Graphing Calculator
EL-9900
Handbook Vol. 2
Programmes
For Advanced Levels
For Basic Levels
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Read this first
This handbook was produced for practical application of the SHARP EL-9900 Graphing Calculator. This
calculator includes a highly convenient programming function, which enables automatic processing of
both simple and complex calculations any number of times.
1. Entering and Editing a Programme (Advanced keyboard mode only):
Programmes can be entered and edited either by pressing the calculator keys or by downloading from a PC.
To download programmes from a PC, you will need the CE-LK2 PC link software (sold separately).
In this handbook, we use the symbol “ ” to represent multiplication, and the symbol “/” to represent
*
division. Please follow this convention when entering and editing programmes via the PC-Link software.
When entering programmes directly through the EL-9900’s keypad, meanwhile, please use the
and
X
keys.
÷
A. Using calculator keys
G
Creating a new programme:
1. Press
to display the programme menu.
PRGM
2. Press
to select the new programme menu. (See right)
ENTER
C
3. Enter the programme title, then press
4. Enter the programme.
.
ENTER
5. Press
to finish programming.
2nd F
QUIT
G
Editing a programme:
1. Press
to display the programme menu.
PRGM
2. Press
3. Press
and choose the number of the programme you wish to edit.
B
to finish editing.
2nd F QUIT
(See right)
B. Downloading from PC
G
Creating a new programme:
1. Using the CE-LK2, select New from the File menu.
2. Enter a programme name in Title:.
3. Enter a programme. (For details on entering a programme, refer to
the operation manual.) (See right)
GG
Programmes can also be downloaded from Sharp’s website at
instead of creating a new programme.
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G
Sending programmes from a PC:
1. Using the CE-LK2, select the Communication Port from
the Link menu and click on the port to be used.
2. Turn off the EL-9900 and connect it to the PC.
3. Turn on the EL-9900
(See right)
4. Select Send… from the Link menu of the CE-LK2
5. Specify the kind of drive, folder, and file, then select the file
to be sent from the file list, and click on the Select button.
6. Click on the OK button.
Note : For further details refer to the manual.
2. Executing a programme:
1. Press
to display the execute menu.
PRGM
2. Press
and choose the number of the programme you wish to
(See right)
A
ENTER
execute.
3. Follow the instructions.
3. Deleting a programme:
Press
and then choose
to select the programme to
2nd F
OPTION
5
C
be deleted.
Note: Do not try to erase a programme by resetting all memories to the initial condition as
programme data to be stored will also be deleted. Also, it is advised to use the CE-
LK2 PC link software to back up any programmes not to be erased.
4. Using the keys:
Press to use secondary functions (in yellow).
2nd F
-1
x
-1
2
-1
To select “x ”:
G Displayed as follows:
2nd F
x
x
2nd F
Press
Press
to use the alphabet keys (in violet).
ALPHA
F
2
To select F:
G Displayed as follows:
x
F
ALPHA
ALPHA
to continue input of violet letters.
2nd F
A-LOCK
To input ABC:
or
2nd F
ALPHA
A-LOCK
A
ALPHA
ALPHA
A
B
C
B
C
(To return to the normal function, press
again.)
ALPHA
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5. Troubleshooting:
Following is a list of error codes and error messages.
When errors occur, refer to pages 233 and 234 of the manual.
Er r o r
Erro r m e ssag e
Erro r c o nte nt
Syntax error found in equation/programme.
c o d e
01
02
03
04
05
07
08
09
10
11
12
13
16
17
20
21
22
23
24
25
26
27
30
31
32
33
34
35
36
37
38
Syntax
Calculate
Nesting
Calculation-related error found (division by 0, calculation beyond range, etc.).
Cannot nest more than 14 numerical values, or 32 functions during execution.
Matrix definition error or entering an invalid value.
Matrix dimension, or STAT list dimension, inconsistent.
Size of list/matrix exceeds calculation range.
Inconsistency found in argument of the structured function.
Invalid data type used in calculation.
Financial calculation error found.
Invalid
Dimension
Invalid DIM
Argument
Data Type
No Sign Change
No define
Domain
Undefined list/matrix used in calculation.
Argument definition outside of domain.
Increment error found.
Increment
Irr Calc
More than two inflection points for Irr calculation.
Med-Med law (statistic) error found.
Argument missing.
Stat Med
No Argument
Not pair ∫ dx
Not pair [ ]
Not pair ( )
Not pair { }
Line over
∫ and dx are not used in a pair.
Brackets are not used in a pair.
Parentheses are not used in a pair.
Braces are not used in a pair.
Line is over the capacity.
Not delete
Buffer over
Edit type
Unable to delete a selected item.
Input/equation exceeds buffer capability.
Invalid editor type found.*
Continue =
No data
“ = ” exists in equation that has been recalled (RCL).
Data does not exist.
Graph Type
Too many var.
No variable
No solution
No title
Graph type setting incorrect.
Too many variables assigned in the SOLVER.
No variable specified in the SOLVER.
No solution found.
No title entered.
Too many obj
More than 30 objects selected.
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Er r o r
c o d e
Erro r m e ssag e
Erro r c o nte nt
40
41
42
43
44
45
46
47
48
49
50
51
52
53
70
71
90
99
Lbl duplicate
Lbl undefined
Lbl over
Labels with identical name found in programme.
Goto/Gosub encountered with no defined label.
More than 50 labels found in programme.
Nesting of more than 10 subroutines found.
Line contains more than 160 characters.
Gosub stack
Line too long
Can’t return
Storage full
Coord type
Without For
Without WEnd
Without While
Without Then
Without EndIf
Without If
Return used without jumping from subroutine.
Cannot create more than 99 files.
Invalid coordinate system for command.
For is missing corresponding to the Next command.
WEnd is missing corresponding to the While command.
While is missing corresponding to the WEnd command.
Then is missing corresponding to the If command.
EndIf is missing corresponding to the If command.
If is missing corresponding to the EndIf command.
Communication error found among devices.
Wrong communication mode set.
I/O device
Wrong Mode
Memory over
System error
Low battery
BREAK!!
Memory is full; cannot store data as requested.
System error found; user memory space is insecure.
Operation interrupted due to low battery power.
Operation break specified.
* The following operations may cause Editor type error. Correct the Editor type to continue.
• Recall the SOLVER equations (EQTN) or Graph data (G_DATA) stored in a different EDITOR mode
than currently in use.
• Receive the Graph equation (Y1 and others) entered in a different EDITOR mode than currently in use.
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6. Page Layout
Programme List
Procedure of data to
be entered
EL-9900 Graphing Calculator
Involute(Inverse Involute)
Introduction
Use the involute function for calculating gears etc. to find the angle of obliquity
from the initial value and involute value.
Brief explanation and
purpose of the section
Calculation
θ
Involute function : inv θ = tan θ - θ[rad]
Use Newton's method to find the inverse involute:
P
f'(θ)
tanθi
-
tan
θ
i
-a
q
S
Exercise
a
θ
i
+1
=
θ
i
-
=
θ
i
-
2
θ
f(θi
)
θi
Rg
f (θ) = a - invθ
SP : involute curve
S
θ
0
Example of problem to be
solved in the section
: involute starting point
: angle of obliquity of point
P
Calculation
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : INVOLUTE
The formula to be used
in calculation and
definition of terms
Start
Label START
ClrT
start
Print "SELECT 1/2
Selection of type
Enter or 2.
1
Input
S
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
EL-9900 Graphing Calculator
Y
To calculation of involute.
S
=
=
1
To inverse involute calculation
Returns to START if entry
neither nor 2.
Label ANGLE
N
Set Up Condition
Important set up condition
before starting the exercise
in order to obtain correct
answers
Print "Inpu
t
B
E
G
I
N
N
1
Input
B
S
Y
2
ANGLE
Entry of initial
value and
B
Z
the involute value is 0.0050912 and the initial
Print "Input INVO
Calculation of involute.
Enter initial value and
involute value.
Input
I
involute value
CALPRESS
I
J
e angle of obliquity is 14.1.
Label CALPRESS
tan
Z/180.0
(T-R-J)/T2
180.0 (R-D)/π
If int (10
Angle of obliquity
calculated.
Calculation of
Z
T
in Deg Mode and decimal point in
π
R
angle of obliquity
Y
Flowchart
D
Judgment on repetition
of calculation of angle
of obliquity.
Z
int(108 D)
0
CL
8
D)≠0 GotoCALPRESS
Z
A
Summary of steps from
start to end
N
Print "ANGLE
Print
End
A
Display of angle of obliquity
INVO
Calculation of inverse
involute. Enter angle
of obliquity.
Ke y O p e ra tio n
Disp la
y
Entry of angle
of obliquity
Label INVO
Print "Input ANGLE
Input
A
PRGM
A
A
θ
tanθ-π
Involute value calculated.
Involute value displayed.
Calculation of involute
value (display)
θ/180
I
Print "INVOLUTE
Print
End
I
End
Key Operation
Illustration of the keys to be
operated
ENTER
PARAMETERS
Parameters
Definition of the
parameters used in the
programme
Name of parameter
Content
Name of parameter
Content
angle of obliquity
involute value
of
D, R, T,
S
J
working variable for calculating
selecting calculation type
(S=1: involute calculation)
(S=2: inverse involute calculation)
initial value, angle of obliquity
θ
I
A
B
inputanidniotiuatlputangle
0
•
ENTER
0
of
input value
Z
0
5
0
9
1
2
NTER
4
Select inverse involute
calculation.
ENTER
4
5
2
ENTER
Enter the value of the angel
of obliquity.
1
4
•
1
ENTER
(Display of involute value)
Display
Step
Illustration of the calculator
screen as it should appear
if each step is carried out
correctly
A step-by-step guide to solving the problems
and an explanation of the display
5
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EL-9900 Graphing Calculator
Heron's Formula
Use Heron's formula to find the area of a triangle when the sides (A,B,C) of the
triangle are known.
Calculation
S = D (D - A) (D - B) (D - C)
C
A
(A + B + C)
2
D =
B
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : HERON
Start
Print "Input LENGTH
Input A
Input B
Enter sides A, B and C.
Entry of sides
Calculation of D
Calculation of area
Display of area
End
Input C
(A+B+C)/2 D
(D (D-A) (D-B) (D-C) ) S
Print "S =
Print S
End
Value of D calculated.
Area S calculated.
Area of triangle
displayed.
PARAMETERS
Name of parameter
Content
value of side A
Name of parameter
Content
A
D
S
value of D
area
B
C
value of side B
value of side C
Exercise
Find the area of a triangle when sides A, B and C are 20, 35 and 40cm respectively.
Ste p
Ke y O p e ra tio n
Disp la y
Specify the programme
mode.
Select the title HERON.
PRGM
A
1
2
Enter the values A, B and C.
(Display of area)
2
0
ENTER
3
5
ENTER
ENTER
4
0
The area is approximately
350cm2.
3
1
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EL-9900 Graphing Calculator
Calculating Tension
Use the law of sines to find the tension when a pole of weight W is suspended with
two strings, and the strings are balanced with the angles from the vertical line A and B.
Calculation
vertical line
T
S
W
=
=
sin B sin A sin (A+B)
A
T
sin B
T = W
B
sin (A+B)
S
G
sin A
S = W
sin (A+B)
B
A
S
W
W
T, S : tension
W : weight
T
A, B : angles (6 sexagesimal numbers)
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : TENSION
Start
Print "Input ANGLE
Input A
Input B
Enter angles and weight
A, B and W.
Entry
Print "Input WEIGHT
Input W
Denominator in law of sines
calculated. C= sin (A + B)
Calculation of denominator
Calculation of tensions
sin (A+B) C
W sin B/C T
W sin A/C S
Print "TENSION
Print "T=
Tensions T and S calculated.
T = W sin B/C
T = W sin A/C
Tensions T and S displayed.
Display of tensions
Print T
Print "S=
Print S
End
PARAMETERS
Name of parameter
Content
Name of parameter
Content
tension S
A
B
C
angle A
angle B
sin(A+B)
S
T
tension T
weight
W
2
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EL-9900 Graphing Calculator
Exercise
Calculate the tension assuming weight=40kg, angle A=30˚ 15' 20", and angle
B=27˚ 45' 40". Enter the angles with sexagesimal numbers.
Set up condition: decimal point digit number in TAB 3 Mode, decimal
point in Fix Mode, and angle unit in Deg Mode.
2nd F
SET UP
C
2
D
3
CL
B
1
Ste p
Disp la y
Ke y O p e ra tio n
Specify the programme mode.
Select the title TENSION.
PRGM
A
1
2
•
•
Enter the values of angles
A and B.
3
0
1
4
5
5
2
4
0
0
ENTER
2
7
ENTER
Enter the value of weight.
4
ENTER
0
3
4
Tension T is 21.840kg and
S is 23.795kg.
3
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EL-9900 Graphing Calculator
Involute(Inverse Involute)
Use the involute function for calculating gears etc. to find the angle of obliquity
from the initial value and involute value.
Conversely, calculate the involute value from the angle of obliquity.
Calculation
θ
Involute function : inv θ = tan θ - θ[rad]
Use Newton's method to find the inverse involute:
P
f'(θ)
tanθi
-
θ
i
-a
q
S
a
θi +1
=
θ
i
-
=
θ
i
-
2
θ
f(θi
)
tan θi
Rg
f (θ) = a - invθ
SP : involute curve
S : involute starting point
θ : angle of obliquity of point P
0
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : INVOLUTE
Start
Label START
ClrT
start
Print "SELECT 1 or 2
Input S
Selection of type
Enter 1 or 2.
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
Label ANGLE
Print "Input BEGIN
Input B
Y
To calculation of involute.
S = 1
To inverse involute calculation
Returns to START if entry
neither 1 nor 2.
N
N
S = 2
ANGLE
Entry of initial
value and
B
Z
Print "Input INVO
Input I
Y
Calculation of involute.
Enter initial value and
involute value.
involute value
CALPRESS
I
J
Label CALPRESS
Angle of obliquity
calculated.
tan Z
T
Calculation of
angle of obliquity
π Z/180.0
R
(T-R-J)/T2
D
Judgment on repetition
of calculation of angle
of obliquity.
180.0 (R-D)/π
Z
Y
int(108 D) 0
If int (10ˆ8 D)≠0 Goto CALPRESS
Z
A
N
Print "ANGLE
Print A
Display of angle of obliquity
INVO
End
Calculation of inverse
involute. Enter angle
of obliquity.
Entry of angle
of obliquity
Label INVO
Print "Input ANGLE
Input A
A
θ
Involute value calculated.
Involute value displayed.
Calculation of involute
value (display)
tanθ -π θ/180
I
Print "INVOLUTE
Print I
End
End
PARAMETERS
Name of parameter
Content
Name of parameter
Content
angle of obliquity
D, R, T, J
S
working variable for calculating
selecting calculation type
(S=1: involute calculation)
(S=2: inverse involute calculation)
initial value, angle of obliquity
θ
I
involute value
A
B
input and output of angle
input of initial value
Z
4
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EL-9900 Graphing Calculator
Exercise
(1) Find the angle of obliquity when the involute value is 0.0050912 and the initial
value is 10.
(2) Find the involute value when the angle of obliquity is 14.1.
Set up condition: angle unit in Deg Mode and decimal point in
Float Pt Mode.
2nd F
CL
SET UP
B
1
C
1
moto
Ste p
Ke y O p e ra tio n
Disp la y
Specify the programme mode.
Select the title INVOLUTE.
PRGM
A
1
2
3
Select involute calculation.
1
ENTER
Enter the initial value and the
involute value.
ENTER
1
0
0
•
0
0
5
0
9
1
2
ENTER
(Display of angle of obliquity)
Select inverse involute
calculation.
ENTER
4
5
2
ENTER
Enter the value of the angle
of obliquity.
•
1
4
1
ENTER
(Display of involute value)
5
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EL-9900 Graphing Calculator
Calculating Illuminance and Luminous Intensity
Enter the luminous intensity of the luminous source, the distance, and the angle between
the perpendicular line and light ray, to find the illuminance of the illuminated side.
Conversely, find the luminous intensity of the source from the illuminance of the
illuminated side.
Calculation
2
Luminous Intensity l
l cos θ
r
i
i =
l =
2
θ
r
cos θ
r
l : luminous intensity [candela]
r : distance [m]
i : illuminance [lux]
θ: angle [˚ ]
Illuminance i
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : CAND LUX
Deg
Start
Label START
ClrT
Print "CANDELA=1 LUX=2
Print "SELECT 1 or 2
Input S
If S=1 Goto CANDELA
If S=2 Goto LUX
Goto START
A
start
Enter 1 or 2.
Selection of type
Y
To calculation of
luminous intensity.
S = 1
N
To calculation of
illuminance.
Label CANDELA
Gosub DISTANCE
Print "Input LUX
Input L
S = 2
LUX
CANDELA
A
Jumps to subroutine
DISTANCE.
To subroutine
To subroutine
L
I
R2 I/cos θ C
Print "CANDELA
Print C
Enter illuminance or
luminous intensity.
Entry of
luminous intensity
Entry of
illuminance
End
Label LUX
Calculation of
luminous intensity
Calculation of
illuminance
Illuminance or luminous
intensity calculated.
Gosub DISTANCE
Print "Input CANDELA
Input C
Display of
luminous intensity
Display of
illuminance
Illuminance or luminous
intensity displayed.
C K
K cos θ /R2
Print "LUX
Print L
L
End
Subroutine
End
Subroutine for entry of
distance and angle.
Label DISTANCE
Print "Input DISTANCE
Input D
DISTANCE
Entry.
Entry of distance and angle
D R
Print "Input ANGLE
Input A
Returns to calling program.
Return
A θ
Return
PARAMETERS
Name of parameter
Content
Name of parameter
Content
angle
I
illuminance of illuminated side
θ
K
R
S
luminous intensity of luminous source
A
L
input of angle
distance
input and calculating luminous intensity
input of distance
selecting calculation type
D
C
(S=1: calculation of luminous intensity
)
input and calculating illuminance
(S=2: calculation of illuminance)
6
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EL-9900 Graphing Calculator
Exercise
(1) Find the luminous intensity of the luminous source of distance 10m, angle 60˚
and illuminance 20 lux.
(2) Find the illuminance of the illuminated side of distance 10m, angle 60˚ and
luminous intensity 4000 candela.
Set up condition: decimal point in Float Pt Mode.
SET UP
2nd F
CL
C
1
Ste p
Disp la y
Ke y O p e ra tio n
Specify the programme mode.
Select the title CAND LUX.
A
PRGM
1
Select calculation of luminous
intensity.
1
ENTER
2
3
Enter the values of distance,
angle, and illuminance.
ENTER
1
2
0
0
ENTER
ENTER
6
0
(Display of luminous intensity)
Select calculation of illuminance.
Enter the values of distance,
angle, and luminous intensity.
ENTER
2
ENTER
ENTER
ENTER
4
1
6
4
0
0
0
ENTER
0
0
(Display of illuminance)
7
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EL-9900 Graphing Calculator
Calculating Simple Harmonic Oscillation
Enter period, amplitude and time to calculate displacement at specified time,
acceleration, angular velocity, and velocity. Also, display the changes during the
entered time period on a graph.
Calculation
2π
angular velocity : ω =
displacement : x = A +sin (ω t)
T
2
acceleration : a = -ω +x
A : amplitude
velocity : v = A +ω +cos (ω t)
x
A
v
0
v
a x
t : time [sec]
T : period [sec]
ω : angular velocity [rad/sec]
ωt
2π
A
ωt
0
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : OSCILLAT
Start
Rad
Print "Input PERIOD
Input P
Entry of period
and amplitude
P F
Print "Input AMPLITUDE
Input A
A D
CALC
Entry of time
Label CALC
Print "Input TIME
Input T
T E
2 π/F W
Angular velocity, displacement,
acceleration and velocity
calculated.
Calculation of
angular velocity, etc.
D sin (W E) H
-(W2) H B
D W cos (W E) V
Print "ANGULAR VELOCITY
Print W
W = angular velocity
H = displacement
B = acceleration,
V = velocity
Print "MAGNITUDE
Print H
Print "ACCELERATION
Print B
Print "VELOCITY
Print V
Wait
E/10 X scl
D/5 Y scl
0 Xmin:E Xmax
-D Ymin:D Ymax
Draw D sin (W X)
Wait
Calculation result of angular
velocity, displacement,
acceleration and velocity
displayed.
Display of
calculation result.
Calculation of
range and scale
Range set and graph displayed.
Function: Y = D sin (W X)
X is time increase.
Graph display
Display clear
ClrT
ClrG
Goto CALC
...
...
...
...
...
...
Xmin 0, Xmax E, Xscl E/10
Ymin -D, Ymax D, Yscl D/5
Text and graph display cleared.
8
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EL-9900 Graphing Calculator
PARAMETERS
Name of parameter
B
E
V
W
H
Xscl
Yscl
Content
acceleration
time
Name of parameter
Content
input of amplitude
input of period
input of time
amplitude
A
P
T
D
F
X
velocity
angle of velocity (ω)
displacement
x-axis scale
y-axis scale
period
time increase
Exercise
Calculate angular velocity, etc., using period π, amplitude 1 and time 3 seconds and
display the changes on a graph.
Set up condition: decimal point in Float Pt Mode.
2nd F
SET UP
E
1
1
CL
C
Ste p
Disp la y
Ke y O p e ra tio n
Specify the programme mode.
Select the title OSCILLAT.
PRGM
A
1
2
Enter the values of period,
amplitude, and time.
2nd F
ENTER
1
ENTER
3
π
ENTER
3
(Display of angular velocity)
(Display of displacement)
(Display of acceleration)
(Display of velocity)
ENTER
ENTER
4
5
(Display of graph of simple
harmonic oscillation)
9
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EL-9900 Graphing Calculator
Electric Power Consumed on an AC Circuit
Enter the voltage effective value, frequency and resistance value to find the power
value of the circuit with resistance R. Draw a graph of the changes in power over a
period of time.
Calculation
P : power consumption I : effective value of current
V : effective value of voltage
R
I
•
•
•
•
•
I
0
= N sin ω t V0 = M sin ω t P0 = l0
V0
P0
: change in amount of power with time
I
V
0
: change in amount of current with time
0: change in amount of voltage with time
N: maximum value of current M: maximum value of voltage
V
ω: angular velocity (2 π S)
t : time S : frequency
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : AC POWER
Start
Rad
Print "Input RESISTANCE
Input R
Enter data (resistance, voltage and
frequency).
Data entry
Print "Input VOLTAGE
Input V
Power calculated.
Print "Input FREQUENCY
Calculation of power
W = angular velocity
M = maximum voltage
N = maximum current
I = effective value of current
Z = power
Input F
R T
V D
F
S
2 π S
W
D √2 M
M/T N
N/√2 I
Range for graph calculated.
Xmax, Xscl, Ymax, Yscl
Calculation of range
D I
Z
1/S Xmax
Xmax/10 Xscl
N M Ymax
Ymax/10 Yscl
Print "WATT=
Print Z
Display of power
Display of graph
Power displayed. (value of Z)
Function: Y = N
M
(sin (W X))2
Wait
0 Xmin
End
0 Ymin
Draw N M (sin (W X))2
End
PARAMETERS
Name of parameter
Content
Name of parameter
Content
S
I
T
D
W
N
frequency
effective value of current
resistance value
effective value of voltage
angular velocity
maximum value of current
maximum value of voltage
maximum value of x-axis
Xscl
Ymax
Yscl
V
R
scale of x-axis
maximum value of y-axis
scale of y-axis
input of voltage
input of resistance value
input of frequency
value of power
F
Z
M
Xmax
10
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EL-9900 Graphing Calculator
Exercise
Find the power value of an AC circuit with resistance value 150Ω, voltage effective
value 100V and frequency 50Hz and display on a graph the changes in power over
a period of time.
Set up condition: decimal point in Float Pt Mode.
1
2nd F
SET UP
1
E
C
CL
Ste p
Disp la y
Ke y O p e ra tio n
Specify the programme mode.
Select the title AC POWER.
PRGM
A
1
2
Enter the resistance value,
voltage effective value, and
frequency.
ENTER
ENTER
1
1
5
5
0
0
0
0
ENTER
(Display of value power)
ENTER
3
(Display of graph)
11
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EL-9900 Graphing Calculator
Angle of Vector
Use the matrix operation feature to find the angle θ which forms the standard vector
and vector. The angle can be calculated at one time against the multiple vectors.
Calculation
← ←
←
←
•
Calculating vector inner product a b = | a | | b | cos θ
Use the above expression to derive the following expression
← ←
•
a b
-1
θ = cos
| a← | | b← |
FLOWCHART
PROGRAMME LIST(MATRIX MODE)
Title : VECTOR
Start
Print " Input NUMBER
Input N
Enter no. of vectors for which
angles are calculated.
Entry of number
of vectors
N M
{M,2} dim (mat A)
{2,1} dim (mat B)
{M,1} dim (mat C)
For K, 1, M, 1
Print " Input VECTOR
Print K
Input X
X mat A(K,1)
Input Y
Arrays defined.
matA, matB, matC.
Definition of arrays
Vector data entry
K = K + 1
Counter for data entry.
Enter x component and Y
component of each vector.
Y mat A(K,2)
NEXT
Print "Input FUNDAMENTAL VECTOR
Input X
X mat B(1,1)
Input Y
Y
Entry repeated by no. of vectors.
K ≤ M
N
Enter x component and Y component
of standard vector.
Entry of standard
vector data
Y mat B(2,1)
√ (mat B(1,1)2+mat B(2,1)2) B
mat A mat B mat C
For I, 1, M, 1
Calculation of
component of
standard vector
Length component of standard
vector (scalar) calculated.
√ (mat A(I,1)2+mat A(I,2)2) A
cos-1 (mat C(I,1) / (A B)) θ
Print "ANGLE OF VECTOR
Print I
Calculation of
inner product
Product of matrices A and B
calculated.
Print "θ=
Print θ
Wait
Counter for calculation of angle.
I = I + 1
NEXT
End
Calculation repeated by no.
of vectors.
Y
I > M
End
N
Calculation of
component of vector
Length component of vector
(scalar) calculated.
Calculation of angle
and display of angle
Angle calculated and displayed.
12
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EL-9900 Graphing Calculator
PARAMETERS
Name of parameter
Content
Name of parameter
Content
A
B
I
vector scalar quantity
θ
vector angle
display
standard vector scalar quantity
calculating counter
input counter
K
N
input of number of vectors
vector components
K
M
X
Y
mat A
mat B
mat C
number of vectors
standard vector components
vector inner product
input of x component
input of y component
Exercise
Calculate the angle formed by the following 3 vectors and standard vector (2,3).
vector 1 (5, 8)
vector 2 (7, 4)
vector 3 (9, 2)
Set up condition: angle unit in Deg mode, and decimal point in Float Pt
mode.
2nd F
1
SET UP
B
1
CL
C
Ke y O p e ra tio n
Ste p
Disp la y
Specify the programme mode.
Select the title VECTOR.
A
PRGM
1
2
3
4
5
6
Enter the number of vectors.
Enter the values of vector 1.
3
ENTER
5
ENTER
8
ENTER
Enter the values of vectors
2 and 3.
ENTER
ENTER
7
9
ENTER
ENTER
4
2
Enter the value of standard
vector.
2
ENTER
3
ENTER
(Display of angle of vector 1)
ENTER
ENTER
(Display of angle of vector 2)
(Display of angle of vector 3)
13
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EL-9900 Graphing Calculator
Linear Transformation
Use the matrix to find four types of the linear transformation of x-axis symmetric
transformation, y-axis symmetric transformation, similar transformation and
revolution around the origin.
Calculation
1. Symmetric transformation to
x-axis (Case 1)
3. Similar transformation with ratio of
similitude K around origin (Case 3)
X'
1 0
X
X'
K 0
X
=
=
(Y') (0 -1) ( Y )
(Y') (0 K ) (Y )
2. Symmetric transformation to
y-axis (Case 2)
4. Transformation revolving around
only angle B at the origin (Case 4)
X'
-1 0
X
X'
(Y') (sin B cos B
cos B -sin B) (XY )
=
=
(Y') ( 0 1 ) ( Y )
FLOWCHART
PROGRAMME LIST
Title : LINE TRN
Start
{2, 2} dim(mat H)
{2, 1} dim(mat D)
{2, 1} dim(mat A)
Print "Input POINT
Input X
Declare array size, etc.
matH(2,2), matD(2,1), matA(2,1)
Enter coordinates before transformation.
Array declaration
Input Y
Entry of coordinates (X,Y)
X
Y
mat D(1, 1)
mat D(2, 1)
TYPE
Type of transformation specified
with no from 1 to 4.
Label TYPE
Entry of type
Print "SELECT 1, 2, 3, 4
Input S
ClrT
Y
Jumps to destination corresponding
to entered number.
s = 1
To label XSYMMETRY
To label YSYMMETRY
To label SYMRATIO
To label ROTATE
If S=1 Goto XSYMMETRY
If S=2 Goto YSYMMETRY
If S=3 Goto SIMRATIO
If S=4 Goto ROTATE
GotoTYPE
N
Y
s = 2
Label XSYMMETRY
N
Y
1
0
0
mat H(1, 1)
mat H(2, 1)
mat H(1, 2)
s = 3
XSYMMETRY
N
s = 4
-1 mat H(2, 2)
Goto TRANS
Data set of x-axis symmetric transformation
matH(1,1) = 1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = -1
Y
Label YSYMMETRY
-1 mat H(1, 1)
N
0
0
1
mat H(2, 1)
mat H(1, 2)
mat H(2, 2)
YSYMMETRY
Data set of y-axis symmetric transformation
matH(1,1) = -1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = 1
Goto TRANS
Label YSYMMETRY
Label XSYMMETRY
Transformation data set
Label SIMRATIO
Print "Input SIMILITUDE RATIO
Input R
SIMRATIO
R
K
0
K
Transformation data set Data set of similar transformation
mat H(1, 1)
mat H(2, 1)
mat H(1, 2)
mat H(2, 2)
Entry of ratio of similitude (R)
matH(1,1) = K, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = θ
0
θ
Label SIMRATIO
Entry of ratio of similitude
Data set of transformation
Label ROTATE
Goto TRANS
Label ROTATE
Print "Input ANGLE
Input A
Entry of angle
Data set of transformation by revolving
Entry of angle (A)
matH(1,1) = cos B, matH(2,1) = sin B,
matH(1,2) = -sin B, matH(2,2) = cos B,
A
B
Data set of transformation
cos B mat H(1, 1)
sin B mat H(2, 1)
-sin B mat H(1, 2)
cos B mat H(2, 2)
Label TRANS
Matrix H multiplied by matrix D.
Coordinate transformation
mat H mat D mat A
Print "mat A(1, 1)
Print mat A(1, 1)
Print "mat A(2, 1)
Print mat A(2, 1)
End
Display of coordinates after transformation
End
Coordinates displayed.
14
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EL-9900 Graphing Calculator
PARAMETERS
Name of parameter
Content
Name of parameter
Content
y-coordinate
B
K
S
angle
Y
A
R
ratio of similitude
selecting type
input of angle
input of ratio of similitude
coordinate after transformation
transformation data
x,y-coordinate
(S=1: case 1, S=2: case 2,
S=3: case 3, S=4: case 4)
x-coordinate
mat A
mat H
mat D
X
Exercise
1. Transform symmetrically the point (3, 5) to the x-axis.
2. Rotate the point (2, 6) at 45˚ around the origin.
Set up condition: angle unit in Deg Mode and decimal point in
Float Pt Mode.
2nd F
SET UP
B
1
C
1
CL
Ste p
Disp la y
Ke y O p e ra tio n
Specify the programme mode.
Select the title LINE TRN.
PRGM
A
1
2
3
Enter the values of the point.
3
1
ENTER
ENTER
5
ENTER
Select symmetric transformation
to x-axis (case 1).
Select transformation revolving
around only angle B at the
origin (case 4).
ENTER
2
4
ENTER
ENTER
6
4
5
4
Enter the angle value.
ENTER
ENTER
5
15
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EL-9900 Graphing Calculator
Moving Average
Plot a moving average graph which helps to understand how the results change over a
specified period. The progress of sales and amounts of consumption and production can
also be seen.
Calculation
Xi-(M-1) / 2 + ... + Xi + ... Xi+(M-1) / 2
H
i
: moving average
M : number of divisions
: data
n : number of data
H
i
=
M
Xi
M-1
2
M-1
2
M-1
2
( I = 1 +
, 2 +
, ... , n +
)
FLOWCHART
PROGRAMME LIST
Title : MVIN AVG
Start
Label MAIN
MAIN
Print "Input DIVISION
Input D
Entry of number of divisions
Enter unit for calculating average.
D
M
Y
1_Stats L1
If M≥n Goto MAIN
Rem RANGE
Returns to entry of no. of divisions if the number
of divisions more than no. of data.
M>=n
N
(xmax-xmin)/10 Yscl
Setting of calculation range
Range for graph set.
0
n
1
Xmin
Xmax
Xscl
Calculation
I = 0, K = int (M/2)
xmin Ymin
xmax Ymax
Gosub count
First calculation. Jumps to subroutine.
Jumps to subroutine.
0
I
LOOP1
int (M/2)
K
Gosub MOVINGSUM
Gosub COUNT
Label LOOP1
Number of calculation times of moving sum judged.
Repeated until calculation of no. of divisions performed.
Y
Gosub MOVINGSUM
If M≥J Goto LOOP1
Gosub AVERAGE
Label LOOP2
M>=J
N
Gosub AVERAGE
Subroutine
Setting of counter
K
H
X
Y
COUNT
LOOP2
X = K, Y = H
Substitution
Gosub COUNT
Label LOOP3
I = I + 1, J = I, S = 0
Return
Jumps to
subroutine.
Gosub COUNT
Gosub MOVINGSUM
If (I+M)>J Goto LOOP3
Gosub AVERAGE
Line (X, Y, K, H)
If K≠(n-int (M/2))Goto LOOP2
Wait
LOOP3
Jumps to
Gosub MOVINGSUM
Subroutine
Calculation of
moving sum
subroutine.
MOVINGSUM
Y
(I+M)>J
End
Label COUNT
Calculation of moving sum
N
Jumps to
Gosub AVERAGE
I+1
I
subroutine.
Return
I
J
0
S
Display of line
Subroutine
Calculation of
average
Line displayed.
Return
Label MOVINGSUM
AVERAGE
K≠
Y
Judgment of end.
S+L1(J)
J+1
Return
Label AVERAGE
S/M
K+1
S
(n-int(M/2))
Calculation of moving average
J
N
End
Return
H
K
Return
16
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EL-9900 Graphing Calculator
Parameters
name of parameter
H
I
content
moving average
counter
name of parameter
S
X
content
moving sum
starting point (x)
J
counter
Y
starting point (y)
K
M
counter
number of divisions
Yscl
B
scale of y-axis
input of number of divisions
Exercise
Find the moving average every three months (number of divisions: 3) from the following
table of monthly sales.
Month
Jan.
Feb.
326
Mar.
323
Apr.
344
May.
300
Jun.
401
Jul.
Aug.
450
Sales[$] 300
398
On the graph, Xmax = 8, Ymin = 300, and Ymax = 450.
Set up condition: decimal point in Float Pt Mode.
2nd F
1
SET UP
C
CL
Ste p
Disp la y
Ke y O p e ra tio n
Enter statistical data into L1.
STAT
ENTER
A
1
3
0
0
ENTER
3
2
6
0
0
ENTER
ENTER
3
2
3
3
4
4
ENTER
3
0
ENTER
ENTER
4
0
1
3
9
8
ENTER
4
5
ENTER
PRGM
Specify the programme mode.
Select the title MVIN AVG.
A
2
3
Enter the number of divisions(3).
3
ENTER
17
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EL-9900 Graphing Calculator
Creating a Graph of Experimental Data
Graph the results of an experiment and examine the trends.
(Example: examined data relating to water vapour pressure and temperature.)
FLOWCHART
PROGRAMME LIST
Title : XY GRAPH
Enter statistical data using
Start
statistics feature before
executing program.
ClrG
Rem DRAWING SD
2 Stats L1,L2
-
Graph plotted using
automatic scaling.
Graph plot
Rem RANGE
xmin Xmin
xmax Xmax
ymin Ymin
ymax Ymax
(Xmax-Xmin) / 10 Xscl
(Ymax-Ymin) / 10 Yscl
Rem BROKEN LINE
For I, 1, n-1, 1
L1(I) X
DRAWLOOP
Counter
Setting of
coordinates
of line
Data as coordinates
(starting point and
finishing point).
Display of line
I = I + 1
Line drawn between
set coordinates.
L2(I) Y
L1(I+1) Z
L2(I+1) W
Line(X,Y,Z,W)
NEXT
Whether or not lines of no.
of data drawn judged.
Repeated until lines drawn
by the no. of data.
Y
I < N
N
Wait
End
End
PARAMETERS
Name of parameter
Content
Name of parameter
Content
y of line starting point
y of line finishing point
counter
I
Y
x of line starting point
x of line finishing point
W
X
Z
*n = number of statistical data
18
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EL-9900 Graphing Calculator
Exercise
The following table shows examined water vapour pressure. Draw a graph
of this data.
Temperature [˚C]
0
10
20
30
40
50
60
70
80
90
100
Pressure [mmHg] 4.581 9.205 17.532 31.826 55.339 92.558 149.47 223.79 355.29 525.90 760.00
Set up condition: decimal point in Float Pt Mode.
2nd F
SET UP
C
1
CL
Ste p
Disp la y
Ke y O p e ra tio n
Enter statistical data into
L1 and L2.
ENTER
STAT
A
1
2
Enter the value for temperature.
…
0
ENTER
1
0
ENTER
1
0
0
(Other numbers not shown)
Enter the value for pressure.
ENTER
•
4
5
8
1
3
4
…
ENTER
0
6
7
Specify the programme mode.
Select the title XY GRAPH.
A
PRGM
(Drawing of graph)
19
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EL-9900 Graphing Calculator
Ordinary Differential Equations
Enter the initial conditions (X, Y) with the step H and interval T. Use Runge Kutta Gill method
to solve the ordinary differential equation of first order.
Calculation
Use the following four steps of Runge Kutta Gill method to find the
equation Xn + 1 and Yn - 1 from Xn and Yn. Input Qo = 0 at the
starting point X0
.
Y
1. K0 = Hf (Xn , Yn), R1 = (1/2) (K0-2Q0), Y(1)= Y
n
+R1
2. Q1 = Q0 + 3R1- (1/2)K0
Y3
(1)
(2)
(1)
K
1
= Hf (Xn + H/2, Y ), R2 = (1 - 1/2) (K1-Q1), Y =Y + R2
Y
2
3. Q2 = Q1 + 3R2 - (1 - 1/2) K1
K2
(2)
(2)
= Hf (Xn + H/2, Y ), R3 = (1 + 1/2) (K2 -Q2),Y(3) = Y + R3
Y1
h
h
4. Q3 = Q2 + 3R3- (1 + 1/2) K2
X
(3)
(3)
0
K
3
= Hf (Xn+1, Y ), R4 = (1/6) (K3-2Q3), Yn+1 = Y + R4
X1
X2
X3
Q
4
= Q3 + 3R4 - (1/2)K3
FLOWCHART
Start
Enter Data.
Subroutine for calculating
built-in function
Entry of data
Initial setting
Initial coordinates (X, Y), step
of x (H), and interval of solutions (T)
Data for calculation set.
Subroutine
FORMULA
Subroutine for
calculating
built-in function
MAIN
f = -I
J
Calculation executed.
Jumps to subroutine.
Gosub
(Another equation can be used.)
Calculation of step 1.
Return
Jumps to subroutine.
Jumps to subroutine.
Jumps to subroutine.
Gosub
Calculation of step 2.
Gosub
PROGRAMME LIST(REAL MODE)
Title : RUNGE
Rem INITIAL
I+H/2 I
Print " Input X0 Rem 2
Gosub FORMULA
Print " Input Y0 H F K
Goto MAIN
Label NEXT
If Z≠I Goto SUB2
I M
J N
Label SUB1
ClrT
Print "XN=
Print M
Print "YN=
Print N
Wait
Z+T Z
Calculation of step 3.
Gosub
Input X
Calculation of step 4.
Input Y
X I
Y J
B (K-Q) R
J+R J
Q+3 R-B K Q
Judgment of calculation end.
If calculation result of I smaller
than value of increase of I,
calculation repeated again.
N
Z <= I
Print " Input H Rem 3
Y
S = I
O = J
Input H
Gosub FORMULA
Print " Input T
Input T
H F K
A (K-Q) R
J+R J
1+√(2-1) A
1- √(2-1) B
I+T Z
O Q
I S
Following calculation
N
Q+3 R - A K Q
I+H/2 I
Rem 4
Gosub FORMULA
H F K
Z ≠ I
performed when calculation
SUB2
I S
J O
Goto MAIN
Label SUB2
result of x not equal to the
value of increase of X.
Y
Processing
in case of
inequality
Label MAIN
Rem 1
(Z - S) (J - O)
H
M = Z
P =
+ O,
N = P
(K - 2 Q) /6 R
J+R J
Q+3 R - K/2 Q
(Z-S) (J-O) /H+O
Z M
P
SUB1
Display of result
Gosub FORMULA
H F K
P N
(K-2 Q) /2 R If Z≤I Goto NEXT
J+R J I S
Q+3 R-K/2 Q J O
Goto SUB1
Label FORMULA
-I J F
Prior processing for next calculation
Z = Z + T, S = X, O = J
Processing for
next calculation
Return
20
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EL-9900 Graphing Calculator
PARAMETERS
Name of parameter
Content
value of 1+ (1/2)
Content
value of Xn-1
Name of parameter
A
B
F
S
T
I
value of 1- (1/2)
f (I,J)
interval
Xn
H
K
O
P
Q
R
step
J
Yn
calculating working area
value of Yn-1
increase of J
value of Qn
value of Rn
Z
X
Y
M
N
value of increase of X
input of X0
input of Y0
indicates Xn
indicates Yn
Exercise
...
Initial settings: Y = 10 when X = 0. Find J when H = 0.01, T = 0.03 and I = 0.03, 0.06 .
(The built-in differential equation is F = -I J.)
Set up condition: angle unit in Rad Mode and decimal point in
Float Pt Mode.
2nd F
SET UP
C
B
2
CL
1
Ste p
Disp la y
Ke y O p e ra tio n
Specify the programme mode.
Select the title RUNGE.
2nd F
A
PRGM
1
2
Enter the values of X0, Y0
H and T.
,
1
ENTER
ENTER
0
0
0
ENTER
0
0
•
1
•
0
3
ENTER
3
4
5
(Display of X1)
(Display of Y1)
ENTER
ENTER
(Display of X2)
(Display of Y2)
(Display of X3)
(Display of Y3)
Similar operation is performed
hereafter.
21
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EL-9900 Graphing Calculator
Analysing with One-way Layout Method
Use the one-way layout method to verify whether there is a relation to the results
achieved based on one condition. Analysis of variance is carried out with this method.
Calculation
Analysis of variance chart of one-way layout method
[X] = (Σ Σ Xij)2 ÷ AN
[A] = Σi (Σj Xij)2 ÷ N
Sum of squares (S)
Degree of freedom (θ)
Variance (V)
Variance ratio (F)
[AS] = Σi Σj (Xij)2
A : number of levels
N: repeated frequency
X : number of data
Factor
Error
Total
S
A
= [A] - [X]
= [AS] - [A]
= [AS] - [X]
θA
= A - 1
VA
= SA ÷ θA
FA
= VA ÷ VE
SE
θ
E
= A (N- 1)
= AN - 1
VE
= SE ÷ θE
ST
θT
FLOWCHART
PROGRAMME LIST(STAT MODE)
Title : VARIANCE
Start
Rem INPUT
Print "Input LEVEL
Input L
Rem SUM OF SQUARES
LOOP2
Y-X
Z-Y
Z-X
E
M
P
Entry of number of levels Enter no. of levels and repeated
and repeat frequency
frequency.
L
A
Print "Input TIMES
Input T
Print "SUM OF SQUARES
Print E
Print "ERROR SUM OF SQUARES
Print M
One variable statistic
(Stat X) declared.
Declaration of one
variable statistic
T
0
0
0
N
W
B
LOOP1
Entry of data
Wait
C
Print "TOTAL SUM OF SQUARES
For S, 1, A, 1
dim(L1)
For K, 1, N, 1
ClrT
Print P
Wait
Accumulation of data
Accumulation of
square of data
Data and square of data
accumulated.
N
Rem DEGREES OF FREEDOM
A-1
Q
S
K
L
T
A (N-1)
A N-1
R
D
K = K + 1
Print "Input DATA
Print "LEVEL
Print L
Print "TIME
Print T
Print "DEGREES OF FREEDOM
Print Q
Print "DEGREES OF FREEDOM
Y
Judgment of repeated frequency
K ≤ N
N
ABOUT ERRORS
Print R
Wait
ΣX (sum of levels) displayed.
ΣX obtained with
statistics feature.
Display of ΣX
(sum of levels)
Input I
Print "SUM OF DEGREES OF FREEDOM
Print D
Wait
Rem VARIANCE
I
L1(K)
B
Accumulation
Square of ΣX accumulated.
B+I
of (ΣX)2
C+I2
C
NEXT
E/Q
M/R
V
U
1_Stats L1
Σx
S = S + 1
J
Print "VARIANCE
Print V
Print "VARIANCE OF ERRORS
Print U
Print "Σx=
Print J
Wait
Repeated frequency corresponding
to no. of levels judged.
Y
S ≤ 1
N
W+(Σx)2
NEXT
W
Wait
X, Y and Z calculated.
Calculation of X,Y and Z
Rem VARIANCE RATIO
Rem CALCULATE
V/U
F
Sum of squares (E, M, P)
calculated and displayed.
B2/A/N
W/N
X
Print "VARIANCE RATIO
Print F
End
Calculation and display
of sum of squares
Y
C
Z
Sum of degree of freedom
(Q, R, D) calculated and
displayed.
Calculation and display
of degree of freedom
Calculation and display
of variance
Variance (V, U) calculated and displayed.
Calculation and display
of variance ratio
Variance ratio (F) calculated and displayed.
End
22
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EL-9900 Graphing Calculator
PARAMETERS
Name of parameter
A
I
K
J
N
S
X
Z
F
E
M
P
Content
number of levels
input of data
loop 1 counter
indicating Σx
Name of parameter
Content
variance factor
V
U
Y
Q
R
D
T
variance error
Σi (Σ jxij)2 / n
degree of freedom factor
degree of freedom error
degree of freedom total
input and indicating frequency
input and indicating number of levels
total sum of squares of each level
total sum (all data)
repeated frequency
loop 2 counter
(ΣΣ xi)2/ a/ n
Σi Σj (xij)2
L
variance ratio factor
sum of squares factor
sum of squares error
sum of squares total
W
B
C
total sum of squares (all data)
Exercise
When a mouse is given a dosage of hormone, the relationship between dosage amount
and increase of mouse weight is as shown in the following table. Find the analysis of
variance. If the value of the variance ratio is larger than the value of the F- distribution
table at the 5% level of significance, the relationship between the hormone amount
and the increase of mouse weight is a causal relation.
Increase mouse weight (grams/day)
10
882
923
933
20
891
915
939
30
864
923
925
40
888
912
940
50
885
930
932
10
20
30
Hormone
(grams/mouse)
The number of levels (number of columns in the table) is A = 3
The repeated frequency (number of rows in the table ) is N = 5
Set up condition: decimal point in Float Pt Mode.
2nd F
SET UP
C
1
CL
Ste p
Disp la y
Ke y O p e ra tio n
Specify the programme mode.
Select the title VARIANCE.
PRGM
A
1
2
3
Enter the number of levels and
the repeated frequency.
5
3
ENTER
ENTER
23
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EL-9900 Graphing Calculator
Ste p
Disp la y
Ke y O p e ra tio n
Enter the statistical data
in level 1.
8
8
2
ENTER
8
9
1
5
4
5
6
4
ENTER
ENTER
8
6
ENTER
8
8
8
8
8
ENTER
(Display of total of hormone 10 g)
Enter the statistical data
in level 2.
ENTER
ENTER
9
2
3
9
1
5
ENTER
9
2
3
5
ENTER
9
1
2
ENTER
ENTER
9
3
0
(Display of total of hormone 20 g)
Enter the statistical data
in level 3.
ENTER
ENTER
9
3
3
9
3
9
ENTER
9
2
ENTER
ENTER
9
4
0
9
3
2
ENTER
(Display of total of hormone 30 g)
ENTER
ENTER
ENTER
7
8
(Display of sum of squares)
(Display of error sum of squares)
(Display of sum of squares)
9
(Display of degrees of freedom)
(Display of degrees of freedom about errors)
ENTER
10
11
12
(Display of sum of degrees of freedom)
ENTER
ENTER
(Display of variance)
(Display of variance of errors)
(Display of variance ratio)
The F-distribution chart shows that the value of F of upper probability P = 5% is 3.89. Since f > 3.98 in this
example, the relationship between the hormone amount and the increase of mouse weight is a causal
relation with 5% level of significance.
24
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EL-9900 Graphing Calculator
Calculating Parabolic Motion
Display on a graph the altitude change and the horizontal distance over a period of time
when an object is thrown at initial velocity V0 and angle θ, and find the horizontal
distance and altitude after t seconds. Specify the angle in Deg.
Calculation
X = V0 cos θ T
y
1
Y = V0 • sin θ T - gT2
•
•
•
2
Initial velocity
Angle
V
θ [˚ ]
0
[m/s]
V0
Gravitational acceleration g = 9.8 [m/s2]
θ
Time
T [s]
x
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : PARABOLA
Start
Deg
C/10 Yscl
Print "V0 (M S),θ,T(S) B/10 Xscl
Enter velocity when thrown.
Print "Input V0
Input V
0
Xmin
Ymin
Xmax
Ymax
Entry of initial velocity
0
B
C
Highest altitude, throwing
distance (horizontal distance),
and time (duration of flight) in
case of released angle 45˚
2 V sin 45/9.8
A
V2/9.8
B
C
Calculation and
display from
released angle 45ß
V2/19.6
For D, 0, T, T/100
Print "HMAX=
Print C
Print "LMAX=
Print B
V cos θ D
X
V sin θ D-(0.5 9.8 D2)
Pnt0N(X,Y)
Y
calculated and displayed.
THETA
NEXT
Angle for throwing entered.
Entry of released angle
Print "TMAX=
Print A
Wait
Label TX
Wait
Label THETA
Input θ
Print "Input TX
Input Z
If Z≤0 Goto THETA
If Z>T Goto THETA
Y
Entered angle less than or equal
to 0˚ or larger than 90˚?
θ≤ 0 or θ> 90
N
If θ ≤ 0 Goto THETA
Highest altitude, throwing distance
(horizontal distance), and time
(duration of flight) for entered angle
calculated and displayed.
Calculation and
display of values
for entered angle
If θ > 90 Goto THETA
V cos θ Z
X
V2 (sin θ)2/19.6
V2 sin (2θ)/9.8
2 V sin θ/9.8
Print "H=
Print H
H
L
V sin θ Z-(0.5 9.8 Z2)
Print "X=
Y
T
Print X
Print "Y=
Print Y
Wait
Line(0,Y,X,Y)
Line(X,0,X,Y)
Wait
Range of graph set based on
values for released angle 45˚.
Range setting
Print "L=
Print L
Print "T=
Print T
LOOP1
Calculation and
Graph (parabola) calculated
and plotted.
plotting of graph
D = (D + T/100)
Wait
Goto TX
Elapsed time counted.
Calculation and plotting repeated
until D (time elapsed) reaches
T (duration of flight).
Y
D ≤ T
TX
N
Entry of time
Entered time less than or equal
to 0 or more than T?
Y
Z
≤
0 or Z > T
N
Altitude and distance after entered
time elapses from throwing
calculated and displayed.
Calculation and
display of distance
and altitude after time Z.
Returns to entry of time.
Display of graph
25
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EL-9900 Graphing Calculator
PARAMETERS
Name of parameter
Content
highest altitude
horizontal distance
time
Name of parameter
Xscl
Z
Content
scale of x-coordinate
input of time period
H
L
T
X
Y
D
V
initial velocity (V0)
distance (after time Z)
altitude (after time Z)
time elapsed
θ
C
B
A
angle (released angle)
highest altitude when released at 90˚
horizontal distance when released at 45˚
time period when released at 45˚
Yscl
scale of y-coordinate
Exercise
Find the horizontal distance and altitude three seconds after an object is thrown, when
the initial velocity is 25m/sec and the angle is 52˚.
Set up condition: angle unit in Deg mode, and decimal point in Float Pt
mode.
2nd F
SET UP
B
1
E
1
CL
1
C
Ke y O p e ra tio n
Ste p
Disp la y
Specify the programme mode.
Select the title PARABOLA.
PRGM
A
1
2
3
4
5
6
7
8
Enter the value of the initial velocity.
2
5
ENTER
(Highest altitude when released at 90˚)
(Distance when released at 45˚)
(Time when released at 45˚)
ENTER
Enter the angle value.
2
ENTER
5
(Display of highest altitude)
(Display of horizontal distance)
(Display of time until dropping of object)
ENTER
ENTER
(Display of graph of parabola)
Enter the value of time period Z.
ENTER
3
(Display of distance after Z seconds)
(Display of altitude after Z seconds)
ENTER
(Altitude and distance after Z seconds are
displayed on the parabola graph.)
26
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Key pad for the SHARP EL-9900 Calculator
Advanced Keyboard
Cursor movement keys
Clear/Quit key
Graphing keys
Power supply ON/OFF key
Secondary function specification key
Alphabet specification key
Display screen
Variable enter key
Calculation execute key
Communication port for peripheral devices
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Key pad for the SHARP EL-9900 Calculator
Basic Keyboard
Cursor movement keys
Clear/Quit key
Graphing keys
Power supply ON/OFF key
Secondary function specification key
Alphabet specification key
Display screen
Variable enter key
Calculation execute key
Communication port for peripheral devices
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Use this form to send us your contribution
Dear Sir/Madam
We would like to take this opportunity to invite you to create a mathematical problem which can be solved
with the SHARP EL-9900 graphing calculator, including the necessary procedures and definitions as out-
lined in the form below.
For this purpose, we would be grateful if you could complete the form and return it to us by fax or mail.
If your contribution is chosen, your name will be included in the next edition of The EL-9900 Graphing
Calculator Handbook or on our homepage. We regret that we are unable to return contributions. Also,
please note that the problems you send us might be opened to the public at Sharp’s home page.
We thank you for your cooperation in this project.
(
)
Name:
Mr.
Ms.
School/College/Univ.:
Address:
Post Code:
Country:
Phone:
E-mail:
Fax:
SUBJECT Write either a title or about the subject matter.
:
INTRODUCTION and CALCULATION:
Write a brief explanation of the subject, and the formula with definitions, including a diagram if relevant.
SHARP Graphing Calculator
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PARAMETERS:
PROGRAMME LIST:
Define the parameters used in the programme.
List the procedure of data to be entered.
EXERCISE and SET UP CONDITION:
Include an example of a problem which can be solved with the
formula. Write a step-by-step guide to solving the problem with
an explanation. Detail any important conditions to be set up
before solving the problem.
SHARP CORPORATION Osaka, Japan
Fax:
SHARP Graphing Calculator
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SH ARP CORPORATION OSAKA,JAPAN
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