Casio ALGEBRA FX 2.0 PLUS_FX 1.0 PLUS_Eng_Users Guide ALGEBRA_FX2.0_FX1.0_PLUS FX2.0 FX1.0 PLUS EN
User Manual: Casio ALGEBRA_FX2.0_FX1.0_PLUS ALGEBRA FX 2.0 PLUS, ALGEBRA FX 1.0 PLUS | Calculators | Manuals | CASIO
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E
ALGEBRA FX 2.0 PLUS
FX 1.0 PLUS
User’s Guide
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 applicable 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 protection 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 user’s 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
Connector FA-123
Power Graphic Unit to Power Graphic Unit
Power Graphic Unit to PC for IBM/Macintosh Machine
Declaration of Conformity
Model Number:
Trade Name:
Responsible party:
Address:
Telephone number:
ALGEBRA FX 2.0 PLUS / FX 1.0 PLUS
CASIO COMPUTER CO., LTD.
CASIO AMERICA, INC.
570 MT. PLEASANT AVENUE, DOVER, NEW JERSEY 07801
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.
IBM is a registered trademark of International Business Machines Corporation.
Macintosh is a registered trademark of Apple Computer, Inc.
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.
1
P
2. Load the four batteries that come with calculator.
• Make sure that the positive (+) and negative (–) ends of the batteries are facing correctly.
BACK UP
3. Remove the insulating sheet at the location marked “BACK UP” by pulling in the direction indicated by the arrow.
BACK UP
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.
2
19990401
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.
P button
* The above shows the ALGEBRA
FX 2.0 PLUS screen.
6. Use the cursor keys (f, c, d, e) to select the SYSTEM icon and press
) to display the contrast adjustment screen.
w, then press 2(
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.
20010102
Quick-Start
Turning Power On And Off
Using Modes
Basic Calculations
Replay Feature
Fraction Calculations
Exponents
Graph Functions
Dual Graph
Box Zoom
Dynamic Graph
Table Function
19990401
1
Quick-Start
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
you’re done, you’ll have mastered the basic operation of this calculator and will be ready
to proceed with the rest of this user’s 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, we’ve indicated it as follows:
Press
fh
Whenever necessary, we’ve included samples of what your screen should look like.
If you find that your screen doesn’t match the sample, you can restart from the beginning by pressing the “All Clear” button
.
o
TURNING POWER ON AND OFF
o.
OFF
To turn power off, press ! o.
To turn power on, press
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, let’s take a look at how to navigate around the modes.
To select the RUN • MAT Mode
1. Press
m to display the Main Menu.
* The above shows the ALGEBRA
FX 2.0 PLUS screen.
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20010102
2
Quick-Start
defc to highlight RUN
and then press w.
2. Use
•
MAT
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. Press
bf*d+gbw.
Parentheses Calculations
Example: 15 × (3 + 61)
1. Press
bf*(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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3
Quick-Start
SET UP
u3 to display the SET UP screen.
1. Press
2. Press
cccc1 (Deg) to specify
degrees as the angle unit.
3. Press
i to clear the menu.
4. Press
o to clear the unit.
5. Press
cf*sefw.
REPLAY FEATURE
d e
With the replay feature, simply press
or
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.
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REPLAY
4
Quick-Start
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. Press
2. Press
o.
b$bf$
bg+dh$
jw.
Indicates 6 7/144
Converting a Mixed Fraction to an Improper Fraction
d/c
While a mixed fraction is shown on the display, press
improper fraction.
!$to convert it to an
d/c
Press
!$again to convert back to a mixed fraction.
Converting a Fraction to Its Decimal Equivalent
While a fraction is shown on the display, press
equivalent.
Press
$ to convert it to its decimal
$ again to convert back to a fraction.
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5
Quick-Start
EXPONENTS
Example: 1250 × 2.065
1. Press
o.
2. Press
bcfa*c.ag.
3. Press
M and the ^ indicator appears on the display.
4. Press
f. The ^5 on the display indicates that 5 is an exponent.
5. Press
w.
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6
Quick-Start
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: θ ; 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.
defc to highlight
GRPH TBL, and then press w.
2. Use
•
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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7
Quick-Start
b(Root).
Press e for other roots.
2. Press
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).
d to move the pointer to the location where
X = –1, and then press w. Next, use e to
3. Use
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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8
Quick-Start
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
SET UP
1. Press
u3ccc2(G+G)
to specify “G+G” for the Dual Screen setting.
i, and then input the two functions.
v(v+b)
(v-c)w
v+b.cw
2. Press
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).
defc
2. Use
to move the pointer
to one corner of the area you want to specify and
.
then press
w
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9
Quick-Start
defc
3. Use
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.
w
4. Press
, 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 = AX
1. Press
2. Use
2
m.
d e f c to highlight DYNA,
w.
and then press
3. Input the formula.
A
avvxw
12356
19990401
10
Quick-Start
4
bw to assign an initial value
4. Press
(VAR)
of 1 to coefficient A.
5. Press
2(RANG) bwdwb
wto specify the range and increment of change
in coefficient A.
6. Press
i.
6
7. Press
(DYNA) to start Dynamic Graph drawing.
The graphs are drawn 10 times.
↓
↓↑
↓↑
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11
Quick-Start
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) (X–2)
1. Press
2. Use
m.
defc to highlight
w.
GRPH • TBL, and then press
3. Input the formula.
v(v+b)
(v-c)w
4. Press
table.
6(g)5(TABL) to generate the number
To learn all about the many powerful features of this calculator, read on and explore!
19990401
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 calculator’s 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 user’s guide and ensure
that the problem is not due to insufficient battery power, programming or operational errors.
19990401
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 user’s guide are subject to change without notice.
• No part of this user’s guide may be reproduced in any form without the express written
consent of the manufacturer.
• The options described in Chapter 10 of this user’s guide may not be available in certain
geographic areas. For full details on availability in your area, contact your nearest CASIO
dealer or distributor.
19990401
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FX 1.0 PLUS
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19990401
20010102
1
Contents
Contents
Getting Acquainted — Read This First!
Chapter 1 Basic Operation
1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
Chapter 2
2-1
2-2
2-3
2-4
2-5
2-6
2-7
2-8
Chapter 3
3-1
3-2
3-3
3-4
Chapter 4
4-1
4-2
4-3
4-4
Keys ................................................................................................. 1-1-1
Display .............................................................................................. 1-2-1
Inputting and Editing Calculations .................................................... 1-3-1
Option (OPTN) Menu ....................................................................... 1-4-1
Variable Data (VARS) Menu ............................................................. 1-5-1
Program (PRGM) Menu ................................................................... 1-6-1
Using the Set Up Screen .................................................................. 1-7-1
When you keep having problems… ................................................. 1-8-1
Manual Calculations
Basic Calculations ............................................................................ 2-1-1
Special Functions ............................................................................. 2-2-1
Specifying the Angle Unit and Display Format ................................. 2-3-1
Function Calculations ....................................................................... 2-4-1
Numerical Calculations ..................................................................... 2-5-1
Complex Number Calculations ......................................................... 2-6-1
Binary, Octal, Decimal, and Hexadecimal Calculations
with Integers ..................................................................................... 2-7-1
Matrix Calculations ........................................................................... 2-8-1
List Function
Inputting and Editing a List ............................................................... 3-1-1
Manipulating List Data ...................................................................... 3-2-1
Arithmetic Calculations Using Lists .................................................. 3-3-1
Switching Between List Files ............................................................ 3-4-1
Equation Calculations
Simultaneous Linear Equations ........................................................ 4-1-1
Higher Degree Equations ................................................................. 4-2-1
Solve Calculations ............................................................................ 4-3-1
What to Do When an Error Occurs ................................................... 4-4-1
19990401
20011101
2
Contents
Chapter 5
5-1
5-2
5-3
5-4
5-5
5-6
5-7
5-8
5-9
5-10
5-11
Chapter 6
6-1
6-2
6-3
6-4
Chapter 7
7-1
7-2
7-3
7-4
Chapter 8
8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
Chapter 9
9-1
9-2
9-3
9-4
9-5
Graphing
Sample Graphs ................................................................................ 5-1-1
Controlling What Appears on a Graph Screen ................................. 5-2-1
Drawing a Graph .............................................................................. 5-3-1
Storing a Graph in Picture Memory .................................................. 5-4-1
Drawing Two Graphs on the Same Screen ...................................... 5-5-1
Manual Graphing .............................................................................. 5-6-1
Using Tables ..................................................................................... 5-7-1
Dynamic Graphing ............................................................................ 5-8-1
Graphing a Recursion Formula ........................................................ 5-9-1
Changing the Appearance of a Graph ............................................ 5-10-1
Function Analysis ........................................................................... 5-11-1
Statistical Graphs and Calculations
Before Performing Statistical Calculations ....................................... 6-1-1
Calculating and Graphing Single-Variable Statistical Data ............... 6-2-1
Calculating and Graphing Paired-Variable Statistical Data .............. 6-3-1
Performing Statistical Calculations ................................................... 6-4-1
Computer Algebra System and Tutorial Modes
(ALGEBRA FX 2.0 PLUS only)
Using the CAS (Computer Algebra System) Mode .......................... 7-1-1
Algebra Mode ................................................................................... 7-2-1
Tutorial Mode .................................................................................... 7-3-1
Algebra System Precautions ............................................................ 7-4-1
Programming
Basic Programming Steps ................................................................ 8-1-1
Program Mode Function Keys .......................................................... 8-2-1
Editing Program Contents ................................................................ 8-3-1
File Management .............................................................................. 8-4-1
Command Reference ....................................................................... 8-5-1
Using Calculator Functions in Programs .......................................... 8-6-1
Program Mode Command List ......................................................... 8-7-1
Program Library ................................................................................ 8-8-1
System Settings Menu
Using the System Settings Menu ..................................................... 9-1-1
Memory Operations .......................................................................... 9-2-1
System Settings ............................................................................... 9-3-1
Reset ................................................................................................ 9-4-1
Tutorial Lock (ALGEBRA FX 2.0 PLUS only) ................................... 9-5-1
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20010102
3
Contents
Chapter 10
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
Data Communications
Connecting Two Units .................................................................. 10-1-1
Connecting the Unit with a CASIO Label Printer .......................... 10-2-1
Connecting the Unit to a Personal Computer ............................... 10-3-1
Performing a Data Communication Operation ............................. 10-4-1
Data Communications Precautions .............................................. 10-5-1
Sending a Screen Shot ................................................................ 10-6-1
Add-ins ......................................................................................... 10-7-1
MEMORY Mode ........................................................................... 10-8-1
Appendix
1
2
3
4
5
6
7
Error Message Table ........................................................................... α-1-1
Input Ranges ....................................................................................... α-2-1
Specifications ....................................................................................... α-3-1
Index .................................................................................................... α-4-1
Key Index ............................................................................................. α-5-1
P Button (In case of hang up) ............................................................. α-6-1
Power Supply ....................................................................................... α-7-1
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4
Contents
Additional Functions
Chapter 1 Advanced Statistics Application
1-1
1-2
1-3
1-4
Chapter 2
2-1
2-2
2-3
2-4
2-5
2-6
2-7
2-8
2-9
2-10
2-11
Chapter 3
3-1
3-2
3-3
3-4
3-5
Chapter 4
4-1
4-2
4-3
4-4
4-5
Advanced Statistics (STAT) .............................................................. 1-1-1
Tests (TEST) .................................................................................... 1-2-1
Confidence Interval (INTR) ............................................................... 1-3-1
Distribution (DIST) ............................................................................ 1-4-1
Financial Calculation (TVM)
Before Performing Financial Calculations ........................................ 2-1-1
Simple Interest ................................................................................. 2-2-1
Compound Interest ........................................................................... 2-3-1
Cash Flow (Investment Appraisal) .................................................... 2-4-1
Amortization ..................................................................................... 2-5-1
Interest Rate Conversion .................................................................. 2-6-1
Cost, Selling Price, Margin ............................................................... 2-7-1
Day/Date Calculations ...................................................................... 2-8-1
Depreciation ..................................................................................... 2-9-1
Bonds ............................................................................................. 2-10-1
TVM Graph ..................................................................................... 2-11-1
Differential Equations
Using the DIFF EQ Mode ................................................................. 3-1-1
Differential Equations of the First Order ........................................... 3-2-1
Linear Differential Equations of the Second Order ........................... 3-3-1
Differential Equations of the Nth Order ............................................ 3-4-1
System of First Order Differential Equations .................................... 3-5-1
E-CON
E-CON Overview .............................................................................. 4-1-1
EA-100 Setup ................................................................................... 4-2-1
Setup Memory .................................................................................. 4-3-1
Program Converter ........................................................................... 4-4-1
Starting a Sampling Operation ......................................................... 4-5-1
Index (Additional Functions)
19990401
20010101
0
Getting Acquainted
— Read This First!
About this User’s 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 user’s 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.
u Menu Titles
• Menu titles in this user’s 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.
19990401
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.
5-1-1
Sample Graphs
5-1 Sample Graphs
5-1-2
Sample Graphs
Example
To graph y = 3x2
Procedure
k How to draw a simple graph (1)
1 m GRPH-TBL
2 dvxw
Description
3 5(DRAW) (or w)
To draw a graph, simply input the applicable function.
Result Screen
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.
19990401
19990401
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)
u Command 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]
u Page 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.
1-2-2
Display
The following explains the meaning of each icon.
Icon
Mode Name
RUN
STATistics
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.
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.
Use this mode to draw graphs of implicit functions.
CONICS
1-2-3
Display
k About the Function Menu
Description
EQUAtion
Use this mode to solve linear equations with two through
six unknowns, quadratic equations, and cubic 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.
Syetem
ALGEBRA
Use this mode for step-by-step solution of expressions.
TUTORial
Use this mode to determine the expression type and
solve mode, and for interactive equation solutions.
LINK
Use this mode for step-by-step solution of expressions.
MEMORY
Use this mode to manage data stored in memory.
SYSTEM
Use this mode to initialize memory, adjust contrast, and
to make other system settings.
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.
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.
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.
19981001
u Supplementary Information
Supplementary information is shown at the bottom of each page in a “
#The contents of each type of screen
are stored in independent memory
19981001
(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.
19990401
Chapter
Basic Operation
1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
Keys
Display
Inputting and Editing Calculations
Option (OPTN) Menu
Variable Data (VARS) Menu
Program (PRGM) Menu
Using the Set Up Screen
When you keep having problems…
19990401
1
1-1-1
Keys
1-1 Keys
COPY
PASTE
CAT/CAL
REPLAY
PRGM
List
H-COPY
Mat
i
19990401
1-1-2
Keys
k Key Table
Page
COPY
Page
Page
Page
Page
Page
1-3-5 PASTE 1-3-5
1-7-1 CAT/CAL 1-3-5
1-1-3
1-3-4
5-2-1
1-4-1
1-6-1
2-4-4
1-5-1
2-4-4
2-4-4
2-4-4
2-4-3
2-4-3
2-4-3
2-4-4
2-4-4
2-4-3
2-4-3
2-4-3
2-4-10
2-4-6
2-4-6
2-4-6
2-4-10
2-4-6
2-1-1
2-1-1
5-3-6 H-COPY 10-6-1
1-2-1
REPLAY
PRGM
1-1-3
Page
Page
Page
2-2-1
Page
Page
1-3-3
1-3-1
3-1-2
List
i
2-1-1
2-1-1
2-1-1
2-1-1
2-8-11
Mat
2-4-3
2-1-1
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20010102
2-2-5
2-1-1
1-1-3
Keys
k Key Markings
Many of the calculator’s 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
l
1
log
2
x
10
!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.
19990401
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.
Currently selected icon
* The above shows the ALGEBRA
FX 2.0 PLUS screen.
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.
The following explains the meaning of each icon.
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.
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19990401
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
System
Use this mode to perform algebraic calculations.
(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
(Financial)
Use this mode to perform financial calculations.
(On the FX 1.0 PLUS menu, the icon has the number 9 in the
lower right corner.)
to make other system settings.
DIFFerential
EQuation
Use this mode to solve differential equations.
(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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1-2-3
Display
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.
• 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.
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.
Text Screen
Graph Screen
The contents of each type of screen are stored in independent memory areas.
Press u5(G↔T) to switch between the graphic screen and text screen.
# The symbol ↑ in the upper left corner of a pullup 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.
19990401
1-2-4
Display
k Normal 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.
u How 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.
1.2E–03 indicates that the result is equivalent to 1.2 × 10–3. 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 .................. 10–2 (0.01) > |x|, |x| > 1010
Norm 2 .................. 10–9 (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.
19990401
1-2-5
Display
k Special Display Formats
This calculator uses special display formats to indicate fractions, hexadecimal values, and
degrees/minutes/seconds values.
u Fractions
12
................. Indicates: 456 ––––
23
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.
k Calculation 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.
19990401
1-3-1
Inputting and Editing Calculations
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
19990401
1-3-2
Inputting and Editing Calculations
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
19990401
1-3-3
Inputting and Editing Calculations
k Using 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)
# 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.
19990401
1-3-4
Inputting and Editing Calculations
k Making 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.
Cursor is positioned automatically at the
location of the cause of the error.
Make necessary changes.
db
Execute again.
w
k Copy 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.
19990401
1-3-5
Inputting and Editing Calculations
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.
u Pasting 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)
k Catalog 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)
19990401
1-3-6
Inputting and Editing Calculations
○ ○ ○ ○ ○
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.
19990401
1-4-1
Option (OPTN) Menu
1-4 Option (OPTN) Menu
The option menu gives you access to scientific functions and features that are not marked on
the calculator’s 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.
u Option 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}
# The option (OPTN) menu does not appear
during binary, octal, decimal, and hexadecimal
calculations.
19990401
1-4-2
Option (OPTN) Menu
The following shows the function menus that appear under other conditions.
u Option Menu when a number table value is displayed in the GRPH • TBL or
RECUR Mode
• {LMEM} … {list memory menu}
•{
° ’ ”}/{ENG}/{
ENG}
u Option 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.
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1-5-1
Variable Data (VARS) Menu
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}
• {Tθ min}/{Tθ max}/{Tθ ptch}
…T, θ {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,θ {minimum value}/{maximum value}/{pitch}
u FACT — Recalling zoom factors
• {Xfact}/{Yfact}
... {x-axis factor}/{y-axis factor}
*1 The 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.
*2 The dot value indicates the display range (Xmax
value – Xmin value) divided by the screen dot
pitch (126).
The dot value is normally calculated automatically from the minimum and maximum values.
Changing the dot value causes the maximum to
be calculated automatically.
19990401
1-5-2
Variable Data (VARS) Menu
u STAT — Recalling statistical data
• {n} … {number of data}
• {X} … {single-variable, paired-variable x-data}
• {o }/{Σ x }/{Σ x 2 }/{x σn }/{x σ n –1 }/{minX}/{maxX}
…{mean}/{sum}/{sum of squares}/{population standard deviation}/{sample
standard deviation}/{minimum value}/{maximum value}
• {Y} ... {paired-variable y-data}
• { p }/{Σ y}/{Σ y 2 }/{Σ xy}/{ yσ n }/{ yσ n –1 }/{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}
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1-5-3
Variable Data (VARS) Menu
u GRPH — Recalling Graph Functions
• {Yn }/{rn }
... {rectangular coordinate or inequality function}/{polar coordinate function}
• {Xtn }/{Yt n }
... 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
The Result item appears only when the TABL
menu is displayed in the RUN • MAT or PRGM
Mode.
19990401
1-5-4
Variable Data (VARS) Menu
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}
... {a 0}/{a1}/{a2} {b 0}/{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
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.
19990401
1-6-1
Program (PRGM) Menu
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”.
19990401
1-7-1
Using the Set Up Screen
1-7 Using the Set Up Screen
The mode’s 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 mode’s
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 mode’s
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.
u Mode (calculation/binary, octal, decimal, hexadecimal mode)
• {Comp} ... {arithmetic calculation mode}
• {Dec}/{Hex}/{Bin}/{Oct}
... {decimal}/{hexadecimal}/{binary}/{octal}
19990401
20011101
1-7-2
Using the Set Up Screen
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, <, ≥, ≤
@ Relational operators =, G
# and (bitwise operation)
$ xnor, xor (bitwise operations)
% or (bitwise operation)
^ And (logical operation)
Or (logical operation)
○ ○ ○ ○ ○
Example
2 + 3 × (log sin2π 2 + 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 120 → ex{In( 120 )}
# Compound functions are executed from right to
left.
# Anything contained within parentheses receives
highest priority.
Otherwise, execution is from left to right.
20011101
19990401
2-1-5
Basic Calculations
k Multiplication 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
2π, 2AB, 3Ans, 3Y1, etc.
• Before an open parenthesis
○ ○ ○ ○ ○
Example
3(5 + 6), (A + 1)(B – 1), etc.
k Overflow 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.
# See the “Error Message Table” on page α-1-1
for information on other errors.
# Other errors can occur during program
execution. Most of the calculator’s 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).
19990401
20010102
2-1-6
Basic Calculations
• 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).
k Memory 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 π. Some of the functions that
take up two bytes are d/dx(, Mat, Xmin, If, For, Return, DrawGraph, SortA(, PxIOn, Sum, and
an+1.
# 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.
19990401
20011101
2-2-1
Special Functions
2-2 Special Functions
k Calculations 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
k Memory
u Variables
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 θ. 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
# Variable contents are retained even when
you turn power off.
19990401
2-2-2
Special Functions
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
u Function 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}
*1
You cannot use “r” or “θ ” as a variable name.
19990401
2-2-3
Special Functions
u To store a function
○ ○ ○ ○ ○
Example
To store the function (A+B) (A–B) 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)
# If the function memory number to which you
store a function already contains a function, the
previous function is replaced with the new one.
19990401
# The recalled function appears at the current
location of the cursor on the display.
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.
19990401
2-2-5
Special Functions
k Answer 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
k Performing 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.
# The largest value that the answer memory
can hold is 15 digits for the mantissa and 2
digits for the exponent.
# Answer memory contents are not cleared
when you press the A key or when you
switch power off.
# Only numeric values and calculation results
can be stored in answer memory.
# Answer memory contents are not changed
by an operation that assigns values to value
memory (such as: faav(A)w).
19990401
2-2-6
Special Functions
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 10level 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
Numeric Value Stack
Command Stack
2
b
2
3
c
3
4
d
4
5
e
5
4
f
...
1
g
...
h
×
(
(
+
×
(
+
# Calculations are performed according to the priority 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.
19990401
2-2-7
Special Functions
k Using Multistatements
Multistatements are formed by connecting a number of individual statements for sequential
execution. You can use multistatements in manual calculations and in programmed calculations. 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, execution 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
# You cannot construct a multistatement in
which one statement directly uses the result
of the previous statement.
# 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
19990401
2-3-1
Specifying the Angle Unit and Display Format
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.
k Setting 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° = 2π radians = 400 grads
90° = π/2 radians = 100 grads
k Setting 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).
# Displayed values are rounded off to the
number of decimal places you specify.
19990401
2-3-2
Specifying the Angle Unit and Display Format
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: 10–2 (0.01)>|x|, |x| >1010
Norm 2: 10–9 (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)
× 10–3
P (Peta)
× 1015
µ (micro)
× 10–6
T (Tera)
× 1012
n (nano)
× 10–9
G (Giga)
× 109
p (pico)
× 10–12
M (Mega)
× 106
f (femto)
× 10–15
k (kilo)
× 103
# 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.
19990401
2-4-1
Function Calculations
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.
u Numeric 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}/{ µ}/{n}/{p}/{f} ... {milli (10–3)}/{micro (10–6)}/{nano (10–9)}/{pico (10–12)}/{femto
(10–15)}
• {k}/{M}/{G}/{T}/{P}/{E} ... {kilo (103)}/{mega (106)}/{giga (109)}/{tera (1012)}/{peta
(1015)}/{exa (1018)}
u Probability/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)}
20010101
20011101
2-4-2
Function Calculations
u Hyperbolic Calculations (HYP)
[OPTN]-[HYP]
• {sinh}/{cosh}/{tanh} ... hyperbolic {sine}/{cosine}/{tangent}
• {sinh–1}/{cosh–1}/{tanh–1} ... inverse hyperbolic {sine}/{cosine}/{tangent}
u Angle 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.
k Angle 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:
243.5070629
u3(SET UP)cccc1(Deg)i
4.25K6(g)3(ANGL)c(r)w
47.3° + 82.5rad = 4774.20181°
47.3+82.5K6(g)3(ANGL)c(r)w
# 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.
20010101
2-4-3
Function Calculations
k Trigonometric and Inverse Trigonometric Functions
• Be sure to set the angle unit before performing trigonometric function and inverse
trigonometric function calculations.
π
(90° = ––– radians = 100 grads)
2
• Be sure to specify Comp for Mode in the SET UP screen.
Example
sin 63° = 0.8910065242
π
cos (–– rad) = 0.5
3
Operation
u3(SET UP)cccc1(Deg)i
s63w
u3(SET UP)cccc2(Rad)i
c(!E(π)/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
sin 30°
sin-10.5 = 30°
(x when sinx = 0.5)
*1 * can be omitted.
1/s30w
!s(sin–1)0.5*2w
*2 Input of leading zero is not necessary.
20010101
2-4-4
Function Calculations
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 × 10–2
l1.23w
In 90 (loge90) = 4.49980967
I90w
101.23 = 16.98243652
(To obtain the antilogarithm of common
logarithm 1.23)
!l(10x)1.23w
e4.5 = 90.0171313
(To obtain the antilogarithm of natural
logarithm 4.5)
!I(ex)4.5w
(–3)4 = (–3) × (–3) × (–3) × (–3) = 81
(-3)M4w
–34 = –(3 × 3 × 3 × 3) = –81
-3M4w
7
1
7
x
123 (= 123 ) = 1.988647795
7!M(
)123w
x
2 + 3 × 3 64 – 4 = 10
2+3*3!M(
*1 ^ (x y) and x
take precedence over
multiplication and division.
20010101
20011101
)64-4w*1
2-4-5
Function Calculations
k Hyperbolic 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
= 0.2231301601
= e –1.5
(Display: –1.5)
K6(g)2(HYP)c(cosh)1.52(HYP)b(sinh)1.5w
I!-(Ans)w
(Proof of cosh x ± sinh x = e±x)
cosh–1
20
15
= 0.7953654612
K6(g)2(HYP)f(cosh–1)(20/15)w
Determine the value of x
when tanh 4 x = 0.88
–1
x = tanh 0.88
K6(g)2(HYP)g(tanh–1)0.88/4w
4
= 0.3439419141
20010101
2-4-6
Function Calculations
k Other Functions
• Be sure to specify Comp for Mode in the SET UP screen.
Example
Operation
2 + 5 = 3.65028154
!x(
)2+!x(
(3 + i) = 1.755317302
+0.2848487846i
!x(
)(d+!a(i))w
(–3)2 = (–3) × (–3) = 9
(-3)xw
–32 = –(3 × 3) = –9
-3xw
1
–––––– = 12
1
1
–– – ––
3
4
8! (= 1 × 2 × 3 × .... × 8)
= 40320
3
36 × 42 × 49 = 42
What is the absolute value of
3
the common logarithm of
?
4
| log 34 | = 0.1249387366
)5w
(3!)(x–1)-4!)(x–1))!)(x–1)w
8K6(g)1(PROB)b(x !)w
!((3
)(36*42*49)w
K5(NUM)b(Abs)l(3/4)w
What is the integer part of
– 3.5?
–3
K5(NUM)c(Int)-3.5w
What is the decimal part of
– 3.5?
– 0.5
K5(NUM)d(Frac)-3.5w
What is the nearest integer
not exceeding – 3.5? – 4
K5(NUM)f(Intg)-3.5w
20010101
2-4-7
Function Calculations
k Random 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
number.)
w
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.)
(Generates the second random number in sequence 1.)
1(PROB)e(Ran#)bw
w
Ran# 0 (Initializes the sequence.)
Ran# 1 (Generates the first random number in sequence 1.)
1(PROB)e(Ran#)aw
1(PROB)e(Ran#)bw
*1 Changing to a different sequence or
generating a totally random number (without
an argument) initializes the sequence.
20010101
2-4-8
Function Calculations
k Coordinate Conversion
u Rectangular Coordinates
u Polar Coordinates
• With polar coordinates, θ can be calculated and displayed within a range of
–180°< θ < 180° (radians and grads have same range).
• Be sure to specify Comp for Mode in the SET UP screen.
Example
Operation
Calculate r and θ ° when x = 14 and y = 20.7
1
24.989
→ 24.98979792 (r)
2
55.928
→ 55.92839019 (θ)
u3(SET UP)cccc1(Deg)i
K6(g)3(ANGL)g(Pol()
14,20.7)w
Calculate x and y when r = 25 and θ = 56°
1
13.979
→ 13.97982259 (x)
2
20.725
→ 20.72593931 (y)
u3(SET UP)cccc1(Deg)i
K6(g)3(ANGL)h(Rec()
25,56)w
20010101
2-4-9
Function Calculations
k Permutation and Combination
u Permutation
u Combination
n!
nPr = –––––
(n – r)!
n!
nCr = –––––––
r! (n – r)!
• 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
P4 = 5040
Operation
10K6(g)1(PROB)c(nPr)4w
10
○ ○ ○ ○ ○
Example
To calculate the possible number of different combinations of 4 items
that can be selected from among 10 items
Formula
C4 = 210
10
Operation
10K6(g)1(PROB)d(nCr)4w
20010101
2-4-10
Function Calculations
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
2
1
13
–– + 3 –– = 3 ––– (Display: 3{13{20)
5
4
20
= 3.65
1
1
––––– + ––––– = 6.066202547 × 10–4
2578
4572
2$5+3$1$4w
$(Conversion to decimal)
$(Conversion to fraction)
1$2578+1$4572w
(Display: 6.066202547E–04*1 )
(Norm 1 display format)
1
–– × 0.5 = 0.25*2
2
1
= ––
4
1$2*.5w
$
1
3
1.5 + 2.3i = 1–– + 2––i
2
10
1
5
–––––– = 1––
1
1
7
–– + ––
3
4
Display:
1{1{2
+2{3{10i
(Display: 1{5{7)
*1 When the total number of characters,
including integer, numerator, denominator
and delimiter marks exceeds 10, the input
fraction is automatically displayed in decimal
format.
*2 Calculations containing both fractions and
decimals are calculated in decimal format.
1.5+2.3!a(i)w
$$*3
1$(1$3+1$4)w*4
*3 Pressing $ once when converting the decimal
part of a complex number to a fraction first
displays the real part and imaginary part on
separate lines.
*4 You can include fractions within the numerator
or denominator of a fraction by putting the
numerator or denominator in parentheses.
20010101
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
999k (kilo) + 25k (kilo)
= 1.024M (mega)
u3(SET UP)cccccccccc
4(Eng)i
999K5(NUM)g(E-SYM)g(k)+255(NUM)
g(E-SYM)g(k)w
9 ÷ 10 = 0.9 = 900m (milli)
= 0.9
= 0.0009k (kilo)
= 0.9
= 900m
9/10w
K6(g)6(g)6(g)3(
3( ENG)*1
2(ENG)*2
2(ENG)*2
*1 Converts the displayed value to the next higher
engineering unit, by shifting the decimal point
three places to the right.
ENG)*1
*2 Converts the displayed value to the next lower
engineering unit, by shifting the decimal point
three places to the left.
20010101
2-5-1
Numerical Calculations
2-5 Numerical Calculations
The following describes the items that are available in the menus you use when performing
differential/ quadratic differential, integration, Σ, 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}/{Σ}/{FMin}/{FMax}/{Solve} ... {differential}/{quadratic differential}/
{integration}/{Σ (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.
20010101
2-5-2
Numerical Calculations
k Differential 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)
(a: point for which you want to determine the
derivative, tol: tolerance)
d
d/dx ( f (x), a) ⇒ ––– f (a)
dx
The differentiation for this type of calculation is defined as:
f (a + Ax) – f (a)
f '(a) = lim –––––––––––––
Ax
Ax→0
In this definition, infinitesimal is replaced by a sufficiently small Ax, with the value in the
neighborhood of f ' (a) calculated as:
f '(a)
f (a + Ax) – f (a)
–––––––––––––
Ax
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.
20010101
2-5-3
Numerical Calculations
○ ○ ○ ○ ○
Example
To determine the derivative at point x = 3 for the function
y = x3 + 4 x2 + 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, θ) 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 automatically 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.
20010101
2-5-4
Numerical Calculations
u Applications of Differential Calculations
• Differentials can be added, subtracted, multiplied or divided with each other.
d
d
––– f (a) = f '(a), ––– g (a) = g'(a)
dx
dx
Therefore:
f '(a) + g'(a), f '(a) × g'(a), etc.
• 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.
d
––– (sinx + cosx, sin0.5, 1E - 8), etc.
dx
# You cannot use a differential, quadratic
differential, integration, Σ, 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.
20010101
20011101
2-5-5
Numerical Calculations
k Quadratic Differential Calculations
[OPTN]-[CALC]-[d 2 /dx2]
After displaying the function analysis menu, you can input quadratic differentials using either of
the two following formats.
K4(CALC)c(d 2/dx 2 ) f(x),a,tol)
(a: differential coefficient point , tol: tolerance)
d2
d2
–––2 (f (x), a) ⇒ –––2 f (a)
dx
dx
Quadratic differential calculations produce an approximate differential value using the following
second order differential formula, which is based on Newton’s 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
# In the function f(x), only X can be used as a
variable in expressions. Other variables (A
through Z, r, θ) 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.
20010101
20011101
2-5-6
Numerical Calculations
u Quadratic Differential Applications
• Arithmetic operations can be performed using two quadratic differentials.
d2
d2
–––2 f (a) = f ''(a), –––
g (a) = g''(a)
dx
dx 2
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.
d2
–––2 (sin x + cos x, sin 0.5, 1E - 8), etc.
dx
# You cannot use a differential, quadratic
differential, integration, Σ, 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)
20010101
2-5-7
Numerical Calculations
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 )
(a: start point, b: end point, tol: tolerance)
∫( f(x), a, b, tol) ⇒ ∫a f(x)dx
b
Area of
∫
b
a
f(x)dx is calculated
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.
# If f (x) < 0 where a a < x < b, the surface area
calculation produces negative values (surface
area × – 1).
20010101
2-5-8
Numerical Calculations
○ ○ ○ ○ ○
Example
To perform the integration calculation for the function shown
below, with a tolerance of “tol” = 1E - 4
∫
5
1
(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
u Application of Integration Calculation
• Integrals can be used in addition, subtraction, multiplication or division.
∫
b
a
f(x) dx +
∫
d
c
g (x) dx, etc.
• Integration results can be used in addition, subtraction, multiplication or division, in
functions.
b
b
2 × f(x) dx, etc. log ( f(x) dx), etc.
∫
a
∫
a
• 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
# In the function f(x), only X can be used as a
variable in expressions. Other variables (A
through Z, r, θ) 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, Σ, maximum/minimum
value or Solve calculation expression inside of
an integration calculation term.
20010101
20011101
2-5-9
Numerical Calculations
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.
Positive
part (S)
Negative part (S)
∫
b
a
f(x)dx =
∫
c
a
∫
f(x)dx + (–
Positive part ( S)
b
c
f(x)dx)
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.
∫
b
a
f(x)dx =
∫
x1
a
f(x)dx +
# Pressing A during calculation of an integral
(while the cursor is not shown on the display)
interrupts the calculation.
∫
x2
x1
f(x)dx +.....+
∫
b
x4
f(x)dx
# An error (Iteration ERROR) occurs whenever
no solution that satisfies the tolerance value
can be obtained.
# Always use radians (Rad Mode) as the angle
unit when performing trigonometric
integrations.
20010101
2-5-10
Numerical Calculations
k Σ Calculations
[OPTN]-[CALC]-[Σ ]
To perform Σ calculations, first display the function analysis menu, and then input the values
shown in the formula below.
K4(CALC)e(Σ) a k , k , α , β , n )
β
Σ (a , k, α, β, n) = Σ a = a
k
α
k
k=α
+ aα +1 +........+ aβ
(n: distance between partitions)
○ ○ ○ ○ ○
Example
To calculate the following:
6
Σ (k
2
– 3k + 5)
k=2
Use n = 1 as the distance between partitions.
AK4(CALC)e(Σ)a,(K)x
-da,(K)+f,
a,(K),c,g,b)w
# You can use only one variable in the function for
input sequence ak.
# Input integers only for the initial term (α) of
sequence ak and last term (β) of sequence ak .
# Input of n and the closing parentheses can be
omitted. If you omit n, the calculator automatically uses n = 1.
20010101
2-5-11
Numerical Calculations
u Σ Calculation Applications
• Arithmetic operations using Σ calculation expressions
n
n
k=1
k=1
Sn = Σ ak, Tn = Σ bk
Expressions:
Sn + Tn, Sn – Tn, etc.
Possible operations:
• Arithmetic and function operations using Σ calculation results
2 × Sn, log (Sn), etc.
• Function operations using Σ calculation terms (ak, k)
Σ (sink, k, 1, 5), etc.
# You cannot use a differential, quadratic
differential, integration, Σ, maximum/minimum
value or Solve calculation expression inside of
a Σ calculation term.
# Make sure that the value used as the final term
β is greater than the value used as the initial
term α. Otherwise, an error will occur.
# To interrupt an ongoing Σ calculation (indicated
when the cursor is not on the display), press the
A key.
20010101
2-5-12
Numerical Calculations
k Maximum/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
20010101
2-5-13
Numerical Calculations
○ ○ ○ ○ ○
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 + 2 x + 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
# In the function f(x), only X can be used as a
variable in expressions. Other variables (A
through Z, r, θ) 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, Σ, 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.
20010101
2-6-1
Complex Number Calculations
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 ^ θ 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 ^ θ i }/{'a + bi } ... converts the result to {polar}/{linear}
# Solutions obtained by the Real and a+bi / re^θ i
modes are different for power root (xy)
calculations when x < 0 and y = m/n when n is
an odd number.
*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)
Example:
3 x (- 8) = – 2 (Real)
= 1 + 1.732050808i(a+bi / re^θ i)
*2 The display range of θ depends on the angle
unit set for the Angle item on the SET UP
screen.
• Deg ... –180 < θ < 180
• Rad ... – π < θ < π
• Gra ... –200 < θ < 200
20010101
20011101
2-6-2
Complex Number Calculations
k Absolute 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 (θ ) for the complex
number 3 + 4i, with the angle unit set for degrees
Imaginary axis
Real axis
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).
20010101
20011101
2-6-3
Complex Number Calculations
k Conjugate 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
k Extraction 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)
# 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, x–1, ^(xy), 3 , x , In, log, 10x, ex, sin,
cos, tan, sin–1, cos–1, tan–1, sinh, cosh, tanh,
sinh–1, cosh–1, tanh–1
Int, Frac, Rnd, Intg, Fix, Sci, ENG, ENG, ° ’ ”,
° ’ ”, a b/c, d/c
20010101
20011101
2-6-4
Complex Number Calculations
k Polar Form and Rectangular Transformation
[OPTN]-[CPLX]-[ ' re ^ θ 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^θi)w
20010101
2-7-1
Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
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 calculations.
• 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 two’s 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
# The alphabetic characters used in the
hexadecimal number appear differently on
the display to distinguish them from text
characters.
Normal Text
A
B
C
D
E
F
Hexadecimal Values
u
v
w
x
y
z
Keys
20010101
20011101
2-7-2
Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
• 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
[SET UP]- [Mode] -[Dec]/[Hex]/[Bin]/[Oct]
1. In the main menu, select RUN • MAT.
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
20010101
20011101
2-7-3
Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
k Selecting 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
k Arithmetic Operations
○ ○ ○ ○ ○
Example 1
To calculate 101112 + 110102
u3(SET UP)4(Bin)i
Ababbb+
bbabaw
20010101
20011101
2-7-4
Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
○ ○ ○ ○ ○
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
k Negative 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
*1 See page 2-7-1.
*2 two’s complement
*3 one’s complement (bitwise complement)
*4 bitwise AND, bitwise OR, bitwise XOR,
bitwise XNOR
20010101
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2-7-5
Binary, Octal, Decimal, and Hexadecimal Calculations with Integers
○ ○ ○ ○ ○
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
u Number 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
*1 See page 2-7-1.
20010101
20011101
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.
20010101
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2-8-2
Matrix Calculations
k Inputting and Editing Matrices
Pressing 1(MAT) displays the matrix editor screen. Use the matrix editor to input and edit
matrices.
m × n … m (row) × n (column) matrix
None… no matrix preset
• {DIM} ... {specifies the matrix dimensions (number of cells)}
• {DEL}/{DEL·A} ... 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.
# 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.
20010101
2-8-3
Matrix Calculations
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 highlighting 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.
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2-8-4
Matrix Calculations
u Deleting 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(DEL·A).
2. Press w(Yes) to delete all matrices in memory or i(No) to abort the operation
without deleting anything.
# 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.
20010101
2-8-5
Matrix Calculations
k Matrix 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)
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2-8-6
Matrix Calculations
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:
Matrix A =
1
2
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 :
Matrix A =
1
2
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)
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2-8-7
Matrix Calculations
u To add two rows together
○ ○ ○ ○ ○
Example
To add row 2 to row 3 of the following matrix :
Matrix A =
1
2
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 :
Matrix A =
1
2
3
4
5
6
c
3(R • DEL)
20010101
2-8-8
Matrix Calculations
u To insert a row
○ ○ ○ ○ ○
Example
To insert a new row between rows one and two of the following
matrix :
Matrix A =
1
2
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 :
Matrix A =
1
2
3
4
5
6
cc
5(R • ADD)
20010101
2-8-9
Matrix Calculations
u Column 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 :
Matrix A =
1
2
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 :
Matrix A =
1
2
3
4
5
6
e
6(g)2(C • INS)
20010101
2-8-10
Matrix Calculations
u To add a column
○ ○ ○ ○ ○
Example
To add a new column to the right of column 2 of the following
matrix :
Matrix A =
1
2
3
4
5
6
e
6(g)3(C • ADD)
k Modifying 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)}
• {M→List} ... {Mat→List command (assign contents of selected column to list file)}
20010101
2-8-11
Matrix Calculations
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
a21 a22
a1n
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
2
3
4
5
6
!+( [ )!+( [ )b,d,f
!-( ] )!+( [ )c,e,g
!-( ] )!-( ] )aK2(MAT)
b(Mat)av(A)
w
Matrix name
# You can also use !c(Mat) in place of
K2 (MAT)b(Mat).
# An error occurs if memory becomes full as you
are inputting data.
# The maximum value of both m and n is 255.
# You can also use the above format inside a
program that inputs matrix data.
20010101
2-8-12
Matrix Calculations
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
20010101
2-8-13
Matrix Calculations
u Modifying 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
20010101
2-8-14
Matrix Calculations
u To 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
2
B=
3
4
K2(MAT)f(Augmnt)
2(MAT)b(Mat)av(A),
2(MAT)b(Mat)al(B)w
# 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.
20010101
2-8-15
Matrix Calculations
u To assign the contents of a matrix column to a list
[OPTN]-[MAT]-[M→List]
Use the following format with the Mat→List 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 :
Matrix A =
1
2
3
4
5
6
K2(MAT)i(M→List)
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 α) → Mat β
• Augment (Mat α, Mat β) → Mat γ
In the above, α, β, and γ are any variable
names A through Z, and n is any value.
The above does not affect the contents of Matrix
Answer Memory.
20010101
2-8-16
Matrix Calculations
k Matrix 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.
20010101
2-8-17
Matrix Calculations
u Matrix Arithmetic Operations
[OPTN]-[MAT]-[Mat]
○ ○ ○ ○ ○
Example 1
To add the following two matrices (Matrix A + Matrix B) :
A=
1
1
2
1
B=
2
3
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.
# 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.
# 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.
20010101
20011101
2-8-18
Matrix Calculations
u Determinant
[OPTN]-[MAT]-[Det]
○ ○ ○ ○ ○
Example
Obtain the determinant for the following matrix :
1
2
3
4
5
6
–1 –2
0
Matrix A =
K2(MAT)d(Det)2(MAT)b(Mat)
av(A)w
u Matrix Transposition
[OPTN]-[MAT]-[Trn]
A matrix is transposed when its rows become columns and its columns become rows.
○ ○ ○ ○ ○
Example
To transpose the following matrix :
Matrix A =
1
2
3
4
5
6
K2(MAT)e(Trn)2(MAT)b(Mat)
av(A)w
# 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 3 × 3 matrix is calculated
as shown below.
a11 a12 a13
a21 a22 a23
a31 a32 a33
= a11a22a33 + a12a23a31 + a13a21a32
– a11a23a32 – a12a21a33 – a13a22a31
|A|=
# The determinant of a 2 × 2 matrix is
calculated as shown below.
|A|=
a11 a12
a21 a22
= a11a22 – a12a21
20010101
2-8-19
Matrix Calculations
u Matrix Inversion
[OPTN]-[MAT]-[x –1]
○ ○ ○ ○ ○
Example
To invert the following matrix :
Matrix A =
1
2
3
4
K2(MAT)b(Mat)
av(A)!) (x–1) w
u Squaring a Matrix
[OPTN]-[MAT]-[x 2]
○ ○ ○ ○ ○
Example
To square the following matrix :
Matrix A =
1
2
3
4
K2(MAT)b(Mat)av(A)xw
# 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 being inverted must satisfy the
conditions shown below.
A A–1 = A–1 A = E =
# A matrix with a determinant of zero cannot be
inverted. Trying to invert a matrix with
determinant of zero produces an error.
1 0
0 1
The following shows the formula used to
invert Matrix A into inverse matrix A–1.
# Calculation precision is affected for matrices
whose determinant is near zero.
A=
a b
c d
A–1=
1
ad – bc
d –b
–c a
Note that ad – bc G 0.
20010101
2-8-20
Matrix Calculations
u Raising 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
u Determining 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
# 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.
# 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 α
In the above, α is any variable name A through
Z. The above does not affect the contents of
Matrix Answer Memory.
# If a matrix calculation result is too large to
fit into Matrix Answer Memory, an error
occurs.
20010101
Chapter
3
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.
Element number
Display range
Cell
Column
1
2
3
4
5
6
7
8
List 1
56
37
21
69
40
48
93
30
List 2
1
2
4
8
16
32
64
128
List 3
107
75
122
87
298
48
338
49
List 4
3.5
6
2.1
4.4
3
6.8
2
8.7
List 5
4
0
0
2
0
3
9
0
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
3-1
3-2
3-3
3-4
Inputting and Editing a List
Manipulating List Data
Arithmetic Calculations Using Lists
Switching Between List Files
19990401
List 20
0
0
0
0
0
0
0
0
•
•
•
•
List name
Row
3-1-1
Inputting and Editing a List
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
# You can also input the result of an expression or a complex number into a cell.
# You can input values up to 255 cells in a single list.
20011101
19990401
3-1-2
Inputting and Editing a List
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
# 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,}
20010102
19990401
3-1-3
Inputting and Editing a List
k Editing 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(䉯)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(䉯)3(DEL) to delete the selected cell and cause everything below it to be
shifted up.
# 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.
20010102
19990401
3-1-4
Inputting and Editing a List
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(䉯)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(䉯)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
neighboring lists, inserting a cell can cause
related values to become misaligned.
20010102
19990401
3-1-5
Inputting and Editing a List
k Sorting 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(䉯)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).
20010102
19990401
3-1-6
Inputting and Editing a List
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(䉯)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
20010102
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.
# 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.
# 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).
19990401
3-2-1
Manipulating List Data
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}/{%}/{A
AList}/
{Augmnt}/{Fill}/{L→Mat}
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.
aK1(LIST)c(Dim)1(LIST)b(List)
w
n = 1 ~ 255
19990401
20011101
3-2-2
Manipulating List Data
○ ○ ○ ○ ○
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.
!*( { ) , !/( } )a
K1(LIST)c(Dim)2(MAT)b(Mat)aw
m, n = 1 ~ 255, matrix name; A ~ Z
○ ○ ○ ○ ○
To create a 2-row × 3-column matrix (each cell of which
contains 0) in Matrix A
Example
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) ,1(LIST)b(List) )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.
19990401
20011101
3-2-3
Manipulating List Data
u To generate a sequence of numbers
[OPTN]-[LIST]-[Seq]
K1(LIST)d(Seq) , ,
, , ) w
• The result of this operation is stored in ListAns Memory.
○ ○ ○ ○ ○
To input the number sequence 12, 62, 112, into a list, using the function
Example
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 don’t, 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 don’t, 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 don’t, an error occurs.
K1(LIST)g(Mean)1(LIST)b(List)
,1(LIST)b(List))w
19990401
3-2-5
Manipulating List Data
○ ○ ○ ○ ○
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 don’t, 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
19990401
3-2-6
Manipulating List Data
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
2+3=
2+3+6=
2+3+6+5=
2+3+6+5+4=
19990401
20011101
3-2-7
Manipulating List Data
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
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 =
u To calculate the differences between neighboring data inside a list
[OPTN]-[LIST]-[A
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)
3–1=
8–3=
5–8=
4–5=
bw
# 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.
19990401
3-2-8
Manipulating List Data
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]-[L→Mat]
K1(LIST)t(L→Mat)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(L→Mat)
1(LIST)b(List)b,
1(LIST)b(List)c)w
19990401
20011101
3-3-1
Arithmetic Calculations Using Lists
3-3 Arithmetic Calculations Using Lists
You can perform arithmetic calculations using two lists or one list and a numeric value.
List
Numeric Value
+
−
×
÷
ListAns Memory
List
=
Numeric Value
List
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.
19990401
3-3-2
Arithmetic Calculations Using Lists
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!/( } )
○ ○ ○ ○ ○
Example 2
To multiply List 3
(
=
41
65
22
)
by the list
6
0
4
K1(LIST)b(List)d*!*( { )g,a,e!/( } )w
The resulting list
246
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
19990401
3-3-3
Arithmetic Calculations Using Lists
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
k Recalling 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.
19990401
3-3-4
Arithmetic Calculations Using Lists
k Graphing 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.
○ ○ ○ ○ ○
Example
41
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.
–8E–3
In place of the K1(LIST)b(List)d operation in the above procedure, you could input
!*( { ) eb,gf,cc!/( } ).
19990401
3-3-5
Arithmetic Calculations Using Lists
○ ○ ○ ○ ○
Example
To use List 1
1
2
3
and List 2
4
5
6
to perform List 1List 2
This creates a list with the results of 14, 25, 36.
K1(LIST)b(List)bM1(LIST)b(List)cw
The resulting list
1
32
is stored in ListAns Memory.
729
19990401
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).
19990401
Chapter
4
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
4-2
4-3
4-4
Simultaneous Linear Equations
Higher Degree Equations
Solve Calculations
What to Do When an Error Occurs
19990401
20011101
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.
19990401
20011101
4-1-2
Simultaneous Linear Equations
○ ○ ○ ○ ○
To solve the following simultaneous linear equations for x, y, and z
Example
4x + y – 2z = – 1
x + 6y + 3z = 1
– 5x + 4y + z = – 7
Procedure
1 m EQUA
2 1(SIML)
2(3)
3 ewbw-cw-bw
bwgwdwbw
-fwewbw-hw
4 6(SOLV)
Result Screen
# Internal calculations are performed using a 15digit 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 simultaneous linear equation with three unknowns.
x1
x2
x3
=
a1 b1 c1
a2 b2 c2
a3 b3 c3
–1
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.
d1
d2
d3
19990401
4-2-1
Higher Degree Equations
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.
# 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.
19990401
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4-2-2
Higher Degree Equations
○ ○ ○ ○ ○
Example
To solve the cubic equation
x3 – 2x2 – x + 2 = 0
Procedure
1 m EQUA
2 2(POLY)
2(3)
3 bw-cw-bwcw
4 6(SOLV)
Result Screen
(Multiple Solutions)
(Complex Number Solution)
19990401
20011101
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
*1 An error occurs if you input more than one equals
sign.
*2 An error occurs if the solution falls outside the
range you specify.
*3 Solutions are approximated using Newton’s
method. Lft and Rgt values are displayed for
confirmation, because Newton’s 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.
19990401
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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
1 m EQUA
2 3(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
19990401
4-4-1
What to Do When an Error Occurs
4-4 What to Do When an Error Occurs
u Error 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.
u Error during calculation
Press the i key to clear the error and display the coefficient. Try inputting values for the
coefficients again.
k Clearing 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.
19990401
20011101
Chapter
5
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
5-2
5-3
5-4
5-5
5-6
5-7
5-8
5-9
5-10
5-11
Sample Graphs
Controlling What Appears on a Graph Screen
Drawing a Graph
Storing a Graph in Picture Memory
Drawing Two Graphs on the Same Screen
Manual Graphing
Using Tables
Dynamic Graphing
Graphing a Recursion Formula
Changing the Appearance of a Graph
Function Analysis
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20011101
5-1-1
Sample Graphs
5-1 Sample Graphs
k How 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.
19990401
5-1-2
Sample Graphs
○ ○ ○ ○ ○
Example
To graph y = 3x 2
Procedure
1 m GRPH • TBL
2 dvxw
3 5(DRAW) (or w)
Result Screen
19990401
5-1-3
Sample Graphs
k How 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 expressions: 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.
19990401
20011101
5-1-4
Sample Graphs
○ ○ ○ ○ ○
Example
Input the functions shown below and draw their graphs
Y1 = 2 x 2 – 3, r 2 = 3sin2θ
Procedure
1 m GRPH • TBL
2 3(TYPE)b(Y=)cvx-dw
3(TYPE)c(r=)dscvw
3 5(DRAW)
Result Screen
(Param)
(INEQUA)
19990401
(Plot)
5-1-5
Sample Graphs
k How 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.
Graph Type
Parabola
Function
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
2
A
B2
3. Input values for the required variables.
4. Graph the function.
19990401
5-1-6
Sample Graphs
○ ○ ○ ○ ○
Example
Graph the circle (X–1)2 + (Y–1)2 = 22
Procedure
1 m CONICS
2 ccccw
3 bwbwcw
4 6(DRAW)
Result Screen
(Parabola)
(Ellipse)
19990401
(Hyperbola)
5-2-1
Controlling What Appears on a Graph Screen
5-2 Controlling What Appears on a Graph Screen
k V-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
Tθ min ... T, θ minimum values
Tθ max ... T, θ maximum values
Tθ ptch ... T, θ 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
*1 Pressing w without inputting anything while k
is displayed exits the View Window setting
screen.
19990401
20011101
5-2-2
Controlling What Appears on a Graph Screen
u V-Window Setting Precautions
• Inputting zero for Tθ 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 Tθ max
is less than Tθ min, Tθ ptch becomes negative.
• You can input expressions (such as 2π) 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, θ pitch value to be too large, relative to the
differential between the T, θ min and T, θ max settings. If the settings you make cause
the T, θ pitch value to be too small relative to the differential between the T, θ min and
T, θ 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
19990401
5-2-3
Controlling What Appears on a Graph Screen
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
Ymin = –3.1,
Ymax = 3.1,
Yscale = 1
Xdot = 0.1
Tθ min = 0,
Tθ max = 2π (rad), Tθ ptch = 2π /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 = – 3π (rad),
Xmax = 3π (rad),
Xscale = π /2 (rad),
Ymin = –1.6,
Ymax = 1.6,
Yscale = 0.5
Xdot = π /21 (rad),
u To standardize the V-Window
The following are the standard V-Window settings of this calculator.
Xmin = –10,
Xmax = 10,
Xscale = 1,
Ymin = –10,
Ymax = 10,
Yscale = 1,
Xdot = 0.15873015,
Tθ min = 0,
Tθ max = 2π (rad), Tθ ptch = 2π /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.
# Initialization and standardization cause Tθ
min, Tθ max, Tθ ptch values to change
automatically in accordance with the current
angle unit setting as shown below.
Gra Mode:
Tθ min = 0, Tθ max = 400, Tθ ptch = 400/60
Deg Mode:
Tθ min = 0, Tθ max = 360, Tθ ptch = 6
19990401
20011101
5-2-4
Controlling What Appears on a Graph Screen
k V-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).
# 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.
19990401
5-2-5
Controlling What Appears on a Graph Screen
k Specifying 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.
19990401
5-2-6
Controlling What Appears on a Graph Screen
○ ○ ○ ○ ○
Example
Graph y = x 2 + 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
1 m GRPH • TBL
2 !K(V-Window) -dwfwbwc
-bawdawfwi
3 3(TYPE)b(Y=)vx+dv-c,
!+( [ )-c,e!-( ] )w
4 5(DRAW)
Result Screen
# You can specify a range when graphing
rectangular expressions, polar expressions,
parametric functions, and inequalities.
19990401
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 operation.
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.
19990401
5-2-8
Controlling What Appears on a Graph Screen
○ ○ ○ ○ ○
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
1 m GRPH • TBL
!K(V-Window) -iwiwcwc
-ewcwbwi
3(TYPE)b(Y=) (v+f)(v+e)
(v+d)w
5(DRAW)
2 2(ZOOM)b(Box)
3 d~dw
4 d~d,f~fw
Result 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.
19990401
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.
19990401
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
1 m GRPH • TBL
!K(V-Window) -iwiwbwc
-dawdawfwi
3(TYPE)b(Y=)(v+e)(v+b)
(v-d)w
dv+ccw
5(DRAW)
2 2(ZOOM)c(Factor)fwfwi
3 2(ZOOM)d(In)
4 f~f,d~dw
Result Screen
# You can repeat factor zoom to enlarge or
reduce a graph even further.
19990401
5-2-11
Controlling What Appears on a Graph Screen
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.
# 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.
19990401
20011101
5-2-12
Controlling What Appears on a Graph Screen
k About 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.
# 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 (regraph) 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.
19990401
20011101
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.
k Specifying 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}
t}/{Ys
s} ... {Y>f( x )}/{Yf( x )}/{Y}/{Y<}/{Yt
• {CONV}
t}/{'Ys
s} ... changes the function type
• {'Y=}/{'Y>}/{'Y<}/{'Yt
2. Press the number key that corresponds to the graph type you want to specify.
k Storing 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 sin3θ
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.
*2 A 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.
19990401
20011101
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 θ 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.
*2 A 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.
19990401
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 Y1°Y2 to Y3, and Y2°Y1 to Y4.
(Y1°Y2 = ((x2 + 3) +1) = (x2 + 4)
2
Y2°Y1 = ( (X + 1)) + 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
19990401
20011101
5-3-4
Drawing a Graph
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
θ
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.
19990401
20010102
5-3-5
Drawing a Graph
k Editing 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.
*1 The 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.
20011101
19990401
5-3-6
Drawing a Graph
k Selecting 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 sin3θ
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 1
Ymin = –5,
Ymax = 5,
Yscale = 1
Tθ min = 0,
Tθ max = π,
Tθ ptch = 2π / 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(G↔T) 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.
20011101
19990401
5-3-7
Drawing a Graph
k Graph 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).
# 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 calculator’s remaining
memory capacity, an error occurs.
# Recalling data from graph memory causes any
data currently on the Graph function list to be
deleted.
20010102
19990401
5-4-1
Storing a Graph in Picture Memory
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).
# 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.
19990401
5-5-1
Drawing Two Graphs on the Same Screen
5-5 Drawing Two Graphs on the Same Screen
k Copying 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
19990401
5-5-2
Drawing Two Graphs on the Same Screen
○ ○ ○ ○ ○
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
Xmin = –4,
Xmax = 4,
Xscale = 1
Ymin = –3,
Ymax = 3,
Yscale = 1
(Sub-screen)
Procedure
1 m GRPH • TBL
2 u3(SET UP)ccc2(G+G)i
3 !K(V-Window) -cwcwa.fwc
-cwcwbw
6(RIGHT)-ewewbwc
-dwdwbwi
4 3(TYPE)b(Y=)v(v+b)(v-b)w
5(DRAW)
5 6(g)4(COPY)
Result Screen
19990401
5-5-3
Drawing Two Graphs on the Same Screen
k Graphing 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.
19990401
5-5-4
Drawing Two Graphs on the Same Screen
○ ○ ○ ○ ○
Graph y = x(x + 1)(x – 1) in the main screen, and y = 2x2 – 3 in the subscreen.
Example
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
1 m GRPH • TBL
2 u3(SET UP)ccc2(G+G)i
3 !K(V-Window) -ewewbwc
-fwfwbw
6(RIGHT)-cwcwa.fwc
-cwcwbwi
4 3(TYPE)b(Y=)v(v+b)(v-b)w
cvx-dw
5 ff1(SEL)
6 5(DRAW)
7 6(g)5(SWAP)
8 i
9 1(SEL)
0 5(DRAW)
Result Screen
19990401
5-5-5
Drawing Two Graphs on the Same Screen
k Using Zoom to Enlarge the Sub-screen
Description
Use the following procedure to enlarge the main screen graph and then move it to the subscreen.
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.
19990401
5-5-6
Drawing Two Graphs on the Same Screen
○ ○ ○ ○ ○
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
1 m GRPH • TBL
2 u3(SET UP)ccc2(G+G)i
3 !K(V-Window) -cwcwa.fwc
-cwcwbwi
4 3(TYPE)b(Y=)v(v+b)(v-b)w
5(DRAW)
5 2(ZOOM)b(BOX)
c~ce~ew
f~fd~dw
Result Screen
19990401
5-6-1
Manual Graphing
5-6 Manual Graphing
k Rectangular 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.
19990401
5-6-2
Manual Graphing
○ ○ ○ ○ ○
Example
Graph y = 2 x 2 + 3 x – 4
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 2
Ymin = –10,
Ymax = 10,
Yscale = 5
Procedure
1 m RUN • MAT
2 !K(V-Window) -fwfwcwc
-bawbawfwi
3 K6(g)6(g)2(SKTCH)b(Cls)w
2(SKTCH)e(GRAPH)b(Y=)
4 cvx+dv-ew
Result Screen
19991201
19990401
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.
19990401
5-6-4
Manual Graphing
○ ○ ○ ○ ○
Example
Graph the integration
∫
1
–2
(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
1 m RUN • MAT
2 !K(V-Window) -ewewbwc
-iwbcwfwi
3 K6(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
20011101
19990401
5-6-5
Manual Graphing
k Drawing Multiple Graphs on the Same Screen
Description
Use the following procedure to assign various values to a variable contained in an expression 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.
19990401
5-6-6
Manual Graphing
○ ○ ○ ○ ○
Example
To graph y = A x 2 – 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
1 m GRPH • TBL
2 !K(V-Window) -fwfwbwc
-bawbawcwi
3 3(TYPE)b(Y=)av(A)vx-d,
!+( [ )av(A)!.(=)d,b,-b!-( ] )w
4 5(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, θ, 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.
19990401
20011101
5-7-1
Using Tables
5-7 Using Tables
k Storing 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.
u Variable 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.
19990401
5-7-2
Using Tables
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.
u Generating 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 generation 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.
19990401
5-7-3
Using Tables
You can use cursor keys to move the highlighting around the table for the following purposes.
• To display the selected cell’s value at the bottom of the screen, using the calculator’s
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 screen’s Derivative item to On causes a number table that
includes the derivative to be displayed whenever you generate a number table.
Locating the cursor at a differential
coefficient displays “dy/dx” in the top line,
which indicates differential.
u Specifying 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.
*1 An error occurs if a graph for which a range is
specified or an overwrite graph is included
among the graph expressions.
*2 The 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.
19990401
5-7-4
Using Tables
k Editing 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.
19990401
5-7-5
Using Tables
k Editing 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}
• {DEL·A} ... {delete table}
• {Re-T} ... {regenerate table from function}
• {G·CON}/{G·PLT } ... {connected type}/{draw plot type} graph draw
• {R·DEL}/{R·INS} /{R·ADD} ... {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
-c.fw
cc
• 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.
19990401
20040901
5-7-6
Using Tables
u Row Operations
u To delete a row
○ ○ ○ ○ ○
Example
To delete Row 2 of the table generated on page 5-7-2
6(g)1(R·DEL)
c
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
6(g)2(R·INS)
c
19990401
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
6(g)3(R·ADD)
cccccc
u Deleting a Table
1. Display the table and then press 2(DEL·A).
2. Press w(Yes) to delete the table or i(No) to abort the operation without deleting
anything.
19990401
5-7-8
Using Tables
k Copying 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
19990401
5-7-9
Using Tables
k Drawing 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
*1 After 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).
*2 Pressing 6(g) 4(G • PLT) on the function
storage screen generates the number table
and plots the graph simultaneously.
19990401
5-7-10
Using Tables
○ ○ ○ ○ ○
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 = 3 x 2 – 2, Y2 = x 2
Use the following V-Window settings.
Xmin = 0,
Xmax = 6,
Xscale = 1
Ymin = –2,
Ymax = 10,
Yscale = 2
Procedure
1 m GRPH • TBL
2 !K(V-Window) awgwbwc
-cwbawcwi
3 3(TYPE)b(Y=)dvx-cw
vxw
4 6(g)2(RANG)-dwdwbwi
5 5(TABL)
6 4(G • CON)
Result Screen
# You can use Trace, Zoom, or Sketch after
drawing a graph.
19990401
20011101
5-7-11
Using Tables
k Specifying 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.
19990401
5-7-12
Using Tables
○ ○ ○ ○ ○
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 = 3x 2 – 2, Y2 = x + 4, Y3 = x 2
Procedure
1 m GRPH • TBL
2 3(TYPE)b(Y=)dvx-cw
v+ew
vxw
3 6(g)2(RANG)-dwdwbwi
4 ff1(SEL)
5 5(TABL)
Result Screen
# 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.
19990401
20011101
5-7-13
Using Tables
k Simultaneously 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
*1 Pressing 6(g) 4(G • PLT) on the function
storage screen generates the number table
and plots the graph simultaneously.
19990401
5-7-14
Using Tables
○ ○ ○ ○ ○
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
1 m GRPH • TBL
2 !K(V-Window) awgwbwc
-cwbawcwi
3 u3(SET UP)ccc1(T+G)i
4 3(TYPE)b(Y=)dvx-cw
5 6(g)2(RANG)
-dwdwbwi
6 5(TABL)
7 4(G • CON)
Result Screen
19990401
20011101
5-7-15
Using Tables
k Using 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
1 m GRPH • TBL
2 !K(V-Window) -bwbawbwc
-bwewbwi
u3(SET UP)ccc1(T+G)i
3 3(TYPE)b(Y=)dlvw
6(g)2(RANG)
cwjwbwi
4 5(TABL)
5(G • PLT)
5 6(g)4(G • Link)
6 c ~ c, f ~ f
Result Screen
…→
←…
19990401
5-8-1
Dynamic Graphing
5-8 Dynamic Graphing
k Using 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 variable.*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.
*1 The following are the seven built-in function
types.
•Y=AX+B
•Y=A(X–B)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
2
* You 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
5-8-2
Dynamic Graphing
○ ○ ○ ○ ○
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
1 m DYNA
2 !K(V-Window)1(INIT)i
3 u3(SET UP)2(Stop)i
4 6(g)3(B-IN)c1(SEL)
5 6(g)4(VAR)cwbw-bw
6 2(RANG)cwfwbwi
7 3(SPEED)3( ) i
8 6(DYNA)
Result Screen
Repeats from 1 through 4.
↓
1
2
→
←
↓↑
4
3
→
←
19990401
5-8-3
Dynamic Graphing
k Dynamic 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.
19990401
5-8-4
Dynamic Graphing
○ ○ ○ ○ ○
Example
The path over time T of a ball thrown in the air at initial velocity V and
an angle of θ degrees from horizontal can be calculated as follows.
X = (Vcos θ ) T, Y = (Vsin θ ) 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
Tθ min = 0,
Tθ max = 6,
Tθ ptch = 0.1
Procedure
1 m DYNA
2 !K(V-Window) -bwecwfwc
-bwbgwcw
awgwa.bwi
3 u3(SET UP)2(Stop)
cccc1(Deg)i
4 3(TYPE)d(Param)
(cacav(A))vw
(casav(A))v-e.jvxw
5 4(VAR)
6 2(RANG)dawgawbfwi
7 3(SPEED)3( ) i
8 6(DYNA)
Result Screen
···→
←···
19990401
20011101
20011001
5-8-5
Dynamic Graphing
k Adjusting 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.
# To clear the speed adjustment menu without
changing anything, press w.
# Press u5 (G↔T) to return to the graph
screen.
19990401
5-8-6
Dynamic Graphing
k Using 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
u To 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.
u To 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.
# 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 calculator’s current graph functions,
draw conditions, and screen data. The previous
data is lost when it is replaced.
19990401
20040901
5-9-1
Graphing a Recursion Formula
5-9 Graphing a Recursion Formula
k Generating 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 {a n }, composed of a n , n
• Linear two-term recursion composed of a n+1, a n , n
• Linear three-term recursion composed of a n+2, a n+1, a n , n
Set Up
1. From the Main Menu, enter the RECUR Mode.
Execution
2. Specify the recursion type.
3(TYPE)b(a n =) ... {general term of sequence a n }
c(a n+1=) ... {linear two-term recursion}
d(a n+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.
19990401
5-9-2
Graphing a Recursion Formula
○ ○ ○ ○ ○
Example
Generate a number table from recursion between three terms as
expressed by a n+2 = a n+1 + a n , with initial terms of a 1 = 1, a 2 = 1
(Fibonacci sequence), as n changes in value from 1 to 6.
Procedure
1 m RECUR
2 3(TYPE)d(a n+2=)
3 4(n. a n ·· )d(a n+1)+2(a n )w
4 5(RANG)2(a 1)bwgwbwbwi
5 6(TABL)
Result Screen
* The first two values correspond to
a 1 = 1 and a 2 = 1.
# Specifying On for the Σ Display of the SET UP
screen causes the sum of each term to be
included in the table.
19990401
20011101
5-9-3
Graphing a Recursion Formula
k Graphing 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
19990401
5-9-4
Graphing a Recursion Formula
○ ○ ○ ○ ○
Example
Generate a number table from recursion between two terms as
expressed by a n+1 = 2a n +1, with an initial term of a 1 = 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
1 m RECUR
2 !K(V-Window) awgwbwc
-bfwgfwfwi
3 3(TYPE)c(a n+1=)c2(a n )+bw
4 5(RANG)2(a 1)bwgwbwi
5 6(TABL)
6 5(G • CON)
Result Screen
19990401
5-9-5
Graphing a Recursion Formula
k Graphing a Recursion Formula (2)
Description
The following describes how to generate a number table from a recursion formula and graph
the values while Σ Display is On.
Set Up
1. From the Main Menu, enter the RECUR Mode.
2. On the SET UP screen, specify On for Σ 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(a n ) ... Line graph with ordinate a n , abscissa n
c(Σa n ) ... Line graph with ordinate Σa n , abscissa n
6(G • PLT) b(a n ) ... Plot type graph with ordinate a n , abscissa n
c(Σa n ) ... Plot type graph with ordinate Σa n , abscissa n
19990401
5-9-6
Graphing a Recursion Formula
○ ○ ○ ○ ○
Example
Generate a number table from recursion between two terms as
expressed by a n+1 = 2a n +1, with an initial term of a 1 = 1, as n changes
in value from 1 to 6. Use the table values to draw a plot line graph with
ordinate Σa n , abscissa n.
Use the following V-Window settings.
Xmin = 0,
Xmax = 6,
Xscale = 1
Ymin = –15,
Ymax = 65,
Yscale = 5
Procedure
1 m RECUR
2 u3(SET UP)1(On)i
3 !K(V-Window) awgwbwc
-bfwgfwfwi
4 3(TYPE)c(a n+1=)c2(a n )+bw
5 5(RANG)2(a 1)bwgwbwi
6 6(TABL)
7 6(G • PLT)c(Σa n )
Result Screen
19990401
5-9-7
Graphing a Recursion Formula
k WEB Graph (Convergence, Divergence)
Description
y = f(x) is graphed by presuming a n+1 = y, a n = x for linear two-term regression a n+1 = f(a n )
composed of a n+1, a n . 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.
19990401
5-9-8
Graphing a Recursion Formula
○ ○ ○ ○ ○
Example
To draw the WEB graph for the recursion formula a n+1 = –3(a n )2 + 3a n ,
b n+1 = 3b n + 0.2, and check for divergence or convergence. Use the
following table range and V-Window Settings.
Table Range
Start = 0, End = 6, a 0 = 0.01, a n Str = 0.01, b 0 = 0.11, b n Str = 0.11
V-Window Settings
Xmin = 0,
Xmax = 1,
Xscale = 1
Ymin = 0,
Ymax = 1,
Yscale = 1
Procedure
1 m RECUR
2 !K(V-Window) awbwbwc
awbwbwi
3 3(TYPE)c(a n+1=)-d2(a n )x+d2(a n )w
d3(b n )+a.cw
4 5(RANG)1(a 0)
awgwa.abwa.bbwc
a.abwa.bbwi
5 6(TABL)
6 4(WEB)
7 1(TRACE)w~w(a n is convergence)
cw~w(b n is divergence)
Result Screen
19990401
5-10-1
Changing the Appearance of a Graph
5-10 Changing the Appearance of a Graph
k Drawing 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
*1 The above shows the function menu that
appears in the GRPH • TBL Mode. Menu items
may differ somewhat in other modes.
*2 In the case of an inverse function graph,
drawing starts immediately after you select
this option.
*3 Some 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
5-10-2
Changing the Appearance of a Graph
○ ○ ○ ○ ○
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
1 m GRPH • TBL
!K(V-Window) -fwfwbwc
-fwfwbwi
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
2 3(SKTCH)g(Tangnt)
3 e~ew*1
Result Screen
*1 You can draw a tangent line in succession by
moving the “ ” pointer and pressing w.
19990401
5-10-3
Changing the Appearance of a Graph
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.
# You can input any of the following characters as
comment text: A~Z, r, θ, space, 0~9, ., +, –, ×,
÷, (–), EXP, π, Ans, (, ), [, ], {, }, comma, →,
x2, ^, log, In,
,x
, 10x, ex, 3
tan, sin–1, cos–1, tan–1, i, List, Mat
19990401
, x–1, sin, cos,
5-10-4
Changing the Appearance of a Graph
○ ○ ○ ○ ○
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
1 m GRPH • TBL
!K(V-Window) -fwfwbwc
-fwfwbwi
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
2 3(SKTCH)e(Text)
3 f~f d~d
a-(Y)!.(=)v(v+c)(v-c)
i
Result Screen
19990401
19991201
5-10-5
Changing the Appearance of a Graph
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.
19990401
5-10-6
Changing the Appearance of a Graph
○ ○ ○ ○ ○
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
1 m GRPH • TBL
!K(V-Window) -fwfwbwc
-fwfwbwi
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
2 3(SKTCH)f(Pen)
3 f~f d~dw
4 cd…, e~e, ef…, d~dw
Result Screen
19990401
19991201
5-10-7
Changing the Appearance of a Graph
k Changing 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
5-11-1
Function Analysis
5-11 Function Analysis
k Reading 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.
19991201
19990401
20011101
5-11-2
Function Analysis
○ ○ ○ ○ ○
Example
Read coordinates along the graph of the function shown below.
Y1 = x 2 – 3
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 1
Ymin = –10,
Ymax = 10,
Yscale = 2
Procedure
1 m GRPH • TBL
!K(V-Window) -fwfwbwc
-bawbawcwi
3(TYPE)b(Y=)vx-dw
5(DRAW)
2 1(TRACE)
3 d~d
4 -bw
Result Screen
# The following shows how coordinates are
displayed for each function type.
• Parametric Graph
• Polar Coordinate Graph
• Inequality Graph
19990401
19991201
5-11-3
Function Analysis
k Displaying 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.
19990401
20011101
5-11-4
Function Analysis
○ ○ ○ ○ ○
Example
Read coordinates and derivatives along the graph of the function
shown below.
Y1 = x 2 – 3
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 1
Ymin = –10,
Ymax = 10,
Yscale = 2
Procedure
1 m GRPH • TBL
u3(SET UP)ccccc1(On)i
2 !K(V-Window) -fwfwbwc
-bawbawcwi
3(TYPE)b(Y=)vx-dw
5(DRAW)
3 1(TRACE)
4 d~d
5 -bw
Result Screen
19990401
19991201
5-11-5
Function Analysis
k Graph 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.
19990401
5-11-6
Function Analysis
○ ○ ○ ○ ○
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
1 m GRPH • TBL
2 u3(SET UP)ccc3(GtoT)i
3 !K(V-Window) -fwfwbwc
-bawbawcwi
4 3(TYPE)b(Y=) vx-dw
-v+cw
5(DRAW)
5 1(TRACE)
6 d~dwe~ewi
7 6(CHNG)
8 K1(LMEM)bw
Result Screen
19990401
20011101
5-11-7
Function Analysis
k Coordinate 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.
19990401
5-11-8
Function Analysis
○ ○ ○ ○ ○
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 = x 2 – 3, Y2 = – x + 2
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 1
Ymin = –10,
Ymax = 10,
Yscale = 2
Procedure
1 m GRPH • TBL
!K(V-Window) -fwfwbwc
-bawbawcwi
3(TYPE)b(Y=)vx-dw
-v+cw
5(DRAW)
2 2(ZOOM)i(Rnd)
3 1(TRACE)
d~d
Result Screen
19990401
5-11-9
Function Analysis
k Calculating 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.
19990401
20011101
5-11-10
Function Analysis
○ ○ ○ ○ ○
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
1 m GRPH • TBL
!K(V-Window) 1(INIT)i
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
2 4(G-SLV)b(Root)
…
4 e
e
Result Screen
# 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.
19990401
20011101
5-11-11
Function Analysis
k Calculating 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
쏆.
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.
19990401
5-11-12
Function Analysis
○ ○ ○ ○ ○
Example
Graph the two functions shown below, and determine the point of
intersection between Y1 and Y2.
Y1 = x + 1, Y2 = x 2
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 1
Ymin = –5,
Ymax = 5,
Yscale = 1
Procedure
1 m GRPH • TBL
!K(V-Window) -fwfwbwc
-fwfwbwi
3(TYPE)b(Y=)v+bw
vxw
5(DRAW)
2 4(G-SLV)f(Isect)
…
6 e
Result Screen
# 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
5-11-13
Function Analysis
k Determining 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.
19990401
5-11-14
Function Analysis
○ ○ ○ ○ ○
Example
Graph the two functions shown below and then determine the ycoordinate 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
1 m GRPH • TBL
!K(V-Window) 1(INIT)i
3(TYPE)b(Y=)v+bw
v(v+c)(v-c)w
5(DRAW)
2 4(G-SLV)g(Y-Cal)
2 4(G-SLV)h(X-Cal)
3 cw
3 cw
4 a.fw
4 c.cw
Result Screen
# 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
5-11-15
Function Analysis
k Calculating 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.
# 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.
19990401
19991201
5-11-16
Function Analysis
○ ○ ○ ○ ○
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
1 m GRPH • TBL
!K(V-Window) -g.dwg.dwbwc
-ewewbwi
3(TYPE)b(Y=)v(v+c)(v-c)w
5(DRAW)
2 4(G-SLV)i(∫dx)
…
4 d~dw
5 e~e(Upper limit; x = 0)
6 w
Result Screen
19990401
5-11-17
Function Analysis
k Conic 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.
u Parabolic 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}
u Circular Graph Analysis
• {Center}/{Radius} ... {center}/{radius}
• {X-Icpt}/{Y-Icpt} ... {x-intercept}/{y-intercept}
u Elliptical Graph Analysis
• {Focus}/{Vertex}/{Center}/{e} ... {focus}/{vertex}/{center}/{eccentricity}
• {X-Icpt}/{Y-Icpt} ... {x-intercept}/{y-intercept}
u Hyperbolic 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.
19990401
20011101
5-11-18
Function Analysis
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.
19990401
5-11-19
Function Analysis
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
(Y – 1)2
(X – 3)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.)
19990401
5-11-20
Function Analysis
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.)
19990401
5-11-21
Function Analysis
u To draw and analyze the asymptotes
[G-SLV]-[Asympt]
○ ○ ○ ○ ○
Example
To draw the asymptotes for the hyperbola
(X – 1)2
(Y – 1)2
––––––––
– ––––––––
=1
2
2
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.)
u To calculate eccentricity
[G-SLV]-[e]
○ ○ ○ ○ ○
Example
To determine the eccentricity of the graph for ellipse
(X – 2)2
+
(Y – 2)2
42
=1
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.)
# 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
6
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
6-2
6-3
6-4
6-5
Before Performing Statistical Calculations
Calculating and Graphing Single-Variable Statistical
Data
Calculating and Graphing Paired-Variable Statistical
Data
Performing Statistical Calculations
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.
19990401
6-1-1
Before Performing Statistical Calculations
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.
# You can use the f, c, d and e keys
to move the highlighting to any cell in the lists
for data input.
# Except for complex numbers, calculation
results can be input as statistical data.
19990401
6-1-2
Before Performing Statistical Calculations
k Changing 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.
*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
6-1-3
Before Performing Statistical Calculations
• 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}/{N·Dis}/{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
19990401
6-1-4
Before Performing Statistical Calculations
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.
# 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.
# 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.
u3(SET UP)2(Man)
i(Returns to previous menu.)
19990401
6-2-1
Calculating and Graphing Single-Variable Statistical Data
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.
k Normal 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.
k Histogram (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.
⇒
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
6-2-2
Calculating and Graphing Single-Variable Statistical Data
k Med-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.
minX
Q1 Med
Q3
maxX
k Modified 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.
# Input a positive integer for frequency data.
Other types of values (decimals, etc.) cause
an error.
# Dimension ERROR usually occurs when two
lists contain a different number of elements.
19990401
6-2-3
Calculating and Graphing Single-Variable Statistical Data
k Normal Distribution Curve (N • Dis)
The normal distribution curve is graphed using the following normal distribution function.
y=
1
(2 π) xσn
e
–
(x–x) 2
2xσn 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.
k Broken 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.
⇒
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
6-2-4
Calculating and Graphing Single-Variable Statistical Data
k Displaying 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 .............
Σx ...........
Σx2 ..........
xσn ..........
xσn–1 ........
n .............
mean
sum
sum of squares
population standard deviation
sample standard deviation
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.
# 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
6-3-2
Calculating and Graphing Paired-Variable Statistical Data
○ ○ ○ ○ ○
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
1 m 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)
19990401
6-3-3
Calculating and Graphing Paired-Variable Statistical Data
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.
# You can perform trace on a regression graph.
You cannot perform trace scroll.
19990401
6-3-4
Calculating and Graphing Paired-Variable Statistical Data
○ ○ ○ ○ ○
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
1 m 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)
3 4(CALC)h(Log)
4 6(DRAW)
Result Screen
20011101
19990401
20010102
6-3-5
Calculating and Graphing Paired-Variable Statistical Data
k Selecting 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
k Displaying 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.
k Graphing Statistical Calculation Results
While the parameter calculation result is on the display, you can graph the displayed
regression formula by pressing 6(DRAW).
19990401
6-3-6
Calculating and Graphing Paired-Variable Statistical Data
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 .............
b .............
r .............
r2 ............
MSe ........
regression coefficient (slope)
regression constant term (y-intercept)
correlation coefficient
coefficient of determination
mean square error
k Med-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
# Input a positive integer for frequency data.
Other types of values (decimals, etc.) cause
an error.
19990401
6-3-7
Calculating and Graphing Paired-Variable Statistical Data
k Quadratic/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
19990401
6-3-8
Calculating and Graphing Paired-Variable Statistical Data
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
19990401
6-3-9
Calculating and Graphing Paired-Variable Statistical Data
k Power 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
k Sinusoidal Regression Graph
Sinusoidal regression is best applied for cyclical data.
The following is the sinusoidal regression model formula.
y = a·sin(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.
19990401
6-3-10
Calculating and Graphing Paired-Variable Statistical Data
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 + ae–bx
4(CALC)l(Lgstic)
6(DRAW)
• Certain types of data may take a long time to calculate. This does not indicate malfunction.
k Residual 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.
# 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
6-3-11
Calculating and Graphing Paired-Variable Statistical Data
k Displaying 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
Σ x ............. sum of data stored in xList
Σ x2 ........... sum of squares of data
stored in xList
xσn ............ population standard
deviation of data stored in
xList
xσn-1 .......... sample standard deviation
of data stored in xList
n ............... number of data
p ............... mean of data stored in yList
Σ y ............. sum of data stored in yList
Σ y2 ...... sum of squares of data stored in yList
yσn ...... population standard deviation of data
stored in yList
yσn-1 .... sample standard deviation of data
stored in yList
Σ 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
k Copying 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 • TBL Mode graph formula area*1.
2. Press w to save the copied graph formula and return to the previous regression
calculation result display.
*1 You cannot edit regression formulas for graph
formulas in the GRPH • TBL Mode.
19990401
6-3-12
Calculating and Graphing Paired-Variable Statistical Data
k Multiple 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 singlevariable 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.
19990401
6-3-13
Calculating and Graphing Paired-Variable Statistical Data
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.
19990401
6-3-14
Calculating and Graphing Paired-Variable Statistical Data
○ ○ ○ ○ ○
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
1 m STAT
2 a.fwb.cw
c.ewewf.cw
e
-c.bwa.dw
b.fwcwc.ew
1(GRPH)b(S-Gph1)
3 5(DefG)
cIvw(Register Y1 = 2In x)
4 6(DRAW)
Result Screen
# 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
6-4-1
Performing Statistical Calculations
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.
u To 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.
19990401
6-4-2
Performing Statistical Calculations
k Single-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).
k Paired-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).
19990401
6-4-3
Performing Statistical Calculations
k Regression 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”.
19990401
6-4-4
Performing Statistical Calculations
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
xi
yi
10
15
20
25
30
1003
1005
1010
1011
1014
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.
# You cannot obtain estimated values for a MedMed, quadratic regression, cubic regression,
quartic regression, sinusoidal regression, or
logistic regression graph.
19990401
6-4-5
Performing Statistical Calculations
k Normal 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
19990401
6-4-6
Performing Statistical Calculations
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)
1(PROB)i(t() bhf.f)w
(Normalized variate t for 175.5cm)
1(PROB)f(P()a.ejg)1(PROB)f(P()-b.gde)w
(Percentage of total)
1(PROB)h(R()a.ejg)w
(Percentile)
Result: –1.633855948
( –1.634)
Result: 0.4963343361
( 0.496)
Result:
0.638921
(63.9% of total)
Result:
0.30995
(31.0 percentile)
*1
You can obtain the normalized variate
immediately after performing single-variable
statistical calculations only.
19990401
6-4-7
Performing Statistical Calculations
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.
19990401
6-4-8
Performing Statistical Calculations
○ ○ ○ ○ ○
Example
To draw a normal probability P (0.5) graph.
Procedure
1 m RUN • MAT
2 K6(g)6(g)2(SKTCH)b(Cls)w
2(SKTCH)e(GRPH)b(Y=)
3 K6(g)1(PROB)f(P()a.fw
Result Screen
19990401
Chapter
7
Computer Algebra
System and Tutorial
Modes (ALGEBRA FX 2.0 PLUS only)
7-1
7-2
7-3
7-4
Using the CAS (Computer Algebra System) Mode
Algebra Mode
Tutorial Mode
Algebra System Precautions
20010102
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.
COPY
H-COPY
PASTE
REPLAY
i
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.
20010102
7-1-2
Using the CAS (Computer Algebra System) Mode
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
20010102
20011101
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.
20010102
20011101
7-1-4
Using the CAS (Computer Algebra System) Mode
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
s} ... {inequality}
• {>}/{<}/{t
•Kkey
• {∞}/{Abs}/{x!}/{sign} ... {infinity}/{absolute value}/{factorial}/{signum function*1}
• {HYP} ... {hyperbolic}/{inverse hyperbolic} functions
• {sinh}/{cosh}/{tanh}/{sinh–1}/{cosh–1}/{tanh–1}
•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 θ. 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
1 (real number, A > 0)
–1 (real number, A < 0)
*1signum (A)
A
(A= imaginary number)
|A|
Undefined (A = 0)
20010102
20011101
7-1-5
Using the CAS (Computer Algebra System) Mode
○ ○ ○ ○ ○
Example
To assign M to row 1 column 2 of variable A when the matrix
is assigned to it
1 2 3
XY Z
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
20010102
7-1-6
Using the CAS (Computer Algebra System) Mode
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.
*1 Up 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.
20010102
20011101
7-1-7
Using the CAS (Computer Algebra System) Mode
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.
# 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
7-1-8
Using the CAS (Computer Algebra System) Mode
SET UP Items
u Angle ... Unit of angular measurement specification
• {Deg}/{Rad} ... {degrees}/{radians}
u Answer Type ... Result range specification
• {Real}/{Cplx} ... {real number}/{complex number}
u Display ... 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.
• {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
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.
• 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.
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
X2 + 4X + 4
1(TRNS)b(expand)(v+c)xw
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
20010102
(X – 2)2
7-1-12
Using the CAS (Computer Algebra System) Mode
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+
X=
al(B)!.(=)aw
–B
A
○ ○ ○ ○ ○
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
sin (A – B)
sin (A + B)
1(TRNS)f(TRIG)c(tCollc)
+
2
2
sav(A)cal(B)w
20010102
20011101
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
ex+ e—x
2
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)+da+(X)w
X + 3Y + 3 = –2Y + 3
20010102
7-1-14
Using the CAS (Computer Algebra System) Mode
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
X3 + 5X2 + 7X + 1
X+2
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+
X2 + (A + B)X
al(B)vw
• 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
20010102
20011101
7-1-15
Using the CAS (Computer Algebra System) Mode
u cExpand (cExpnd)
Function: Expands xth root of imaginary number.
Syntax: cExpand( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
○ ○ ○ ○ ○
Example
To expand
2i
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
1(TRNS)l(approx)!x(
2
)cw
1.414213562
○ ○ ○ ○ ○
Example
920
Normal:jMcaw
12157665459056928801
approx: 1(TRNS)l(approx)jMcaw 1. 215766546E+19 (Display: Norm1)
# 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.
20010102
7-1-16
Using the CAS (Computer Algebra System) Mode
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
X3
3
• 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
• Direction can be positive (from right) or negative (from left).
20010102
1
7-1-17
Using the CAS (Computer Algebra System) Mode
uΣ
Function: Calculates a sum.
Syntax: Σ( {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(Σ)vx,v,b,baw
385
uΠ
Function: Calculates a product.
Syntax: Π( {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(Π)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
X5
X3
2(CALC)g(taylor)sv,v,f,aw
+X
–
120
6
• 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
20010102
In(2)
5
In (4 5 + 8)
–
+
4
2
2
7-1-18
Using the CAS (Computer Algebra System) Mode
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,vxdv-ew
X+1
20010102
20011101
7-1-19
Using the CAS (Computer Algebra System) Mode
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!.(=)
X2 – 4X + 3 = 0
fv-vxw
20010102
20011101
7-1-20
Using the CAS (Computer Algebra System) Mode
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
20010102
20011101
2Y = X
7-1-21
Using the CAS (Computer Algebra System) Mode
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)(
2X – 3 = 9
cv-d)!.(=)jw
or 2X – 3 = – 9 2
1
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
20010102
6X = X + 8
7-1-22
Using the CAS (Computer Algebra System) Mode
u clear (clrVar)
Function: Clears the contents of specific equation (A to Z, r, θ ).*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, θ).
Syntax: clearVarAll
{ }
*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
7-1-23
Using the CAS (Computer Algebra System) Mode
k List Calculation Commands
[OPTN]-[LIST]
u Dim
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
u Min
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
20010102
{1, 1, 2 }
7-1-24
Using the CAS (Computer Algebra System) Mode
u Max
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
7-1-25
Using the CAS (Computer Algebra System) Mode
○ ○ ○ ○ ○
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
5
3
u Median
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
3
2
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
20010102
7-1-26
Using the CAS (Computer Algebra System) Mode
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
u Cuml
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
20010102
{ 503 , 1003 , 50 {
7-1-27
Using the CAS (Computer Algebra System) Mode
u A 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 }
u StdDev
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
21
3
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
20010102
20011101
7
3
7-1-28
Using the CAS (Computer Algebra System) Mode
u Seq
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
20010102
20011101
{ X, X, X, X, X, X, X, X }
7-1-29
Using the CAS (Computer Algebra System) Mode
u SortA
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.
20010102
7-1-30
Using the CAS (Computer Algebra System) Mode
u List→Mat (L→Mat)
Function: Converts lists into a matrix.
Syntax: List→Mat( List [ , ... ,List ] [ ) ]
○ ○ ○ ○ ○
Example
To convert list {3, 5} and list {2, 4} into a matrix
K1(LIST)d(LIST→)b(L→Mat)!*( { )d,f
3 2
!/( } ),!*( { )c,e!/( } )w
5 4
u List→Vect (L→Vect)
Function: Converts a list into a vector.
Syntax: List→Vect List
○ ○ ○ ○ ○
Example
To convert list {3, 2} into a vector
K1(LIST)d(LIST→)c(L→Vect)!*( { )d,c
!/( } )w
[ 3, 2 ]
20010102
7-1-31
Using the CAS (Computer Algebra System) Mode
k Matrix Calculation Commands
[OPTN]-[MAT]
u Dim
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
20010102
20011101
46
7-1-32
Using the CAS (Computer Algebra System) Mode
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, (0.894427191 0.4472135955) are the eigenvectors that correspond to 5,
while (– 0.894427191 0.4472135955) 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
20010102
20011101
{ 5, 1 }
7-1-33
Using the CAS (Computer Algebra System) Mode
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!-( ] )
66
71
147
0 1 0
71
62
0 0 1–
71
1 0 0
!+( [ )-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!-( ] )
1 1 0
3
0 1 –
9
6
2
0 0 1
–
!+( [ )-f,c,e,-e
!-( ] )!-( ] )w
20010102
62
71
7-1-34
Using the CAS (Computer Algebra System) Mode
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
1
5
6
1
2
0
0
1
0
1
2
1
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
20010102
7-1-35
Using the CAS (Computer Algebra System) Mode
u Augment (Augmnt)
Function: Combines two matrices.
Syntax: Augment( Mat, Mat [ ) ]
○ ○ ○ ○ ○
Example
To combine the two matrices below
1 2
3 4
5
7
6
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
○ ○ ○ ○ ○
To create a 2 × 2 identity matrix
Example
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
20010102
7-1-36
Using the CAS (Computer Algebra System) Mode
○ ○ ○ ○ ○
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.
20010102
7-1-37
Using the CAS (Computer Algebra System) Mode
u Diag
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 ]
u Mat→List (M→List)
Function: Converts a specific column of a matrix into a list.
Syntax: Mat→List( Mat, column number [ ) ]
○ ○ ○ ○ ○
Example
To convert column 2 of the matrix below to a list
1 2
3 4
K2(MAT)d(MAT→)b(M→List)!+( [ )!+( [ )
b,c!-( ] )!+( [ )d,e
!-( ] )!-( ] ),cw
{ 2, 4 }
u Mat→Vect (M→Vect)
Function: Converts a specific column of a matrix into a vector.
Syntax: Mat→Vect( Mat, column number [ ) ]
○ ○ ○ ○ ○
Example
To convert column 2 of the matrix below to a vector
1 2
3 4
K2(MAT)d(MAT→)c(M→Vect)!+( [ )!+( [ )
b,c!-( ] )!+( [ )d,e
!-( ] )!-( ] ),cw
20010102
20011101
[ 2, 4 ]
7-1-38
Using the CAS (Computer Algebra System) Mode
u Swap
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
20010102
7-1-39
Using the CAS (Computer Algebra System) Mode
u Row+
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
20010102
7-1-40
Using the CAS (Computer Algebra System) Mode
k Vector Calculation Commands
[OPTN]-[VECT]
u Dim
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
u CrossP
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 ]
u DotP
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
u Norm
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
20010102
20011101
7-1-41
Using the CAS (Computer Algebra System) Mode
u UnitV
Function: Normalizes a vector.
Syntax: UnitV Vect
○ ○ ○ ○ ○
Example
To normalize a vector (1 2 3)
K3(VECT)b(CALC)f(UnitV)
!+( [ )b,c,d
14 14 3 14
14 , 7 , 14
!-( ] )w
u Angle
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
cos–1
11 5
25
u Augment (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 ]
20010102
20011101
7-1-42
Using the CAS (Computer Algebra System) Mode
u Vect→List (V→List)
Function: Converts a vector into a list.
Syntax: Vect→List Vect
○ ○ ○ ○ ○
Example
To convert vector (3 2) into a list
K3(VECT)d(VECT→)b(V→List)!+( [ )d,c
!-( ] )w
{ 3, 2 }
u Vect→Mat (V→Mat)
Function: Converts vectors into a matrix.
Syntax: Vect→Mat( Vect [, ... ,Vect ] ( ] )
○ ○ ○ ○ ○
Example
To convert vector (3 5) and (2 4) into a matrix
K3(VECT)d(VECT→)c(V→Mat)!+( [ )d,f
3 2
!-( ] ),!+( [ )c,e!-( ] )w
5 4
20010102
7-2-1
Algebra Mode
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)+dfa+(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
19990401
20011101
3X + 2 (2X + 1)
7-3-1
Tutorial Mode
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.
19990401
7-3-2
Tutorial Mode
The following shows the formulas available for each type of expression.
Linear Equation — 6 Types
• AX = B
• AX + B = C
• A(BX + C) = D(EX + F)
•X +A= B
• AX + B = CX + D
•AX + B= C
Linear Inequality — 6 × 4 Types
• AX { > < > < } B
• AX + B { > < > < } C
• A(BX + C) { > < > < } D(EX + F)
•X +A{ > < ><} B
• AX + B { > < > < } CX + D
•AX + B{ > < > < } C
Quadratic Equation — 5 Types
• AX2 = B
• AX2 + BX + C = 0
• AX2 + BX + C = DX2 + EX + F
• (AX + B)2 = C
• AX2 + BX + C = D
Simul Equation — 10 Types
• AX + BY = C
DX + EY = F
• AX + BY + C = 0
DX + EY + F = 0
• AX + BY = C
Y = DX + E
• AX + BY = C
DX + EY + F = GX + HY + I
• AX + BY + C = DX + EY + F
Y = GX + H
• Y = AX + B
Y = CX + D
• AX + BY + C = DX + EY + F
GX + HY + I = JX + KY + L
• AX + BY = C
DX + EY + F = 0
• AX + BY + C = 0
Y = DX + E
• AX + BY + C = 0
DX + EY + F = GX + HY + I
Pressing 6(EXCH) reverses the left side and right side elements of the expression.
19990401
7-3-3
Tutorial Mode
k Defining 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.
• {L • COP}/{R • COP} ... copy {left side element}/{right side element} as a graph function
(Simultaneous Equation Mode*2)
• {1 • COP}/{2 • COP} ... copy {first}/{second} expression as a graph function
*1 In the case of an inequality, the inequality
symbols are also copied.
*2 Simultaneous equations are transformed to the
format Y = AX + B when copied.
19990401
7-3-4
Tutorial Mode
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
19990401
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)
19990401
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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20010102
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.
20010102
19990401
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)
*1 You 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.
20011101
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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)
∫a f (x)dx = F(b) – F(a)
b
19990401
20011101
Chapter
Programming
8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
Basic Programming Steps
Program Mode Function Keys
Editing Program Contents
File Management
Command Reference
Using Calculator Functions in Programs
Program Mode Command List
Program Library
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.
19990401
8
8-1-1
Basic Programming Steps
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.
# 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, θ, 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.
19990401
8-1-2
Basic Programming Steps
○ ○ ○ ○ ○
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.
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.
2
S = 2 3 A2, V = –––– A3
3
A
Procedure
1 m PRGM
2 3(NEW)OCTAw*1
3 !J(PRGM)3(?)aav(A)6(g)6(g)3(:)*2
c*!x(
!x(
)d*av(A)x6(g)4(^)
)c/d*av(A)Md
ii
4 1(EXE) or w
hw(Value of A)
w
S when A = 7
V when A = 7
w
wbaw
w
S when A = 10
V when A = 10
w
wbfw
w*3
S when A = 15
V when A = 15
*1 Press 3(NEW) and the cursor changes form
to indicate alpha character input.
*2 The 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*
xw
Volume V ............ !x(
)c/d*
Mdw
*3 Pressing 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 ”” w.
# 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
”” cannot be found.
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8-2-1
Program Mode Function Keys
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
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}/{Σ DSP}
See “SET UP Screen Function Key Menus” on page 1-7-1 for details about each of these
commands.
19990401
8-2-2
Program Mode Function Keys
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}/{DEL·A}
... {specific program}/{all program} delete
• {SRC}/{REN}
... file name {search}/{change}
*1 Programs input after pressing 2(BASE) are
indicated by B to the right of the file name.
19990401
8-3-1
Editing Program Contents
8-3 Editing Program Contents
k Debugging 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
u To 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 α-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.
u To 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
19990401
8-3-2
Editing Program Contents
k Using 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.
A
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.
2
S = 3 A2, V = –––– A3
12
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(
Volume V ..................... !x(
)d*av(A)x6(g)4(^)
)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)
19990401
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
19990401
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
*1 The message “Not Found” appears when the
search data you specify cannot be found in
the program.
*2 If 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.
19990401
8-4-2
File Management
k Editing 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.
k Deleting 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.
19990401
8-4-3
File Management
u To delete all programs
1. While the program list is on the display, press 5(DEL·A).
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 SYSTEM Mode from the Main Menu, and
then pressing 1(Mem) to display the memory management screen.
See “9-2 Memory Operations” for details.
k Registering 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.
19990401
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.
k Recalling 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.
19990401
8-5-1
Command Reference
8-5 Command Reference
k Command 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
DrawRΣ-Con, DrawRΣ-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
19990401
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 command.
[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).
k Basic 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, “?” appears to prompt input. Up to 255 bytes of text can be used for a
prompt.
• 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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19991201
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.
19990401
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8-5-4
Command Reference
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 IfEndstatement is always executed following either the Then-statement or Else-statement.
Syntax:
If
numeric expression
_
:
^
_
:
^
Then
Else
_
:
^
_
:
^
_
:
^
IfEnd
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 Nextstatement. 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:
For → To Step
Next
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)
19990401
_
:
^
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 (nonzero).
Syntax:
Do
_
:
^
_
:
^
LpWhile
numeric expression
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.
19990401
8-5-6
Command Reference
While~WhileEnd
Function: This command repeats specific commands as long as its condition is true (nonzero).
Syntax:
While
numeric expression
_
:
^
_
:
^
WhileEnd
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.
k Program 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.
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
A
Subroutines
D
Prog ”D”
Prog ”C”
C
E
Prog ”E”
Prog ”I”
Level 1
I
J
Prog ”J”
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 statement 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.
19990401
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.
19990401
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:
Variable Value G 0
Dsz :
_
:
^
Variable Value = 0
Parameters: variable name: A to Z, r, θ
[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 (_).
19990401
8-5-10
Command Reference
Goto~Lbl
Function: This command performs an unconditional jump to a specified location.
Syntax: Goto
Source Exif Data:
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