Casio fx-7400G PLUS Installation and operation manual

The Graphic Calculator fx-7400G PLUS,
your powerful math companion.
Printed in Japan SA0202-002001A
A booklet of practical examples for students using the graphic scientific calculator.
A booklet of practical examples for students using the graphic scientific calculator.
Worldwide
Education Web
http://world.casio.com/edu_e/

This activities book introduces practical examples of problems and exercises that are
covered in secondary school and college classes using the CASIO Graphic Scientific
Calculator.
As you will see as you go through the problems and exercises, using a graphic scientific
calculator does much more than take the work out of calculations. It is also a highly
effective educational tool that can help students grasp important concepts and stimulate
their imagination. Today, the graphic scientific calculator is highly evaluated as a vital
educational tool and is being used extensively in classrooms in Europe, the United
States, and other countries around the world.
This manual is a collection of actual problems and exercises, including actual
operations. It is intended as the first step for educators who want to start using the
graphic scientific calculator in their own classrooms. The material presented here is
designed to make problem solving more enjoyable and to cultivate a deeper
understanding of mathematics by showing how the graphic scientific calculator can be
used to solve a blend of textbook problems and problems faced in everyday life.
Finally, everyone at CASIO would like to express their sincere appreciation to all of the
teachers and educators whose cooperation made this activities book possible.
CASIO COMPUTER CO., LTD.

** CONTENTS **
SUBJECT TITLE UNIT AUTHOR PAGE
Engineering E-1 Speed and Distance Equation Mr. Yuji Kudo 1
E-2 Function Expressing the Relationship Quadratic Equation Mr. Yuji Kudo
Between Time Taken and Distance Traveled
E-3 Automobile Transmission and Engine Speed Division Mr. Yuji Kudo
E-4 Automobile Gasoline Engine Efficiency Regression (Linear, Quadratic) Mr. Mitsugu Tatara
Engineering EM-1 Water Depth and Flow Velocity Regression (Exponential) Mr. Mitsugu Tatara 9
Mathematics
Algebra A-1 The Calculator 10-key Pad Addition 11
A-2 Confirmation of the Expression Quadratic Equation Mr. Hideyo Makishita
A-3 Straight Line Passing Through Two Points Linear Regression
A-4 Parabola Passing Through Three Points Quadratic Regression
Statistics S-1 Histogram Standard Deviation 13
S-2 Circle Graph Ratio Mr. Hideyo Makishita
S-3 Bar Graph Graph
S-4 Bar Graph and Line Graph Graph
Electrical EE-1 Relationship Between Voltage, Current, Regression (Linear, Quadratic) Mr. Mitsugu Tatara 19
Engineering and Power
EE-2 Ohm’s Law Linear Regression Mr. Takashi Fukazawa
EE-3 Small Signal Amplification Factor of a Mr. Takashi Fukazawa
Transistor
Engineering EC-1 Density of a Liquid Quadratic Regression 32
Chemistry EC-2 Viscosity of a Liquid Quadratic Regression
EC-3 Index of Refraction of a Liquid Linear Regression Mr. Mitsugu Tatara
EC-4 Solubility Curve Quadratic Regression
EC-5 Specific Gravity of Gas Division
Mechanics M-1 Cam Diagram Data Collection Mr. Yuji Kudo 39
M-2 Stepping Motor Excitation Systems Optional Device Control
Algebra AC-1 Sum of Products Multiplication and Addition 43
Calculation AC-2 Sum of Products and Mean Multiplication, Division, and Addition
AC-3 Sum Addition
AC-4 Percent Division Mr. Hiroaki Hashimoto
AC-5 Calculations Including Trigonometric Trigonometry
Functions
AC-6 Permutation and Combination Permutation and Combination
Architecture AR-1 Economy of Materials (Cross-sectional Area) Quadratic Equation 49
AR-2 Economy of Materials (Volume) Cubic Equation Mr. Akihiro Shimizu
AR-3 Concrete Mix Design (Circle Graph) Ratio
Quality Q-1 Material Quality Control (Histogram) Standard Deviation 55
Control Q-2 Component Quality Variation Control Data Processing Mr. Yuji Kudo
(X-R Control Chart)
Others Z-1 Using a Graphic Calculator 67
(Displaying Calculation Results)
Z-2 Using a Graphic Calculator
(Inputting Statistical Data)
Z-3 Using a Graphic Calculator
(Determining the Slope of a Line)
Z-4 Creating Text Materials

– 1 –
E-1 Speed and Distance
1. Input the formula.
From the Main Menu, enter the GRAPH Mode.
Make sure that Y1: is highlighted and then input the following.
90Tw
Move the highlighting to Y2: and then input the following.
60T+72w
2. Use the View Window to configure graph settings.
Specify the ranges of the X-axis and Y-axis, and their scales.
Input the X-axis range and scale values shown to the right.
!3(V-WIN) 0w5w1w
Next, input the Y-axis range and scale values shown to the right.
c0w400 w100 ww
3. Display the graph.
Press 4(DRAW) to draw the graphs.
4. Observe the point where the lines intersect.
•Pressing !1(TRCE) displays a pointer on the graph, along with the X and Y values at
that point. Use fand cto select the graph Y2 =60X +72
•Pressing dto move the cursor the point where the graph intersects the Y-axis produces
values of X = 0, Y = 72. Using the cursor this way is called “tracing.”
Two Cars Traveling at Different Speeds
Two cars, one in Tokyo and one in the Ayuzawa Parking
Area (72 kilometers from Tokyo) set off for Nagoya at the
same time. Both cars run at constant speeds without
stopping, the Tokyo car at 90 km/h and the Ayuzawa car
at 60 km/h. Draw a graph that shows at what point the
Tokyo car will overtake the Ayuzawa car.
Exercise
Tokyo (0)
Atsugi
(35)
Gotenba
(83.7)
Fuji
(121.5)
Shizuoka
(161.8)
Okazaki
(293.4)
Nagoya
(325.5)
Hamamatsu
(230)
Ayuzawa (72)
JIKKYO SHUPPAN CO., LTD.: SHIN KOGYO SURI
(NEW EDITION)

– 2 –
•Keep pressing euntil the cursor is at the point where the two graphs intersect. This pro-
duces values that provide an approximate result for the exercise.
•Press 2(Zoom) and then 3(IN) to enlarge the graph with the cursor location as the
center. Repeat this step a number of times and use !1(TRCE) eto move the
cursor closer to the intersect point and produce a more accurate value.
Summary
If, when you use other formulas for the above exercise, the graphs do not intersect, try in-
creasing the X-axis and Y-axis ranges. Check the results on the display and make further
adjustments, if required.
E-1 Speed and Distance

– 3 –
E-2 Function Expressing the Relationship
Between Time Taken and Distance Traveled
1. Input the table.
From the Main Menu, enter the STAT Mode.
After making sure the first line of List 1 is highlighted, input the
following.
30w60w90w• • • 180w
After making sure the first line of List 2 is highlighted, input the
following.
125w500w1125w• • • 4500w
2. Configure graph settings.
Press 1(GRPH) [4(SET) and check the graph set-
tings.
Use fand cto move the highlighting to G-Type.
Press 2(xy) so the screen appears as shown to the right.
3. Draw the graph.
Press Q1(GRPH)1(GPH1) to display a graph in which
plotted points are linked.
4. Configure graph 2.
Press Qand then 1(GRPH)[4(SET), and check
the graph settings.
Move the highlighting to G-Type and then press 1(Scat).
The display should change as shown to the right.
Function Expressing the Relationship Between
Time and Distance Traveled
The nearby table is being configured for s= f(t)[m],
when it is assumed that distance covered s [m] is a
function of time taken t [sec]. Complete the table
and graph the expression f(t).
Exercise
Time tDistance s
[min] [sec] [km] [m]
0.5 0.125
1.0 0.500
1.5 1.125
2.0 2.000
2.5 3.125
3.0 4.500
JIKKYO SHUPPAN CO., LTD.: SHIN KOGYO SURI
(NEW EDITION)

– 4 –
5. Draw graph 2.
Press Q1(GRPH)1(GPH1).
The graph that appears is a scatter diagram.
6. Perform quadratic regression.
Press 3(X^2) to perform quadratic regression and obtain
the function.
Press 4(DRAW) to draw the graph, which is overlaid onto
the scatter diagram as shown to the right.
7. Check the function.
Check 3(X^2) again to display the parameter screen shown
to the right. This provides us with the following function.
s= f(t) = 0.13888 t 2= 1 t 2
7.2
In this exercise, the quadratic regression overlaid nicely onto the scatter diagram. When the
overlay is not as successful the one used here, try returning to the graph screen and using
linear regression, logarithmic regression, or some other type of regression.
Summary
E-2 Function Expressing the Relationship Between Time Taken and Distance Traveled

– 5 –
E-3 Automobile Transmission and Engine Speed
1. Program
From the Main Menu, enter the PRGM Mode.
Input “NP” as the program name.
3(NEW)i(N)e(P)w
Line 1 !J(PRGM)[1(?)aaT(A)w
Line 2 2000/aT(A)aal(B)w
Line 3 Q[2(”)!a( A -LOCK)i(N)e(P)!.(=)2(”)
!J(PRGM)[[3(:)al(B)wQQ
2. Program Description
•Program name (NP)
•Assigns input gear ratio to variable A.
•Assigns calculated result (2000 ÷Variable A) to variable B.
•Displays “NP=” followed by the value assigned to variable B.
*“_” marks indicate return (enter) symbols.
3. Program Execution
From the Main Menu, enter the PRGM Mode.
Use fand cto select “NP,” and then press w.
Input a gear ratio and press w. This calculates and displays the engine speed.
Relationship between an Automobile’s Transmission
and Engine Speed
Create a program that determines the rotation speed np
[rpm] of an automobile’s propeller shaft in each gear for
an engine running at ne= 2000 rpm.
Engine Transmission
Drive Shaft
Wheel
Flywheel
Clutch Shift Lever
Differential Gear
Exercise
Gear Shift Position 1st 2nd 3rd 4th 5th R
Gear Ratio 3.6 2.1 1.4 1.0 0.8 4.2
JIKKYO SHUPPAN CO., LTD.: SHIN KOGYO SURI
(NEW EDITION)

– 6 –
4. Practical Example
The screen to the right shows an example of what appears
when a gear ratio of 3.6 is input.
The program can be made even more useful by modifying it to accept input of engine speed
as well. You can also control the number of decimal places and significant digits.
Summary
E-3 Automobile Transmission and Engine Speed

– 7 –
11040 7.05 10.24 327.66
21505 7.51 15.79 279.61
32000 7.78 21.74 257.26
42560 7.88 28.17 240.67
53020 7.58 32.00 233.02
63500 7.27 35.53 233.15
74010 6.61 37.02 241.72
Sample Engine Speed
n [rpm]
Torque
T0 [kgf.m]
Output
N0 [PS]
Fuel Efficiency
f0 [gf/PSh]
E-4 Automobile Gasoline Engine Efficiency
The following is a table of fuel efficiency measurement results for an automobile gasoline
engine. Draw a graph of the rate of change in the data.
■ Measurement Results
■ Graphic Calculator Operation
1. Data Input
From the Main Menu, enter the STAT Mode.
Input the data into List 1 to List 4.
List 1: Engine speed
List 2: Torque
List 3: Output
List 4: Fuel Efficiency
2. Engine Speed – Torque Graph: Graph 1
Stat Graph 1: Make List 2 the YList.
Q
1(GRPH)
1(GPH1)
Graph 1
Exercise
1(GRPH)
[
4(SET)

– 8 –
3. Engine Speed – Output Graph: Graph 2
Stat Graph 2: Make List 3 the YList.
Q
1(GRPH)
[
4(SET)
Q
1(GRPH)
2(GPH2)
Graph 2
4. Engine Speed – Fuel Efficiency Graph: Graph 3
Stat Graph 3: Make List 4 the YList.
Q
1(GRPH)
[
4(SET)
Q
1(GRPH)
3(GPH3)
Graph 3
E-4 Automobile Gasoline Engine Efficiency

– 9 –
EM-1 Water Depth and Flow Velocity
Exercise 1
When t [s] is the time it takes for 1000 [cm3] to flow from each hole, and Q [cm3/s] is the flow
rate and v [cm/s] is flow velocity from each hole, calculate flow rates and the flow velocities.
Solution:
Q = V [cm3/s] , v = Q [cm/s],
t A
A = πd2 =3.14(0.6)2= 0.283 [cm2]
4 4
Graphic Calculator Operation
(1) In the STAT Mode, input the h data into List 1 and the t
data into List 2 as shown in the illustration to the right.
(2) Input the calculation formula for v into List 3.
Calculation: (1000 ÷List 2) ÷0.283
Move the cursor to the List 3 title and input the formula.
Use K1(LIST) 1(List) to input the List characters.
Industrial Mathematics (Water Depth and Flow Velocity)
■ Experiment
(1) Cut off the top of an old oil can. Then, starting
5 cm from the top of can, punch 6mm diam-
eter holes at 5cm intervals into the side of the
can, as shown in the illustration.
(2) First, use tape to cover all the holes except for
hole A. Next, fill the can with water so it
overflows from the top.
(3) Allow the water from hole A to flow into a
measuring cylinder. Use the stopwatch to
measure how long it takes for the water in the
cylinder to reach 1000 cm3.
(4) Repeat the same process for holes B through
F, and record the data.
(5) Use the data obtained to study the relation-
ship between water depth and flow velocity.
Exercise
Water Depth h [cm] and Duration t [sec]
Hole A B C D E F
h51015 20 25 30
t43.1 30.8 25.8 21.6 20.2 17.9
A
B
C
D
E
F
A
B
C
D
E
F
5 cm
10 cm
15 cm
20 cm
25 cm
30 cm 1000 cm
3
Stopwatch
Oil Can
Oil Can
()
JIKKYO SHUPPAN CO., LTD.: SHIN KOGYO SURI
(NEW EDITION)
A: area of a hole.
d: diameter of a hole.

– 10 –
(3) This makes it possible to obtain flow velocity v in List 3.
Exercise 2
From the data in Excercise 1, graph the relationship between water depth h [cm] and flow
velocity v [cm/s].
Solution:
With the h [cm] on the horizontal axis and v [cm/s] on the vertical axis, point data points and
then draw a regression curve.
Graphic Calculator Operation
(1) From the Main Menu, enter the STAT Mode.
(2) Assign List 1 to the X-axis (XList) and List 3 to the Y-axis
(YList).
Use 1(GRPH) [4(SET) to configure the settings
shown in the illustration to the right.
Press Q1(GRPH) 1(GPH1) to draw the graph.
(3) Regression by Function
The formula for this exercise can be expressed as v = 36.0 h ,
which is power regression.
Coefficients can be obtained by [3(Pwr).
4(DRAW)
When the hole position is 0 [cm] in this exercise, the flow rate is 0. When h = 0 then v = 0.
Adding this data to the top of the list makes drawing of the regression curve easier.
Note
EM-1 Water Depth and Flow Velocity

– 11 –
Mathematics with the Graphic Calculator
A-1 The Calculator 10-key Pad
(1) Take one counter-clockwise lap around the calculator 10-key
pad, pressing the three keys and adding the values produced
along each side. Make a note of the result obtained.
(2) Next, take a clockwise lap and compare with results (1).
This simple exercised produces results that are quite interesting.
(1) 123 + 369 + 987 + 741 = 2220
(2) 147 + 789 + 963 + 321 = 2220
Amazingly, the same result is produced by both the clockwise and the counter-clockwise
laps. Most of today’s senior high school students have been playing around with calculators
since elementary school and so they should already be aware of this fact. However, even
when conducting this exercise in high school, you can see the excitement and wonder in the
eyes of the students.
Why it works: 123 + 369 + 987 + 741
= 100 (1+ 3 + 9 + 7) + 10 (2 + 6 + 8 + 4) + 1 (3 + 9 + 7 + 1)
= 100  (1+ 7 + 9 + 3) + 10 (4 + 8 + 6 + 2) + 1 (7 + 9 + 3 + 1)
= 147 + 789 + 963 + 321
This is the place value system of decimal notation.
A-2 Confirmation of the Expression
Is the following expression correct?
(x+ 3)2= x2+ 9
What other explanation is available besides the algebraic method?
You can also use the area of a square like the one shown to the right.
Let’s try using the graphic calculator.
Graph the following expression:
y= (x+ 3)2 – (x2+ 9)
Viewing this graph, we can see that the following is never true:
y= 0
This tells us visually that y= 0 would be an incorrect solution of the above expression.
In the GRAPH Mode, input the following.
Y1= (X + 3)2 – (X2+ 9)
789
456
123
The Calculator 10-key Pad
9
x
2
3
x
x
3

– 12 –
A-3 Straight Line Passing Through Two Points
Find the equation for the straight line passing through the two points (–2, 1) and
(–1, –4).
This problem is easy for students.
The straight line is found by substituting two points (–2, 1) and (–1, –4) into y= ax+ b,
creating a system of simultaneous linear equations with two unknowns (a, and b).
Here we will use a regression line to obtain the result.
From the Main Menu, enter STAT Mode.
Input the following.
List 1 List 2
–2 1
–1 –4
Press1(GRPH) and then select 1(GPH1) .
This displays the two points on the screen. The straight line that passes between these two
points is the one we are trying to obtain.
Next, press 2(X) .
This calculates a= –5, b= –9 for y= ax + b.
Pressing 3(COPY) wsubstitutes y= –5x– 9 for GRAPH. Pressing 4(DRAW) draws
the straight line.
A-4 Parabola Passing Through Three Points
Find the equation of the parabola that passes through the following three
points: (–2, 1), (–1, –4), (1, 1).
This problem is difficult for students.
Here we will use the regression function to obtain the result.
From the Main Menu, enter the STAT Mode.
Input the following.
List 1 List 2
–2 1
–1 –4
11
Press1(GRPH) and then select 1(GPH1) .
This displays the three points on the screen. The parabola that passes through these three
points is the one we are trying to obtain.
Next, press 3(X^2) .
This calculates a= 2.5, b= 2.5, c= –4 for y= ax2+ bx+ c.
Pressing 3(COPY) wsubstitutes y= 2.5x2+ 2.5x–4 for GRAPH.
Pressing 4(DRAW) draws the parabola.
Mathematics with the Graphic Calculator

– 13 –
S-1 Histogram
Use a graphic scientific calculator to graph statistics.
Procedure: Input data into List 1. Select the input data and graph type.
Solution: From the Main Menu, enter the STAT Mode.
1. Input data into List 1.
2. Specify the data and graph.
3. This draws a histogram.
4. Pressing 2(CALC) calculates the mean and standard deviation of the input data.
The following data represents the distances a handball is thrown by 12 students.
14 20 25 28 18 26 (Unit: meters)
23 21 24 32 15 22
(The Entrance Examination of Hokkaido Public High School, 2000)
Press 1(GRPH) to display the
data and graph setting screen.
[4(SET) Configure settings as shown
above, and then press w.
1(1VAR)
1(GPH1) 1(1VAR)
Exercise 1
Q
2(CALC)
*Select G-Type, and press
[, 1(Hist)

– 14 –
Reference
You can also change the width of the class.
Operation
(4) Draw the histogram.
w,1(GRPH),1(GPH1)
4(DRAW)
(1) !m(SET UP)
The display settings are also changed.
(3) !3(V-WIN)
x-axis y-axis
Drill 1
The following shows the results recorded for a side step drill by 25 students. Use the
data to draw a histogram. (The Entrance Examination of Yamaguchi Public High School, 2000)
55 34 47 54 39 48 44 37 44 49
43 40 51 38 43 49 38 45 53 39
51 47 48 42 56
Data Input Start
Abbreviated Solution
Input Complete Data and Graph Type
Selection
Histogram Display Statistical Data
Q
(2) Change the start value of the class
to 10, and the width to 5.
w,1(GRPH),1(GPH1)
S-1 Histogram
S
10 w5w
2(Man)
c
*Use List 6.

– 15 –
S-2 Circle Graph
The data to the right shows the percent-
ages of new subscribers that use various
available methods to subscribe to an
Internet service provider. Draw a circle
graph of this data.
Solution
1. Input the data into List 2.
Set up the drawing conditions.
!m(SET UP)1(AUTO)Q
2. Select 1(GRPH).
Configure settings and press w.
3. Display the circle graph.
Press2(GPH2).
4. Use 1(TRCE).
Pressing the round cursor key e moves the pointer in the sequence A →B →C →D →E, and so on.
Drill 2
The nearby table shows Japanese lum-
ber production data by tree type. Create
a circle graph of this data. Note that the
values shown here are not percents.
Tree Type Volume
Japanese Cedar 7788
White Cedar 2338
Fir, Spruce 1609
Red Pine, Black Pine 1581
Larch 1526
Other 372
Unit: 1,000 mm2
Lumber Production in Japan by Tree Type – 1988
Subscription Method %
From provider Website 28.4
Off-line by mail 27.2
Software that comes with new computer 18.8
CD-ROM provided through a magazine 9.7
CD-ROM distributed through retailers 9.1
CD-ROM requested from provider 6.8
Total 100
Users Employing Each Provider Subscription Method (%)
Exercise 2
This draws the circle graph.
(Yahoo! Internet Guide <2002. February>, Japan)
[4(SET)

– 16 –
S-3 Bar Graph
The nearby table shows the number of people visiting
Hawaii from Japan and other countries during June
2000. It shows the total number of visitors on each day
of the week.
Drill 2 Solution
Note the setting for
Display.
Explanation: Input the data into List 4 and draw a bar graph.
Solution
1. Input the data into List 4.
2. Press 1(GRPH) and configure settings.
3. Display the bar graph.
[4(SET) Configure settings as shown
above, and then press w.
Press 1(GPH1) to select Graph 1.
Day Total Visitors
SUN 22596
MON 22777
TUE 21962
WED 23481
THU 21662
FRI 23995
SAT 26732
Exercise 3
S-2 Circle Graph S-3 Bar Graph

– 17 –
S-4 Bar Graph and Line Graph
The following shows the monthly average temperature and precipitation for Tokyo.
Use this data to draw a graph that includes a bar graph of the precipitation and a line graph
of the temperature.
Explanation When specifying the data graph type, select 3(Both).
Solution
1. Input the data into any available lists. In this exercise, we input the data into List 5 and List 6.
List 5: Temperature
List 6: Precipitation
Press 1(GRPH)
and then [.
Press 4(SET).
[[[[
Select 3(Both)
for G-Type.
2. Specify the data and graph.
The bar graph shows the precipitation data in List 6.
The line graph shows the temperature data in List 5.
Drill 4
The nearby table shows the volume of
PET bottles produced in Japan and
the percentage of bottle recycled
during each year. Draw a bar graph
that shows the production volume,
together with a line graph that shows
the recycle rate.
Production Volume Recycle Rate
1993 123,798 0.4
1994 150,282 0.9
1995 142,110 1.8
1996 172,902 2.9
1997 218,806 9.8
1998 281,927 16.9
1999 332,202 22.8
2000 361,944 31.8
PET Bottle Production Volume (t) and Recycle Rate (%)
Exercise 4
Tokyo JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Tem perature 5.2 6.6 8.5 14.1 18.6 21.7 25.2 27.1 23.2 17.6 12.8 7.9
Precipitation 45.1 80.4 60.4 99.5 125.0 138.0 185.2 126.1 147.5 179.8 89.1 45.7