usage screen.
1(Main) ... {display the Main Memories screen}
2(Strg) ... {display the Storage Memories screen.}
Pressing 1(Main) displays data currently assigned to Main Memories.
To delete data 1. Use the f and c cursor keys to move the highlighting to the memory item whose
data you want to delete.
2. Depending on the screen that is on your display, press the function key assigned to the DEL function.
From the Main Memories screen, press 1(DEL).*1
From the Storage Memories screen, press 6(DEL).
3. If you selected List File, Graph Memory, V-Win Memory, Picture or H-Copy Memory in step 1, a menu appears so you can select which data you want to delete.
Input a number to specify the data and then press w.
4. In response to the confirmation message that appears, press w(Yes) to delete the data you specified, or i(No) to cancel.
Pressing i or !i(QUIT) returns to the initial System Settings Mode screen.
9-2-1 Memory Operations
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*1Pressing 6(DEL A) deletes all the data in the currently selected memory item.
# Performing the procedure to delete add-in applications clears all currently installed add-ins. You cannot delete add-ins individually.
19990401
9-2-2 Memory Operations
To view memory usage information Use f and c to move the highlighting and view the amount of memory (in bytes) used for storage of each type of data.
The following table shows all of the data types that appear on the memory status screen.
Main Memories
Data Type Meaning
Program Program data
Matrix Matrix memory data
Statistics Statistical calculations and graphs
List File List data
Y=Data Graph functions
Draw Memory Graph drawing conditions (View Window, enlargement/reduction factor)
Graph Memory Graph memory data
V-Win Memory View Window memory data
Picture Picture memory data
Table Function Table & Graph data
Dynamic Graph Dynamic Graph data
Recursion Recursion Table & Graph data
Equation Equation calculation data
Algebra Algebra variable data (ALGEBRA FX 2.0 PLUS only)
Financial Financial data
Diff Eq Differential equation and graphing conditions
E-Con E-CON setup memory, custom probe list
Alpha Memory Alpha memory data
Function Mem Function memory data
H-Copy Memory Screen shot transfer memory
System System Variable data
Others Other data
Storage Memories*1
Data Type Meaning
ADD-IN APP. Add-in applications
[B]~ Backup data
Pressing 1(Ver) displays the application names and versions of all currently installed add- ins.
122001 1 2
*1Any item that does not contain any data does not appear on the screen.
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9-3 System Settings
kContrast Adjustment
Use the (Contrast) item to adjust display contrast.
While the initial System Settings Mode screen is displayed, press 2( ) to display the Contrast Adjustment screen.
The e cursor key makes display contrast darker.
The d cursor key makes display contrast lighter.
1(INIT) returns display contrast to its initial default.
Pressing i or !i(QUIT) returns to the initial System Settings Mode screen.
You can adjust contrast while any screen besides the Main Menu is on the display by pressing ! and then e or d. To exit contrast adjustment, press ! again.
kAPO Settings
You can specify either six minutes or 60 minutes as the Auto Power Off trigger time. The initial default setting is six minutes.
While the initial System Settings Mode screen is displayed, press 3(APO) to display the APO Setting screen.
1(6) ... 6 minutes
2(60) ... 60 minutes
Pressing i or !i(QUIT) returns to the initial System Settings Mode screen.
9-3-1 System Settings
19990401
kSystem Language Setting
Use Lang to specify the display language for built-in applications. You can also use add-ins to install various other languages.
1. From the initial System Setting Mode screen, press 4(Lang) to display the system language setting screen.
2. Use the f and c cursor keys to select the language you want, and then press 1(Sel).
3. The pop up window appears using the language you selected. Check the contents and then press i.
Press i or !i(QUIT) to return to the initial System Setting Mode screen.
9-3-2 System Settings
# Installing a language with an add-in causes the installed language to be selected as the system language automatically.
# English display only is supported for the following functions. Differential equations E-CON
This means that all displays are in English, even if another display language is selected.
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9-4 Reset 1. While the initial System Settings Mode screen is displayed, press 5(Reset) to display
the Reset Menu screen.
1(S/U) ... {set up initialization}
2(Main) ... {main memory data clear}
4(Init) ... {all memory clear}
Pressing 3(Strg) on the above screen displays the Storage Memories screen shown below.
1(A&B) ... {Add-in application and backup data clear}
2(ADDIN) ... {Add-in application clear}
3(BACK) ... {Backup data clear}
4(B&M) ... {Backup data and Main Memories data clear}
2. Press the function key that corresponds to the reset operation you want to perform.
3. In response to the confirmation message that appears, press w(Yes) to perform the reset operation you specified, or i(No) to cancel.
4. A message appears to let you know when the reset operation is complete. Press m to return to the Main Menu.
9-4-1 Reset
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9-5-1 Tutorial Lock
9-5 Tutorial Lock (ALGEBRA FX 2.0 PLUS only) You can temporarily disable the Tutorial Mode (for 180 minutes).
1. From the initial System Setting Mode screen, press 6(T-Lock) to display the Tutorial Lock screen.
2. Pressing 1(Lock) displays the pop-up menu.
3. Pressing w(Yes) locks the Tutorial Mode so it cannot be used for 180 minutes.
Pressing i or !i(QUIT) returns to the initial System Settings Mode screen.
Attempting to enter the Tutorial Mode while Tutorial Lock is enabled displays a screen that shows the remaining Tutorial Lock time.
Press i to return to the Main Menu.
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Data Communications This chapter tells you everything you need to know to transfer programs between two CASIO Power Graphic calculators connected using the cable that is equipped as a standard accessory. You can also use the cable to connect the calculator to a CASIO Label Printer to print screen data.
To transfer data between a calculator and a personal computer, you need to purchase the separately available CASIO FA-123 Connection Kit.
10-1 Connecting Two Units 10-2 Connecting the Unit with a CASIO Label Printer
10-3 Connecting the Unit to a Personal Computer
10-4 Performing a Data Communication Operation
10-5 Data Communications Precautions 10-6 Sending a Screen Shot
10-7 Add-ins
10-8 MEMORY Mode
Chapter
10
19990401
10-1-1 Connecting Two Units
10-1 Connecting Two Units The following procedure describes how to connect two units with the connecting cable that comes equipped as a standard accessory.
uTo connect two units 1. Check to make sure that the power of both units is off.
2. Remove the covers from the connectors of the two units.
3. Connect the two units using the cable.
Cable
# Models that are supported for this configura- tion are shown below.
ALGEBRA FX 2.0/FX 2.0 PLUS FX 1.0/FX 1.0 PLUS
# Be sure you keep the connector covers in a safe place so you can replace them after you finish your data communications.
# Keep the connectors covered when you are not using them.
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10-2-1 Connecting the Unit with a CASIO Label Printer
10-2 Connecting the Unit with a CASIO Label Printer
After you connect the unit to a CASIO Label Printer with cable, you can use the Label Printer to print screen shot data from the unit (see 10-6 Sending a Screen Shot). See the users guide that comes with your Label Printer for details on how to perform this operation.
The operation described above can be performed using the following Label Printer models: KL-2000, KL-2700, KL-8200, KL-8700 (as of February 1999).
uTo connect the unit to a Label Printer 1. Check to make sure that the power of the unit and the Label Printer is off.
2. Connect the cable to the Label Printer.
3. Remove the cover from the connector of the unit.
4. Connect the other end of the cable to the unit.
5. Turn on the power of the unit, followed by the Label Printer.
After you finish data communications, turn off power in the sequence: the unit first, and then the Label Printer. Finally, disconnect the equipment.
Label Printer
Cable
# Be sure you keep the connector cover in a safe place so you can replace it after you
finish your data communications.
19990401
10-3 Connecting the Unit to a Personal Computer
To transfer data and screen shots between the unit and a personal computer, you must connect them through a separately available CASIO FA-123 Connection Kit.
For details on operation, the types of computer that can be connected, and hardware limitations, see the users manual that comes with the FA-123.
Some types of data may not be able to be exchanged with a personal computer.
u To connect the unit to a personal computer 1. Check to make sure that the power of the unit and the personal computer is off.
2. Connect the personal computer to the FA-123 Connection Kit.
3. Remove the cover from the connector of the unit.
4. Connect the unit to the FA-123 Connection Kit.
5. Turn on the power of the unit, followed by the personal computer.
10-3-1 Connecting the Unit to a Personal Computer
# The ALGEBRA calculator also supports to PC transfer of programs created with a CASIO CFX-9850 Series calculator.
# Be sure you keep the connector cover in a safe place so you can replace it after you finish your data communications.
After you finish data communications, turn off power in the sequence: the unit first, and then the personal computer. Finally, disconnect the equipment.
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10-4 Performing a Data Communication Operation
From the Main Menu, enter the LINK Mode. The following data communication main menu appears on the display.
{TRNS}/{Recv} ... menu of {send settings}/{receive settings}
Communication parameters are fixed at the following settings.
Speed (BPS): 38.4 kbps (sending a data)
9,600bps (sending a screen shot)
Parity (PARITY): NONE
kPerforming a Data Transfer Operation
Connect the two units and then perform the following procedures.
Receiving unit
To set up the calculator to receive data, press 2(Recv) while the data communication main menu is displayed.
The calculator enters a data receive standby mode and waits for data to arrive. Actual data receive starts as soon as data is sent from the sending unit.
10-4-1 Performing a Data Communication Operation
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Sending unit
To set up the calculator to send data, press 1(TRNS) while the data communication main menu is displayed.
Press the number key that corresponds to the type of data you want to send.
{Select} ... {selects data items and sends them}
{Currnt} ... {selects data items from among previously selected data items and sends them}
{Backup} ... {sends all memory contents, including mode settings}
{H-Copy} ... {selects H-Copy screen shot data and sends it}
u To send selected data items Press b(Select) or c(Currnt) to display a data item selection screen.
{Sel} ... {selects data item where cursor is located}
{All} ... {selects all data}
{Trns} ... {sends selected data items}
Use the f and c cursor keys to move the cursor to the data item you want to select and press 1(Sel) to select it. Currently selected data items are marked with '. Pressing 6 (Trns) sends all the selected data items.
To deselect a data item, move the cursor to it and press 1(Sel) again.
Only items that contain data appear on the data item selection screen. If there are too many data items to fit on a single screen, the list scrolls when you move the cursor to the bottom line of the items on the screen.
10-4-2 Performing a Data Communication Operation
19990401
uTo execute a send operation After selecting the data items to send, press 6(Trns). A message appears to confirm that you want to execute the send operation.
w(Yes) ... sends data
i(No)... returns to data selection screen
Press w(Yes) to send the data.
You can interrupt a data operation at any time by pressing A.
The following shows what the displays of the sending and receiving units look like after the data communication operation is complete.
Sending Unit Receiving Unit
Press i to return to the data communication main menu.
10-4-3 Performing a Data Communication Operation
19990401
u To send backup data This operation allows you to send all memory contents, including mode settings.
While the transmit data type selection menu is on the screen, press d(Backup), to display the screen shown below.
Press w(Yes) to start the send operation.
The following shows what the displays of the sending and receiving units look like after the data communication operation is complete.
Sending Unit Receiving Unit
Press i to return to the data communication main menu.
10-4-4 Performing a Data Communication Operation
# Data can become corrupted, necessitating a RESET of the receiving unit, should the connecting cable become disconnected during data transfer.
Make sure that the cable is securely connected to both units before performing any data communi- cation operation.
19990401
10-5 Data Communications Precautions The following are the types of data items that can be sent.
Data Item Contents Overwrite Password Check*1 Check*2
Program names Program contents Yes Yes(All programs are listed.)
Mat n Matrix memory (A to Z) contents Yes
List n List memory (1 to 20) contents Yes
File n List file memory (1 to 6) contents Yes
Y=Data Graph expressions, graph write/ non-write status, V-Window contents, No zoom factors
G-Mem n Graph memory (1 to 20) contents Yes
V-Win n V-Window memory contents No
Picture n Picture (graph) memory (1 to 20) data No
DynaMem Dynamic Graph functions Yes
Equation Equation calculation coefficient values No
Alpha Memory Variable memory contents No
F-Mem n Function memory contents No
CAS CAS formula data contents (ALGEBRA FX 2.0 PLUS only) No
Algebra Algebra data contents (ALGEBRA FX 2.0 PLUS only) No
DIFF Equation Differencial Equation data No
E-CON Data E-CON data No
Add-in application Add-in application data Nonames (All add-in applications are listed.)
*1 No overwrite check: If the receiving unit already contains the same type of data, the existing data is overwritten with the new data.
With overwrite check: If the receiving unit already contains the same type of data, a message appears to ask if the existing data should be overwritten with the new data.
10-5-1 Data Communications Precautions
Data item name
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1(YES) ... {replaces the receiving units existing data with the new data}
6(NO) ... {skips to next data item}
*2 With password check: If a file is password protected, a message appears asking for input of the password.
2
After inputting the password, press w.
Note the following precautions whenever you perform data communications.
An error occurs whenever you try to send data to a receiving unit that is not yet standing by to receive data. When this happens, press i to clear the error and try again, after setting up the receiving unit to receive data.
An error occurs whenever the receiving unit does not receive any data approximately six minutes after it is set up to receive data. When this happens, press i to clear the error.
An error occurs during data communications if the cable becomes disconnected, if the parameters of the two units do not match, or if any other communications problem occurs. When this happens, press i to clear the error, then correct the problem before trying data communications again. If data communications are interrupted by the i key operation or an error, any data successfully received up to the interruption will be in the memory of the receiving unit.
An error occurs if the receiving unit memory becomes full during data communications. When this happens, press i to clear the error and delete unneeded data from the receiving unit to make room for the new data, and then try again.
The E-CON item contains the following data.
1. Current Setup Data 2. Setup Memory Data 3. Custom Probe Memory Data
The corresponding data is overwritten on the receiver. Setup Memory data and Custom Probe Memory data overwrites the data for the same memory number on the receiver. If you want to keep data from being overwritten on the receiver, change its memory number.
10-5-2 Data Communications Precautions
20010102
Name of password protected file
Password input field
20 1 1
19990401
10-6 Sending a Screen Shot Use the following procedures to send a hardcopy of the screen directly to a connected personal computer (or CASIO Label Printer) or to save a screen shot in memory to send later. Screen shots can also be sent to a CASIO Label Printer.
Use the LINK Mode set up (u3(SET UP)) to specify whether you want to send the screen shot now or save it in memory.
u H-Copy {Dirct}/{Mem} ............. {direct send}/{save}
uTo send a screen shot directly to a connected computer (or CASIO Label Printer) (Direct) 1. Connect the unit to the computer (or CASIO Label Printer).
On the computer (or CASIO Label Printer), perform the procedures required to set it up to receive data.
2. Display the screen you want to send.
3. Press u6(H-COPY).
uTo save a screen shot in memory (Memory) 1. Display the screen you want to save.
2. Press u6(H-COPY).
You can store up to 20 screen shots in memory. Saved screen shots are automatically assigned file names from Hcopy1 to Hcopy20.
10-6-1 Sending a Screen Shot
# You cannot send the following types of screens to a computer or a Label Printer. The screen that appears while a data
communication operation is in progress. A screen that appears while a calculation is
in progress. The screen that appears following the reset
operation. The low battery message.
# The flashing cursor is not included in the screen image that is sent from the unit.
# You cannot use 6mm wide tape to print a screen shot of a graph.
19990401
uTo send a saved screen shot to a computer or CASIO Label Printer 1. Connect the unit to the computer (or CASIO Label Printer). On the computer (or CASIO
Label Printer), perform the procedures required to set it up to receive data.
2. In the LINK Mode, press 1(TRNS)e(H-Copy) to display the list of screen shots in memory.
3. Use the f and c cursor keys to highlight the name of the screen shot you want to send, and then press 6(Trns).
10-6-2 Sending a Screen Shot
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10-7-1 Add-ins
10-7 Add-ins Add-in capabilities let you install separately available applications and other software to tailor the calculator to suit your particular needs. Add-ins are installed from a computer using the data communication described on page 10-4-1. The following are the types of software that can be installed as add-ins.
u Add-in Application
After you install an application, its icon appears in the Main Menu, and you can run it just as you would a built-in application.
u Built-in Application Upgrades
These are upgrades for the applications that are pre-programmed in the calculators ROM.
u On-screen Message Language Data
This data is required to display on-screen messages in other languages. Installing this data causes all on-screen messages to appear in the corresponding language.
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10-8-1 MEMORY Mode
10-8 MEMORY Mode This calculator has two separate memory areas: a current area and a storage area. The current area is a work area where you can perform input data, perform calculations and run programs. Data in the current area is relatively safe, but it can be deleted when batteries go dead or when you perform a full reset.
The storage area uses flash memory, so data is safe even when power is interrupted. Normally, you would use the storage area for data you need to store securely for long periods and load it into the current area only when you need it.
Use the MEMORY Mode to transfer data between the current area and storage area, and to perform other memory management operations.
From the Main Menu, select the MEMORY icon to enter the MEMORY Mode and display its initial screen.
{PROG} ...... {program file save, load, delete, search}
{BACK} ...... {current area data backup and restore}
{OPT} ......... {optimization of the storage area}
k Storing and Loading Program Files
Use the following procedures to store a current area program file into the storage area, and to load a file from the storage area into the current area.
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u To store a program file into the storage area 1. On the initial MEMORY Mode screen press 1(PROG).
This displays a list of program files that are in the current area.*1
2. Select the program file you want to store.
Use the cursor f and c keys to highlight the name of the program file you want to store, and then press 1(SEL).
3. Press 5(SAVE).
The message Complete! appears when the store operation is finished.
Press i to return to the screen displayed in step 1.
A Memory ERROR occurs and the store operation is terminated if the storage area becomes full.
The following message appears if there is already a program file in the storage area with the same name as the program file you are trying to save.
Press w(Yes) to save the new program file, or i(No) to cancel the save operation.
10-8-2 MEMORY Mode
*1This screen appears as shown to the right if there are no program files in the current area when you start the save operation.
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19990401
u To load a program file from the storage area 1. On the initial MEMORY Mode screen press 1(PROG).
2. Press 6(STRG).
This displays a list of program files that are in the storage area. *1
3. Select the program file you want to load.
Use the cursor f and c keys to highlight the name of the program file you want to load, and then press 1(SEL).
4. Press 5(LOAD).
The message Complete! appears when the load operation is finished.
Press i to return to the screen displayed in step 1.
A Memory ERROR occurs and the load operation is terminated if the current area becomes full.
The following message appears if there is already a program file in the current area with the same name as the program file you are trying to load.
Press w(Yes) to load the new program file, or i(No) to cancel the load operation.
*1The screen appears as shown below if there are no program files in the storage area when you start the load operation.
10-8-3 MEMORY Mode
19990401
kDeleting Program Files
Use the following procedures to delete individual files or all files in the current area or storage areas.
u To delete a current area program file 1. On the initial MEMORY Mode screen press 1(PROG).
This displays a list of program files that are in the current area.
2. Use the cursor f and c keys to highlight the name of the program file you want to delete, and then press 2(DEL).
Press w(Yes) to delete the program file.
Press i(No) to cancel the delete operation.
u To delete a storage area program file 1. On the initial MEMORY Mode screen press 1(PROG).
2. Press 6(STRG).
This displays a list of program files that are in the storage area.
3. Use the cursor f and c keys to highlight the name of the program file you want to delete, and then press 2(DEL).
Press w(Yes) to delete the program file.
Press i(No) to cancel the delete operation.
u To delete all the program files in the current area 1. On the initial MEMORY Mode screen press 1(PROG).
This displays a list of program files that are in the current area.
2. Press 3(DELA).
Press w(Yes) to delete all the program files in the current area.
Press i(No) to cancel the delete operation.
10-8-4 MEMORY Mode
19990401
u To delete all the program files in the storage area 1. On the initial MEMORY Mode screen press 1(PROG).
2. Press 6(STRG).
This displays a list of program files that are in the storage area.
3. Press 3(DELA).
Press w(Yes) to delete all the program files in the storage area.
Press i(No) to cancel the delete operation.
k Searching for a Program File
Use the following procedures to search for a specific program file in the current area or in the storage area.
u To search for a program file in the current area *1
Example To search for all program files in the current area whose names begin with the letter C
1. On the initial MEMORY Mode screen press 1(PROG).
This displays a list of program files that are in the current area.
2. Press 4(SRC).
Input the letter C for the keyword.
The first program file name that begins with the letter C appears highlighted on display.
10-8-5 MEMORY Mode
*1 You can input up to eight characters for the keyword.
The message Not Found appears if there are no program file names that match your keyword.
19990401
u To search for a program file in the storage area
Example To search for all program files in the storage area whose names begin with the letter S
1. On the initial MEMORY Mode screen press 1(PROG).
2. Press 6(STRG).
This displays a list of program files that are in the storage area.
3. Press 4(SRC).
Input the letter S for the keyword.
The first program file name that begins with the letter S appears highlighted on display.
Press c or 1(SRC) to highlight the next file name that matches your keyword.
Press f to highlight the previous file name that matches your keyword.
The message Not Found appears if there are no program file names that match your keyword.
Press i to exit the search.
10-8-6 MEMORY Mode
19990401
kBacking Up Current Area Data
You can back up all the data in the current area and store it in the storage area. Later you can restore the backed up data to the current area when necessary.
u To back up current area data 1. On the initial MEMORY Mode screen press 2(BACK).
Screen A appears if there is already backup data in the storage area. Screen B appears if there is no backup data in the storage area.
Screen A Screen B
2. Press 1(SAVE) to backup the data.
The message Complete! appears when the backup operation is finished.
Press i to return to the screen displayed in step 1.
The following message appears if there is already backup data in the storage area.
Press w(Yes) to back up the data, or i(No) to cancel the backup operation.
A Memory ERROR occurs when there is not enough space available in the storage area to complete the backup operation.
10-8-7 MEMORY Mode
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19990401
u To restore backup data to the current area 1. On the initial MEMORY Mode screen press 2(BACK).
On the screen that appears, you can confirm whether or not there is backup data in the storage area.
2. Press 2(LOAD).
A message appears to confirm whether or not you really want to restore the backed up data.
Press w(Yes) to restore the data and delete any data currently in the area.
Press i(No) to cancel the data backup operation.
The message Complete! appears when the restore operation is finished.
Press i to return to the screen displayed in step 1.
u To delete backup data from the storage area 1. On the initial MEMORY Mode screen press 2(BACK).
On the screen that appears, you can confirm whether or not there is backup data in the storage area.
2. Press 3(DEL).
A message appears to confirm whether or not you really want to delete the backed up data.
Press w(Yes) to delete the backed up data from the storage area.
Press i(No) to cancel the backup data delete operation.
The message Complete! appears when the delete operation is complete.
Press i to return to the screen displayed in step 1, which now contains the message No Backup Data.
10-8-8 MEMORY Mode
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19990401
kOptimizing the Storage Area
Storage area memory can become fragmented after many store and load operations. Fragmentation can cause blocks of memory to become unavailable for data storage. Because of this, you should periodically perform the storage area optimization procedure, which rearranges the data in the storage area and makes memory usage more economical.
u To optimize the storage area On the initial MEMORY Mode screen press 3(OPT) to start storage area optimization.
The message Complete! appears when the optimize operation is complete.
Press i to return to the initial MEMORY Mode screen.
10-8-9 MEMORY Mode
19990401
Appendix 1 Error Message Table
2 Input Ranges
3 Specifications 4 Index
5 Key Index
6 P Button (In case of hang up)
7 Power Supply
19990401
Meaning
Illegal syntax Attempt to input an illegal
command
Calculation result exceeds the display range.
Calculation is outside the input range of a function.
Mathematical error (division by zero, etc.)
Sufficient precision could not be obtained for calculation, differential calculation, etc.
Solution could not be obtained for equation calculation, etc.
1 No corresponding Lbl n for Goto n.
2 No program stored in program area Prog file name.
Nesting of subroutines by Prog file name exceeds 10 levels.
Execution of calculations that exceed the capacity of the stack for numeric values or stack for commands.
Message
Syntax ERROR
Ma ERROR
Go ERROR
Nesting ERROR
Stack ERROR
Countermeasure
Press i to display the error and make necessary correc- tions.
Check input values and make corrections to ensure that values are within allowable limits.
1 Correctly input a Lbl n to corres- pond to the Goto n , or delete the Goto n if not required.
2 Store a program in program area Prog file name, or delete the Prog file name if not required.
Ensure that Prog file name is not used to return from subroutines to main routine. If used, delete any unnecessary Prog file name.
Trace the subroutine jump destinations and ensure that no jumps are made back to the original program area. Ensure that returns are made correctly.
Simplify the formulas to keep stacks within 10 levels for the numeric values and 26 levels for the commands.
Divide the formula into two or more parts.
-1-1 Error Message Table
1 Error Message Table
19990401
MeaningMessage Countermeasure
-1-2 Error Message Table
Memory ERROR
Argument ERROR
Dimension ERROR
Range ERROR
Condition ERROR
Non-Real ERROR
Operation or memory storage operation exceeds remaining memory capacity.
Incorrect argument specification for a command that requires an argument.
Illegal dimension or list used during matrix calculations.
1 Input of an improper V-Window value.
2 V-Window range settings exceeded when a graph is redrawn.
3 Input of an improper value on the range screen and use of that value for execution.
Execution of a calculation or function before all conditions required for execution are met.
1 Calculation that produces a complex number when Real is specified for the Complex Mode setting on the SET UP screen, even though the argument is a real number.
2 Calculation that produces a complex number when Real is specified for the Answer Type setting on the SET UP screen, even though the argument is a real number. (ALGEBRA FX 2.0 PLUS only)
Keep the number of variables you use for the operation within the number of variables currently available.
Simplify the data you are trying to store to keep it within the available memory capacity.
Delete no longer needed data to make room for the new data.
Correct the argument.
Check the matrix or list dimension.
1 Change the V-Window value so it is within range.
2 Redraw using the proper settings.
3 Input a proper range value.
Check the conditions and make any necessary corrections.
1 Change the Complex Mode setting to something other than Real.
2 Change the Answer Type setting to something other than Real. (ALGEBRA FX 2.0 PLUS only)
2001 1 2
19990401
-1-3 Error Message Table
MeaningMessage Countermeasure
Complex Number In List
Complex Number In Matrix
Cant Solve! Adjust Initial Value Or Bounds. Then Try Again
No Variable
Iteration ERROR
Com ERROR
Transmit ERROR
Receive ERROR
Memory Full
List containing complex number used in a calculation or operation for which complex number data is invalid.
Matrix containing complex number used in a calculation or operation for which complex number data is invalid.
Solve could not obtain a solution within the specified range.
No variable specified within a graph function being used for Dynamic Graph.
No variable within a Solve equation.
1 No convergence of Solve solutions.
2 No integration or differential calculation solution that satisfies operation ending condition (tol value).
Problem with cable connection or parameter setting during program data communications.
Problem with cable connection or parameter setting during data communications.
Problem with cable connection or parameter setting during data communications.
Memory of receiving unit became full during program data communications.
Change all data in the list to real numbers.
Change all data in the matrix to real numbers.
Change the specified range. Correct the input expression.
Specify a variable for the graph function.
1 Change the initial estimated value to one that is nearer to the solution.
2 Increase the tol value to reduce precision.
Check the cable connection.
Check the cable connection.
Check the cable connection.
Delete some data stored in the receiving unit and try again.
12
19990401
-1-4 Error Message Table
MeaningMessage Countermeasure
Download ERROR
Model Mismatch
Overflow ERROR *
Domain ERROR *
Data communication cable disconnect during add-in installation, or incorrect data transfer conditions.
Attempt to perform back up between two different models.
Overflow of the calculation range in the Algebre Mode.
Overflow of the input element range in the Algebre Mode.
Press w and try again. Press i and try again.
Use two identical models.
Correct the input expression.
Correct the input expression.
2001 1 2
* ALGEBRA FX 2.0 PLUS only
19990401
-2-1 Input Ranges
2 Input Ranges
sinx cosx tanx
sin1x cos1x
tan1x
sinhx coshx
tanhx
sinh1x
cosh1x
tanh1x
logx Inx
10x
ex
x
x2
1/x
3 x
x!
nPr nCr
As a rule, precision is 1 at the 10th digit.*
"
"
"
"
"
"
"
"
"
However, for tanx: |x| G 90(2n+1):DEG |x| G /2(2n+1):RAD |x| G 100(2n+1):GRA * Complex numbers can be
used as arguments.
* Complex numbers can be used as arguments.
* Complex numbers can be used as arguments.
* Complex numbers can be used as arguments.
* Complex numbers can be used as arguments.
* Complex numbers can be used as arguments.
* Complex numbers can be used as arguments.
* Complex numbers can be used as arguments.
(DEG) |x| < 9 (109) (RAD) |x| < 5 107rad (GRA) |x| < 1 1010grad
|x| < 1
|x| < 1 10100
|x| < 230.2585092
|x| < 1 10100
|x| < 5 1099
1< x < 5 1099
|x| < 1
1 1099 < x < 1 10100
1 10100 < x < 100
1 10100
< x < 230.2585092
0 < x < 1 10100
|x| <1 1050
|x| < 1 10100, x G 0
|x| < 1 10100
0 < x < 69 (x is an integer)
Result < 1 10100
n, r (n and r are integers) 0 < r < n, n < 1 1010
15 digits
"
"
"
"
"
"
"
"
"
Function Input range for real number solutions
Internal digits
Precision Notes
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19990401
-2-2 Input Ranges
Pol (x, y)
Rec (r ,)
^(x y)
x y
ab/c
15 digits
"
"
"
"
"
As a rule, precision is 1 at the 10th digit.*
"
"
"
"
"
However, for tan : | | G 90(2n+1):DEG | | G /2(2n+1):RAD | | G 100(2n+1):GRA
|r| < 1 10100
(DEG) | | < 9 (109) (RAD) | | < 5 107 rad (GRA) | | < 1 1010grad
|a|, b, c < 1 10100
0 < b, c
|x| < 1 10100
Sexagesimal display: |x| < 1 107
x > 0: 1 10100 < y logx < 100 x = 0 : y > 0 x < 0 :
1y = n, (n is an integer 2n+1 or a fraction)
However;
1 10100 < y log |x| < 100
y > 0 : x G 0 11 10100 < logy < 100x
y = 0 : x > 0 1y < 0 : x = 2n +1, n
(n G 0, n is an integer or a fraction) However;
11 10100 < log |y| < 100x
Total of integer, numerator and denominator must be within 10 digits (includes division marks).
*For a single calculation, calculation error is 1 at the 10th digit. (In the case of exponential display, calculation error is 1 at the last significant digit.) Errors are cumulative in the case of consecutive calculations, which can also cause them to become large. (This is also true of internal consecutive calculations that are performed in the case of ^(xy), x y, x!, 3 x, nPr, nCr, etc.) In the vicinity of a functions singular point and point of inflection, errors are cumulative and may become large.
Function Input range for real number solutions
Internal digits
Precision Notes
< 1 10100x2 + y2
* Complex numbers can be used as arguments.
* Complex numbers can be used as arguments.
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19990401
-2-3 Input Ranges
Function
Binary, octal, decimal, hexadecimal calculation
Input range
Values fall within following ranges after conversion: DEC: 2147483648 < x < 2147483647 BIN: 1000000000000000 < x
< 1111111111111111 (negative) 0 < x < 0111111111111111 (0, positive)
OCT: 20000000000 < x < 37777777777 (negative) 0 < x < 17777777777 (0, positive)
HEX: 80000000 < x < FFFFFFFF (negative) 0 < x < 7FFFFFFF (0, positive)
19990401
-3-1 Specifications
3 Specifications Variables: 28
Calculation range:
1 1099 to 9.999999999 1099 and 0. Internal operations use 15-digit mantissa.
Exponential display range: Norm 1: 102 > |x|, |x| > 1010
Norm 2: 109 > |x|, |x| > 1010
Program capacity: 144 kbytes (max.)
Power supply:
Main: Four AAA-size batteries (LR03 (AM4) or R03 (UM-4))
Back-up: One CR2032 lithium battery
Power consumption: 0.2 W
Approximate battery life
Main (ALGEBRA FX 2.0 PLUS):
LR03 (AM4): 230 hours (continuous display of main menu)
150 hours continuous operation (5 minutes calculation, 55 minutes display)
R03 (UM-4): 140 hours (continuous display of main menu)
90 hours continuous operation (5 minutes calculation, 55 minutes display)
Main (FX 1.0 PLUS):
LR03 (AM4): 200 hours (continuous display of main menu)
140 hours continuous operation (5 minutes calculation, 55 minutes display)
R03 (UM-4): 120 hours (continuous display of main menu)
80 hours continuous operation (5 minutes calculation, 55 minutes display)
Back-up: 2 years
Auto power off:
Power is automatically turned off approximately six minutes or 60 minutes after last operation.
Ambient temperature range: 0 C to 40 C
Dimensions: 19.5 mm (H) 82 mm (W) 178 mm (D) 3/4" (H) 3 1/4" (W) 6 7/8" (D)
Weight: Approx. 213 g (including batteries)
2001 1 2
19990401
-3-2 Specifications
Data Communications
Method: Start-stop (asynchronous), half-duplex
Transmission speed (BPS): 38400 bits/second (normal)
9600 bits/second (H-Copy & Send/Receive)
Parity: None
Bit length: 8 bits
Stop bit:
Send: 3 bits
Receive: 2 bits
Includes parity (None) 1-bit
X ON/X OFF Control: None
19990401
Symbols
AList .................................................. 3-2-7
calculation .....................................2-5-10
A
Absolute value .................................. 2-6-2
Add-ins ........................................... 10-7-1
Algebra Mode ................................... 7-2-1
Algebra Mode operation ................... 7-1-3
Angle unit ................................ 2-3-1, 2-4-2
Ans ................................................... 2-2-5
Answer function ................................ 2-2-5
Answer memory ...................... 2-2-5, 7-1-7
APO settings ..................................... 9-3-1
Argument ...........................................2-6-2
Arithmetic calculations ...................... 2-1-1
Asymptotes ................................... 5-11-21
Auto Mode ........................................ 7-3-8
Auto power off ......................... 9-3-1, -7-5
Axis of symmetry .......................... 5-11-20
B
Backing up data .............................. 10-8-7
Backup data, sending ..................... 10-4-4
Bar graph ...........................................6-2-1
Binary calculation ..............................2-7-1
Bitwise operation .............................. 2-7-4
Box zoom ...........................................5-2-7
Broken line graph .............................. 6-2-3
C
Calc window.....................................5-2-12
Calculation execution indicator ......... 1-2-5
Calculation priority sequence ........... 2-1-3
Calculation results of a paired-variable graph............................... 6-3-11, 6-4-2
Calculation results of a single-variable graph ................................ 6-2-4, 6-4-2
CAS Mode ........................................ 7-1-1
Catalog ............................................. 1-3-5
Cell, editing ....................................... 3-1-3
Center ............................................ 5-11-19
Circle ................................................ 5-1-5
Clipboard ...........................................1-3-4
Column operations ........................... 2-8-9
Combination ..................................... 2-4-9
Comments ...................................... 5-10-3
Complex number calculations .......... 2-6-1
Composite function ................. 2-1-3, 5-3-3
Conic section ................................ 5-11-17
CONICS Mode .................................. 5-1-5
Conjugate complex number .............. 2-6-3
Connecting the unit to a personal computer ................................... 10-3-1
Connecting the unit with a CASIO Label Printer ....................................... 10-2-1
Connecting two units ...................... 10-1-1
Continuous calculations .......... 2-2-5, 7-1-7
Contrast adjustment ......................... 9-3-1
Coordinate conversion ............ 2-4-2, 2-4-8
Coordinate rounding ........................ 5-11-7
Coordinates for given points .......... 5-11-13
Coordinates on a grah line .............. 5-11-1
Copy range ....................................... 1-3-4
Copying a regression graph formula ................................................... 6-3-11
Copying a table column to a list ........ 5-7-8
Corrections ....................................... 1-3-4
Cubic regression graph ..................... 6-3-7
-4-1 Index
4 Index
200111
19990401200111
-4-2 Index
Current area ................................... 10-8-1
D
Data communication operation ........10-4-1
DATA ERROR message ................... -6-1
Debugging ........................................ 8-3-1
Decimal calculations ......................... 2-7-1
Decimal places ....................... 2-1-2, 2-3-1
Degrees/minutes/seconds ...... 1-2-5, 2-4-2
Derivative item ...................... 5-7-3, 5-11-3
Determinant .....................................2-8-18
Differential calculations ..................... 2-5-2
Directrix ......................................... 5-11-20
Display format ................................... 2-3-1
Display screens ................................ 1-2-3
Draw/non draw status of a graph ...... 5-3-6
Drawing a line ..................................5-10-1
Dual graph ........................................ 5-5-1
DYNA Mode ...................................... 5-8-1
Dynamic graph ..................................5-8-1
Dynamic graph functions in a program .................................................... 8-6-5
Dynamic graph memory ................... 5-8-6
E
Eccentricity .................................... 5-11-21
Editing calculations ........................... 1-3-1
Ellipse ............................................... 5-1-5
Eng ....................................... 2-3-2, 2-4-11
Eqn memory ..................................... 7-1-6
EQUA Mode ...................................... 4-1-1
Error message ........................ 2-1-5, -1-1
Estimated value ................................ 6-4-4
Exponential function ......................... 2-4-4
Exponential regression graph ........... 6-3-8
F
Factor zoom ...................................... 5-2-9
File name, editing ..............................8-4-2
File name, registering ............. 8-1-1, 8-1-2
Flash memory ..................................10-8-1
FMEM ............................................... 2-2-2
Focus ............................................. 5-11-18
Formula memory .............................. 7-1-4
Formula number area ....................... 7-1-1
Fraction ................................. 1-2-5, 2-4-10
Freehand drawing ............................5-10-5
Function analysis ............................. 5-11-1
Function memory .................... 2-2-2, 7-1-6
Function menu ...................... 1-2-3, 5-2-11
Function, edit/change/delete ............ 5-3-5
G
Generating a table ............................ 5-7-2
Graph background .......................... 5-10-7
Graph function, recall ....................... 5-3-7
Graph functions in a program ........... 8-6-3
Graph functions, store ...................... 5-3-7
Graph memory ........................ 5-3-7, 7-1-6
Graph parameters, changing ............ 6-1-2
Graph screen .................................... 1-2-3
Graph to table .................................. 5-11-5
Graph type, specifying ...................... 5-3-1
Graph, store/recall ............................ 5-4-1
Graph-Table linking ......................... 5-7-15
GRPH TBL Mode ..............................5-1-1
H
Hexadecimal calculation ......... 1-2-5, 2-7-1
Higher degree equations .................. 4-2-1
19990401
-4-3 Index
Histogram ......................................... 6-2-1
Hyperbola ......................................... 5-1-5
Hyperbolic function (HYP) ...... 2-4-2, 2-4-5
I
Icon ................................................... 1-2-1
Imaginary part ................................... 2-6-3
Inequality ...........................................5-3-2
Input area ......................................... 7-1-1
Input ranges ...................................... -2-1
Inputting calculations ........................ 1-3-1
Integral value for a given range ..... 5-11-15
Integration calculation ....................... 2-5-7
Integration graph .............................. 5-6-3
Intercepts ....................................... 5-11-19
Inverse hyperbolic function ..... 2-4-2, 2-4-5
Inverse trigonometric function .......... 2-4-3
K
Key markings .................................... 1-1-3
Key table ........................................... 1-1-2
L
Latus rectum .................................. 5-11-18
Linear equation ..................................7-3-2
Linear inequality ............................... 7-3-2
Linear regression graph .................... 6-3-6
LINK Mode ...................................... 10-4-1
List data, manipulating ...................... 3-2-1
List data in the CAS Mode .................7-1-2
List files, switching ............................ 3-4-1
List sort functions in a program ........ 8-6-8
List, arithmetic calculations ............... 3-3-1
List, inputting and editing .................. 3-1-1
Logarithmic function ......................... 2-4-4
Logarithmic regression graph ........... 6-3-8
Logistic regression graph ................6-3-10
Low battery message ............. 1-8-2, -7-1
M
Main Memories ..................................9-2-1
Main screen ...................................... 5-5-1
Manual graphing ............................... 5-6-1
Manual Mode .................................... 7-3-6
MatAns ............................................. 2-8-1
Matrices using matrix commands ...................................... 2-8-10, 2-8-13
Matrix arithmetic operation ............. 2-8-17
Matrix Data in the CAS Mode ........... 7-1-2
Matrix inversion .............................. 2-8-19
Matrix row operations in a program .. 8-6-1
Matrix transposition .........................2-8-18
Matrix, dimension ................. 2-8-2, 2-8-12
Matrix, inputting and editing .............. 2-8-2
Maximum/minimum value calculation ...................................................2-5-12
Med-box graph ..................................6-2-2
Med-Med graph ................................ 6-3-6
Memory ............................................. 2-2-1
Memory capacity .............................. 2-1-6
Memory Mode ..................................10-8-1
Memory operations ........................... 9-2-1
Memory Usage ..................................9-2-1
Menu bar command .......................... 1-2-3
Mode set up ...................................... 1-7-1
Modified box graph ........................... 6-2-2
Multi-Replay ...................................... 1-3-3
Multiple graphs ................................6-3-12
Multiplication sign ..............................2-1-5
Multistatements ................................ 2-2-7
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19990401
-4-4 Index
N
Natural result display area .................7-1-1
Negative value .................................. 2-7-4
Norm 1/2 mode ....................... 1-2-4, 2-3-2
Normal display .............. 1-2-4, 2-1-2, 2-3-2
Normal distribution curve .................. 6-2-3
Normal probability distribution calculation ................................... 6-4-5
Normal probability plot ...................... 6-2-1
Number system ................................ 2-7-3
Number system transformation ......... 2-7-5
Numeric calculations (NUM) ............. 2-4-1
O
Octal calculations ..............................2-7-1
Optimizing the storage area............ 10-8-9
Option (OPTN) menu ........................ 1-4-1
Output area ....................................... 7-1-1
Overflow ............................................ 2-1-5
Overwrite the graphs ........................ 5-6-5
P
P button ............................................ -6-1
Paired-variable statistical graph ........ 6-3-1
Parabola ........................................... 5-1-5
Parametric function .......................... 5-3-2
Parentheses ...................................... 2-1-1
Password ...........................................8-4-3
Pasting text ....................................... 1-3-5
Permutation ...................................... 2-4-9
Picture memory ................................ 5-4-1
Plot ................................................... 5-1-4
Point of intersection of two graphs ................................................ 5-11-11
Polar coordinate function .................. 5-3-1
Polar form transformation ................. 2-6-4
POLY ................................................. 4-2-1
Power regression graph .................... 6-3-9
Power supply .................................... -7-1
PRGM Mode ..................................... 8-1-1
Probability distribution graph ............ 6-4-7
Probability/distribution calculations (PROB) ....................................... 2-4-1
Program (PRGM) menu .................... 1-6-1
Program file, load .............................10-8-3
Program file, searching ......... 8-4-1, 10-8-5
Program file, store .......................... 10-8-2
Program files, deleting .....................10-8-4
Program library ..................................8-8-1
Program mode command ................. 8-7-1
Program, BASE Mode ...................... 8-2-2
Program, deleting ..............................8-4-2
Program, editing ............................... 8-3-1
Program, inputting ............................ 8-2-1
Program, running .............................. 8-1-1
Program, searching for data ............. 8-3-4
Pull-up menu ..................................... 1-2-3
Q
Quadratic differential calculation ....... 2-5-5
Quadratic equation ........................... 7-3-2
Quadratic regression graph .............. 6-3-7
Quartic regression graph .................. 6-3-7
R
Radius ...........................................5-11-19
Raising a matrix to a power ............ 2-8-20
Random number ............................... 2-4-7
Real part ........................................... 2-6-3
Rectangular coordinate function ....... 5-3-1
Rectangular transformation .............. 2-6-4
RECUR Mode ................................... 5-9-1
200111
19990401200111
-4-5 Index
Recursion formula number table ...... 5-9-1
Recursion Table & Graph functions in a program ...................................... 8-6-7
Regression calculation ..................... 6-4-3
Regression graph ..............................6-3-3
Replay .................................... 1-3-3, 7-1-7
Reset ................................................ 9-4-1
Residual calculation .........................6-3-10
Root ................................................. 5-11-9
Row calculations ............................... 2-8-5
RUN MAT Mode ............................... 2-1-1
S
Scalar multiplication .......................... 2-8-6
Scatter diagram ................................ 6-3-1
Screen shot, saving .........................10-6-1
Screen shot, sending ...................... 10-6-1
Set up screen ................................... 1-7-1
Sexagesimal operations ......... 1-2-5, 2-4-2
Significant digits ...................... 2-1-2, 2-3-2
SIML ................................................. 4-1-1
Simultaneous linear equations .......................................... 4-1-1, 7-3-1
Single-variable statistical graph ........ 6-2-1
Sinusoidal regression graph ............. 6-3-9
Sketch ..............................................5-10-1
Solution Memory ............................... 7-1-8
Solve calculation ..................... 2-5-1, 4-3-1
Solve calculation function in a program .................................................... 8-6-9
Solve Mode ....................................... 7-3-4
Sorting list values ..............................3-1-5
Squaring a matrix ............................2-8-19
Stacks ............................................... 2-2-6
STAT Mode ....................................... 6-1-1
Statistical calculation data lists ......... 6-4-1
Statistical calculations and graphs in a program ...................................... 8-6-9
Statistical data list ..............................6-1-1
Storage area ................................... 10-8-1
Storage Memories ............................ 9-2-1
Sub-screen ....................................... 5-5-1
Submenu ...........................................1-2-3
System language setting .................. 9-3-2
SYSTEM Mode ..................................9-1-1
System setting menu ........................ 9-1-1
T
Table & Graph functions in a program .................................................... 8-6-6
Table range ....................................... 5-7-1
Table, deleting .................................. 5-7-7
Tables ............................................... 5-7-1
Tables, editing ................................... 5-7-5
Text display ....................................... 8-6-1
Text screen ....................................... 1-2-3
Trace ................................................ 5-11-1
Trigonometric function ...................... 2-4-3
TUTOR ............................................. 7-3-1
Tutorial lock ...................................... 9-5-1
Tutorial Mode .................................... 7-3-1
V
V-Window ......................................... 5-2-1
V-Window memory ........................... 5-2-4
Variable ............................................. 2-2-1
Variable data (VARS) menu .............. 1-5-1
Vector Data in the CAS Mode ........... 7-1-2
Verify Mode ....................................... 7-3-4
Vertex ............................................ 5-11-18
W
WEB graph ....................................... 5-9-7
19990401
X
X = constant expression ................... 5-3-2
xy line graph ..................................... 6-3-1
Z
Zoom ................................................ 5-2-7
-4-6 Index
2001 1 2
199904012001 1 2
-4-7 Index
CAS, ALGEBRA, TUTOR Command Index ........................................................7-1-16
.......................................................7-1-17
......................................................7-1-17
absExpand ...................................... 7-1-21
andConnect .....................................7-1-21
approx ..............................................7-1-15
arcLen ..............................................7-1-17
arrange ............................................. 7-2-1
cExpand ...........................................7-1-15
clear ................................................ 7-1-22
clearVarAll ....................................... 7-1-22
collect ..............................................7-1-14
combine ...........................................7-1-14
denominator .....................................7-1-18
diff ................................................... 7-1-16
eliminate ..........................................7-1-20
eqn ...................................................7-1-21
exchange .........................................7-1-20
expand ............................................. 7-1-11
expToTrig .........................................7-1-13
factor ................................................ 7-1-11
gcd ...................................................7-1-18
getRight ...........................................7-1-20
invert ............................................... 7-1-20
lcm ...................................................7-1-19
lim ................................................... 7-1-16
numerator ....................................... 7-1-18
rclAllEqn ..........................................7-1-19
rclEqn ..............................................7-1-19
replace ...............................................7-2-1
rewrite ..............................................7-1-19
rFactor ............................................. 7-1-11
simplify .............................................7-1-13
solve ............................................... 7-1-12
substitute .........................................7-1-14
tanLine .............................................7-1-18
taylor ............................................... 7-1-17
tCollect .............................................7-1-12
tExpand ...........................................7-1-12
trigToExp ..........................................7-1-13
(List Commands)
AList .................................................... 7-1-27
Augment .............................................. 7-1-28
Cuml .................................................... 7-1-26
Dim ...................................................... 7-1-23
Fill ........................................................ 7-1-28
List Mat ........................................... 7-1-30
List Vect .......................................... 7-1-30
Max ...................................................... 7-1-24
Mean.................................................... 7-1-24
Median ................................................. 7-1-25
Min ....................................................... 7-1-23
Percent ................................................ 7-1-26
Prod ..................................................... 7-1-26
Seq ...................................................... 7-1-28
SortA .................................................... 7-1-29
SortD ................................................... 7-1-29
StdDev ................................................. 7-1-27
SubList ................................................ 7-1-29
Sum ..................................................... 7-1-25
Variance ............................................... 7-1-27
(Matrix Commands)
`Row .................................................. 7-1-38
`Row+................................................ 7-1-38
Augment .............................................. 7-1-35
Det ....................................................... 7-1-31
Diag ..................................................... 7-1-37
Dim ...................................................... 7-1-31
19990401
EigVc ................................................... 7-1-32
EigVl .................................................... 7-1-32
Fill ........................................................ 7-1-35
Identify ................................................. 7-1-35
LU ........................................................ 7-1-34
Mat List ........................................... 7-1-37
Mat Vect .......................................... 7-1-37
Norm .................................................... 7-1-31
Ref ....................................................... 7-1-33
Row+ ................................................... 7-1-39
Rref ...................................................... 7-1-33
SubMat ................................................ 7-1-36
Swap.................................................... 7-1-38
Trn ....................................................... 7-1-34
(Vector Commands)
Angle ................................................... 7-1-41
Augment .............................................. 7-1-41
CrossP ................................................. 7-1-40
Dim ...................................................... 7-1-40
DotP .................................................... 7-1-40
Fill ........................................................ 7-1-41
Norm .................................................... 7-1-40
UnitV .................................................... 7-1-41
Vect List .......................................... 7-1-42
Vect Mat .......................................... 7-1-42
-4-8 Index
2001 1 2
19990401
-4-90 Index
PRGM Command Index Break ................................................ 8-5-6
ClrGraph .......................................... 8-5-11
ClrList ............................................... 8-5-11
ClrMat ..............................................8-5-12
ClrText .............................................8-5-12
DispF-Tbl, DispR-Tbl ...................... 8-5-12
Do~LpWhile ...................................... 8-5-5
DrawDyna ....................................... 8-5-12
DrawFTG-Con, DrawFTG-Plt ......... 8-5-13
DrawGraph ......................................8-5-13
DrawR-Con, DrawR-Plt ....................8-5-13
DrawR-Con, DrawR-Plt ...............8-5-14
DrawStat ..........................................8-5-14
DrawWeb .........................................8-5-14
Dsz ................................................... 8-5-9
For~To~(Step~)Next ......................... 8-5-4
Getkey .............................................8-5-15
Goto~Lbl ..........................................8-5-10
If~Then~(Else~)IfEnd ....................... 8-5-4
Isz .................................................... 8-5-11
Locate ..............................................8-5-16
Prog .................................................. 8-5-7
Receive ( /Send ( .............................8-5-17
Return ............................................... 8-5-8
Stop .................................................. 8-5-8
While~WhileEnd ............................... 8-5-6
? (Input Command) ........................... 8-5-2
^ (Output Command) ...................... 8-5-3
: (Multi-statement Command) ........... 8-5-3
_ (Carriage Return) ......................... 8-5-3
(Comment Text Delimiter) ............... 8-5-3
=, G, >, <, , (Relational Operators) .....................8-5-18
2001 1 2
19990401
-5-1 Key Index
5 Key Index
H-COPY
6
a
Key Primary Function Combined withu Combined with
Key Primary Function Combined with Combined with
a
! a
COPY
1
PASTE
2
SET UP
CAT/CAL
3 Selects 3rd function menu item. Shows the set up display.
Enters number 0. Toggles function menu display on and off.
Shows the Catalog or opens the Calc Window.
Displays View Window parameter input screen.
4 Selects 4th function menu item.
G T
5 Switches display between graph and text screens.
Selects 5th function menu item.
Selects 6th function menu item. Sends a shot of the current screen to a connected device.
! Activates shift functions of other keys and function menus.
u
V-Window
K
PRGM
J
Displays option menu.
Activates functions marked above function keys.
m Returns to the Main Menu.
A -LOCK
a Allows entry of alphanumeric characters shown in red.
Locks/Unlocks entry of alphanumeric characters.
r
x
Displays the variable data menu. Displays program command menu.
Enters character r.
M
Press between two values to make second value exponent of first.
Press between entering values for X & Y to show xth root of y.
Enters character .
QUIT
i Back steps to the previous screen without making any changes.
Returns directly to initial screen of the mode.
Selects 1st function menu item. Performs copy operation.
Selects 2nd function menu item. Performs paste operation.
19990401
-5-2 Key Index
H
x
Key Primary Function Combined with! Combined with a
e Moves cursor to right. Scrolls screen. Press after w to display calculation from beginning.
A
v Allows input of variable X, , and T.
Enters letter A.
10 x B
l Press before entering value to calculate common logalithm.
Press before entering exponent value of 10.
Enters letter B.
e x C
sin1 D
cos1 E
tan1 F
I Press before entering value to calculate natural logarithm.
Press before entering exponent value of e.
Enters letter C.
s Press before entering value to calculate sine.
Press before entering value to calculate inverse sine.
Enters letter D.
c Press before entering value to calculate cosine.
Press before entering value to calculate inverse cosine.
Enters letter E.
t Press before entering value to calculate tangent.
Press before entering value to calculate inverse tangent.
Enters letter F.
d/c G
$
Press between entering fraction values. Converts fraction to decimal.
Displays improper fractions. Enters letter G.
Enters letter H.
I
( Enters open parenthesis in formula.
Press before entering value to calculate cube root.
Enters letter I.
x 1 J
) Enters close parenthesis in formula.
Press after entering value to calculate reciprocal.
Enters letter J.
K
, Enters comma. Enters letter K.
L
a Assigns value to a value memory name.
Enters letter L.
M
h Enters number 7. Enters letter M.
N
i Enters number 8. Enters letter N.
3
Press after entering value to calculate square.
Press before entering value to calculate square root.
d Moves cursor to left. Scrolls screen. Press after w to display calculation from end.
f Moves cursor upward. Scrolls screen. Switches to previous function in trace mode.
c Moves cursor downward. Scrolls screen. Switches to next function in trace mode.
19990401
-5-3 Key Index
Key Primary Function Combined with! Combined with a
INS
D Deletes character at current cursor location.
Allows insertion of characters at cursor location.
OFF
o Turns power on. Clears the display.
Turns power off.
P
e Enters number 4. Enters letter P.
Q
f Enters number 5. Enters letter Q.
R
g Enters number 6. Enters letter R.
{ S
* Multiplication function. Enters open curly bracket. Enters letter S.
} T
/ Division function. Enters close curly bracket.
Inputs List command.
Inputs Mat command.
Enters letter T.
UList
Mat
b Enters number 1. Enters letter U.
V
c Enters number 2. Enters letter V.
W
d Enters number 3. Enters letter W.
[ X
+ Addition function. Specifies positive value.
Enters open bracket. Enters letter X.
] Y
- Subtraction function. Specifies negative value.
Enters close bracket.
Inputs imaginary number unit.
Enters letter Y.
i Z
a Enters number 0. Enters letter Z.
= SPACE
. Enters decimal point. Enters character =.
Enters a blank
Enters double quotation mark.
space.
E
Enables entry of exponent. Inputs value of pi. Enters pi symbol.
Ans
- Enter before value to specify as negative.
Recalls most recent calculation result.
_
w Displays result of calculation. Inputs a new line.
O
j Enters number 9. Enters letter O.
19990401
-6-1 P Button (In case of hang up)
6 P Button (In case of hang up) Pressing the P button resets the calculator to its initial defaults.
Warning!
Never perform this operation unless you want to totally clear the memory of the calculator. If you need the data currently stored in memory, be sure to write it down somewhere before performing the P button operation.
Pressing the P button while a calculation operation is being performed (while the calculator is performing a calculation internally) deletes all data in memory.
You can also reset the calculator using front panel key operations (see 9-4 Reset). Use the P button to reset only while the front panel keys are disabled for some reason.
uDATA ERROR Message A data error indicates that data in calculator memory is seriously corrupted. This can be due to exposure of the calculator to strong electrostatic charge, temperature extremes, high humidity, etc. A data error is indicated by appearance of the screen shown below.
Press the w key to reset the calculator.
The data error screen appears when you press the P button to reset the calculator or when you turn on calculator power.
Warning!
Pressing w deletes all data in calculator memory. If a data error occurs when you press w, it could mean that your calculator is malfunctioning. If the data error screen keeps appearing, press i to turn off power. Next, take the calculator to the retailer where you purchased it or to your local CASIO service provider.
P button
19990401
-7-1 Power Supply
7 Power Supply This calculator is powered by four AAA-size (LR03 (AM4) or R03 (UM-4)) batteries. In addition, it uses a single CR2032 lithium battery as a back up power supply for the memory.
If either of the following messages appears on the display, immediately turn off the calculator and replace main batteries or the back up battery as instructed.
If you try to continue using the calculator, it will automatically turn off in order to protect memory contents. You will not be able to turn power back on until you replace batteries.
Be sure to replace the main batteries at least once every two years, no matter how much you use the calculator during that time.
The batteries that come with this calculator discharge slightly during shipment and storage. Because of this, they may require replacement sooner than the normal expected battery life.
Warning!
All memory contents will be deleted if you remove both the main power supply and the memory back up batteries at the same time. If you ever remove both batteries, correctly reload them and then perform the reset operation.
19990401
kReplacing Batteries
Precautions:
Incorrectly using batteries can cause them to burst or leak, possibly damaging the interior of the calculator. Note the following precautions:
Be sure that the positive (+) and negative () poles of each battery are facing in the proper directions.
Never mix batteries of different types.
Never mix old batteries and new ones.
Never leave dead batteries in the battery compartment.
Remove the batteries if you do not plan to use the calculator for long periods.
Never try to recharge the batteries supplied with the calculator.
Do not expose batteries to direct heat, let them become shorted, or try to take them apart.
(Should a battery leak, clean out the battery compartment of the calculator immediately, taking care to avoid letting the battery fluid come into direct contact with your skin.)
Keep batteries out of the reach of small children. If swallowed, consult with a physician immediately.
uTo replace the main power supply batteries * Before replacing the main power supply batteries, turn on the calculator and check to see if
the Low Backup Battery! message appears on the display. If it does, replace the memory back up battery before replacing the main power supply batteries.
* Never remove the main power supply and the memory back up batteries from the calcula- tor at the same time.
* Never turn on the calculator while the main power supply batteries are removed or not loaded correctly. Doing so can cause memory data to be deleted and malfunction of the calculator. If mishandling of batteries causes such problems, correctly load batteries and then perform the RESET operation to resume normal operation.
* Be sure to replace all four batteries with new ones.
-7-2 Power Supply
19990401
1. Press !o(OFF) to turn off the calculator.
Warning!
* Be sure to turn the calculator off before replacing batteries. Replacing batteries with power on will cause data in memory to be deleted.
2. Making sure that you do not accidently press the o key, slide the case onto the calculator and then turn it over.
P
3. Remove the back cover from the calculator by 1
pulling with your finger at the point marked 1.
4. Remove the four old batteries.
5. Load a new set of four batteries, making sure that their positive (+) and negative () ends are facing in the proper directions.
BACK UP
6. Replace the back cover.
7. Turn the calculator front side up and slide off its case. Next, press o to turn on power.
-7-3 Power Supply
# Power supplied by memory back up battery while the main power supply batteries are removed for replacement retains memory contents.
# Do not leave the calculator without main power supply batteries loaded for long periods. Doing so can cause deletion of data stored in memory.
# If the figures on the display appear too light and hard to see after you turn on power, adjust the tint.
19990401
uTo replace the memory back up battery * Before replacing the memory back up battery, check to make sure the main batteries
are not dead.
* Never remove the main power supply and the memory back up batteries from the calculator at the same time.
* Be sure to replace the back up power supply battery at least once 2 years, regardless of how much you use the calculator during that time. Failure to do so can cause data in memory to be deleted.
1. Press !o(OFF) to turn off the calculator.
Warning!
* Be sure to turn the calculator off before replacing battery. Replacing battery with power on will cause data in memory to be deleted.
2. Making sure that you do not accidently press the o key, slide the case onto the calculator and then turn it over.
3. Remove the back cover from the calculator by 1
pulling with your finger at the point marked 1.
4. Remove screw i on the back of the calculator, and remove the back up battery compartment cover.
5. Insert a thin, pointed non-metal object (such as a toothpick) into the hole maked j and remove the old battery.
-7-4 Power Supply
P
AB
BACK UP
19990401
6. Wipe off the surfaces of a new battery with a soft, dry cloth. Load it into the calculator so that its positive (+) side is facing up.
7. Install the memory protection battery cover onto the calculator and secure it in place with the screw. Next, replace the back cover.
8. Turn the calculator front side up and slide off its case. Next, press o to turn on power.
kAbout the Auto Power Off Function
Calculator power turns off automatically if you do not perform any operation within the Auto Power Off trigger time you specify. You can specify either six minutes or 60 minutes as the trigger time (see APO Settings on page 9-3-1). To restore power, press o.
-7-5 Power Supply
BACK UP
20010101
ALGEBRA FX 2.0 PLUS FX 1.0 PLUS
(Additional Functions)
20010101
Advanced Statistics Application
1-1 Advanced Statistics (STAT) 1-2 Tests (TEST)
1-3 Confidence Interval (INTR)
1-4 Distribution (DIST)
1
Chapter
20010101
1-1 Advanced Statistics (STAT)
uFunction Menu
The following shows the function menus for the STAT Mode list input screen.
Pressing a function key that corresponds to the added item displays a menu that lets you select one of the functions listed below.
3(TEST) ... Test (page1-2-1)
4(INTR) ... Confidence interval (page1-3-1)
5(DIST) ... Distribution (page1-4-1)
SORT and JUMP functions are located in the TOOL menu (6(g)1(TOOL)).
uCalculation of the Coefficient of Determination (r2) and MSE
You can use the STAT Mode to calculate the coefficient of determination (r2) for quadratic regression, cubic regression, and quartic regression. The following types of MSE calculations are also available for each type of regression.
Linear Regression ... MSE = 1 n 2 i=1
n
(yi (axi+ b))2
Quadratic Regression ... MSE = 1 n 3 i=1
n
(yi (axi + bxi+ c))22
Cubic Regression ... MSE = 1 n 4 i=1
n
(yi (axi 3+ bxi + cxi +d ))22
Quartic Regression ... MSE = 1 n 5 i=1
n
(yi (axi 4+ bxi
3 + cxi + dxi
+ e))22
1-1-1 Advanced Statistics (STAT)
20010101
Logarithmic Regression ... MSE = 1 n 2 i=1
n
(yi (a + b ln xi ))2
Exponential Repression ... MSE = 1 n 2 i=1
n
(ln yi (ln a + bxi ))2
Power Regression ... MSE = 1 n 2 i=1
n
(ln yi (ln a + b ln xi ))2
Sin Regression ... MSE = 1 n 2 i=1
n
(yi (a sin (bxi + c) + d ))2
Logistic Regression ... MSE = 1 n 2 1 + ae-bxi
C i=1
n
yi 2
uEstimated Value Calculation for Regression Graphs
The STAT Mode also includes a Y-CAL function that uses regression to calculate the estimated y-value for a particular x-value after graphing a paired-variable statistical regression.
The following is the general procedure for using the Y-CAL function.
1. After drawing a regression graph, press 6(g)2(Y-CAL) to enter the graph selection mode, and then press w.
If there are multiple graphs on the display, use f and c to select the graph you want, and then press w.
This causes an x-value input dialog box to appear.
2. Input the value you want for x and then press w.
This causes the coordinates for x and y to appear at the bottom of the display, and moves the pointer to the corresponding point on the graph.
3. Pressing v or a number key at this time causes the x-value input dialog box to reappear so you can perform another estimated value calculation if you want.
1-1-2 Advanced Statistics (STAT)
1
20010101
4. After you are finished, press i to clear the coordinate values and the pointer from the display.
The pointer does not appear if the calculated coordinates are not within the display range.
The coordinates do not appear if [Off] is specified for the [Coord] item of the [SETUP] screen.
The Y-CAL function can also be used with a graph drawn by using DefG feature.
uRegression Formula Copy Function from a Regression Calculation Result Screen
In addition to the normal regression formula copy function that lets you copy the regression calculation result screen after drawing a statistical graph (such as Scatter Plot), the STAT Mode also has a function that lets you copy the regression formula obtained as the result of a regression calculation. To copy a resulting regression formula, press 6(COPY).
k Tests, Confidence Interval, and Distribution Calculations
The STAT Mode includes functions for performing tests, and confidence interval and distribution calculations. You can find explanations of each of these functions in the following sections: 1-2 Tests, 1-3 Confidence Interval, and 1-4 Distribution.
uParameter Settings
The following describes the two methods you can use to make parameter settings for test, confidence interval, and distribution calculations.
Selection With this method, you press the function key that corresponds to the setting you want to select from the function menu.
Value Input With this method, you directly input the parameter value you want to input. In this case, nothing appears in the function menu.
Pressing i returns to the list input screen, with the cursor in the same position it was at before you started the parameter setting procedure.
Pressing ! i(QUIT) returns to the top of list input screen.
Pressing w without pressing 1(CALC) under Execute item advances to calculation execution. To return to the parameter setting screen, press i, A, or w.
1-1-3 Advanced Statistics (STAT)
20010101
uCommon Functions
The symbol appears in the upper right corner of the screen while execution of a calculation is being performed and while a graph is being drawn. Pressing A during this time terminates the ongoing calculation or draw operation (AC Break).
Pressing i or w while a calculation result or graph is on the display returns to the parameter setting screen. Pressing ! i(QUIT) returns to the top of list input screen.
Pressing A while a calculation result is on the display returns to the parameter setting screen.
Pressing u 5(GT) after drawing a graph switches to the parameter setting screen (GT function). Pressing u 5(GT) again returns to the graph screen.
The GT function is disabled whenever you change a setting on the parameter setting screen, or when you perform a u 3(SET UP) or ! K(V-Window) operation.
You can perform the PICT menu's screen save or recall functions after drawing a graph.
The ZOOM function and SKETCH function are disabled.
The TRACE function is disabled, except for the graph display of two-way ANOVA.
The graph screen cannot be scrolled.
After drawing a graph, you can use a Save Result feature to save calculation results to a specific list. Basically, all items are saved as they are displayed, except for the first line title.
Each time you execute Save Result, any existing data in the list is replaced by the new results.
1-1-4 Advanced Statistics (STAT)
1
20010101
1-2 Tests (TEST) The Z Test provides a variety of different standardization-based tests. They make it possible to test whether or not a sample accurately represents the population when the standard deviation of a population (such as the entire population of a country) is known from previous tests. Z testing is used for market research and public opinion research, that need to be performed repeatedly.
1-Sample Z Test tests for the unknown population mean when the population standard deviation is known.
2-Sample Z Test tests the equality of the means of two populations based on independent samples when both population standard deviations are known.
1-Prop Z Test tests for an unknown proportion of successes.
2-Prop Z Test tests to compare the proportion of successes from two populations.
The t Test tests the hypothesis when the population standard deviation is unknown. The hypothesis that is the opposite of the hypothesis being proven is called the null hypothesis, while the hypothesis being proved is called the alternative hypothesis. The t-test is normally applied to test the null hypothesis. Then a determination is made whether the null hypothesis or alternative hypothesis will be adopted.
1-Sample t Test tests the hypothesis for a single unknown population mean when the population standard deviation is unknown.
2-Sample t Test compares the population means when the population standard deviations are unknown.
LinearReg t Test calculates the strength of the linear association of paired data.
2 Test tests hypothesis concerning the proportion of samples included in each of a number of independent groups. Mainly, it generates cross-tabulation of two categorical variables (such as yes, no) and evaluates the independence of these variables. It could be used, for example, to evaluate the relationship between whether or not a driver has ever been involved in a traffic accident and that persons knowledge of traffic regulations.
2-Sample F Test tests the hypothesis for the ratio of sample variances. It could be used, for example, to test the carcinogenic effects of multiple suspected factors such as tobacco use, alcohol, vitamin deficiency, high coffee intake, inactivity, poor living habits, etc.
ANOVA tests the hypothesis that the population means of the samples are equal when there are multiple samples. It could be used, for example, to test whether or not different combinations of materials have an effect on the quality and life of a final product.
One-Way ANOVA is used when there is one independent variable and one dependent variable.
Two-Way ANOVA is used when there are two independent variables and one dependent variable.
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The following pages explain various statistical calculation methods based on the principles described above. Details concerning statistical principles and terminology can be found in any standard statistics textbook.
On the initial STAT Mode screen, press 3(TEST) to display the test menu, which contains the following items.
3(TEST)b(Z) ... Z Tests (p. 1-2-2)
c(T) ... t Tests (p. 1-2-10)
d(2) ... 2 Test (p. 1-2-18)
e(F) ... 2-Sample F Test (p. 1-2-20)
f(ANOVA) ... ANOVA (p. 1-2-22)
k Z Tests
uZ Test Common Functions
You can use the following graph analysis functions after drawing a graph.
1(Z) ... Displays z score.
Pressing 1 (Z) displays the z score at the bottom of the display, and displays the pointer at the corresponding location in the graph (unless the location is off the graph screen). Two points are displayed in the case of a two-tail test. Use d and e to move the pointer. Press i to clear the z score.
2(P) ... Displays p-value.
Pressing 2 (P) displays the p-value at the bottom of the display without displaying the pointer. Press i to clear the p-value.
u1-Sample Z Test
This test is used when the population standard deviation is known to test the hypothesis. The 1-Sample Z Test is applied to the normal distribution.
Z = o 0
n
o : mean of sample o : assumed population mean : population standard deviation n : size of sample
# The following V-Window settings are used for drawing the graph. Xmin = 3.2, Xmax = 3.2, Xscale = 1, Ymin = 0.1, Ymax = 0.45, Yscale = 0.1
# Executing an analysis function automatically stores the z and p values in alpha variables Z and P, respectively.
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Perform the following key operations from the statistical data list.
3(TEST)
b(Z)
b(1-Smpl)
The following shows the meaning of each item in the case of list data specification.
Data ............................ data type
.................................. population mean value test conditions (G 0 specifies two-tail test, < 0 specifies lower one-tail test, > 0 specifies upper one-tail test.)
0 ................................. assumed population mean
.................................. population standard deviation ( > 0)
List .............................. list whose contents you want to use as data (List 1 to 20)
Freq ............................. frequency (1 or List 1 to 20)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
The following shows the meaning of parameter data specification items that are different from list data specification.
o .................................. mean of sample
n .................................. size of sample (positive integer)
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
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Calculation Result Output Example
G11.4 ........................ direction of test
z .................................. z score
p .................................. p-value
o .................................. mean of sample
xn-1 ............................. sample standard deviation (Displayed only for Data: List setting.)
n .................................. size of sample
# [Save Res] does not save the condition in line 2.
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u2-Sample Z Test
This test is used when the standard deviations for two populations are known to test the hypothesis. The 2-Sample Z Test is applied to the normal distribution.
Z = o1 o2
n1
1 2
n2
2 2
+
o1 : mean of sample 1 o2 : mean of sample 2 1 : population standard deviation of sample 1 2 : population standard deviation of sample 2 n1 : size of sample 1 n2 : size of sample 2
Perform the following key operations from the statistical data list.
3(TEST)
b(Z)
c(2-Smpl)
The following shows the meaning of each item in the case of list data specification.
Data ............................ data type
1 ................................. population mean value test conditions (G 2 specifies two- tail test, < 2 specifies one-tail test where sample 1 is smaller than sample 2, > 2 specifies one-tail test where sample 1 is greater than sample 2.)
1 ................................. population standard deviation of sample 1 (1 > 0)
2 ................................. population standard deviation of sample 2 (2 > 0)
List(1) .......................... list whose contents you want to use as sample 1 data (List 1 to 20)
List(2) .......................... list whose contents you want to use as sample 2 data (List 1 to 20)
Freq(1) ........................ frequency of sample 1 (1 or List 1 to 20)
Freq(2) ........................ frequency of sample 2 (1 or List 1 to 20)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
The following shows the meaning of parameter data specification items that are different from list data specification.
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o1 ................................. mean of sample 1
n1 ................................. size (positive integer) of sample 1
o2 ................................. mean of sample 2
n2 ................................. size (positive integer) of sample 2
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
Calculation Result Output Example
1G2 ........................... direction of test
z ................................... z score
p .................................. p-value
o1 ................................. mean of sample 1
o2 ................................. mean of sample 2
x1n-1 ............................ standard deviation of sample 1 (Displayed only for Data: List setting.)
x2n-1 ............................ standard deviation of sample 2 (Displayed only for Data: List setting.)
n1 ................................. size of sample 1
n2 ................................. size of sample 2
# [Save Res] does not save the 1 condition in line 2.
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u1-Prop Z Test
This test is used to test for an unknown proportion of successes. The 1-Prop Z Test is applied to the normal distribution.
Z = n x
n p0(1 p0)
p0
p0 : expected sample proportion n : size of sample
Perform the following key operations from the statistical data list.
3(TEST)
b(Z)
d(1-Prop)
Prop ............................ sample proportion test conditions (G p0 specifies two-tail test, < p0 specifies lower one-tail test, > p0 specifies upper one-tail test.)
p0 ................................. expected sample proportion (0 < p0 < 1)
x .................................. sample value (x > 0 integer)
n .................................. size of sample (positive integer)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
Calculation Result Output Example
PropG0.5 .................... direction of test
z ................................... z score
p .................................. p-value
p .................................. estimated sample proportion
n .................................. size of sample
# [Save Res] does not save the Prop condition in line 2.
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u2-Prop Z Test
This test is used to compare the proportion of successes. The 2-Prop Z Test is applied to the normal distribution.
Z = n1
x1
n2
x2
p(1 p ) n1
1 n2
1+
x1 : data value of sample 1 x2 : data value of sample 2 n1 : size of sample 1 n2 : size of sample 2 p : estimated sample proportion
Perform the following key operation from the statistical data list.
3(TEST)
b(Z)
e(2-Prop)
p1 ................................. sample proportion test conditions (G p2 specifies two-tail test, < p2 specifies one-tail test where sample 1 is smaller than sample 2, > p2 specifies one-tail test where sample 1 is greater than sample 2.)
x1 ................................. data value (x1 > 0 integer) of sample 1
n1 ................................. size (positive integer) of sample 1
x2 ................................. data value (x2 > 0 integer) of sample 2
n2 ................................. size (positive integer) of sample 2
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
Calculation Result Output Example
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p1>p2 ............................ direction of test
z .................................. z score
p .................................. p-value
p 1 ................................. estimated proportion of sample 1
p 2 ................................. estimated proportion of sample 2
p .................................. estimated sample proportion
n1 ................................. size of sample 1
n2 ................................. size of sample 2
# [Save Res] does not save the p1 condition in line 2.
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k t Tests
u t Test Common Functions
You can use the following graph analysis functions after drawing a graph.
1(T) ... Displays t score.
Pressing 1 (T) displays the t score at the bottom of the display, and displays the pointer at the corresponding location in the graph (unless the location is off the graph screen).
Two points are displayed in the case of a two-tail test. Use d and e to move the pointer.
Press i to clear the t score.
2(P) ... Displays p-value.
Pressing 2 (P) displays the p-value at the bottom of the display without displaying the pointer.
Press i to clear the p-value.
# The following V-Window settings are used for drawing the graph. Xmin = 3.2, Xmax = 3.2, Xscale = 1, Ymin = 0.1, Ymax = 0.45, Yscale = 0.1
# Executing an analysis function automatically stores the t and p values in alpha variables T and P, respectively.
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u1-Sample t Test
This test uses the hypothesis test for a single unknown population mean when the population standard deviation is unknown. The 1-Sample t Test is applied to t-distribution.
t = o 0
x n1
n
o : mean of sample 0 : assumed population mean xn-1 : sample standard deviation n : size of sample
Perform the following key operations from the statistical data list.
3(TEST)
c(T)
b(1-Smpl)
The following shows the meaning of each item in the case of list data specification.
Data ............................ data type
.................................. population mean value test conditions (G 0 specifies two- tail test, < 0 specifies lower one-tail test, > 0 specifies upper one-tail test.)
0 ................................. assumed population mean
List .............................. list whose contents you want to use as data (List 1 to 20)
Freq ............................. frequency (1 or List 1 to 20)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
The following shows the meaning of parameter data specification items that are different from list data specification.
o .................................. mean of sample
xn-1 ............................. sample standard deviation (xn-1 > 0)
n .................................. size of sample (positive integer)
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
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Calculation Result Output Example
G 11.3 ...................... direction of test
t ................................... t score
p .................................. p-value
o .................................. mean of sample
xn-1 ............................. sample standard deviation
n .................................. size of sample
# [Save Res] does not save the condition in line 2.
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u2-Sample t Test
2-Sample t Test compares the population means when the population standard deviations are unknown. The 2-Sample t Test is applied to t-distribution.
The following applies when pooling is in effect.
t = o1 o2
n1
1 + n2
1xp n1 2
xp n1 = n1 + n2 2 (n11)x1 n12 +(n21)x2 n12
df = n1 + n2 2
The following applies when pooling is not in effect.
t = o1 o2
x1 n1 2
n1 +
x2 n1 2
n2
df = 1 C 2
n11 +
(1C )2
n21
C = x1 n1
2 n1
+ x2 n1
2 n2
x1 n1 2
n1
Perform the following key operations from the statistical data list.
3(TEST)
c(T)
c(2-Smpl)
1-2-13 Tests (TEST)
o1 : mean of sample 1 o2 : mean of sample 2
x1n-1 : standard deviation of sample 1
x2n-1 : standard deviation of sample 2
n1 : size of sample 1 n2 : size of sample 2
xpn-1 : pooled sample standard deviation
df : degrees of freedom
o1 : mean of sample 1 o2 : mean of sample 2
x1n-1 : standard deviation of sample 1
x2n-1 : standard deviation of sample 2
n1 : size of sample 1 n2 : size of sample 2 df : degrees of freedom
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The following shows the meaning of each item in the case of list data specification.
Data ............................ data type
1 ................................. sample mean value test conditions (G 2 specifies two-tail test, < 2 specifies one-tail test where sample 1 is smaller than sample 2, > 2 specifies one-tail test where sample 1 is greater than sample 2.)
List(1) .......................... list whose contents you want to use as data of sample 1 (List 1 to 20)
List(2) .......................... list whose contents you want to use as data of sample 2 (List 1 to 20)
Freq(1) ........................ frequency of sample 1 (1 or List 1 to 20)
Freq(2) ........................ frequency of sample 2 (1 or List 1 to 20)
Pooled ......................... pooling On (in effect) or Off (not in effect)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
The following shows the meaning of parameter data specification items that are different from list data specification.
o1 ................................. mean of sample 1
x1n-1 ............................ standard deviation (x1n-1 > 0) of sample 1
n1 ................................. size (positive integer) of sample 1
o2 ................................. mean of sample 2
x2n-1 ............................ standard deviation (x2n-1 > 0) of sample 2
n2 ................................. size (positive integer) of sample 2
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation. 6(DRAW) ... Draws the graph.
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Calculation Result Output Example
1G2 ........................... direction of test
t ................................... t score
p .................................. p-value
df ................................. degrees of freedom
o1 ................................. mean of sample 1
o2 ................................. mean of sample 2
x1n-1 ............................ standard deviation of sample 1
x2n-1 ............................ standard deviation of sample 2
xpn-1 ............................ pooled sample standard deviation (Displayed only when Pooled: On setting.)
n1 ................................. size of sample 1
n2 ................................. size of sample 2
# [Save Res] does not save the 1 condition in line 2.
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uLinearReg t Test
LinearReg t Test treats paired-variable data sets as (x, y) pairs, and uses the method of least squares to determine the most appropriate a, b coefficients of the data for the regression formula y = a + bx. It also determines the correlation coefficient and t value, and calculates the extent of the relationship between x and y.
b = ( x o)( y p) i=1
n
(x o)2
i=1
n a = p bo t = r n 2
1 r2
a : intercept b : slope of the line n : size of sample (n > 3) r : correlation coefficient r2 : coefficient of
determination
Perform the following key operations from the statistical data list.
3(TEST)
c(T)
d(LinReg)
The following shows the meaning of each item in the case of list data specification.
& ............................ p-value test conditions (G 0 specifies two-tail test, < 0 specifies lower one-tail test, > 0 specifies upper one-tail test.)
XList ............................ list for x-axis data (List 1 to 20)
YList ............................ list for y-axis data (List 1 to 20)
Freq ............................. frequency (1 or List 1 to 20)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
# You cannot draw a graph for LinearReg t Test.
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Calculation Result Output Example
G 0 & G 0 .............. direction of test
t ................................... t score
p .................................. p-value
df ................................. degrees of freedom
a .................................. constant term
b .................................. coefficient
s .................................. standard error
r .................................. correlation coefficient
r2 ................................. coefficient of determination
Pressing 6 (COPY) while a calculation result is on the display copies the regression formula to the graph formula editor.
When there is a list specified for the [Resid List] item on the SET UP screen, regression formula residual data is automatically saved to the specified list after the calculation is finished.
# [Save Res] does not save the & conditions in line 2.
# When the list specified by [Save Res] is the same list specified by the [Resid List] item on the SET UP screen, only [Resid List] data is saved in the list.
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k 2 Test
2 Test sets up a number of independent groups and tests hypothesis related to the proportion of the sample included in each group. The 2 Test is applied to dichotomous variables (variable with two possible values, such as yes/no).
Expected counts
Fij = xij i=1
k
xij j=1
k
i=1 j=1
xij
2 = Fiji=1
k (xij Fij)2
j=1
Perform the following key operations from the statistical data list.
3(TEST)
d(2)
Next, specify the matrix that contains the data. The following shows the meaning of the above item.
Observed .................... name of matrix (A to Z) that contains observed counts (all cells positive integers)
Expected ..................... name of matrix (A to Z) that is for saving expected frequency
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
# The matrix must be at least two lines by two columns. An error occurs if the matrix has only one line or one column.
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# Pressing 2 ('MAT) while setting parameters enters the MATRIX editor, which you can use to edit and view the contents of matrices.
20010101
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
Calculation Result Output Example
2 ................................. 2 value
p .................................. p-value
df ................................. degrees of freedom
You can use the following graph analysis functions after drawing a graph.
1(CHI) ... Displays 2 value.
Pressing 1 (CHI) displays the 2 value at the bottom of the display, and displays the pointer at the corresponding location in the graph (unless the location is off the graph screen).
Press i to clear the 2 value.
2(P) ... Displays p-value.
Pressing 2 (P) displays the p-value at the bottom of the display without displaying the pointer.
Press i to clear the p-value.
# Pressing 6('MAT) while a calculation result is displayed enters the MATRIX editor, which you can use to edit and view the contents of matrices.
# The following V-Window settings are used for drawing the graph. Xmin = 0, Xmax = 11.5, Xscale = 2, Ymin = 0.1, Ymax = 0.5, Yscale = 0.1
# Executing an analysis function automatically stores the 2 and p values in alpha variables C and P, respectively.
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k 2-Sample F Test
2-Sample F Test tests the hypothesis for the ratio of sample variances. The F Test is applied to the F distribution.
F = x1 n1
2 x2 n1
2
Perform the following key operations from the statistical data list.
3(TEST)
e(F)
The following is the meaning of each item in the case of list data specification.
Data ............................ data type
1 ................................. population standard deviation test conditions (G 2 specifies two-tail test, < 2 specifies one-tail test where sample 1 is smaller than sample 2, > 2 specifies one-tail test where sample 1 is greater than sample 2.)
List(1) .......................... list whose contents you want to use as data of sample 1 (List 1 to 20)
List(2) .......................... list whose contents you want to use as data of sample 2 (List 1 to 20)
Freq(1) ........................ frequency of sample 1 (1 or List 1 to 20)
Freq(2) ........................ frequency of sample 2 (1 or List 1 to 20)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
The following shows the meaning of parameter data specification items that are different from list data specification.
x1n-1 ............................ standard deviation (x1n-1 > 0) of sample 1
n1 ................................. size (positive integer) of sample 1
x2n-1 ............................ standard deviation (x2n-1 > 0) of sample 2
n2 ................................. size (positive integer) of sample 2
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After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
Calculation Result Output Example
1G2 .......................... direction of test
F .................................. F value
p .................................. p-value
o1 ................................. mean of sample 1 (Displayed only for Data: List setting.)
o2 ................................. mean of sample 2 (Displayed only for Data: List setting.)
x1n-1 ............................ standard deviation of sample 1
x2n-1 ............................ standard deviation of sample 2
n1 ................................. size of sample 1
n2 ................................. size of sample 2
You can use the following graph analysis functions after drawing a graph.
1(F) ... Displays F value.
Pressing 1 (F) displays the F value at the bottom of the display, and displays the pointer at the corresponding location in the graph (unless the location is off the graph screen).
Two points are displayed in the case of a two-tail test. Use d and e to move the pointer.
Press i to clear the F value.
2(P) ... Displays p-value.
Pressing 2 (P) displays the p-value at the bottom of the display without displaying the pointer.
Press i to clear the p-value.
# [Save Res] does not save the 1 condition in line 2.
# V-Window settings are automatically optimized for drawing the graph.
# Executing an analysis function automatically stores the F and p values in alpha variables F and P, respectively.
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k ANOVA
ANOVA tests the hypothesis that the population means of the samples are equal when there are multiple samples. One-Way ANOVA is used when there is one independent variable and one dependent variable. Two-Way ANOVA is used when there are two independent variables and one dependent variable.
Perform the following key operations from the statistical data list.
3(TEST)
f(ANOVA)
The following is the meaning of each item in the case of list data specification.
How Many ................... selects One-Way ANOVA or Two-Way ANOVA (number of levels)
Factor A ....................... category list (List 1 to 20)
Dependnt .................... list to be used for sample data (List 1 to 20)
Save Res ..................... first list for storage of calculation results (None or List 1 to 16)*1
Execute ....................... executes a calculation or draws a graph (Two-Way ANOVA only)
The following item appears in the case of Two-Way ANOVA only.
Factor B ....................... category list (List 1 to 20)
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph (Two-Way ANOVA only).
Calculation results are displayed in table form, just as they appear in science books.
*1 [Save Res] saves each vertical column of the table into its own list. The leftmost column is saved in the specified list, and each subsequent column to the right is saved in
the next sequentially numbered list. Up to five lists can be used for storing columns. You can specify an first list number in the range of 1 to 16.
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Calculation Result Output Example
One-Way ANOVA
Line 1 (A) .................... Factor A df value, SS value, MS value, F value, p-value
Line 2 (ERR) ............... Error df value, SS value, MS value
Two-Way ANOVA
Line 1 (A) .................... Factor A df value, SS value, MS value, F value, p-value
Line 2 (B) .................... Factor B df value, SS value, MS value, F value, p-value
Line 3 (AB) .................. Factor A Factor B df value, SS value, MS value, F value, p-value
*Line 3 does not appear when there is only one observation in each cell.
Line 4 (ERR) ............... Error df value, SS value, MS value
F .................................. F value
p .................................. p-value
df ................................. degrees of freedom
SS ................................ sum of squares
MS ............................... mean squares
With Two-Way ANOVA, you can draw Interaction Plot graphs. The number of graphs depends on Factor B, while the number of X-axis data depends on the Factor A. The Y-axis is the average value of each category.
You can use the following graph analysis function after drawing a graph.
1(TRACE) ... Trace function
Pressing d or e moves the pointer on the graph in the corresponding direction. When there are multiple graphs, you can move between graphs by pressing f and c.
Press i to clear the pointer from the display.
# Graphing is available with Two-Way ANOVA only. V-Window settings are performed automatically, regardless of SET UP screen settings.
# Using the TRACE function automatically stores the number of conditions to alpha variable A and the mean value to variable M, respectively.
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k ANOVA (Two-Way)
uDescription
The nearby table shows measurement results for a metal product produced by a heat treatment process based on two treatment levels: time (A) and temperature (B). The experiments were repeated twice each under identical conditions.
Perform analysis of variance on the following null hypothesis, using a significance level of 5%.
Ho : No change in strength due to time Ho : No change in strength due to heat treatment temperature Ho : No change in strength due to interaction of time and heat treatment temperature
uSolution
Use two-way ANOVA to test the above hypothesis. Input the above data as shown below.
List1={1,1,1,1,2,2,2,2} List2={1,1,2,2,1,1,2,2} List3={113,116,139,132,133,131,126,122}
Define List 3 (the data for each group) as Dependent. Define List 1 and List 2 (the factor numbers for each data item in List 3) as Factor A and Factor B respectively. Executing the test produces the following results.
Time differential (A) level of significance P = 0.2458019517 The level of significance (p = 0.2458019517) is greater than the significance level (0.05), so the hypothesis is not rejected.
Temperature differential (B) level of significance P = 0.04222398836 The level of significance (p = 0.04222398836) is less than the significance level (0.05), so the hypothesis is rejected.
Interaction (A B) level of significance P = 2.78169946e-3 The level of significance (p = 2.78169946e-3) is less than the significance level (0.05), so the hypothesis is rejected.
The above test indicates that the time differential is not significant, the temperature differential is significant, and interaction is highly significant.
B (Heat Treatment Temperature) B1 B2
A1 113 , 116
133 , 131
139 , 132
126 , 122A2
A (Time)
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uInput Example
uResults
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1-3 Confidence Interval (INTR) A confidence interval is a range (interval) that includes a statistical value, usually the population mean.
A confidence interval that is too broad makes it difficult to get an idea of where the population value (true value) is located. A narrow confidence interval, on the other hand, limits the population value and makes it difficult to obtain reliable results. The most commonly used confidence levels are 95% and 99%. Raising the confidence level broadens the confidence interval, while lowering the confidence level narrows the confidence level, but it also increases the chance of accidently overlooking the population value. With a 95% confidence interval, for example, the population value is not included within the resulting intervals 5% of the time.
When you plan to conduct a survey and then t test and Z test the data, you must also consider the sample size, confidence interval width, and confidence level. The confidence level changes in accordance with the application.
1-Sample Z Interval calculates the confidence interval for an unknown population mean when the population standard deviation is known.
2-Sample Z Interval calculates the confidence interval for the difference between two population means when the population standard deviations of two samples are known.
1-Prop Z Interval calculates the confidence interval for an unknown proportion of successes.
2-Prop Z Interval calculates the confidence interval for the difference between the propotion of successes in two populations.
1-Sample t Interval calculates the confidence interval for an unknown population mean when the population standard deviation is unknown.
2-Sample t Interval calculates the confidence interval for the difference between two population means when both population standard deviations are unknown.
On the initial STAT Mode screen, press 4 (INTR) to display the confidence interval menu, which contains the following items.
4(INTR)b(Z) ... Z intervals (p. 1-3-3)
c(T) ... t intervals (p. 1-3-8)
# There is no graphing for confidence interval functions.
1-3-1 Confidence Interval (INTR)
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uGeneral Confidence Interval Precautions
Inputting a value in the range of 0 < C-Level < 1 for the C-Level setting sets you value you input. Inputting a value in the range of 1 < C-Level < 100 sets a value equivalent to your input divided by 100.
# Inputting a value of 100 or greater, or a negative value causes an error (Ma ERROR).
1-3-2 Confidence Interval (INTR)
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k Z Interval
u1-Sample Z Interval
1-Sample Z Interval calculates the confidence interval for an unknown population mean when the population standard deviation is known.
The following is the confidence interval.
Left = o Z 2
n
Right = o + Z 2
n
However, is the level of significance. The value 100 (1 ) % is the confidence level.
When the confidence level is 95%, for example, inputting 0.95 produces 1 0.95 = 0.05 = .
Perform the following key operations from the statistical data list.
4(INTR)
b(Z)
b(1-Smpl)
The following shows the meaning of each item in the case of list data specification.
Data ............................ data type
C-Level ........................ confidence level (0 < C-Level < 1)
.................................. population standard deviation ( > 0)
List .............................. list whose contents you want to use as sample data (List 1 to 20)
Freq ............................. sample frequency (1 or List 1 to 20)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of parameter data specification items that are different from list data specification.
o .................................. mean of sample
n .................................. size of sample (positive integer)
1-3-3 Confidence Interval (INTR)
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After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
Left .............................. interval lower limit (left edge)
Right ............................ interval upper limit (right edge)
o .................................. mean of sample
xn-1 ............................. sample standard deviation (Displayed only for Data: List setting.)
n .................................. size of sample
u 2-Sample Z Interval
2-Sample Z Interval calculates the confidence interval for the difference between two population means when the population standard deviations of two samples are known. The following is the confidence interval. The value 100 (1 ) % is the confidence level.
Left = (o1 o2) Z 2
Right = (o1 o2) + Z 2
n1
1 2 +
n2
2 2
n1
1 2 +
n2
2 2
o1 : mean of sample 1 o2 : mean of sample 2 1 : population standard deviation
of sample 1 2 : population standard deviation
of sample 2 n1 : size of sample 1 n2 : size of sample 2
Perform the following key operations from the statistical data list.
4(INTR)
b(Z)
c(2-Smpl)
1-3-4 Confidence Interval (INTR)
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The following shows the meaning of each item in the case of list data specification.
Data ............................ data type
C-Level ........................ confidence level (0 < C-Level < 1)
1 ................................. population standard deviation of sample 1 (1 > 0)
2 ................................. population standard deviation of sample 2 (2 > 0)
List(1) .......................... list whose contents you want to use as data of sample 1 (List 1 to 20)
List(2) .......................... list whose contents you want to use as data of sample 2 (List 1 to 20)
Freq(1) ........................ frequency of sample 1 (1 or List 1 to 20)
Freq(2) ........................ frequency of sample 2 (1 or List 1 to 20)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of parameter data specification items that are different from list data specification.
o1 ................................. mean of sample 1
n1 ................................. size (positive integer) of sample 1
o2 ................................. mean of sample 2
n2 ................................. size (positive integer) of sample 2
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
Left .............................. interval lower limit (left edge)
Right ............................ interval upper limit (right edge)
o1 ................................. mean of sample 1
o2 ................................. mean of sample 2
x1n-1 ............................ standard deviation of sample 1 (Displayed only for Data: List setting.)
x2n-1 ............................ standard deviation of sample 2 (Displayed only for Data: List setting.)
n1 ................................. size of sample 1
n2 ................................. size of sample 2
1-3-5 Confidence Interval (INTR)
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u1-Prop Z Interval
1-Prop Z Interval uses the number of data to calculate the confidence interval for an unknown proportion of successes.
The following is the confidence interval. The value 100 (1 ) % is the confidence level.
Left = Z 2
Right = + Z
x n n
1 n x
n x1
x n
2 n
1 n x
n x1
n : size of sample x : data
Perform the following key operations from the statistical data list.
4(INTR)
b(Z)
d(1-Prop)
Data is specified using parameter specification. The following shows the meaning of each item.
C-Level ........................ confidence level (0 < C-Level < 1)
x .................................. data (0 or positive integer)
n .................................. size of sample (positive integer)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
Left .............................. interval lower limit (left edge)
Right ............................ interval upper limit (right edge)
p .................................. estimated sample proportion
n .................................. size of sample
1-3-6 Confidence Interval (INTR)
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u 2-Prop Z Interval
2-Prop Z Interval uses the number of data items to calculate the confidence interval for the defference between the proportion of successes in two populations.
The following is the confidence interval. The value 100 (1 ) % is the confidence level.
Left = Z 2
x1 n1
x2 n2 n1
n1
x1 1 n1
x1
+ n2
n2
x2 1 n2
x2
Right = + Z 2
x1 n1
x2 n2 n1
n1
x1 1 n1
x1
+ n2
n2
x2 1 n2
x2
n1, n2 : size of sample x1, x2 : data
Perform the following key operations from the statistical data list.
4(INTR)
b(Z)
e(2-Prop)
Data is specified using parameter specification. The following shows the meaning of each item.
C-Level ........................ confidence level (0 < C-Level < 1)
x1 ................................. data value (x1 > 0) of sample 1
n1 ................................. size (positive integer) of sample 1
x2 ................................. data value (x2 > 0) of sample 2
n2 ................................. size (positive integer) of sample 2
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
1-3-7 Confidence Interval (INTR)
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Left .............................. interval lower limit (left edge)
Right ............................ interval upper limit (right edge)
p 1 ................................. estimated sample propotion for sample 1
p 2 ................................. estimated sample propotion for sample 2
n1 ................................. size of sample 1
n2 ................................. size of sample 2
k t Interval
u 1-Sample t Interval
1-Sample t Interval calculates the confidence interval for an unknown population mean when the population standard deviation is unknown.
The following is the confidence interval. The value 100 (1 ) % is the confidence level.
Left = o tn 1 2
Right = o+ tn 1 2
x n1 n
x n1 n
Perform the following key operations from the statistical data list.
4(INTR)
c(T)
b(1-Smpl)
The following shows the meaning of each item in the case of list data specification.
Data ............................ data type
C-Level ........................ confidence level (0 < C-Level < 1)
List .............................. list whose contents you want to use as sample data (List 1 to 20)
Freq ............................. sample frequency (1 or List 1 to 20)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of parameter data specification items that are different from list data specification.
1-3-8 Confidence Interval (INTR)
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o .................................. mean of sample
xn-1 ............................. sample standard deviation (xn-1 > 0)
n .................................. size of sample (positive integer)
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
Left .............................. interval lower limit (left edge)
Right ............................ interval upper limit (right edge)
o .................................. mean of sample
xn-1 ............................. sample standard deviation
n .................................. size of sample
u 2-Sample t Interval
2-Sample t Interval calculates the confidence interval for the difference between two population means when both population standard deviations are unknown. The t interval is applied to t distribution.
The following confidence interval applies when pooling is in effect. The value 100 (1 ) % is the confidence level.
Left = (o1 o2) t 2
Right = (o1 o2)+ t 2
n1+n2 2 n1
1 + n2
1xp n1 2
n1+n2 2 n1
1 + n2
1xp n1 2
xp n1 = n1 + n2 2 (n11)x1 n12 +(n21)x2 n12
1-3-9 Confidence Interval (INTR)
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The following confidence interval applies when pooling is not in effect. The value 100 (1 ) % is the confidence level.
Left = (o1 o2) tdf 2
Right = (o1 o2)+ tdf 2
+n1
x1 n1 2
n2
x2 n1 2
+n1
x1 n1 2
n2
x2 n1 2
C =
df = 1 C
2
n11 +
(1C )2
n21
+n1
x1 n1 2 n1
x1 n1 2
n2
x2 n1 2
Perform the following key operations from the statistical data list.
4(INTR)
c(T)
c(2-Smpl)
The following shows the meaning of each item in the case of list data specification.
Data ............................ data type
C-Level ........................ confidence level (0 < C-Level < 1)
List(1) .......................... list whose contents you want to use as data of sample 1 (List 1 to 20)
List(2) .......................... list whose contents you want to use as data of sample 2 (List 1 to 20)
Freq(1) ........................ frequency of sample 1 (1 or List 1 to 20)
Freq(2) ........................ frequency of sample 2 (1 or List 1 to 20)
Pooled ......................... pooling On (in effect) or Off (not in effect)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of parameter data specification items that are different from list data specification.
1-3-10 Confidence Interval (INTR)
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o1 ................................. mean of sample 1
x1n-1 ............................ standard deviation (x1n-1 > 0) of sample 1
n1 ................................. size (positive integer) of sample 1
o2 ................................. mean of sample 2
x2n-1 ............................ standard deviation (x2n-1 > 0) of sample 2
n2 ................................. size (positive integer) of sample 2
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
Left .............................. interval lower limit (left edge)
Right ............................ interval upper limit (right edge)
df ................................. degrees of freedom
o1 ................................. mean of sample 1
o2 ................................. mean of sample 2
x1n-1 ............................ standard deviation of sample 1
x2n-1 ............................ standard deviation of sample 2
xpn-1 ............................ pooled sample standard deviation (Displayed only when Pooled: On setting.)
n1 ................................. size of sample 1
n2 ................................. size of sample 2
1-3-11 Confidence Interval (INTR)
20010101
1-4 Distribution (DIST) There is a variety of different types of distribution, but the most well-known is normal distribution, which is essential for performing statistical calculations. Normal distribution is a symmetrical distribution centered on the greatest occurrences of mean data (highest frequency), with the frequency decreasing as you move away from the center. Poisson distribution, geometric distribution, and various other distribution shapes are also used, depending on the data type.
Certain trends can be determined once the distribution shape is determined. You can calculate the probability of data taken from a distribution being less than a specific value.
For example, distribution can be used to calculate the yield rate when manufacturing some product. Once a value is established as the criteria, you can calculate normal probability when estimating what percent of the products meet the criteria. Conversely, a success rate target (80% for example) is set up as the hypothesis, and normal distribution is used to estimate the proportion of the products will reach this value.
Normal probability density calculates the probability density of normal distribution from a specified x value.
Normal distribution probability calculates the probability of normal distribution data falling between two specific values.
Inverse cumulative normal distribution calculates a value that represents the location within a normal distribution for a specific cumulative probability.
Student- t probability density calculates t probability density from a specified x value.
Student- t distribution probability calculates the probability of t distribution data falling between two specific values.
Like t distribution, distribution probability can also be calculated for 2, F, Binomial, Poisson, and Geometric distributions.
On the initial STAT Mode screen, press 5 (DIST) to display the distribution menu, which contains the following items.
5(DIST)b(Norm) ... Normal distribution (p. 1-4-3)
c(T) ... Student-t distribution (p. 1-4-7)
d(2) ... 2 distribution (p. 1-4-9)
e(F) ... F distribution (p. 1-4-12)
f(Binmal) ... Binomial distribution (p. 1-4-16)
g(Poissn) ... Poisson distribution (p. 1-4-19)
h(Geo) ... Geometric distribution (p. 1-4-21)
1-4-1 Distribution (DIST)
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uCommon Distribution Functions
After drawing a graph, you can use the P-CAL function to calculate an estimated p-value for a particular x value.
The following is the general procedure for using the P-CAL function.
1. After drawing a graph, press 1 (P-CAL) to display the x value input dialog box.
2. Input the value you want for x and then press w.
This causes the x and p values to appear at the bottom of the display, and moves the pointer to the corresponding point on the graph.
3. Pressing v or a number key at this time causes the x value input dialog box to reappear so you can perform another estimated value calculation if you want.
4. After you are finished, press i to clear the coordinate values and the pointer from the display.
# Executing an analysis function automatically stores the x and p values in alpha variables X and P, respectively.
1-4-2 Distribution (DIST)
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k Normal Distribution
uNormal Probability Density
Normal probability density calculates the probability density of nomal distribution from a specified x value. Normal probability density is applied to standard normal distribution.
2 f(x) = 1 e
2 2
(x )2
( > 0)
Perform the following key operations from the statistical data list.
5(DIST)
b(Norm)
b(P.D)
Data is specified using parameter specification. The following shows the meaning of each item.
x .................................. data
.................................. standard deviation ( > 0)
.................................. mean
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
Specifying = 1 and = 0 specifies standard normal distribution.
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
Calculation Result Output Example
p .................................. normal probability density
# V-Window settings for graph drawing are set automatically when the SET UP screen's [Stat Wind] setting is [Auto]. Current V-
Window settings are used for graph drawing when the [Stat Wind] setting is [Manual].
1-4-3 Distribution (DIST)
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uNormal Distribution Probability
Normal distribution probability calculates the probability of normal distribution data falling between two specific values.
2 p = 1 e
dx 2 2
(x )2
a
b a : lower boundary b : upper boundary
Perform the following key operations from the statistical data list.
5(DIST)
b(Norm)
c(C.D)
Data is specified using parameter specification. The following shows the meaning of each item.
Lower .......................... lower boundary
Upper .......................... upper boundary
.................................. standard deviation ( > 0)
.................................. mean
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
# There is no graphing for normal distribution probability.
1-4-4 Distribution (DIST)
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Calculation Result Output Example
p .................................. normal distribution probability
z:Low ........................... z:Low value (converted to standardize z score for lower value)
z:Up ............................. z:Up value (converted to standardize z score for upper value)
uInverse Cumulative Normal Distribution
Inverse cumulative normal distribution calculates a value that represents the location within a normal distribution for a specific cumulative probability.
f (x)dx = p f (x)dx = p
+
f (x)dx = p
Specify the probability and use this formula to obtain the integration interval.
Perform the following key operations from the statistical data list.
5(DIST)
b(Norm)
d(Invrse)
Data is specified using parameter specification. The following shows the meaning of each item.
Tail ............................... probability value tail specification (Left, Right, Central)
Area ............................ probability value (0 < Area < 1)
.................................. standard deviation ( > 0)
.................................. mean
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
Tail: Left upper boundary of integration interval = ?
Tail: Right lower boundary of integration interval = ?
Tail: Central upper and lower boundaries of integration interval = ? = ?
1-4-5 Distribution (DIST)
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After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Examples
x ....................................... inverse cumulative normal distribution (Tail:Left upper boundary of integration interval) (Tail:Right lower boundary of integration interval) (Tail:Central upper and lower boundaries of integration interval)
# There is no graphing for inverse cumulative normal distribution.
1-4-6 Distribution (DIST)
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k Student-t Distribution
uStudent-t Probability Density
Student-t probability density calculates t probability density from a specified x value.
f (x) =
df
df+1 2
2 df 2
df + 1 df x2
1+
Perform the following key operations from the statistical data list.
5(DIST)
c(T)
b(P.D)
Data is specified using parameter specification. The following shows the meaning of each item.
x .................................. data
df ................................. degrees of freedom (df > 0)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
Calculation Result Output Example
p .................................. Student-t probability density
# Current V-Window settings are used for graph drawing when the SET UP screen's [Stat Wind] setting is [Manual]. The V- Window settings below are set automatically
when the [Stat Wind] setting is [Auto].
Xmin = 3.2, Xmax = 3.2, Xscale = 1,
Ymin = 0.1, Ymax = 0.45, Yscale = 0.1
1-4-7 Distribution (DIST)
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uStudent-t Distribution Probability
Student-t distribution probability calculates the probability of t distribution data falling between two specific values.
p =
df2 df
2 df + 1
df+1 2
df x2
1+ dx a
b
a : lower boundary b : upper boundary
Perform the following key operations from the statistical data list.
5(DIST)
c(T)
c(C.D)
Data is specified using parameter specification. The following shows the meaning of each item.
Lower .......................... lower boundary
Upper .......................... upper boundary
df ................................. degrees of freedom (df > 0)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
# There is no graphing for Student-t distribution probability.
1-4-8 Distribution (DIST)
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Calculation Result Output Example
p .................................. Student-t distribution probability
t:Low ........................... t:Low value (input lower value)
t:Up ............................. t:Up value (input upper value)
k 2 Distribution
u2 Probability Density
2 probability density calculates the probability density function for the 2 distribution at a specified x value.
f(x) =
1
2 df
df 2 x e
2 1
df 2
1 x 2
Perform the following key operations from the statistical data list.
5(DIST)
d(2)
b(P.D)
Data is specified using parameter specification. The following shows the meaning of each item.
x .................................. data
df ................................. degrees of freedom (positive integer)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
1-4-9 Distribution (DIST)
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Calculation Result Output Example
p .................................. 2 probability density
# Current V-Window settings are used for graph drawing when the SET UP screen's [Stat Wind] setting is [Manual]. The V- Window settings below are set automatically
when the [Stat Wind] setting is [Auto].
Xmin = 0, Xmax = 11.5, Xscale = 2,
Ymin = -0.1, Ymax = 0.5, Yscale = 0.1
1-4-10 Distribution (DIST)
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u2 Distribution Probability
2 distribution probability calculates the probability of 2 distribution data falling between two specific values.
p =
1
2 df
df 2
x e dx2 1 df
2 1
x 2
a
b
a : lower boundary b : upper boundary
Perform the following key operations from the statistical data list.
5(DIST)
d(2)
c(C.D)
Data is specified using parameter specification. The following shows the meaning of each item.
Lower .......................... lower boundary
Upper .......................... upper boundary
df ................................. degrees of freedom (positive integer)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
# There is no graphing for 2 distribution probability.
1-4-11 Distribution (DIST)
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Calculation Result Output Example
p .................................. 2 distribution probability
k F Distribution
u F Probability Density
F probability density calculates the probability density function for the F distribution at a specified x value.
n 2 x
d n
n 2
1
2 n
2
n + d
2 d d
nx1 +
n + d 2
f (x) =
Perform the following key operations from the statistical data list.
5(DIST)
e(F)
b(P.D)
Data is specified using parameter specification. The following shows the meaning of each item.
x .................................. data
n:df .............................. numerator degrees of freedom (positive integer)
d:df .............................. denominator degrees of freedom (positive integer)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation or draws a graph
After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
1(CALC) ... Performs the calculation.
6(DRAW) ... Draws the graph.
1-4-12 Distribution (DIST)
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Calculation Result Output Example
p .................................. F probability density
# V-Window settings for graph drawing are set automatically when the SET UP screen's [Stat Wind] setting is [Auto]. Current V-
Window settings are used for graph drawing when the [Stat Wind] setting is [Manual].
1-4-13 Distribution (DIST)
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u F Distribution Probability
F distribution probability calculates the probability of F distribution data falling between two specific values.
p =
n 2
dxxd n
n 2
1
2 n
2
n + d
2 d d
nx1 +
n + d 2
a
b
a : lower boundary b : upper boundary
Perform the following key operations from the statistical data list.
5(DIST)
e(F)
c(C.D)
Data is specified using parameter specification. The following shows the meaning of each item.
Lower .......................... lower boundary
Upper .......................... upper boundary
n:df .............................. numerator degrees of freedom (positive integer)
d:df .............................. denominator degrees of freedom (positive integer)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
# There is no graphing for F distribution probability.
1-4-14 Distribution (DIST)
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Calculation Result Output Example
p .................................. F distribution probability
1-4-15 Distribution (DIST)
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k Binomial Distribution
u Binomial Probability
Binomial probability calculates a probability at a specified value for the discrete binomial distribution with the specified number of trials and probability of success on each trial.
f (x) = nCxpx(1p)n x (x = 0, 1, , n) p : success probability (0 < p < 1)
n : number of trials
Perform the following key operations from the statistical data list.
5(DIST)
f(Binmal)
b(P.D)
The following shows the meaning of each item when data is specified using list specification.
Data ............................ data type
List .............................. list whose contents you want to use as specified data (List 1 to 20)
Numtrial ....................... number of trials
p .................................. success probability (0 < p < 1)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of a parameter data specification item that is different from list data specification.
x .................................. integer from 0 to n
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
# There is no graphing for binomial distribution.
1-4-16 Distribution (DIST)
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Calculation Result Output Example
p .................................. binomial probability
uBinomial Cumulative Density
Binomial cumulative density calculates a cumulative probability at a specified value for the discrete binomial distribution with the specified number of trials and probability of success on each trial.
Perform the following key operations from the statistical data list.
5 (DIST)
f (Binmal)
c (C.D)
The following shows the meaning of each item when data is specified using list specification.
Data ............................ data type
List .............................. list whose contents you want to use as specified data (List 1 to 20)
Numtrial ....................... number of trials
p .................................. success probability (0 < p < 1)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of a parameter data specification item that is different from list data specification.
x .................................. integer from 0 to n
1-4-17 Distribution (DIST)
1
20010101
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
p ......................................... probability of success
1-4-18 Distribution (DIST)
1
20010101
k Poisson Distribution
uPoisson Probability
Poisson probability calculates a probability at a specified value for the discrete Poisson distribution with the specified mean.
f(x) = x!
e x (x = 0, 1, 2, ) : mean ( > 0)
Perform the following key operations from the statistical data list.
5(DIST)
g(Poissn)
b(P.D)
The following shows the meaning of each item when data is specified using list specification.
Data ............................ data type
List .............................. list whose contents you want to use as specified data (List 1 to 20)
.................................. mean ( > 0)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of a parameter data specification item that is different from list data specification.
x .................................. ( x > 0)
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
p .................................. Poisson probability
# There is no graphing for Poisson distribution.
1-4-19 Distribution (DIST)
1
20010101
u Poisson Cumulative Density
Poisson cumulative density calculates a cumulative probability at specified value for the discrete Poisson distribution with the specified mean.
Perform the following key operations from the statistical data list.
5(DIST)
g(Poissn)
c(C.D)
The following shows the meaning of each item when data is specified using list specification.
Data ............................ data type
List .............................. list whose contents you want to use as specified data (List 1 to 20)
.................................. mean ( > 0)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a caluculation
The following shows the meaning of a parameter data specification item that is different from list data specification.
x .................................. ( x > 0)
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
p .................................. Poisson cumulative probability
1-4-20 Distribution (DIST)
1
20010101
k Geometric Distribution
uGeometric Probability
Geometric probability calculates the probability at a specified value, and the number of the trial on which the first success occurs, for the geometric distribution with a specified probability of success.
f (x) = p(1 p) x 1 (x = 1, 2, 3, )
Perform the following key operations from the statistical data list.
5(DIST)
h(Geo)
b(P.D)
The following shows the meaning of each item when data is specified using list specification.
Data ............................ data type
List .............................. list whose contents you want to use as specified data (List 1 to 20)
p .................................. success probability (0 < p < 1)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of a parameter data specification item that is different from list data specification.
x .................................. positive integer (x > 1)
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
p .................................. geometric probability
1-4-21 Distribution (DIST)
# There is no graphing for geometric distribu- tion.
# Positive integer number is calculated whether list data (Data:List) or x value (Data:variable) is specified.
1
20010101
uGeometric Cumulative Density
Geometric cumulative density calculates a cumulative probability at specified value, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success.
Perform the following key operations from the statistical data list.
5(DIST)
h(Geo)
c(C.D)
The following shows the meaning of each item when data is specified using list specification.
Data ............................ data type
List .............................. list whose contents you want to use as specified data (List 1 to 20)
p .................................. success probability (0 < p < 1)
Save Res ..................... list for storage of calculation results (None or List 1 to 20)
Execute ....................... executes a calculation
The following shows the meaning of a parameter data specification item that is different from list data specification.
x .................................. positive integer (x > 1)
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
1(CALC) ... Performs the calculation.
Calculation Result Output Example
p .................................. geometric cumulative probability
# Positive integer number is calculated whether list data (Data:List) or x value (Data:variable) is specified.
1-4-22 Distribution (DIST)
1
Financial Calculation (TVM)
2-1 Before Performing Financial Calculations
2-2 Simple Interest 2-3 Compound Interest
2-4 Cash Flow (Investment Appraisal)
2-5 Amortization
2-6 Interest Rate Conversion 2-7 Cost, Selling Price, Margin
2-8 Day/Date Calculations
2-9 Depreciation
2-10 Bonds 2-11 TVM Graph
2
Chapter
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2-1 Before Performing Financial Calculations
k TVM Mode
On the Main Menu, select the TVM icon.
Entering the TVM Mode displays the Financial screen like the one shown below.
Financial 1 screen Financial 2 screen
1(SMPL) .... Simple interest
2(CMPD) ... Compound interest
3(CASH) .... Cash flow (investment appraisal)
4(AMT) ...... Amortization
5(CNVT) .... Interest rate conversion
6(g)1(COST) ... Cost, selling price, margin
2(DAYS) ... Day/date calculations
3(DEPR) ... Depreciation
4(BOND) ... Bonds
5(TVMG) ... TVM (compound interest simulation) graph
2-1-1 Before Performing Financial Calculations
* The above shows the ALGEBRA FX 2.0 PLUS screen.
20010101
k SET UP Items
u Payment
{BGN}/{END} ........ Specifies {beginning of the period} / {end of the period} payment
u Date Mode
{365}/{360} ......... Specifies calculation according to a {365-day} / {360-day} year
u Periods/YR. (Bond)
{Annual}/{SEMI} ... Indicates an {annual} / {semi-annual} period
Note the following points regarding SET UP screen settings whenever using the Financial Mode.
Drawing a financial graph while the Label item is turned on, displays the label CASH for the vertical axis (deposits, withdrawals), and TIME for the horizontal axis (frequency). Axis labels do not appear on the TVM graph.
The number of display digits applied in the Financial Mode is different from the number of digits used in other modes. The calculators automatically reverts to Norm 1 whenever you enter the Financial Mode, which cancels a Sci (number of significant digits) or Eng (engineering notation) setting made in another mode.
k Graphing in the TVM Mode
After performing a financial calculation, you can use 6 (GRPH) to graph the results as shown below.
Pressing 1 (TRACE) while a graph is on the display activates Trace, which can be used to look up other financial values. In the case of simple interest, for example, pressing e displays PV, SI, and SFV. Pressing d displays the same values in reverse sequence.
Zoom, Scroll, and Sketch cannot be used in the Financial Mode.
Whether you should use a positive or a negative value for the present value (PV) or the purchase price (PRC) depends on the type of calculation you are trying to perform.
Note that graphs should be used only for reference purposes when viewing TVM Mode calculation results.
Note that calculation results produced in this mode should be regarded as reference values only.
Whenever performing an actual financial transaction, be sure to check any calculation results obtained using this calculator with against the figures calculated by your financial institution.
2-1-2 Before Performing Financial Calculations
20010101
2-2 Simple Interest This calculator uses the following formulas to calculate simple interest.
uFormula
365-day Mode SI' = n 365
PV i
SI' = n 360
PV i
I% 100
i =
I% 100
i =
SI : interest n : number of interest
360-day Mode periods PV : principal I% : annual interest SFV : principal plus interest
SI = SI' SFV = (PV + SI')
Press 1(SMPL) from the Financial 1 screen to display the following input screen for simple interest.
1(SMPL)
n .................................. number of interest periods (days)
I% ............................... annual interest rate
PV ............................... principal
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1(SI) ....... Simple interest
2(SFV) ... Simple future value
2-2-1 Simple Interest
20010101
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function keys to maneuver between calculation result screens.
1(REPT) ... Parameter input screen
6(GRPH) ... Draws graph
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph.
Each press of e while trace is turned on cycles the displayed value in the sequence: present value (PV) simple interest (SI) simple future value (SFV). Pressing d cycles in the reverse direction.
Press i to turn off trace.
Press i again to return to the parameter input screen.
2-2-2 Simple Interest
20010101
2-3 Compound Interest This calculator uses the following standard formulas to calculate compound interest.
uFormula I
PV+PMT + FV i(1+ i)n (1+ i)n
(1+ i S)[(1+ i)n1] 1 = 0 i =
100
I %
Here:
PV= (PMT + FV )
FV=
PMT + PV
PMT= PV + FV
n =
log{ } log(1+ i)
(1+ i S ) PMT+PVi
(1+ i S ) PMTFVi
i(1+ i)n
(1+ i S)[(1+ i)n1] =
(1+ i)n
1 =
F(i) = Formula I
+ (1+ i S)[n(1+ i)n1]+S [
nFV(1+ i)n1
ii
PMT (1+ i S)[1 (1+ i)n] F(i) = [
+S [1(1+ i)n] ] uFormula II (I% = 0)
PV + PMT n + FV = 0
Here:
PV = (PMT n + FV )
PV : present value FV : future value PMT : payment n : number of compound periods I% : annual interest rate
i is calculated using Newtons Method.
S = 0 assumed for end of term S = 1 assumed for beginning of term
2-3-1 Compound Interest
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20010101
FV = (PMT n + PV )
n PMT =
PV + FV
PMT n =
PV + FV
A deposit is indicated by a plus sign (+), while a withdrawal is indicated by a minus sign ().
uConverting between the nominal interest rate and effective interest rate
The nominal interest rate (I% value input by user) is converted to an effective interest rate (I%') when the number of installments per year (P/Y ) is different from the number of compound interest calculation periods (C/Y ). This conversion is required for installment savings accounts, loan repayments, etc.
P/Y : installment periods per year
C/Y: compounding periods per year
When calculating n, PV, PMT, FV
The following calculation is performed after conversion from the nominal interest rate to the effective interest rate, and the result is used for all subsequent calculations.
i = I%'100
When calculating I%
After I% is obtained, the following calculation is performed to convert to I%'.
I%' = I%
(1+ ) 1 [C / Y ] [P / Y ]
100 { }[C / Y ]100 P/Y : installment
periods per year C/Y: compounding
periods per year
The value of I%' is returned as the result of the I% calculation.
2-3-2 Compound Interest
I%' = I%
(1+ ) 1 [C / Y ] [P / Y ]
100 [C / Y ]{ }100
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20010101
Press 2(CMPD) from the Financial 1 screen to display the following input screen for compound interest.
2(CMPD)
n .................................. number of compound periods
I% ............................... annual interest rate
PV ............................... present value (loan amount in case of loan; principal in case of savings)
PMT ............................ payment for each installment (payment in case of loan; deposit in case of savings)
FV ............................... future value (unpaid balance in case of loan; principal plus interest in case of savings)
P/Y .............................. installment periods per year
C/Y .............................. compounding periods per year
Important! Inputting Values
A period (n) is expressed as a positive value. Either the present value (PV ) or future value (FV ) is positive, while the other (PV or FV ) is negative.
Precision
This calculator performs interest calculations using Newtons Method, which produces approximate values whose precision can be affected by various calculation conditions. Because of this, interest calculation results produced by this calculator should be used keeping the above limitation in mind or the results should be verified.
2-3-3 Compound Interest
20010101
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1(n) ............ Number of compound periods
2(I%) .......... Annual interest rate
3(PV) ......... Present value (Loan: loan amount; Savings: balance)
4(PMT) ....... Payment (Loan: installment; Savings: deposit)
5(FV) .......... Future value (Loan: unpaid balance; Savings: principal plus interest)
6(AMT) ....... Amortization screen
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function keys to maneuver between calculation result screens.
1(REPT) ..... Parameter input screen
4(AMT) ....... Amortization screen
6(GRPH) .... Draws graph
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph.
Press i to turn off trace.
Press i again to return to the parameter input screen.
2-3-4 Compound Interest
20010101
2-4 Cash Flow (Investment Appraisal) This calculator uses the discounted cash flow (DCF) method to perform investment appraisal by totalling cash flow for a fixed period. This calculator can perform the following four types of investment appraisal.
Net present value (NPV )
Net future value (NFV )
Internal rate of return (IRR )
Pay back period (PBP )
A cash flow diagram like the one shown below helps to visualize the movement of funds.
CF0
CF1
CF2 CF3
CF4
CF5 CF6
CF7
With this graph, the initial investment amount is represented by CF0. The cash flow one year later is shown by CF1, two years later by CF2, and so on.
Investment appraisal can be used to clearly determine whether an investment is realizing profits that were originally targeted.
uNPV
NPV = CF0 + + + + + (1+ i) CF1
(1+ i)2
CF2
(1+ i)3
CF3
(1+ i)n
CFn i =
100
I %
n: natural number up to 254
uNFV
NFV = NPV (1 + i )n
uIRR
0 = CF0 + + + + + (1+ i) CF1
(1+ i)2
CF2
(1+ i)3
CF3
(1+ i)n
CFn
In this formula, NPV = 0, and the value of IRR is equivalent to i 100. It should be noted, however, that minute fractional values tend to accumulate during the subsequent calculations performed automatically by the calculator, so NPV never actually reaches exactly zero. IRR becomes more accurate the closer that NPV approaches to zero.
2-4-1 Cash Flow (Investment Appraisal)
20010101
uPBP
PBP is the value of n when NPV > 0 (when investment can be recovered).
Press 3(CASH) from the Financial 1 screen to display the following input screen for Cash Flow.
3(CASH)
I% ............................... interest rate (%)
Csh .............................. list for cash flow
If you have not yet input data into a list, press 5('LIST) and input data into a list.
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1(NPV) ......... Net present value
2(IRR) .......... Internal rate of return
3(PBP) ......... Pay back period
4(NFV) ......... Net future value
5('LIST) ..... Inputs data from a list
6(LIST) ......... Specifies a list for data input
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function keys to maneuver between calculation result screens.
1(REPT) ...... Parameter input screen
6(GRPH) ..... Draws graph
2-4-2 Cash Flow (Investment Appraisal)
1
20010101
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph.
Press i to turn off trace.
Press i again to return to the parameter input screen.
2-4-3 Cash Flow (Investment Appraisal)
20010101
2-5 Amortization This calculator can be used to calculate the principal and interest portion of a monthly installment, the remaining principal, and amount of principal and interest repaid up to any point.
uFormula
b
a
d
e
c
1 2 m n
a: interest portion of installment PM1 (INT )
b: principal portion of installment PM1 (PRN )
c: balance of principal after installment PM2 (BAL )
d: total principal from installment PM1 to payment of installment PM2 (PRN )
e: total interest from installment PM1 to payment of installment PM2 (INT )
*a + b = one repayment (PMT )
a : INTPM1 = I BALPM11 i I (PMT sign) b : PRNPM1 = PMT + BALPM11 i c : BALPM2 = BALPM21 + PRNPM2
d : PRN = PRNPM1 + PRNPM1+1 + + PRNPM2
e : INT = INTPM1 + INTPM1+1 + + INTPM2
PM2
PM1
PM2
PM1
BAL0 = PV (INT1 = 0 and PRN1 = PMT at beginning of installment term)
(Number of payments)
Amount of single payment
2-5-1 Amortization
20010101
uConverting between the nominal interest rate and effective interest rate
The nominal interest rate (I% value input by user) is converted to an effective interest rate (I%') for installment loans where the number of installments per year is different from the number of compound interest calculation periods.
I%' = I%
(1+ ) 1 [C / Y ] [P / Y ]
100 [C / Y ]{ }100
The following calculation is performed after conversion from the nominal interest rate to the effective interest rate, and the result is used for all subsequent calculations.
i = I%'100
Press 4(AMT) from the Financial 1 screen to display the following input screen for interest rate conversion.
4(AMT)
PM1 ............................. first installment of installments 1 through n
PM2 ............................. second installment of installments 1 through n
n .................................. installments
I% ............................... interest rate
PV ............................... principal
PMT ............................ payment for each installment
FV ............................... balance following final installment
P/Y .............................. installments per year
C/Y .............................. compoundings per year
2-5-2 Amortization
20010101
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1(BAL) ......... Balance of principal after installment PM2
2(INT) .......... Interest portion of installment PM1
3(PRN) ......... Principal portion of installment PM1
4( INT) ....... Total interest paid from installment PM1 to installment PM2
5( PRN) ...... Total principal paid from installment PM1 to installment PM2
6(CMPD) ...... Compound interest screen
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function keys to maneuver between calculation result screens.
1(REPT) ....... Parameter input screen
4(CMPD) ...... Compound interest screen
6(GRPH) ...... Draws graph
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph.
The first press of 1(TRACE) displays INT and PRN when n = 1. Each press of e shows INT and PRN when n = 2, n = 3, and so on.
Press i to turn off trace.
Press i again to return to the parameter input screen.
2-5-3 Amortization
20010101
2-6 Interest Rate Conversion The procedures in this section describe how to convert between the annual percentage rate and effective interest rate.
uFormula
EFF = n
APR/1001+ 1 100 n
APR = 100 EFF1+ 1 n 100
1 n
Press 5(CNVT) in the Financial 1 screen to display the following input screen for interest rate conversion.
5(CNVT)
n ....................................... number of compoundings
I% ............................... interest rate
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1('EFF) ... Converts annual percent rate to effective interest rate
2('APR) ... Converts effective interest rate to annual percent rate
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function key to maneuver between calculation result screens.
1(REPT) ... Parameter input screen
APR : annual percentage rate (%) EFF : effective interest rate (%) n : number of compoundings
2-6-1 Interest Rate Conversion
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2-7 Cost, Selling Price, Margin Cost, selling price, or margin can be calculated by inputting the other two values.
uFormula
CST = SEL 100 MRG1
SEL =
100 MRG1
CST
MRG(%) = SEL CST1 100
Press 1(COST) from the Financial 2 screen to display the following input screen.
6(g)1(COST)
Cst ............................... cost
Sel ............................... selling price
Mrg .............................. margin
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1(COST) .... Cost
2(SEL) ....... Selling price
3(MRG) ...... Margin
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function key to maneuver between calculation result screens.
1(REPT) ... Parameter input screen
CST : cost SEL : selling price MRG : margin
2-7-1 Cost, Selling Price, Margin
20010101
2-8 Day/Date Calculations You can calculate the number of days between two dates, or you can determine what date comes a specific number of days before or after another date.
Press 2(DAYS) from the Financial 2 screen to display the following input screen for day/ date calculation.
6(g)2(DAYS)
d1 ................................ date 1
d2 ................................ date 2
D ................................. number of days
To input a date, first highlight d1 or d2. Pressing a number key to input the month causes an input screen like the one shown below to appear on the display.
2-8-1 Day/Date Calculations
# The set up screen can be used to specify either a 365-day or 360-day year for financial calculations. Day/date calculations are also performed in accordance with the current setting for number of days in the year, but the following calculations cannot be performed
when the 360-day year is set. Attempting to do so causes an error.
(Date) + (Number of Days)
(Date) (Number of Days)
# The allowable calculation range is January 1, 1901 to December 31, 2099.
20010101
Input the month, day, and year, pressing w after each.
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1(PRD) ........ Number of days from d1 to d2 (d2 d1)
2(d1+D) ....... d1 plus a number of days (d1 + D)
3(d1 D) ..... d1 minus a number of days (d1 D)
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function key to maneuver between calculation result screens.
1(REPT) ...... Parameter input screen
360-day Date Mode Calculations
The following describes how calculations are processed when 360 is specified for the Date Mode item in the SET UP screen.
If d1 is day 31 of a month, d1 is treated as day 30 of that month is used.
If d2 is day 31 of a month, d2 is treated as day 1 of the following month, unless d1 is day 30.
2-8-2 Day/Date Calculations
20010101
2-9 Depreciation Any of the following four methods can be used to calculated depreciation.
uStraight-Line Method
The straight-line method calculates depreciation for a given period.
{Y1}(PVFV ) SL1 =
n 12 u
(PVFV ) SLj =
n 12{Y1}
({Y1}G12)
(PVFV ) n 12
uSLn+1 =
Depreciation for an item acquired part way through a year can be calculated by month.
uFixed Percentage Method
Fixed percentage method can be used to calculate depreciation for a given period, or to calculate the depreciation rate.
100 I%
FPj = (RDVj1 + FV )
100 {Y1}I%
FP1 = PV 12
FPn+1 = RDVn ({Y1}G12)
RDV1 = PV FV FP1
RDVj = RDVj1 FPj
RDVn+1 = 0 ({Y1}G12)
Depreciation for an item acquired part way through a year can be calculated by month.
SL j : depreciation charge for the jth year
n : useful life in years PV : original cost (basis) FV : scrap value (salvage value) j : year Y1 : number of depreciable months
in first year
FPj : depreciation charge for the jth year RDVj : remaining depreciable value at the
end of jth year I% : depreciation rate
2-9-1 Depreciation
20010101
uSum-of-the-Year's Digits Method
The sum-of-the-year's-digits method calculates depreciation for a given period.
12 {Y1}
n' = n
n (n +1) Z =
2
2 (n' integer part +1)(n' integer part + 2*n' fraction part )
Z' =
SYD1 = {Y1}
12 n Z
(PV FV )
n' j+2 Z'
)(PV FV SYD1) ( jG1)SYDj = (
RDV1 = PV FV SYD1
RDVj = RDVj 1 SYDj
n' (n +1)+2 Z'
)(PV FV SYD1) ({Y1}G12) 12{Y1}
12 SYDn+1 = (
Depreciation for an item acquired part way through a year can be calculated by month.
uDeclining Balance Method
The declining balance method calculates depreciation for a given period.
RDV1 = PV FV DB1
({Y1}G12)
({Y1}G12)
100n Y1I%
DB1 = PV
100n I%
12
DBj = (RDVj1 + FV )
RDVj = RDVj1 DBj
DBn +1 = RDVn
RDVn+1 = 0
Depreciation for an item acquired part way through a year can be calculated by month.
SYDj : depreciation charge for the jth year RDVj : remaining depreciable value at the
end of jth year
DBj : depreciation charge for the jth year
RDVj : remaining depreciable value at the end of jth year
I% : factor (%)
2-9-2 Depreciation
1
20010101
Press 3(DEPR) from the Financial 2 screen to display the following input screen for depreciation.
6(g)3(DEPR)
n .................................. useful life in years
I% ............................... depreciation rate/factor
PV ............................... original cost (basis)
FV ............................... scrap value (salvage value)
j ................................... year
Y1 .............................. number of depreciable months in first year
Parameters can be displayed as integer or decimal values only. Inputting a fraction causes it to be converted to a decimal value.
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1(SL) ........... Straight-Line Method
2(FP) ........... 1.Fixed Percentage Method
........... 2.Depreciation ratio
3(SYD) ........ Sum-of-the-Year's Digits Method
4(DB) .......... Declining Balance Method
2-9-3 Depreciation
1
20010101
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function keys to maneuver between calculation result screens.
1(REPT) ...... Parameter input screen
6(TABL) ....... Calculation result table
The following function keys are on the calculation result table screen.
1(REPT) ...... Parameter input screen
6(GRPH) ..... Draws graph
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph.
Press i to turn off trace.
Press i again to return to the parameter input screen.
2-9-4 Depreciation
1
20010101
2-10 Bonds The bond calculation function calculates the price and yield of a bond.
uFormula
PRC : price per $100 of face value CPN : annual coupon rate (%) YLD : yield to maturity (%) A : accrued days M : number of coupon payments per year (1=annual, 2=semi annual) N : number of coupon payments between settlement date and maturity date RDV : redemption price or call price per $100 of face value D : number of days in coupon period where settlement occurs B : number of days from settlement date until next coupon payment date = D A INT : accrued interest CST : price including interest
Less than six months to redemption
PRC = ( )
RDV + M
CPN
1+ ( ) D
B
M
YLD/100
D
A
M
CPN
Six months or more to redemption
D
A
M
CPN PRC = +
RDV
(1+ ) M
YLD/100 (1+ )
M
YLD/100
M
CPN
N
k=1 (N1+B/D ) (K1+B/D )
D
A
M
CPN INT =
CST = PRC + INT
D
Issue date
Redemption date
Purchase date Coupon Payment dates
A B
2-10-1 Bonds
1
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Press 4(BOND) from the Financial 2 screen to display the following input screen for band calculation.
6(g)4(BOND)
d1 ................................ purchase date
d2 ................................ redemption date
RDV ............................ redemption price or call price per $100 of face value
CPN ............................ annual coupon rate (%)
PRC ............................ price per $100 of face value
YLD ............................. yield to maturity (%)
To input a date, first highlight d1 or d2. Pressing a number key to input the month causes an input screen like the one shown below to appear on the display.
Input the month, day, and year, pressing w after each.
After configuring the parameters, press one of the function keys noted below to perform the corresponding calculation.
1(PRC) ..... Price per $100 of face value
2(YLD) ..... Yield to maturity
2-10-2 Bonds
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An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function keys to maneuver between calculation result screens.
1(REPT) .......Parameter input screen
5(MEMO) .....Screen of various bond calculation values*
6(GRPH) ......Draws Graph
Pressing 5(MEMO) displays various bond calculation values, like those shown here.
*The interest payment date is calculated from d2 when 365 is specified for the Date Mode item in the SET UP screen.
w~w
6(GRPH)
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph.
Press i to turn off trace.
Press i again to return to the parameter input screen.
2-10-3 Bonds
1
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2-11 TVM Graph The TVM Graph lets you assign two of the five parameters (n, I%, PV, PMT, FV) to the x-axis and y-axis of a graph, and plot changes in y as the value of x changes.
Press 5(TVMG) from the Financial 2 screen to display the following input screen for TVM Graph.
6(g)5(TVMG)
After configuring the parameters, press the function keys noted below to assign parameters to the x-axis and y-axis.
1(X) ... Assigns highlighted parameter to the x-axis
2(Y) ... Assigns highlighted parameter to the y-axis
After making the required settings, draw the graph.
6(GRPH) ... Draws graph
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation results along the graph.
Press i to turn off trace.
2-11-1 TVM Graph
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Pressing 6(Y-CAL) after drawing a graph displays the screen shown below.
Inputting an x-axis value on this screen and pressing w displays the corresponding y-axis value.
Press i again to return to the parameter input screen.
Calculation may take some time to perform when you specify I% as the y-axis parameter.
2-11-2 TVM Graph
Chapter
This chapter explains how to solve the four types of differential equations listed below.
Differential equations of the first order Linear differential equations of the second order Differential equations of the Nth order System of first order differential equations
3-1 Using the DIFF EQ Mode
3-2 Differential Equations of the First Order
3-3 Linear Differential Equations of the Second Order
3-4 Differential Equations of the Nth Order 3-5 System of First Order Differential Equations
Differential Equations 3
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3-1-1 Using the DIFF EQ Mode
3-1 Using the DIFF EQ Mode You can solve differential equations numerically and graph the solutions. The general procedure for solving a differential equation is described below.
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution 2. Select the differential equation type.
1(1st) ........ Four types of first order differential equations
2(2nd) ...... Second order linear differential equations
3(N-th) ...... Differential equations of the first order through ninth order
4(SYS) ..... System of the first order differential equations
5(RCL) ..... Displays a screen for recalling a previous differential equation.
With 1(1st), you need to make further selections of differential equation type. See Differential equations of the first order for more information.
With 3(N-th), you also need to specify the order of the differential equation, from 1 to 9.
With 4(SYS), you also need to specify the number of unknowns, from 1 to 9.
3. Enter the differential equation.
4. Specify the initial values.
5. Press 5(SET) and select b(Param) to display the Parameter screen. Specify the calculation range. Make the parameter settings you want.
h ................... Step size for the classical Runge-Kutta method (fourth order)
Step ............. Number of steps for graphing*1 and storing data in LIST.
SF ................ The number of slope field columns displayed on the screen (0 100). The slope fields can be displayed only for differential equations of the first order.
*1When graphed for the first time, a function is always graphed with every step. When the function is graphed again, however, it is
graphed according to a value of Step. For example, when Step is set to 2, the function is graphed with every two steps.
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3-1-2 Using the DIFF EQ Mode
6. Specify variables to graph or to store in LIST. Press 5(SET) and select c(Output) to display the list setting screen. x, y, y(1), y(2), ....., y(8) stand for the independent variable, the dependent variable, the first order derivative, the second order derivative, ....., and the eighth order derivative, respectively. 1st, 2nd, 3rd, ...., 9th stand for the initial values in order. To specify a variable to graph, select it using the cursor keys (f, c) and press 1(SEL). To specify a variable to store in LIST, select it using the cursor keys (f, c) and press 2(LIST).
7. Press !K(V-Window) to display the V-Window setting screen. Before you solve a differential equation, you need to make V-Window settings.
Xmin x-axis minimum value
max x-axis maximum value
scale x-axis value spacing
dot value corresponding to one x-axis dot
Ymin y-axis minimum value
max y-axis maximum value
scale y-axis value spacing
8. Press 6(CALC) to solve the differential equation.
The calculated result is graphed or stored in the list.
# Only the slope fields are displayed if you do not input initial values or if you input the wrong type of initial values.
# An error occurs if you set SF to zero and you do not input the initial values, or if you input the initial values inappropriately.
# You are advised to input parentheses and a multiplication sign between a value and an expression in order to prevent calculation errors.
# Do not confuse the - key and the - key. A syntax error occurs if you use the - key as the subtraction symbol.
# An error occurs if you input variable y in the function f(x). Variable x is treated as a variable. Other variables (A through , r, , excluding X and Y) are treated as constants and the value currently assigned to that variable is applied during the calculation.
# An error occurs if you input variable x in the function g(y). Variable y is treated as a variable. Other variables (A through , r, , excluding X and Y) are treated as constants and the value currently assigned to that variable is applied during the calculation.
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3-2-1 Differential Equations of the First Order
3-2 Differential Equations of the First Order
k Separable Equation
Description To solve a separable equation, simply input the equation and specify the initial values.
dy/dx = f(x)g(y)
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution 2. Press 1(1st) to display the menu of first order differential equations, and then select b(Separ).
3. Specify f(x) and g(y).
4. Specify the initial value for x0, y0.
5. Press 5(SET)b(Param).
6. Specify the calculation range.
7. Specify the step size for h.
8. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results.
9. Make V-Window settings.
10. Press 6(CALC) to solve the differential equation.
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3-2-2 Differential Equations of the First Order
Example To graph the solutions of the separable equation dy/dx = y2 1, x0 = 0, y0 = {0, 1}, 5 < x < 5, h = 0.1.
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1 (initial defaults)
Procedure 1m DIFF EQ
21(1st)b(Separ)
3 bw
a-(Y)Mc-bw
4 aw
!*( { )a,b!/( } )w
55(SET)b(Param)
6-fw
fw
7 a.bwi
85(SET)c(Output)4(INIT)i
9!K(V-Window)1(INIT)i
06(CALC)
Result Screen
# To graph a family of solutions, enter a list of initial conditions.
(x0, y0) = (0,0)
(x0, y0) = (0,1)
1
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3-2-3 Differential Equations of the First Order
k Linear Equation
To solve a linear equation, simply input the equation and specify initial values.
dy/dx + f(x)y = g(x)
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution 2. Press 1(1st) to display the menu of differential equations of the first order, and then
select c(Linear).
3. Specify f(x) and g(x).
4. Specify the initial value for x0, y0.
5. Press 5(SET)b(Param).
6. Specify the calculation range.
7. Specify the step size for h.
8. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results.
9. Make V-Window settings.
10. Press 6(CALC) to solve the differential equation.
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3-2-4 Differential Equations of the First Order
Example To graph the solution of the linear equation dy/dx + xy = x, x0 = 0, y0 = 2, 5 < x < 5, h = 0.1.
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1 (initial defaults)
Procedure 1m DIFF EQ
21(1st)c(Linear)
3vw
vw
4 aw
-cw
55(SET)b(Param)
6-fw
fw
7 a.bwi
85(SET)c(Output)4(INIT)i
9!K(V-Window)1(INIT)i
06(CALC)
Result Screen
1
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3-2-5 Differential Equations of the First Order
kBernoulli equation
To solve a Bernoulli equation, simply input the equation and specify the power of y and the initial values.
dy/dx + f(x)y = g(x)y n
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution 2. Press 1(1st) to display the menu of differential equations of the first order, and then
select d(Bern).
3. Specify f(x), g(x), and n.
4. Specify the initial value for x0, y0.
5. Press 5(SET)b(Param).
6. Specify the calculation range.
7. Specify the step size for h.
8. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results.
9. Make V-Window settings.
10. Press 6(CALC) to solve the differential equation.
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3-2-6 Differential Equations of the First Order
Example To graph the solution of the Bernoulli equation dy/dx 2y = y2, x0 = 0, y0 = 1, 5 < x < 5, h = 0.1.
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1 (initial defaults)
Procedure 1m DIFF EQ
21(1st)d(Bern)
3-cw
-bw
cw
4 aw
bw
55(SET)b(Param)
6-fw
fw
7 a.bwi
85(SET)c(Output)4(INIT)i
9!K(V-Window)1(INIT)i
06(CALC)
Result Screen
1
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3-2-7 Differential Equations of the First Order
kOthers
To solve a general differential equation of the first order, simply input the equation and specify the initial values. Use the same procedures as those described above for typical differential equations of the first order.
dy/dx = f(x, y)
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution 2. Press 1(1st) to display the menu of differential equations of the first order, and then
select e(Others).
3. Specify f(x, y).
4. Specify the initial value for x0, y0.
5. Press 5(SET)b(Param).
6. Specify the calculation range.
7. Specify the step size for h.
8. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results.
9. Make V-Window settings.
10. Press 6(CALC) to solve the differential equation.
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3-2-8 Differential Equations of the First Order
Example To graph the solution of the first order differential equation dy/dx = cos x, x0 = 0, y0 = 1, 5 < x < 5, h = 0.1.
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1 (initial defaults)
Procedure 1m DIFF EQ
21(1st)e(Others)
3-cvw
4 aw
bw
55(SET)b(Param)
6-fw
fw
7 a.bwi
85(SET)c(Output)4(INIT)i
9!K(V-Window)1(INIT)i
06(CALC)
Result Screen
1
20010101
3-3-1 Linear Differential Equations of the Second Order
3-3 Linear Differential Equations of the Second Order
Description To solve a linear differential equation of the second order, simply input the equation and specify the initial values. Slope fields are not displayed for a linear differential equation of the second order.
y + f(x) y + g(x)y = h(x)
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution 2. Press 2(2nd).
3. Specify f(x), g(x), and h(x).
4. Specify the initial value for x0, y0, y0.
5. Press 5(SET)b(Param).
6. Specify the calculation range.
7. Specify the step size for h.
8. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results.
9. Make V-Window settings.
10. Press 6(CALC) to solve the differential equation.
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3-3-2 Linear Differential Equations of the Second Order
Example To graph the solution of the linear differential equation of the second order y + 9y = sin 3x, x0 = 0, y0= 1, y0 = 1, 0 < x < 10, h = 0.1.
Use the following V-Window settings.
Xmin = 1, Xmax = 11, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1
Procedure 1m DIFF EQ
22(2nd)
3 aw
jw
sdvw
4 aw
bw
bw
55(SET)b(Param)
6 aw
baw
7 a.bw*1i
85(SET)c(Output)4(INIT)i
9!K(V-Window)
-bw
bbw
bwc
-d.bw
d.bw
bw*2i
06(CALC)
Result Screen
*1 *2
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3-4-1 Differential Equations of the Nth Order
3-4 Differential Equations of the Nth Order You can solve differential equations of the first through ninth order. The number of initial values required to solve the differential equation depends on its order.
Enter dependent variables y, y, y, y(3), ....., y(9) as follows.
y .................... a-(Y)
y ................... 3(y(n))b(Y1)
y ................... 3(y(n))c(Y2)
y(3)(=y) ......... 3(y(n))d(Y3)
y(8) ................. 3(y(n))i(Y8)
y(9) ................. 3(y(n))j(Y9)
kDifferential Equation of the Fourth Order
The following example shows how to solve a differential equation of the fourth order.
y(4) = f(x, y, ...... , y(3))
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution 2. Press 3(N-th).
3. Press 3(n)e to select a differential equation of the fourth order.
4. Specify y(4).
5. Specify the initial value for x0, y0, y0, y0, and y(3) 0.
6. Press 5(SET)b(Param).
7. Specify the calculation range.
8. Specify the step size for h.
9. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results.
10. Make V-Window settings.
11. Press 6(CALC) to solve the differential equation.
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3-4-2 Differential Equations of the Nth Order
Example To graph the solution of the differential equation of the fourth order below y(4) = 0, x0 = 0, y0 = 0, y0 = 2, y0 = 0, y(3)0 = 3, 5 < x < 5, h = 0.1.
Use the following V-Window settings.
Xmin = 6.3, Xmax = 6.3, Xscale = 1
Ymin = 3.1, Ymax = 3.1, Yscale = 1 (initial defaults)
Procedure 65(SET)b(Param)
7-fw
fw
8 a.bw*1i
95(SET)c(Output)4(INIT)i
0!K(V-Window)1(INIT)i
!6(CALC)
1m DIFF EQ
23(N-th)
33(n)ew
4 aw
5 aw
aw
-cw
aw
dw
Result Screen
*1
1
20010101
3-4-3 Differential Equations of the Nth Order
kConverting a High-order Differential Equation to a System of First Order Differential Equations
You can convert a single N-th order differential equation to a system of n first order differential equations.
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution (N = 3) 2. Press 3(N-th).
3. Press 3(n)d to select a differential equation of the third order.
4. Perform substitutions as follows.
y Y1 (3(y(n))b)
y Y2 (3(y(n))c)
5. Specify the initial value for x0, y0, y0, and y0.
6. Press 2(SYS).
7. Press w(Yes).
The entered differential equation is converted to a system of three first order differential equations. Initial values are also converted accordingly.
1
20010101
Example Express the differential equation below as a set of first order differential equations. y(3) = sinx y y, x0 = 0, y0 = 0, y0 = 1, y0 = 0.
Procedure 1m DIFF EQ
23(N-th)
33(n)dw
4sv-3(y(n)) b-3(y(n))cw
5 aw
aw
bw
aw
62(SYS)
7w(Yes)
The differential equation is converted to a set of first order differential equations as shown below.
(y1) = dy/dx = (y2)
(y2) = d2y/dx2 = (y3)
(y3) = sin x (y2) (y3).
Initial values are also converted to (x0 = 0), ((y1)0 = 0), ((y2)0 = 1), and ((y3)0 = 0)).
# On the system of first order differential equations screen, dependent valuables are expressed as follows.
(y1) (Y1) (y2) (Y2) (y3) (Y3)
Result Screen
3-4-4 Differential Equations of the Nth Order
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3-5 System of First Order Differential Equations A system of first order differential equations, for example, has dependent variables (y1), (y2), ....., and (y9), and independent variable x. The example below shows a system of first order differential equations.
(y1)= (y2)
(y2)= (y1) + sin x
Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Execution 2. Press 4(SYS).
3. Enter the number of unknowns.
4. Enter the expression as shown below.
(y1) Y1 (3(yn)b)
(y2) Y2 (3(yn)c)
(y9) Y9 (3(yn)j)
5. Specify the initial value for x0, (y1)0, (y2)0 and so on, if necessary.
6. Press 5(SET)b(Param).
7. Specify the calculation range.
8. Specify the step size for h.
9. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results.
10. Make V-Window settings.
11. Press 6(CALC) to solve the system of first order equations for y1, y2, and so on.
3-5-1 System of First Order Differential Equations
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Example 1 To graph the solution of first order differential equations with two unknowns below. (y1)= (y2), (y2) = (y1) + sin x, x0 = 0, (y1)0 = 1, (y2)0 = 0.1, 2 < x < 5, h = 0.1.
Use the following V-Window settings.
Xmin = 3, Xmax = 6, Xscale = 1
Ymin = 2, Ymax = 2, Yscale = 1
Procedure 1m DIFF EQ
24(SYS)
32(2)
43(yn)cw
-3(yn)b+svw
5 aw
bw
a.bw
65(SET)b(Param)
7-cw
fw
8 a.bw*1i
95(SET)c(Output)4(INIT)
cc1(SEL)
(Select (y1) and (y2) to graph)*2
i
0!K(V-Window)
-dw
gw
bwc
-cw
cw
bwi
!6(CALC)
Result Screen
3-5-2 System of First Order Differential Equations
*1 *2
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Example 2 To graph the solution of the system of first order differential equations below. (y1) = (2 (y2)) (y1) (y2) = (2 (y1) 3) (y2) x0 = 0, (y1)0 = 1, (y2)0 = 1/4, 0 < x < 10, h = 0.1.
Use the following V-Window settings.
Xmin = 1, Xmax = 11, Xscale = 1
Ymin = 1, Ymax = 8, Yscale = 1
Procedure 1m DIFF EQ
24(SYS)
32(2)
4 (c-3(yn)c)*3(yn)
bw
(c*3(yn)b-d
)*3(yn)cw
5 aw
bw
b/ew
65(SET)b(Param)
7 aw
baw
8 a.bw*1i
95(SET)c(Output)4(INIT)
cc1(SEL) (Select (y1) and (y2) to graph.)
ff2(LIST)bw(Select LIST1 to store the values for x in LIST1)
c2(LIST)cw (Select LIST2 to store the values for (y1) in LIST2)
c2(LIST)dw (Select LIST3 to store the values for (y2) in LIST3)*2
i
0!K(V-Window)
-bwbbwbwc
-bwiwbwi
!6(CALC)
3-5-3 System of First Order Differential Equations
*1 *2
Result Screen
(y2)
(y1)
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k Further Analysis
To further analyze the result, we can graph the relation between (y1) and (y2).
Procedure 1m STAT
2 List 1, List 2, and List 3 contain values for x, (y1), and (y2), respectively.
31(GRPH)f(Set)
41(GPH1)
5c2(xy)
6c1(LIST)cw (XLIST = LIST2: (y1))
7c1(LIST)dw (YLIST = LIST3: (y2))
i
81(GRPH)b(S-Gph1)
Result Screen
3-5-4 System of First Order Differential Equations
(y1)
(y2)
20010101
Important! This calculator may abort calculation part way through when an overflow occurs part way
through the calculation when calculated solutions cause the solution curve to extend into a discontinuous region, when a calculated value is clearly false, etc.
The following steps are recommended when the calculator aborts a calculation as described above.
1. If you are able to determine beforehand the point where the solution curve overflows, stop the calculation before the point is reached.
2. If you are able to determine beforehand the point where the solution curve extends into a discontinuous region, stop the calculation before the point is reached.
3. In other cases, reduce the size of the calculation range and the value of h (step size) and try again.
4. When you need to perform a calculation using a very wide calculation range, store intermediate results in a list and perform a new calculation starting from step 3 using the stored results as initial values. You can repeat this step multiple times, if necessary.
k SET UP Items
G-Mem {G-Mem 20}/{1 20} ...... Specifies a memory location {G-Mem No.} for storage of the latest graph functions.
Note the following regarding SET UP screen settings whenever using the DIFF EQ Mode.
The DIFF EQ Mode temporarily stores data into Graph Memory whenever a differential equation calculation is performed. Before the calculation, DIFF EQ stores the latest graph functions into the currently specified Graph Memory (G-Mem) location. After the calculation, it recalls the graph functions from the specified G-Mem location, without deleting the G-Mem data. Because of this, you should specify the G-Mem location (number) where the DIFF EQ Mode stores the graph functions.
3-5-5 System of First Order Differential Equations
Chapter
4-1 E-CON Overview
4-2 EA-100 Setup 4-3 Setup Memory
4-4 Program Converter
4-5 Starting a Sampling Operation
E-CON
4
All of the explanations provided here assume that you are already familiar with the operating precautions, terminology, and operational procedures of the calculator and the EA-100.
20010101
20010101
4-1-1 E-CON Overview
4-1 E-CON Overview From the Main Menu, select E-CON to enter the E-CON Mode.
The E-CON provides the functions listed below for simple and more efficient data sampling using the CASIO EA-100.
1(SETUP) ... Displays a screen for setting up the EA-100.
2(MEM) ....... Displays a screen for saving EA-100 setup data under a file name.
3(PRGM) ..... Performs program conversion.
This function converts EA-100 setup data created by E-CON to a program.
It can also be used to convert data to a program that can be run on a CFX-9850 Series/fx-7400 Series calculator, and to transfer the data to the calculator.
4(START) .... Starts data collection.
6(HELP) ...... Displays E-CON help.
Pressing the K key (Setup Preview) or a cursor key while the E-CON main menu is on the screen displays a preview dialog box that shows the contents of the setup in the current setup memory area.
To close the preview dialog box, press i.
About online help Pressing the 6(HELP) key displays online help about the E-CON Mode.
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4-2 EA-100 Setup You can use the E-CON Mode to set up the EA-100 for sampling and then start sampling immediately or save the setup in calculator memory. You can use either of the following two methods to set up the EA-100.
Setup Wizard: With this method, you set up the EA-100 simply by replying to questions as they appear.
Advanced Setup: Advanced setup gives you control over a variety of sampling parameters, which means you can set up the EA-100 for exactly the type of sampling you want.
kUsing Setup Wizard to Create an EA-100 Setup
With Setup Wizard, you set up the EA-100 simply by replying to questions as they appear.
uSetup Wizard parameters Setup Wizard lets you make changes to the following three EA-100 basic sampling parameters using an interactive wizard format.
Sensor (Select Sensor) Specify a CASIO or VERNIER*1 sensor from a menu of choices.
Sampling Interval (Sampling Time) When you have Photogate specified as the sensor type, you can specify the sampling timing (Gate Status) and sampling time recording method (Record Time) with this parameter.
Number of Samples (Number of Samples) You can specify a value from 1 to 255.
Note the following limitations that apply to a setup made using Setup Wizard.
You can use Setup Wizard only when the EA-100 sampling channel is CH1 or SONIC.
The trigger for a Setup Wizard setup is always the w key.
Sampling results are always stored in List 1 (for the sampling time) and List 2 (for sample values).
4-2-1 EA-100 Setup
*1Vernier Software & Technology
20010101
u To create an EA-100 setup using Setup Wizard
Before getting started...
Before starting the procedure below, make sure you first decide if you want to start sampling immediately using the setup you create with Setup Wizard, or if you want to store the setup for later sampling.
See sections 4-3, 4-4, and 4-5 of this manual for information about procedures required to start sampling and to store a setup. We recommend that you read through the entire procedure first, referencing the other sections and pages as noted, before actually trying to perform it.
To terminate Setup Wizard part way through and cancel the setup, press !i(QUIT).
1. Display the E-CON main menu.
2. Press 1(SETUP). This displays the Setup EA-100 sub-menu.
3. Press b(Wizard). This displays the Setup Wizard initial screen.
4-2-2 EA-100 Setup
4. Press any key to start Setup Wizard and display the sensor specification screen.
Press 1 to specify a CASIO sensor, or 2 to specify a VERNIER sensor. From the menu of supported sensors that appears, select the one you want.
5. The screen that appears after you select a sensor in step 4 depends on whether or not you specified Photogate as the sensor.
If you did not specify Photogate, a screen for setting the sampling interval appears after step 4.
1. Use the number keys to input the sampling interval.
Inputting a value in the range of 0.52 to 300 enables real-time sampling. Inputting a value outside this range enables non-real-time sampling.
2. Press w.
If you specified Photogate as the sensor, a screen for setting the sampling timing appears after step 4.
1. Press either 1(Open) or 2(Close) to specify the sampling timing. Pressing either key advances to a screen for setting the time recording method.
See online help (GATE TRIGGER STATUS HELP) for details about the Open and Close settings.
2. Press 1(Abs) or 2(Rel) to specify the sampling time recording method.
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6. After you complete step 5, a screen for setting the number of samples appears on the display.
Use the number keys to input the number of samples, and then press w.
7. After you complete step 6, a screen like the one shown below appears on the display.
Press one of the function keys described below to specify what you want to do with the setup you have created with the above steps.
1(YES) ........ Starts sampling using the setup (page 4-5-1).
2(NO) .......... Returns to the E-CON main menu (page 4-1-1).
3(SAVE) ...... Saves the setup (page 4-3-1).
4(PRGM) ..... Converts the setup to a program (page 4-4-1).
Pressing 2(NO) in step 7 returns to the E-CON main menu and stores the setup in the E-CON Modes current setup memory area. You can use the following function key operations from the E-CON main menu to manipulate the contents of the current setup memory area.
2(MEM), then 2(SAVE) ....................... Saves the current setup memory area setup (page 4-3-1).
3(PRGM) ..... Converts the setup in the current setup memory area to a program (page 4-4-1).
4(START) .... Starts sampling using the setup in the current setup memory area (page 4-5-1).
Pressing 1(SETUP) and then c(Advan) displays an Advanced Setup screen for more detailed control over the parameters that make up the setup in the current setup memory area. See Creating an EA-100 Setup Using Advanced Setup for more information about changing advanced setup parameters.
4-2-3 EA-100 Setup
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kCreating an EA-100 Setup Using Advanced Setup
Advanced Setup provides you with total control over a number of parameters that you can adjust to create the EA-100 setup that suits your particular needs.
u To create an EA-100 setup using Advanced Setup The following procedure describes the general steps for using Advanced Setup. Refer to the pages as noted for more information.
1. Display the E-CON main menu.
2. Press 1(SETUP). This displays the Setup EA-100 sub-menu.
3. Press c(Advan). This displays the Advanced Setup menu.
4. If you want to configure a custom probe at this point, press f(Custom Probe). Next, follow the steps under To configure a custom probe starting from the Advanced Setup menu on page 4-2-12.
You can also configure a custom probe during the procedure under To change Channel parameter settings on page 4-2-6.
Custom probe configurations you have stored in memory can be selected using Channel in step 5, below.
5. Use the Advanced Setup function keys described below to set other parameters.
b(Channel) .... Displays a screen for setting the following parameters: sampling channel, sensor, sensor configuration, and storage location for sample data (page 4-2-5).
c(Sample) ..... Displays a screen for setting the following parameters: real-time settings, sampling interval, number of samples, measurement time recording method, and storage location for measurement time records (page 4-2-7).
d(Trigger) ...... Displays a screen for setting sampling start (trigger) conditions (page 4-2-8).
e(Option) ....... Displays a screen for making View Window settings, real-time settings (channel for real-time sampling), and filter settings (page 4-2-10).
4-2-4 EA-100 Setup
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You can return the settings on the above setup screens (b through e) using the procedure described under To return setup parameters to their initial defaults.
6. After you create a setup, you can use the function key operations described below to start sampling or perform other operations.
1(START) .... Starts sampling using the setup (page 4-5-1).
2(MULT) ...... Starts MULTIMETER Mode sampling using the setup (page 4-2-14).
3(MEM) ....... Saves the setup (page 4-3-1).
4(PRGM) ..... Converts the setup to a program (page 4-4-1).
u To return setup parameters to their initial defaults Perform the following procedure when you want to return the parameters of the setup in the current setup memory area to their initial defaults.
1. While the Advanced Setup menu is on the display, press g(Initialize).
2. In response to the confirmation message that appears, press w to initialize the setup.
To clear the confirmation message without initializing the setup, press i.
uAdvanced setup parameters This section provides detailed information about the parameters you can change in step 5 of the procedure under To create an EA-100 setup using Advanced Setup on page 4-2-4.
Channel Selecting this parameter displays a screen where you can specify the EA-100 channel to be used for sampling, the type of sensor used for each channel, and the storage location for saving sample data.
4-2-5 EA-100 Setup
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To change Channel parameter settings
1. While the Advanced Setup menu is on the display, press b(Channel).
This displays the Channel parameter setting screen.
4-2-6 EA-100 Setup
# If the list you specify for the Sample Data Storage Location (Store Data) in step 2 is already being used, data is overwritten according to the priority sequence shown below. 1. (Highest) SONIC 4. CH1 2. CH3 5. (Lowest) Record Time 3. CH2
Example: Specifying the same list number for CH3 sample data and SONIC sample data causes the CH3 data to be overwritten by the SONIC data.
2. Use the function key operations described below to change Channel parameter settings.
(1) Selected Channel 1(CH1) ........ Channel 1
2(CH2) ........ Channel 2
3(CH3) ........ Channel 3
4(SONIC) .... Sonic channel
(2) Selected Sensor (Sensor) 1(CASIO) .... CASIO sensor
2(VERN) ..... VERNIER sensor
3(CSTM) ..... Custom probe
4(None) ....... No sensor
(3) Sample Data Storage Location (Store Data) 1(LIST) ........ Displays a dialog box for specifying the list for storage of
measurement data. Specify a list number from 1 to 20.
To change the setting of an item, first use the f and c cursor keys to move the highlighting to the item. Next, use the function keys to select the setting you want. Note that the Channel parameter settings you make affect the Selected Channel only. You need to make separate settings for each channel you plan to use for sampling.
Specifying a sensor causes its sampling range (Range) and measurement unit (Unit) to appear on the display.
3. After all the settings are the way you want, press w to return to the Advanced Setup menu.
Current setting of selected item
Selected item
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Sample Selecting this parameter displays a screen for making real-time settings, and for specifying the sampling interval, number of samples, measurement time recording method, and storage location for measurement time records.
To change Sample Setup settings
1. While the Advanced Setup menu is on the display, press c(Sample).
This displays the Sample Setup screen.
2. Use the function key operations described below to change Sample Setup settings.
To change the setting of an item, first use the f and c cursor keys to move the highlighting to the item. Next, use the function keys to select the setting you want.
(1) Real-time Settings (Real-Time)
1(NO) .......... Disables real-time sampling.
2(YES) ........ Enables real-time sampling.
(2) Sampling Interval (Interval)
1(TIMER) .... Displays a dialog box for specifying a timer value, and enables fixed- interval sampling.
2(KEY) ........ Starts sampling operation that uses the EA-100 [TRIGGER] key. The [TRIGGER] key must be pressed the number of times specified for the number of samples.
3(GATE) ...... Starts sampling in accordance with the Photogate Gate Status trigger timing. Press 1, 2, or 3 to specify the channel of the Photogate sensor. Photogate is assigned to the sensor of the specified channel.
(3) Number of Samples (Number)
1(NUM) ....... Displays a dialog box for specifying the number of samples by inputting a value from 1 to 255.
4-2-7 EA-100 Setup
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(4) Measurement Time Recording Method (Rec Time)
1(None) ....... No time recorded.
2(Abs) ......... Absolute time in seconds from start of sampling
3(Rel) .......... Relative time (interval between samples) in seconds
4(Int A) ........ Absolute time calculated from sampling interval and number of samples
5(Int R) ........ Relative time calculated from sampling interval and number of samples
(5) Sample Data Storage Location (Store Data)
1(LIST) ........ Displays a dialog box for specifying the list (1 to 20) for storing sample data.
3. After all the settings are the way you want, press w to return to the Advanced Setup menu.
Trigger Use the Trigger Setup screen to specify the following measurement start (trigger) conditions: trigger source, trigger threshold, trigger edge.
To change Trigger Setup settings
1. While the Advanced Setup menu is on the display, press d(Trigger).
This displays the Trigger Setup screen.
4-2-8 EA-100 Setup
Current setting of selected item
Selected item
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2. Use the function key operations described below to change Trigger Setup settings.
To change the setting of an item, first use the f and c cursor keys to move the highlighting to the item. Next, use the function keys to select the setting you want.
(1) Trigger Source (Source)
1(KEY)
b([EXE]) .......... Calculator w key press starts sampling.
c(TRIGER) ...... EA-100 [TRIGGER] key press starts sampling.
2(CH1) ........ Channel 1
3(CH2) ........ Channel 2
4(CH3) ........ Channel 3
Specifying CH1, CH2, or CH3 as the trigger source displays the specified channels sensor name, trigger threshold initial value, measurement unit, and trigger edge initial value.
(2) Trigger Threshold (Threshold)
1(EDIT) ....... Displays a dialog box for inputting the trigger threshold. This option is available only when CH1, CH2, or CH3 is specified as the trigger source.
(3) Trigger Edge (Edge)
1(Rise) ........ Rising edge triggers sampling
2(Fall) .......... Falling edge triggers sampling
3. After all the settings are the way you want, press w to return to the Advanced Setup menu.
4-2-9 EA-100 Setup
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Option Use the Option Setup screen to make View Window settings, to specify the channel for real- time sampling, and to make filter settings.
To change Option Setup settings
1. While the Advanced Setup menu is on the display, press e(Option).
This displays the Option Setup screen.
2. Use the function key operations described below to change Option Setup settings.
To change the setting of an item, first use the f and c cursor keys to move the highlighting to the item. Next, use the function keys to select the setting you want.
(1) View Window Settings (V-Window)
1(Auto) ........ Makes View Window settings automatically.
2(Man) ........ Enables manual View Window settings.
3(SetY) ...... Displays screens for specifying the Y-axis (sample data) minimum value (Ymin) and maximum value (Ymax).
(2) Real-time Settings (Real-Time)
1(NO) .......... Disables real-time sampling.
2(YES) ........ Enables real-time sampling.
Note that this item is linked with the Real-Time item of the Sample Setup on page 4-2-7.
4-2-10 EA-100 Setup
Current setting of selected item
Selected item
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(3) Real-time Sampling Channel (Use CH)
1(CH1) ........ Channel 1
2(CH2) ........ Channel 2
3(CH3) ........ Channel 3
4(SONIC) .... Sonic channel
Note that the above options appear only when real-time sampling is turned on (by pressing 1(YES) for the Real-Time item).
(4) Filter Settings (Filter)
1(None) ....... No setting
2(S-G) ......... S-G Smoothing
b(5-p): 5-point c(9-p): 9-point
d(17-p): 17-point e(25-p): 25-point
3(MED) ....... Median Filter
b(3-p): 3-point c(5-p): 5-point
Note that the above options appear only when real-time sampling is turned off (by pressing 2(NO) for the Real-Time item).
3. After all the settings are the way you want, press w to return to the Advanced Setup menu.
u To configure a custom probe You can use the procedures in this section to configure a custom probe*1 for use with the EA-100.
Creating a New Custom Probe Configuration To configure a custom probe, you must input values for the constants of the fixed linear transformation formula (ax + b). The required constants are slope (a) and intercept (b). x in the above expression (ax + b) is the sampled voltage value (sampling range: 0 to 5 volts). You can use either of the two following procedures to create a new custom probe configuration while creating an EA-100 setup using Advanced Setup.
4-2-11 EA-100 Setup
*1The term custom probe means any sensor other than the CASIO or VERNIER sensors specified as standard for the E-CON Mode.
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To configure a custom probe starting from the Advanced Setup menu
1. From the E-CON main menu, press 1(SETUP) and then c(Advan) to display the Advanced Setup menu.
See Creating an EA-100 Setup Using Advanced Setup on page 4-2-4 for more information.
2. On the Advanced Setup menu, press f(Custom Probe) to display the Custom Probe List.
The message No Custom Probe appears if the Custom Probe List is empty.
3. Press 2(NEW).
This displays the screen for inputting the name of the new custom probe.
4. Input up to 18 characters for the custom probe name, and then press w.
This displays the screen for configuring a new custom probe.
5. Use the function key operations described below to make custom probe configuration settings.
To change the setting of an item, first use the f and c cursor keys to move the highlighting to the item. Next, use the function keys to select the setting you want.
(1) Slope Press 1(EDIT) to display a dialog box for inputting the slope for the linear transformation formula.
(2) Intercept Press 1(EDIT) to display a dialog box for inputting the intercept for the linear transformation formula.
(3) Unit Name Press 1(EDIT) to display a dialog box for inputting up to eight characters for the unit name.
6. Press wand then input a memory number (1 to 99).
This saves the custom probe configuration and returns to the Custom Probe List, which should now contain the new custom probe you configured.
4-2-12 EA-100 Setup
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To configure a custom probe starting from the Channel parameter setting screen
1. From the E-CON main menu, press 1(SETUP) and then c(Advan) to display the Advanced Setup menu.
See Creating an EA-100 Setup Using Advanced Setup on page 4-2-4 for more information.
2. On the Advanced Setup menu, press b(Channel).
3. On the Channel parameter setting screen, press the function key (1, 2, or 3) for the channel whose parameter settings you want to change.
4. Next press c 3(CSTM) to display the Custom Probe List.
5. Perform steps 3 through 6 under To configure a custom probe starting from the Advanced Setup menu on page 4-2-12.
Editing an Existing Custom Probe Configuration Use the following procedure when you want to edit the configuration of an existing custom probe.
1. Display the Custom Probe List.
2. Select the custom probe whose configuration you want to edit.
Use the f and c cursor keys to highlight the name of the custom probe you want.
3. Press 3(EDIT).
This displays the screen for configuring a custom probe.
To edit the custom probe settings, perform the procedure starting from step 5 under To configure a custom probe starting from the Advanced Setup menu on page 4-2-12.
Deleting a Custom Probe Configuration Use the following procedure when you want to delete the configuration of a custom probe.
1. Display the Custom Probe List.
2. Select the custom probe whose configuration you want to delete.
Use the f and c cursor keys to highlight the name of the custom probe you want.
3. Press 4(DEL).
4. In response to the confirmation message that appears, press w to delete the custom probe configuration.
To clear the confirmation message without deleting anything, press i.
4-2-13 EA-100 Setup
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u To use the MULTIMETER Mode You can use the Channel parameter settings of Advanced Setup to configure a channel so that EA-100 MULTIMETER Mode sampling is triggered by a calculator operation.
1. Use the Channel parameter setting Sensor item to configure a sensor.
See To create an EA-100 setup using Advanced Setup on page 4-2-4 for more information.
2. After making the required settings, press w to display the Advanced Setup menu and then press 2(MULT).
This displays the channel selection screen for MULTIMETER Mode sampling.
3. Specify a channel for sampling.
Pressing a function key to specify a channel causes the EA-100 to enter the MULTIMETER Mode and start sampling over the specified channel.
4. To stop MULTIMETER Mode sampling, first press the A key. After the Break screen appears, press i.
Sample data is updated at intervals of 0.52 second.
Do not have sensors connected to channels other than the one you specify in step 3. However, it is not necessary to specify None for the Channel parameter Sensor item for the unused channels.
Sample data is not stored in memory.
4-2-14 EA-100 Setup
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4-3-1 Setup Memory
4-3 Setup Memory You can use setup memory to save EA-100 setups you create using Setup Wizard or Advanced Setup in calculator memory for later recall when you need them.
k Saving a Setup
A setup can be saved when any one of the following conditions exist.
After creating a new setup with Setup Wizard See step 7 under To create an EA-100 setup using Setup Wizard on page 4-2-2.
After creating a new setup with Advanced Setup See step 6 under To create an EA-100 setup using Advanced Setup on page 4-2-4 for more information.
While the E-CON main menu is on the display Performing the setup save operation while the E-CON main menu is on the display saves the contents of the current setup memory area (which were created using Setup Wizard or Advanced Setup).
Details on saving a setup are listed below.
u To save a setup 1. Start the save operation by performing one of the function key operations described
below.
If the final Setup Wizard screen is on the display, press 3(SAVE).
If the Advanced Setup menu screen is on the display, press 3(MEM).
If the E-CON main menu screen is on the display, press 2(MEM).
Performing any one of the above operations causes the setup memory list to appear.
The message No Setup-MEM appears if setup memory is empty.
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2. Press 2(SAVE).
This displays the screen for inputting the setup name.
4-3-2 Setup Memory
3. Press w and then input a memory number (1 to 99).
If you start from the final setup screen, this saves the setup and the message Complete! appears. Press w to return to the final setup screen.
If you start from the Advanced Setup menu or the E-CON main menu, this saves the setup and returns to the setup memory list which includes the name you assigned it.
kUsing and Managing Setups in Setup Memory
All of the setups you save are shown in the setup memory list. After selecting a setup in the list, you can use it to sample data or you can edit it.
u To preview saved setup data You can use the following procedure to check the contents of a setup before you use it for sampling.
1. On the E-CON main menu, press 2(MEM) to display the setup memory list.
2. Use the f and c cursor keys to highlight the name of the setup you want.
3. Press K(Setup Preview).
This displays the preview dialog box.
4. To close the preview dialog box, press i.
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u To recall a setup and use it for sampling Be sure to perform the following steps before starting sampling with the EA-100.
1. Connect the calculator to the EA-100.
2. Turn on EA-100 power.
3. In accordance with the setup you plan to use, connect the proper sensor to the appropriate EA-100 channel.
4. Prepare the item whose data is to be sampled.
To recall a setup and use it for sampling
1. On the E-CON main menu, press 2(MEM) to display the setup memory list.
2. Use the f and c cursor keys to highlight the name of the setup you want.
3. Press 1(START).
4. In response to the confirmation message that appears, press w.
Pressing w sets up the EA-100 and then starts sampling.
To clear the confirmation message without sampling, press i.
u To change the name of setup data 1. On the E-CON main menu, press 2(MEM) to display the setup memory list.
2. Use the f and c cursor keys to highlight the name of the setup you want.
3. Press 3(REN).
This displays the screen for inputting the setup name.
4-3-3 Setup Memory
4. Input up to 18 characters for the setup name, and then press w.
This changes the setup name and returns to the setup memory list.
# See Operations during a sampling operation on page 4-5-2 for information about
operations you can perform while a sampling operation is in progress.
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u To delete setup data 1. On the E-CON main menu, press 2(MEM) to display the setup memory list.
2. Use the f and c cursor keys to highlight the name of the setup you want.
3. Press 4(DEL).
4. In response to the confirmation message that appears, press w to delete the setup.
To clear the confirmation message without deleting anything, press i.
u To recall setup data Recalling setup data stores it in the current setup memory area. You can then use Advanced Setup to edit the setup. This capability comes in handy when you need to perform a setup that is slightly different from one you have stored in memory.
1. On the E-CON main menu, press 2(MEM) to display the setup memory list.
2. Use the f and c cursor keys to highlight the name of the setup you want.
3. Press 5(LOAD).
4. In response to the confirmation message that appears, press w to recall the setup.
To clear the confirmation message without recalling the setup, press i.
4-3-4 Setup Memory
# Recalling setup data replaces any other data currently in the current setup memory area.
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4-4 Program Converter Program Converter converts an EA-100 setup you created using Setup Wizard or Advanced Setup to a program that can run on the calculator. You can also use Program Converter to convert a setup to a CFX-9850 Series/fx-7400 Series-compatible program and transfer it to a calculator.*1 *2
kConverting a Setup to a Program
A setup can be converted to a program when any one of the following conditions exists.
After creating a new setup with Setup Wizard See step 7 under To create an EA-100 setup using Setup Wizard on page 4-2-2.
After creating a new setup with Advanced Setup See step 6 under To create an EA-100 setup using Advanced Setup on page 4-2-4 for more information.
While the E-CON main menu is on the display Performing the program converter operation while the E-CON main menu is on the display converts the contents of the current setup memory area (which were created using Setup Wizard or Advanced Setup).
The program converter procedure is identical in all of the above cases.
u To convert a setup to a program 1. Start the converter operation by performing one of the function key operations described
below.
If the final Setup Wizard screen is on the display, press 4(PRGM).
If the Advanced Setup menu screen is on the display, press 4(PRGM).
If the E-CON main menu screen is on the display, press 3(PRGM).
This displays the program name input screen.
4-4-1 Program Converter
*1See the documentation that came with your scientific calculator or EA-100 for information about how to use a converted program.
*2See online help (PROGRAM CONVERTER HELP) for information about supported CFX- 9850 Series and fx-7400 Series models.
2. Input the name you want to assign to the program.
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3. Press w.
This starts conversion of the setup data to a program.
The message Complete! appears when conversion is complete.
u To convert setup data to a program and transfer it to a CFX-9850 Series/ fx-7400 Series calculator
1. Connect the scientific calculator (CFX-9850 Series or fx-7400 Series) to the ALGEBRA calculator.
Perform the necessary procedure on the scientific calculator to set it up to receive data.
2. Perform steps 1 and 2 of the procedure under To convert a setup to a program on page 4-4-1.
3. Press 1 (TRNS). On the sub-menu that appears, specify the type of scientific calculator (b: FX9850 or c: fx7400) for which you want to create a program.
Program conversion and transfer starts as soon as you specify a calculator model.
The message Complete! appears when conversion is complete.
4-4-2 Program Converter
# When you convent setup data to a CFX-9850 Series or fx-7400 Series program, any sample value storage list number greater than 5 is changed to 5.
# CFX-9850 Series or fx-7400 Series calculators support up to six lists only.
# List 6 is used for EA-100 setup.
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4-5 Starting a Sampling Operation The section describes how to use a setup created using the E-CON Mode to start an EA-100 sampling operation.
kBefore getting started...
Be sure to perform the following steps before starting sampling with the EA-100.
1. Connect the calculator to the EA-100.
2. Turn on EA-100 power.
3. In accordance with the setup you plan to use, connect the proper sensor to the appropriate EA-100 channel.
4. Prepare the item whose data is to be sampled.
k Starting a Sampling Operation
A sampling operation can be started when any one of the following conditions exist.
After creating a new setup with Setup Wizard See step 7 under To create an EA-100 setup using Setup Wizard on page 4-2-2.
After creating a new setup with Advanced Setup See step 6 under To create an EA-100 setup using Advanced Setup on page 4-2-4.
While the E-CON main menu is on the display Starting a sampling operation while the E-CON main menu is on the display performs sampling using the contents of the current setup memory area (which were created using Setup Wizard or Advanced Setup).
While the setup memory list is on the display You can select the setup you want on the setup memory list and then start sampling.
The following procedures explain the first three conditions described above. See To recall a setup and use it for sampling on page 4-3-3 for information about starting sampling from the setup memory list.
4-5-1 Starting a Sampling Operation
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u To start sampling 1. Start the sampling operation by performing one of the function key operations described
below.
If the final Setup Wizard screen is on the display, press 1(YES).
If the Advanced Setup menu screen is on the display, press 1(START).
If the E-CON main menu screen is on the display, press 4(START).
This sets up the EA-100 using the setup data in the current setup memory area.
To interrupt a setup while the above screen is on the display, press A.
2. The sampling start dialog box appears after setup of the EA-100 is complete.
The content of the sampling start dialog box depends on the settings contained in the setup. See Operations during a sampling operation below for information about this dialog box and other display screens.
uOperations during a sampling operation Sending a sample start command from the calculator to the EA-100 causes the following sequence to be performed.
Setup Data Transfer Sampling Start Sampling End Transfer of Sample Data from the EA-100 to the Calculator
The table on the next page shows how the trigger conditions and sensor type specified in the setup data affects the above sequence.
4-5-2 Starting a Sampling Operation
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4-5-3 Starting a Sampling Operation
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20010101
4-5-4 Starting a Sampling Operation
# Conductivity, heart rate, and pH sensors Sample values produced by these types of sensors lose accuracy unless the sensors are allowed to warm up. Perform the following procedure to ensure better sampling accuracy.
Using a Heart Rate Sensor
1. Select [TRIGGER] as the Trigger Source item of Advanced Setups Trigger parameter.
2. When the EA-100 is in the Ready state prior to sampling, hold down the EA-100s [TRIGGER] key for about 20 to 30 seconds, and then release it.
3. Press the EA-100s [TRIGGER] key when you want to start sampling.
Using a Conductivity or pH Sensor
1. Select [Yes] for the [Real-Time] setting on the Sample Setup screen of the Advanced Setup menu.
# Initial samples using conductivity, heart rate, and pH sensors are always inaccurate when starting from Setup Wizard.
# For detailed information about a sensor, see the documentation that comes with it.
1
20010101
Symbols
2 Distribution .................................... 1-4-9
2 Test ................................... 1-2-1, 1-2-18
A
Advanced Setup ............................... 4-2-4
Advanced Statistics .......................... 1-1-1
Amortization ...................................... 2-5-1
ANOVA ................................. 1-2-1, 1-2-22
B
Bernoulli equation ..............................3-2-5
Binomial Distribution ........................1-4-16
Bonds ..............................................2-10-1
C
Calculation range .............................. 3-1-1
Cash Flow ......................................... 2-4-1
Channel ............................................ 4-2-5
Compound Interest ........................... 2-3-1
Confidence Interval ........................... 1-3-1
Copy ................................................. 1-1-3
Cost .................................................. 2-7-1
Custom Probe .................................. 4-2-11
D
Date Calculation ............................... 2-8-1
Days Calculation ............................... 2-8-1
Dependent variable .......................... 3-1-2
Depreciation .................................... 2-9-1
Derivative ...........................................3-1-2
DIFF EQ Mode ..................................3-1-1
Differential equation .......................... 3-1-1
Differential equation of the first order ........................................... 3-2-1
Differential equation of the fourth order ........................................... 3-4-1
Differential equation of the Nth order ........................................... 3-4-1
Distribution ....................................... 1-4-1
E
E-CON HELP .................................... 4-1-1
E-CON Mode .................................... 4-1-1
EA-100 Setup ................................... 4-2-1
F
F Distribution .................................. 1-4-12
F Test .................................... 1-2-1, 1-2-20
Financial Calculations ....................... 2-1-1
G
Geometric Distribution .....................1-4-21
Graph Memory .................................. 3-5-5
H
h (step size) ...................................... 3-1-1
I
Independent variable ........................ 3-1-2
Initial value .............................. 3-1-1, 3-1-2
Interest Rate Conversion .................. 2-6-1
Investment Appraisal ........................ 2-4-1
1 Index
Index (Additional Functions)
20010101
2 Index
L
Linear differential equation of the second order ............................... 3-3-1
Linear equation ..................................3-2-3
List setting screen ..............................3-1-2
M
Margin ............................................... 2-7-1
MSE .................................................. 1-1-1
MULTIMETER Mode........................4-2-14
N
Normal Distribution ........................... 1-4-3
O
Option Setup ................................... 4-2-10
P
Parameter screen ..............................3-1-1
Poisson Distribution .........................1-4-19
Program Converter ........................... 4-4-1
R
Runge-Kutta method ........................ 3-1-1
S
Sample Setup ................................... 4-2-7
Selling Price ...................................... 2-7-1
Separable equation .......................... 3-2-1
Setup Memory .................................. 4-3-1
Setup Wizard .................................... 4-2-1
SF (slope field) ....................... 3-1-1, 3-1-2
Simple Interest .................................. 2-2-1
Slope field ............................... 3-1-1, 3-1-2
Starting a Sampling Operation ......... 4-5-1
STAT Mode ....................................... 1-1-1
Step .................................................. 3-1-1
Step size ........................................... 3-1-1
Student-t Distribution ........................ 1-4-7
System of the first order differential equations .......................... 3-4-3, 3-5-1
T
t Interval .................................. 1-3-1, 1-3-8
t Tests ................................... 1-2-1, 1-2-10
Tests ................................................. 1-2-1
Trigger Setup .................................... 4-2-8
TVM Graph ...................................... 2-11-1
TVM Mode ........................................ 2-1-1
V
V-Window ......................................... 3-1-2
Y
Y-CAL ............................................... 1-1-2
Z
Z Interval ................................. 1-3-1, 1-3-3
Z Tests .................................... 1-2-1, 1-2-2
CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Ci
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