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CHAPTER 7

Calculator Notes for the fx-7400G Plus
Note 7A Function Notation
Functions are usually entered from GRAPH mode and are referred to by name as Y1, Y2,. , Y9, Y10. To evaluate a function for a particular x-value, for example, Y1 when x 4, enter RUN mode. Press 4 , EXE to assign a value of 4 to x. Then, press VARS F2 (GRAPH) F1 (Y) 1 EXE to see the value of Y1.

Note 7B Some Functions

To use the command for squaring, in RUN mode, enter a number and press X2 EXE. To use the command for square root, press enter a number and press EXE.

SHIFT [ ]

in RUN mode. Then
To use the command for the sum of a list, in RUN mode press OPTN F1 (LIST) F2 (Sum). Then, press SHIFT [ { ] and enter the numbers in the list, separating each number with a comma. Close the braces and press EXE. Alternatively, from either RUN or STAT mode, enter numbers into a list, for example, List 1. (See Note 1B.) Then, on the Run screen, enter sum List 1 by pressing OPTN F1 (LIST) F2 (Sum) F1 (List) F1 (List) 1 EXE.
The command for random number generates a random ten-digit decimal number between 0 and 1. From RUN mode, press OPTN F4 (PROB) F4 (Ran#) EXE.

Note 7C Absolute Value

To find the absolute value of a number, from the Run screen, press OPTN F1 (NUM) F1 (Abs). Then, enter a number and press EXE.
Discovering Algebra Calculator Notes for the Casio fx-7400G Plus
2007 Key Curriculum Press
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fx-7400G Plus Note 7D Friendly Windows
When you trace a function or locate a point on the screen, you often see long, ugly decimal values for the coordinates of your points. Sometimes, however, the values are nice, friendly values, like 2.4 or 4.84, or repeating decimals, like 4.3333333. When the proper values are set for Xmin and Xmax in the View Window screen, the coordinate values of your points will be friendly numbers for most functions. This is because the calculator screen is made of tiny square dots called pixels, and when you move horizontally across the screen, the x-coordinate changes by one pixel with each trace step. When the total number of pixels across the screen (78 pixels) is either equal to, or a multiple of, the breadth of the domain, Xmax Xmin, the window will be friendly. For example, if Xmin 0 and Xmax 78 or Xmin 1 and Xmax 8.8, the window will be friendly. (Note: The y-coordinate is calculated by evaluating the function for the x-coordinate. So if the coefficients in a function are irrational, the y-coordinates will not be nice even in a friendly window.)
Two Friendly Square Windows
If you press SHIFT [V-Window] F1 (INIT), you get a special type of small friendly window, called a friendly square window. It is friendly because it has the view window values [3.9, 3.9, 1, 2.3, 2.3, 1]. It is square because the horizontal and vertical scales on the screen are equal in size. In a square window, circles appear symmetric and round, and the line y x makes a 45-degree angle with both axes. A square window is often the preferred window to use because it displays no visual distortion. However, this window, [3.9, 3.9, 1, 2.3, 2.3, 1], is sometimes too small to show much of the graph.
[3.9, 3.9, 1, 2.3, 2.3, 1]

Ymin, and Ymax

To see more of the graph in the window, you can double the Xmin, Xmax, values to [7.8, 7.8, 1, 4.6, 4.6, 1]. This square window is referred to as the friendly window with a factor of 2.

[7.8, 7.8, 1, 4.6, 4.6, 1]

(continued)

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Note 7D Friendly Windows (continued)
The friendly window with a factor of 2 is often a convenient window to use. To save it and recall it quickly, follow these steps. a. First, enter the values [7.8, 7.8, 1, 4.6, 4.6, 1] into your View Window screen.

fx-7400G Plus

b. From the View Window screen, press

F3 (Sto).

c. The next time you need this windowfor example, for the graph of y x 2press SHIFT [V-Window] F4 (Rcl).

[10, 10, 1, 10, 10, 1]

Other Friendly Square Windows
To assure that a window is square, the size of a horizontal step, called x, must equal the size of a vertical step, called y. x is the step size of the trace. In the square window [3.9, 3.9, 1, 2.3, 2.3, 1], x is 0.1. In the square window [7.8, 7.8, 1, 4.6, 4.6, 1], x is 0.2. Values for origin-centered friendly square windows are [39 x, 39 x, 1, 23 y, 23 y, 1]. For example, if x and y equal 0.3, then.
First-quadrant friendly square window values are [0, 78 x, 1, 0, 46 y, 1]. Again, if x and y equal 0.3, then.

[0, 23.4, 1, 0, 13.8, 1]

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Note 7D Friendly Windows (continued) Friendly Windows That Are Not Square
The Ymin and Ymax values of a friendly window can be changed to show a larger or smaller range. The graph will look distorted and it will no longer be square, but this might be necessary to see more of the graph. For example, the graph of y x 2 in the friendly square window [7.8, 7.8, 1, 4.6, 4.6, 1] runs off the top of the graph for x-coordinates greater than 2. If you want to see more of the graph, change the window to [7.8, 7.8, 1, 10, 100, 10]. This is a friendly window because the coordinates are still nice, but it is not square.
[7.8, 7.8, 1, 10, 100, 10] You can also see more of a graph without first changing the view window settings. Without using the trace option, use the arrow key to automatically scroll the graph in any direction. As you scroll, the view window settings change to reflect the current screen.

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CHAPTER 0

Calculator Notes for the fx-7400G Plus
To display the Main Menu screen of this calculator while in any mode, press MENU. If the Main Menu screen is not immediately displayed, press QUIT MENU or AC/ON MENU. There are nine modes that can be accessed from the Main Menu screen. To access a mode, use the arrow key to highlight the icon you want, and press EXE to display the first screen of the mode you selected. You can also enter a mode without highlighting an icon in the Main Menu by inputting the number marked in the lower-right corner of the icon. Many of the operations performed by this calculator can be executed by pressing function keys F1 through F4. Pressing sometimes shows more options. The operation assigned to each function key changes according to the mode. Function menus are at the bottom of the display in each mode. This calculator has nine different modes or work areas, depending on the type of operation you want to perform. When you first turn on your calculator, you see the Main Menu, which is a screen containing icons for the nine different modes. Pressing MENU also displays the Main Menu. You choose an icon from the Main Menu either by pressing its number or by using the arrow keys to highlight its icon and pressing EXE. Arithmetic calculations including calculations using fractions are performed in RUN mode.

Note 0A Fractions

This calculator has two special keys to facilitate work with fractions. From the Main Menu, select RUN and press EXE. To ensure that the calculator has the correct settings, press SHIFT [SET UP] to display the setup screen. Make sure that Simplify is set to Auto and that Frac is set to a b/c. The Frac setting is below Simplify. Just arrow down and the screen will scroll. (See Note 1J for an explanation of the setup options.) a. abc is used to enter a number as a fraction or as a mixed number. A mixed number contains two symbols. The first separates the whole number and the fraction, and the second separates the numerator and denominator. To enter 3, press 3 abc 4 EXE. To enter 4 31, press 3 abc 1 abc 2 EXE. Fractions are automatically displayed in 2 reduced form. (If you dont want fractions to be automatically reduced, see Note 1J.)
FD converts fractions to decimal numbers, and vice versa. A nonrepeating decimal number that has a fraction equivalent with fewer than nine digits in the numerator and denominator combined will convert. (If the number is a repeating decimal number, you can use the RPT DEC program in Note 0H to find the equivalent fraction.) To change a decimal to a fraction, enter the decimal and press EXE FD. The symbol separates the numerator from the

(continued)

2007 Key Curriculum Press
Discovering Algebra Calculator Notes for the Casio fx-7400G Plus
DA2_FX7400G_00.qxd 01/03/2006 02:48 PM Page 2
Note 0A Fractions (continued)
denominator. FD is also used to send images to a computer, so if the conversion does not seem to work, select LINK from the Main Menu and press EXE F4 (IMGE) F1 (Off).

fx-7400G Plus

SHIFT [d/c]
converts mixed numbers to improper fractions, and

vice versa.

To enter and solve 2 1, press 2 abc abc 2 EXE. The answer to a problem that involves only fractions will be in the form of a fraction or a whole number. However, the answer to a problem that involves a decimal will be in decimal form. To convert the terminal decimal answer to a fraction, and vice versa, press FD.
As an alternative to using the special fraction keys, you can enter a fraction as a division problem. To work with simple fractions like 4 and improper 7 fractions like 7, simply enter them into your calculator as division problems. 4 To see the answer displayed as a fraction, you must press FD. Often you dont need to use parentheses around a fraction entered as a division problem, but when in doubt, put in the parentheses.

Note 0B Exponents

There are several ways to raise a number to a power by using the calculator. The simplest way to square a number (raise it to the second power) is to use X2. Enter the number you want to square and then press X2. When you press EXE , the calculator will multiply the number by itself. For all powers (including the second power), you can use ^.
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Note 0B Exponents (continued)
The order of operations requires that you do all operations within parentheses first, evaluate all powers second, multiply and divide from left to right third, and add and subtract from left to right last.
Note 0C Negation and Subtraction
Negation and subtraction are performed with different keys on this calculator. Negation, () , changes the sign of a number or a variable. It is slightly shorter than the subtraction symbol. If you enter the wrong symbol, you may get an error message. In the order of operations, negation is treated like multiply by negative 1, so it is performed before addition and subtraction but after evaluation of powers. Sometimes you may need to use parentheses to get the correct result.

Note 0D Recursion

The Ans command on the calculator allows you to use the result of your last calculation in your next calculation. If you press EXE without pressing another key, the calculator will repeat the last operation on the previous result. Combining these two features allows you to perform on-screen recursion, calculating a new number by repeating the operation using the result of the previous calculation. To create patterns of numbers (sequences), follow this procedure: a. Enter the starting number of your sequence and press EXE. b. Enter an expression using Ans. You can get Ans by pressing any of the operation keys, such as , , , , ^ , X2 , or by pressing SHIFT [Ans]. c. Press EXE EXE EXE and so on. Each time you press EXE , you will get one more term in the sequence.

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fx-7400G Plus Note 0E The Chaos Game
To play the Chaos game, follow these steps: a. Link or manually enter the CHAOS program into your calculator. (See Note 0F and Note 0G.) b. From the Main Menu, arrow to PRGM and press EXE. Arrow down to select CHAOS and press EXE. c. You are asked to choose a Chaos shape. Press the appropriate number and EXE to select the shape. d. You are then asked to enter a fraction between 0 and 1. You can enter this value either as a fraction or as a decimal number. Press EXE. The calculator will plot 1000 points by following the Chaos rules to plot a fractal. e. When the program is done, press EXE to play again or AC/ON to quit.
File Name:CHAOS ClrText "CHAOS SHAPES" Lbl 0 "1.RT TRIANGLE2.EQUILAT TRI3.RAND TRIANG4.MORE"?A A<4Goto 1 ClrText "5.SQUARE" "6.PENTAGON" "7.HEXAGON" "8.GO BACK" ?A Lbl 1 A=1Goto 2 A=2Goto 3 A=3Goto 4 A=5Goto 5 A=6Goto 6 A=7Goto 7 A=8Goto 0 Lbl 2 " RT TRIANGLE" {.05,.95,.05}List 1 {.05,.05,.65}List 2
Goto 8 Lbl 3 " EQUILAT TRI" {.05,.95,.5}List 1 {.05,.05,.65}List 2 Goto 8 Lbl 4 " RANDOM TRI" {Ran#,Ran#,Ran#}List 1 {.7Ran#,.7Ran#,.7Ran#}List 2 Goto 8 Lbl 5 " SQUARE" {.2,.8,.8,.2}List 1 {.05,.05,.65,.65}List 2 Goto 8 Lbl 6 " PENTAGON".5+.35sin (72{0,1,2,3,4})List 1.35+.35cos (72{0,1,2,3,4})List 2 Goto 8 Lbl 7 " HEXAGON".5+.35sin (60{0,1,2,3,4,5})List 1.35+.35cos (60{0,1,2,3,4,5})List 2
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Note 0E The Chaos Game (continued)
(File Name: CHAOS continued)
Lbl 8 ClrGraph ViewWindow 0,1.1,.25,-.2,.7,.25 S-Gph2 DrawOff S-Gph3 DrawOff S-WindMan S-Gph1 DrawOn,xyLine,List 1,List 2,1, Square DrawStat List 1[1]X:List 2[1]Y Dim List 1N F-Line X,Y,List 1[N],List 2[N] " ENTER A " " FRACTION" " BETWEEN 0" " AND 1"?F "WHEN DONE" "PRESS AC TO" "QUIT OR EXE" "TO PLAY AGAIN" For 1J To 500 Next For 1J To 1000 Int (NRan#+1)P X+(List 1[P]-X)FX Y+(List 2[P]-Y)FY Plot X,Y Next
Note 0F Linking Programs or Lists
To transfer a program or list from one calculator to another, follow these steps: a. Connect two calculators by using a link cable. Be sure that the connection is tight on each unit. b. Turn on both calculators, and on each one select LINK from the Main Menu and press EXE.
c. On the receiving calculator, press F2 (RECV) so that the calculator displays Receiving. d. On the sending calculator, press F1 (TRAN).
e. Arrow down to the program or data you want to send. Press F1 (SEL) to select a program or list. You can select more than one program and/or list and send them simultaneously. Just continue to arrow down, pressing F1 (SEL) at each program or list you want to transmit. Then, press F4 (TRAN) to display the transmit menu. When you are ready to transmit, press F1 (YES).

f. When the transfer is complete, the screen will display Communication Complete! on both calculators.
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Note 0F Linking Programs or Lists (continued) Errors
If you get a Transmit ERROR! message, check each calculator to be sure the link cable is pushed all the way in and try again. Remember that after you arrow to the program or list you want to send, you must press F1 (SEL) to select it to transmit. Also, the receiving calculator must be Receiving before the sending calculator transmits. If the receiving calculator already has a program or list that has the same name as the one you are sending, the sending calculator will ask if you want to overwrite the item on the other calculator. Select F1 (YES) to overwrite, or F2 (NO) to skip transferring that item.
Note 0G Entering a Program
Your calculator is like a small computer. You can instruct (or program) it to do calculations or to communicate with other devices. What follows is not instructions for writing a program, but instructions for entering a calculator program that has already been written. You must be very careful to enter the commands exactly as they are written. Changing the program in any way will alter how it runs and may cause an error. There are three ways to enter a program into your calculator. Two easy ways are to download a program from either a computer or another calculator. To use a computer, download the program from a CD-ROM or website directly into your calculator by using the Casio FA-122 or FA-123 Program-Link software and the appropriate cable. To use another calculator that has the program in its memory, link the two calculators with a link cable and transfer the program. (See Note 0F.) The third way to enter a program is to do it manually by following these steps: a. Select PRGM from the Main Menu.
b. Press F3 (NEW) to name the program. (Use the red letters above the number and operation keys.) You are already in Alpha Lock, so do not press ALPHA unless you want to enter a number in the program name. When the name is complete, press EXE.
c. Enter the program exactly as you see it. Lowercase letters in the command indicate that you must find the command on the calculator. You can find many programming commands by pressing SHIFT [PRGM] and looking under COM, CTL, and JUMP. The key will often give you more options. Use the function keys to access the commands shown at the bottom of the screen. To find other commands, press the appropriate function key or look at the function options by pressing OPTN ALPHA VARS SHIFT [SET UP] SHIFT.

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Note 0G Entering a Program (continued)
You can look in the back cover of your fx-7400G Plus Users Guide to determine which calculator key to press. If you enter a command from the calculator text screen, all the letters will be uppercase. The command wont look the same, and it wont work.
d. Use SHIFT [INS] EXE to insert a new line between two lines. Use on a blank line to delete that line. e. Press QUIT twice when you finish entering the program.

Errors

You can edit the program if there is an error or if you need to make a change. a. Select PRGM from the Main Menu. Arrow down to the program name and press F2 (EDIT). b. Scroll down through the program to find the error. Studying the entire program on paper is often easier than working from the calculator screen, where you can see only a small portion at one time. Use SHIFT [INS] or DEL as needed to make changes. When you are finished making corrections, press QUIT. c. If you get an error message when you execute a program, press the arrow key to the right. The calculator will automatically switch to the EDIT mode and scroll to the line with the error. Then proceed as in step b.
Note 0H Generating Random Integers
You can generate random integers within an interval by using the Int and Ran# commands. From the Run screen, press OPTN F4 F1 (NUM) F2 (Int) to access the integer part command. Press OPTN F4 F4 (PROB) F4 (Ran#) to access the random number command.
To randomly generate integers between two values, enter Int (Ran#(H L 1)) where H is the highest integer and L is the lowest integer. For example, to generate integers between 43 and 57, enter Int(Ran#(15))43. Pressing EXE will generate as many of these integers as you like.
To randomly generate a particular number of integers in an intervalfor example, five integers between 43 and 57select the Seq command by
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Note 0H Generating Random Integers (continued)
pressing OPTN F1 (LIST) F4 F1 (Seq), enter the formula as before, and then add ,x,1,5,1 to generate five random numbers in this interval.
Note 0I The Repeating Decimal Program
The RPT DEC program can be used to convert a repeating decimal to a fraction. Follow the steps below: a. Link or manually enter the program into your calculator. (See Note 0F and Note 0G.) b. In the Main Menu, arrow to PRGM and press EXE. Toggle the arrow key down to select the program labeled RPT DEC and press EXE. c. You are asked to enter your decimal. Enter your decimal, including at least one digit more than one repeating cycle, and press EXE. For example, if your number is.133333. , you could enter.133,.1333, or.13333, and so on. d. You are then asked how many digits repeat. In our example, the 3 is the only digit that repeats, so press 1 EXE.
e. You are next asked how many digits come before the repeating digits. In our example,.133333. , there is one digit (the 1), so press 1 EXE.

f. The equivalent fraction will be displayed on the screen. You can then use FD to convert back and forth between fraction and decimal.
File Name:RPT DEC "ENTER DECIMAL" ?N "HOW MANY " "DIGITS " "REPEAT"?P "HOW MANY " "DIGITS COME" "BEFORE THE"
"REPEATING" "DIGITS"?L Int (10^LN)R Frac (10^LN)S Int (S10^P)C (10^P-1)10^LB 10^LA RA+CB