Sharp EL-9650, EL-9600c, EL-9450, EL-9400 User Manual

Graphing Calculator

EL-9650/9600c/9450/9400

Handbook Vol. 2

Programmes

EL-9650

EL-9450

1. Heron's Formula 1

2. Calculating Tension 2

3. Involute (Inverse Involute) 4

4. Calculating Illuminance and Luminous Intensity 6

5. Calculating Simple Harmonic Oscillation 8

6. Electric Power Consumed on an AC Circuit 10

7. Angle of Vector* 12

8. Linear Transformation* 14

9. Moving Average 16

10. Creating a Graph of Experimental Data 18

11. Ordinary Differ ential Equations 20

12. Analysing with One-way Layout Method 22

13. Calculating Parabolic Motion 25

*only for EL-9650/9600c

Contents

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1. Entering and Editing a Programme:

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-LK1P PC link software (sold separately).

A. Using calculator keys

●

Creating a new programme:

1. Press

to display the programme menu.

2. Press

to select the new programme menu. (See right)

3. Enter the programme title, then press

.

4. Enter the programme.

5. Press

to finish programming.

●

Editing a programme:

1. Press

to display the programme menu.

2. Press

and choose the number of the programme you wish to edit.

3. Press

to finish editing.

B. Downloading from PC

●

Creating a new programme:

1. Using the CE-LK1P, select the M odel Type from the Tools menu
and click on the same model as your calculator.

2. Select New from the File menu.

3. Enter a programme name in Title:.

4. Enter a programme. (For details on entering a programme, refer to
the operation manual.)

●

Programmes can also be downloaded from Sharp’s website at

http://sharp-world.com/products/calculator/education/program/index.html

instead of creating a new programme.

Read this first

This handbook was produced for practical application of the SHARP EL-9650/9600c and EL-9450/9400
Graphing Calculator. Both calculators include a highly convenient programming function, which enables
automatic processing of both simple and complex calculations any number of times.

Note: Certain problems can not be solved with the EL-9450/9400 as indicated in contents.

(See right)

ENTER

ENTER

PRGM

2nd F

2nd F

QUIT

PRGM

2nd F

2nd F

QUIT

C

B

(See right)

2. Executing a programme:

1. Press to display the execute menu.

2. Press

and choose the number of the programme you wish to

execute.

3. Follow the instructions.

●

Sending programmes from a PC:

1. Using the CE-LK1P, select the Communication Port from
the Link menu and click on the port to be used.

2. Turn off the EL-9650/9600c/9450/9400 and connect it to the PC.

3. Turn on the EL-9650/9600c/9450/9400

4. Select Send… from the Link menu of the CE-LK1P (See right)

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.

ENTER

PRGM

2nd F

3. Deleting a programme:

Press and then choose to select the programme to
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 CE­LK1P PC link software to back up any programmes not to be erased.

C

5

OPTION

2nd F

4. Using the keys:

Press to use secondary functions (in yellow).

To select “sin

-1

”: ➔ Displayed as follows:

Press to use the alphabet keys (in blue).

To select A:

➔ Displayed as follows:

Press to continue input of blue letters.

To input ABC:

or

(To return to the normal function, press again.)

2nd F

A

2nd F

2nd Fsin

sin

-1

ALPHA

ALPHA

sin

ALPHA

2nd F

A-LOCK

ALPHA

ALPHA ALPHA

ALPHA

A

B

CA

BC

2nd F

A-LOCK

sin

-1

A

(See right)

A

5. Troubleshooting:

Following is a list of error codes and error messages.
When errors occur, refer to pages 12, 254, or 27 of the manual.

01 Syntax Syntax error in equation or programme
02 Calculate Execution of a division using 0, calculation beyond calculation range, etc.
03 Nesting Reservation of 14 or more numerical values or 32 or more functions during execution.
04 Invalid Matrix definition error
05 Dimension Inconsistency in the dimension of matrix during arithmetic of a matrix or dimension of list for

STAT calculation.

07 Invalid DIM Size of list and matrix input for calculation exceeds calculation range.
08 Argument Inconsistency in argument of the structured function
09 Data Type Invalid data type used in calculation
11 No define Undefined list or matrix
12 Domain Argument definition outside of domain
13 Increment Increment error
17 Stat Med Med-Med law (statistic) error
20 No Argument No argument entered
21 Not pair ∫ dx Equation definition (∫ and dx as a pair) for integral calculus does not follow syntax.
22 Not pair [ ] Not paired with specified “[ ]”
23 Not pair ( ) Not paired with specified “( )”
24 Not pair { } Not paired with specified “{ }”
32 No data Data does not exist
33 Graph Type Error in graph type setting
37 No title No title entered
38 Too many obj More than 30 objects selected
40 Lbl duplicate Same label name is used more than once within a programme
41 Lbl undefined Label is not defined for Goto or Gosub
42 Lbl over More than 50 labels are used within a programme
43 Gosub stack Nesting of more than 10 subroutine stacks
44 Line too long One line of programme exceeds more than 160 characters
45 Can’t return Use of return command without jumping from subroutine
46 Strage full Attempt to create a file exceeding 99 (delete unnecessary files)
47 Coord type Invalid coordinate system for command
90 Memory over Over memory capacity
99 System error User memory space cannot be secured

Error content

Error
code

Error message

EL-9650/9600c Graphing Calculator

3

DisplayStep Key Operation

1

2

Specify the program mode.
Select the title INVOLUTE.

(Display of angle of obliquity)

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.

* * * *

4

(Display of involute value)

5

*

Select involute calculation.

Select inverse involute
calculation.

Enter the initial value and the
involute value.

Enter the value of the angel
of obliquity.

5

CL

1B

SET UP

2nd F

1C

2nd F

PRGM

A

ENTER

0005091•

ENTER

1

ENTER

01

ENTER

2

ENTER

ENTER

14 1•

EL-9650/9600c 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

Involute function : inv θ = tan θ - θ[rad]
Use Newton's method to find the inverse involute:

FLOWCHART

PARAMETERS

PROGRAM LIST

(REAL MODE)

Selection of type

Entry of initial

value and

involute value
Calculation of

angle of obliquity

Display of angle of obliquity

Start

End

start

Y

ANGLE

INVO

CALPRESS

Y

Y

N

N

N

Calculation of involute

value (display)

Entry of angle

of obliquity

Enter 1 or 2.

To calculation of involute.

Calculation of involute.
Enter initial value and
involute value.

Angle of obliquity
calculated.

Judgment on repetition
of calculation of angle
of obliquity.

Calculation of inverse
involute. Enter angle
of obliquity.

Involute value calculated.
Involute value displayed.

To inverse involute calculation
Returns to START if entry
neither 1 nor 2.

θ

i +1

= θi -= qi -

f(θ

i

)

f'(θ)

tan2 θ

i

tanθi - θi -a

f (θ) = a - invq SP : involute curve
S : involute starting point

θ : angle of obliquity of point P

Name of parameter
D, R, T, J
S

Z

Content
working variable for calculating
selecting calculation type
(S=1: involute calculation)
(S=2: inverse involute calculation)
initial value, angle of obliquity

Name of parameter

θ

I
A
B

Content
angle of obliquity
involute value
input and output of angle
input of initial value

S = 2

int(10

8

D) 0

S = 1

0

q

Rg

P

S

a

θ

θ

Label START
ClrT
Print "SELECT 1/2
Input S
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
Label ANGLE
Print "Input BEGIN
Input B
B Z
Print "Input INVO
Input I
I J
Label CALPRESS
tan Z T

π

Z/180.0 R

(T-R-J)/T

2

D

180.0 (R-D)/π Z
If int (

10

8 D)≠0 Goto CALPRESS
Z A
Print "ANGLE
Print A
End
Label INVO
Print "Input ANGLE
Input A
A θ
tanθ -π θ/180 I
Print "INVOLUTE
Print I
End

Title : INVOLUTE

4

6. Page Layout

Note: This handbook is only an example of how to use programming function of the EL-9650/9600c. The layout may v ary with each screen.

2

Introduction

Brief explanation and
purpose of the section

Exercise

Example of problem to be
solved in the section

Set Up Condition

Important set up condition
before starting the exercise
in order to obtain correct
answers

Step

A step-by-step guide to solving the problems
and an explanation of the display

Key Operation

Illustration of the keys to be
operated

Display

Illustration of the calculator
screen as it should appear
if each step is carried out
correctly

Calculation

The formula to be used
in calculation and
definition of terms

Flowchart

Summary of steps from
start to end

Programme List

Procedure of data to
be entered

Parameters

Definition of the
parameters used in the
programme

When the mark

✽

appears on the key:

●

Same series of key strokes can be done
with screen touch.

●

Key operations may also be carried out
with the cursor (not shown).

(When using EL-9650/9600c)

EL-9650/9600c/9450/9400 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)

(A + B + C)

D =

2

FLOWCHART

Start

Entry of sides

Calculation of D

Calculation of area

Display of area

End

Name of parameter
A
B
C

Content
value of side A
value of side B
value of side C

Enter sides A, B and C.

Value of D calculated.

Area S calculated.

Area of triangle
displayed.

PARAMETERS

Name of parameter
D
S

A

C

B

PROGRAMME LIST

Title : HERON

Print "Input LENGTH
Input A
Input B
Input C
(A+B+C)/2 D
(D (D-A) (D-B) (D-C) ) S
Print "S =
Print S
End

Content
value of D
area

(REAL MODE)

Exercise

Find the area of a triangle when sides A, B and C are 20, 35 and 40cm respectiv ely.

Specify the programme

1

mode.
Select the title HERON.

Enter the values A, B and C.

Key OperationStep

2nd F

PRGM

A

*

2

ENTER

035

Display

(When using EL-9650/9600c)

2

(Display of area)

The area is approximately
350cm

2

.

3

ENTER ENTER

40

1

EL-9650/9600c/9450/9400 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

T

vertical line

W

B

S

G

T

sin B

T = W

S = W

T, S : tension W : weight
A, B : angles (6 sexagesimal numbers)

=

sin A

sin (A+B)

S

=

sin (A+B)

sin B

sin (A+B)

sin A

W

A

B

S

W

A

T

FLOWCHART

Start

Entry

Calculation of denominator

Calculation of tensions

Display of tensions

Name of parameter
A
B
C

Content
angle A
angle B
sin(A+B)

Enter angles and weight
A, B and W.

Denominator in law of sines
calculated. C= sin (A + B)

Tensions T and S calculated.
T = W sin B/C
T = W sin A/C

Tensions T and S displayed.

PARAMETERS

Name of parameter
S
T
W

PROGRAMME LIST

Title : TENSION

Print "Input ANGLE
Input A
Input B
Print "Input WEIGHT
Input W
sin (A+B) C
W sin B/C T
W sin A/C S
Print "TENSION
Print "T=
Print T
Print "S=
Print S
End

Content
tension S
tension T
weight

(REAL MODE)

2

EL-9650/9600c/9450/9400 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.

* * * * * *

SET UP

2nd F

Specify the programme mode.

1

Select the title TENSION.

Enter the values of angles

2

A and B.

Enter the value of weight.

3

3D1B

Key Operation

2nd F

3

ENTER

27 4540

ENTER

40

CL2C

PRGM

A

*

0 1520

•

•

ENTER

moto

motomotomotomoto

DisplayStep

(When using EL-9650/9600c)

Tension T is 21.840kg and

4

S is 23.795kg.

3

EL-9650/9600c/9450/9400 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

Involute function : inv θ = tan θ - θ[rad]
Use Newton's method to find the inverse involute:

θ

i +1

f (θ) = a - inv

f'(θ)

= θi -=

f(θi)

θ

Start

Selection of type

S = 1

N

N

S = 2

Y

CALPRESS

angle of obliquity

INVO

Display of angle of obliquity

Entry of angle

of obliquity

Calculation of involute

value (display)

End

FLOWCHART

Entry of initial

value and

involute value
Calculation of

int(10

start

Y

tanθ

i

θi

-

- θi -a

tan2 θ

i

SP: involute curve
S : involute starting point
θ : angle of obliquity of point P

Enter 1 or 2.

To calculation of involute.
To inverse involute calculation

Returns to START if entry
neither 1 nor 2.

Calculation of involute.
Enter initial value and
involute value.

Angle of obliquity
calculated.

Judgment on repetition
of calculation of angle
of obliquity.

Calculation of inverse
involute. Enter angle
of obliquity.

Involute value calculated.
Involute value displayed.

8

D) 0

N

ANGLE

Y

PROGRAMME LIST

Title : INVOLUTE

Label START
ClrT
Print "SELECT 1/2
Input S
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
Label ANGLE
Print "Input BEGIN
Input B
B Z
Print "Input INVO
Input I
I J
Label CALPRESS
tan Z T
π Z/180.0 R
(T-R-J)/T

180.0 (R-D)/π Z
If int (108 D)≠0 Goto CALPRESS
Z A
Print "ANGLE
Print A
End
Label INVO
Print "Input ANGLE
Input A
A θ
tanθ -π θ/180 I
Print "INVOLUTE
Print I
End

2

θ

P

S

a

q

θ

Rg

0

(REAL MODE)

D

Name of parameter
D, R, T, J
S

Z

Content
working variable for calculating
selecting calculation type
(S=1: involute calculation)
(S=2: inverse involute calculation)
initial value, angle of obliquity

4

PARAMETERS

Name of parameter

θ

I
A
B

Content
angle of obliquity
involute value
input and output of angle
input of initial value

EL-9650/9600c/9450/9400 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

SET UP

1B

* * * *

1C

CL

motomoto

DisplayStep Key Operation

(When using EL-9650/9600c)

Specify the programme mode.

1

Select the title INVOLUTE.

Select involute calculation.

2

Enter the initial value and the

3

involute value.

(Display of angle of obliquity)

○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○

Select inverse involute

4

calculation.

2nd F

PRGM

A

*

ENTER

1

ENTER

01

0005091•2

ENTER

ENTER

ENTER

2

Enter the value of the angle

5

of obliquity.

(Display of involute value)

14 1•

ENTER

5

EL-9650/9600c/9450/9400 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

i =

l cos θ

2

r

l =

2

r

i

cos θ

l : luminous intensity [candela] i : illuminance [lux]
r : distance [m] θ: angle [˚ ]

FLOWCHART

Start

A

Selection of type

Y

CANDELA

To subroutine To subroutine

Entry of

illuminance

Calculation of

luminous intensity

Display of

luminous intensity

Subroutine

Entry of distance and angle

Return

start

S = 1

N

S = 2

A

Entry of

luminous intensity

Calculation of

illuminance

Display of

illuminance

End

DISTANCE

LUX

Enter 1 or 2.

To calculation of
luminous intensity.

To calculation of
illuminance.

Jumps to subroutine
DISTANCE.

Enter illuminance or
luminous intensity.

Illuminance or luminous
intensity calculated.

Illuminance or luminous
intensity displayed.

Subroutine for entry of
distance and angle.

Entry.

Returns to calling program.

Luminous Intensity l

θ

r

Illuminance i

PROGRAMME LIST

(REAL MODE)

Title : CAND LUX

Label START
ClrT
Print "CANDELA=1 LUX=2
Print "SELECT 1/2
Input S
If S=1 Goto CANDELA
If S=2 Goto LUX
Goto START
Label CANDELA
Gosub DISTANCE
Print "Input LUX
Input L
L I

2

R

I/cos θ C
Print "CANDELA
Print C
End
Label LUX
Gosub DISTANCE
Print "Input CANDELA
Input C
C K
K cos θ /R

2

L
Print "LUX
Print L
End
Label DISTANCE
Print "Input DISTANCE
Input D
D R
Print "Input ANGLE
Input A
A θ
Return

Name of parameter
I
K
R
S

6

PARAMETERS

Content
illuminance of illuminated side
luminous intensity of luminous source
distance

selecting calculation type
(S=1:

calculation of luminous intensity

(S=2: calculation of illuminance)

)

Name of parameter

θ

A
L
D
C

Content
angle
input of angle
input and calculating luminous intensity
input of distance
input and calculating illuminance

EL-9650/9600c/9450/9400 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: angle unit in Deg Mode and decimal point in
Float Pt Mode.

2nd F

SET UP

1B

* * * *

CL

1C

Specify the programme mode.

1

Select the title CAND LUX.

Select calculation of luminous

2

intensity.

Enter the values of distance,

3

angle, and illuminance.

(Display of luminous intensity)

Select calculation of illuminance.

4

Enter the values of distance,
angle, and luminous intensity.

Key Operation

2nd F

PRGM

A

*

ENTER

1

10
20

ENTER ENTER

10

ENTER ENTER

ENTER

2

ENTER

DisplayStep

(When using EL-9650/9600c)

60

(Display of illuminance)

60

4000

ENTER

ENTER

7

EL-9650/9600c/9450/9400 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

angular velocity : ω =
acceleration : a = -ω

A : amplitude
t : time [sec]
T : period [sec]
ω : angular velocity [rad/sec]

2π

T

2

x velocity : v = A ω cos (ω t)

+

displacement : x = A sin (ω t)

0

+

Ax

2π

ωt

+

+

A

ωt

0

v

v
ax

FLOWCHART

Start

Entry of period

and amplitude

CALC

Entry of time

Calculation of

angular velocity, etc.

Display of

calculation result.

Calculation of

range and scale

Graph display

Display clear

Angular velocity, displacement,
acceleration and velocity
calculated.

W = angular velocity
H = displacement
B = acceleration,
V = velocity

Calculation result of angular
velocity, displacement,
acceleration and velocity
displayed.

Range set and graph displayed.
Function: Y = D sin (W X)
X is time increase.

...

Xmin

0, Xmax

...

Ymin

-D, Ymax

Text and graph display cleared.

...

E, Xscl

...

D, Yscl

...

E/10

...

D/5

PROGRAMME LIST

Title : OSCILLAT

Print "Input PERIOD
Input P
P F
Print "Input AMPLITUDE
Input A
A D
Label CALC
Print "Input TIME
Input T
T E
2 π/F W
D sin (W E) H

2

-(W

) H B
D W cos (W E) V
Print "ANGULAR VELOCITY
Print W
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
ClrT
ClrG
Goto CALC

(REAL MODE)

8

Name of parameter
B
E
V
W
H
Xscl
Yscl

Exercise

Content
acceleration
time
velocity
angle of velocity (ω)
displacement
x-axis scale
y-axis scale

EL-9650/9600c/9450/9400 Graphing Calculator

PARAMETERS

Name of parameter
A
P
T
D
F
X

Content
input of amplitude
input of period
input of time
amplitude
period
time increase

Calculate angular velocity, etc., using period

ππ

π, amplitude 1 and time 3 seconds and

ππ

display the changes on a graph.

Set up condition: angle unit in Rad Mode and decimal point in
Float Pt Mode.

2nd F

SET UP

Specify the programme mode.

1

Select the title OSCILLAT.

Enter the values of period,

2

amplitude, and time.

3

(Display of angular velocity)
(Display of displacement)
(Display of acceleration)
(Display of velocity)

2B

* * * *

1C

CL

Key Operation

2nd F

PRGM

A

*

2nd F

ENTER

π

ENTER

1

ENTER

3

DisplayStep

(When using EL-9650/9600c)

4

(Display of graph of simple
harmonic oscillation)

5

ENTER

ENTER

9

EL-9650/9600c/9450/9400 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

•

•

I0 = N

sin ω

t V0 = M

•

sin ω

•

t P0 = l0

•

V0
P0 : change in amount of power with time
I0 : change in amount of current with time

0: change in amount of voltage with time

V
N: maximum value of current M: maximum value of voltage
ω: angular velocity (2 π S) t : time S : frequency

V

I

FLOWCHART

Start

Data entry

Calculation of power

Calculation of range

Display of power

Display of graph

End

Enter data (resistance, voltage and
frequency).

Power calculated.
W = angular velocity
M = maximum voltage
N = maximum current
I = effective value of current
Z = power

Range for graph calculated.
Xmax, Xscl, Ymax, Yscl

Power displayed. (value of Z)

Function: Y = N M (sin (W X))

2

PROGRAMME LIST

Title : AC POWER

Print "Input RESISTANCE
Input R
Print "Input VOLTAGE
Input V
Print "Input FREQUENCY
Input F
R T
V D
F S
2 π S W
D √2 M
M/T N
N/√2 I
D I Z
1/S Xmax
Xmax/10 Xscl
N M Ymax
Ymax/10 Yscl
Print "WATT=
Print Z
Wait
0 Xmin
0 Ymin
Draw N M (sin (W X))
End

2

(REAL MODE)

Name of parameter
S
I
T
D
W
N
M
Xmax

Content
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

10

PARAMETERS

Name of parameter
Xscl
Ymax
Yscl
V
R
F
Z

Content
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

EL-9650/9600c/9450/9400 Graphing Calculator

Exercise

Find the power value of an A C cir cuit with r esistance value 150 Ω, voltage effective
value 100V and frequency 50Hz and display on a graph the changes in power o ver
a period of time.

Set up condition: angle unit in Rad Mode and decimal point in
Float Pt Mode.

2nd F

SET UP

* * * *

CL2B

1C

Specify the programme mode.

1

Select the title AC POWER.

Enter the resistance value,

2

voltage effective value, and
frequency.

(Display of value power)

3

(Display of graph)

Key Operation

2nd F

PRGM

15

10

5

ENTER

0

0

0

ENTER

A

*

ENTER

ENTER

DisplayStep

(When using EL-9650/9600c)

11

A

EL-9650/9600c Graphing Calculator

ngle 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

θ = cos

-1

←←

| a | | b |

←←←

END

End

FLOWCHART

Start

Entry of number

of vectors

Definition of arrays

K = K + 1

Vector data entry

Y

CALC

K < M

N

Entry of standard

vector data

Calculation of

component of

standard vector

Calculation of
inner product

I = I + 1

Y

component of vector

Calculation of angle
and display of angle

I > M

N

Calculation of

DATA

PROGRAMME LIST

Title : VECTOR

0 I

Enter no. of vectors for which
angles are calculated.

Arrays defined.
matA, matB, matC.

Counter for data entry.

Enter x component and Y
component of each vector.

Entry repeated by no. of vectors.

Enter x component and Y component
of standard vector.

Length component of standard
vector (scalar) calculated.

Product of matrices A and B
calculated.

Counter for calculation of angle.

Calculation repeated by no.
of vectors.

Length component of vector
(scalar) calculated.

Angle calculated and displayed.

0 K
Print " Input NUMBER
Input N
N M
{M,2} dim (mat A)
{2,1} dim (mat B)
{M,1} dim (mat C)
Label DATA
K + 1 K
Print " Input VECTOR
Print K
Input X
X mat A(K,1)
Input Y
Y mat A(K,2)
If K<M Goto DATA
Print "Input FUNDAMENTAL VECTOR
Input X
X mat B(1,1)
Input Y
Y mat B(2,1)
√ (mat B(1,1)
mat A mat B mat C
Label CALC
Ι + 1 Ι
If I>M Goto END
√ (mat A(I,1)
cos
Print "ANGLE OF VECTOR
Print I
Print "θ=
Print θ
Wait
Goto CALC
Label END
End

2

+mat B(2,1)2) B

2

-1

(mat C(I,1) / (A B)) θ

+mat A(I,2)2) A

(MATRIX MODE)

12

EL-9650/9600c Graphing Calculator

PARAMETERS

Name of parameter
A
B
I
K
M
X
Y

Content
vector scalar quantity
standard vector scalar quantity
calculating counter
input counter
number of vectors
input of x component
input of y component

Name of parameter

θ

K
N
mat A
mat B
mat C

Content
vector angle
display
input of number of vectors
vector components
standard vector components
vector inner product

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

SET UP

Specify the programme mode.

1

Select the title VECTOR.

1B

* * * *

CL

1C

Key Operation

2nd F

PRGM

A

*

DisplayStep

Enter the number of vectors.

2

Enter the values of vector 1.

3

Enter the values of vectors

4

2 and 3.

Enter the value of standard

5

vector.

(Display of angle of vector 1)

6

(Display of angle of vector 2)

3

ENTER

5

ENTER

7

ENTER

9

ENTER

2

ENTER

ENTER

8

4
2

3

ENTER

ENTER

ENTER

ENTER

(Display of angle of vector 3)

ENTER

13

EL-9650/9600c 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)

X'

() ()

Y'

1 0

=

() ()

0 -1

X
Y

2. Symmetric transformation to
y-axis (Case 2)

X'

() ()()

Y'

Start

Array declaration

Entry of coordinates (X,Y)

Entry of type

s = 1

s = 2

s = 3

s = 4

Label XSYMMETRY

Transformation data set

Label SIMRATIO

Entry of ratio of similitude

Data set of transformation

Display of coordinates after transformation

-1 0

=

01

Y

N

Y

N

Y

N

Y

N

Coordinate transformation

X
Y

FLOWCHART

TYPE

To label XSYMMETRY

To label YSYMMETRY

To label SYMRATIO

To label ROTATE

Label YSYMMETRY

Transformation data set

Label ROTATE

Entry of angle

Data set of transformation

End

3. Similar transformation with ratio of
similitude K around origin (Case 3)

X'
Y'

=

K0

0 K

X

()()

Y

4. Transformation revolving around
only angle B at the origin (Case 4)

X'

(())()

Y'

Declare array size, etc.
matH(2,2), matD(2,1), matA(2,1)
Enter coordinates before transformation.

Type of transformation specified
with no from 1 to 4.

Jumps to destination corresponding
to entered number.

XSYMMETRY
Data set of x-axis symmetric transformation
matH(1,1) = 1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = -1

YSYMMETRY
Data set of y-axis symmetric transformation
matH(1,1) = -1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = 1

SIMRATIO
Data set of similar transformation
Entry of ratio of similitude (R)
matH(1,1) = K, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = θ

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,

Matrix H multiplied by matrix D.

Coordinates displayed.

cos B -sin B

=

sin B cos B

X
Y

PROGRAMME LIST

(MATRIX MODE)

Title : LINE TRNS

{2, 2} dim(mat H)
{2, 1} dim(mat D)
{2, 1} dim(mat A)
Print "Input POINT
Input X
Input Y
X mat D(1, 1)
Y mat D(2, 1)
Label TYPE
Print "SELECT 1/2/3/4
Input S
ClrT
If S=1 Goto XSYMMETRY
If S=2 Goto YSYMMETRY
If S=3 Goto SIMRATIO
If S=4 Goto ROTATE
GotoTYPE
Label XSYMMETRY
1 mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)

-1 mat H(2, 2)
Goto TRANS
Label YSYMMETRY

-1 mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)
1 mat H(2, 2)
Goto TRANS
Label SIMRATIO
Print "Input
Input R
R K
K mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)
θ mat H(2, 2)
Goto TRANS
Label ROTATE
Print "Input ANGLE
Input A
A B
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
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

SIMILITUDE RATIO

14

EL-9650/9600c Graphing Calculator

PARAMETERS

Name of parameter
B
K
S

X

Content
angle
ratio of similitude
selecting type
(S=1: case 1, S=2: case 2,
S=3: case 3, S=4: case 4)
x-coordinate

Name of parameter
Y
A
R
mat A
mat H
mat D

Content

y-coordinate

input of angle

input of ratio of similitude

coordinate after transformation

transformation data

x,y-coordinate

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.

* * * *

Specify the programme mode.

1

Select the title LINE TRNS.

2nd F

SET UP

1C

CL1B

Key Operation

2nd F

PRGM

A

*

DisplayStep

Enter the values of the point.

2

Select symmetric transformation

3

to x-axis (case 1).

○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○

Select transformation revolving

4

around only angle B at the
origin (case 4).

Enter the angle value.

5

3

ENTER

1

ENTER

ENTER

5

2

ENTER

ENTER

4

4

5

ENTER

ENTER

6

ENTER

15

EL-9650/9600c/9450/9400 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

X

i-(M-1) / 2

Hi =
( I = 1 +

+ ... + Xi + ... X

M

M-1

2 2 2

, 2 +

M-1

i+(M-1) / 2

, ... , n +

M-1

Hi: moving average
M : number of divisions
X

i

)

: data

n : number of data

FLOWCHART

Start

MAIN

Entry of number of divisions

Y

Setting of calculation range

Gosub MOVINGSUM

Y

Gosub MOVINGSUM

Y

Y

M>=n

N

Calculation

Gosub count

M>=J

N

Gosub AVERAGE

Substitution

Gosub COUNT

(I+M)>J

N

Gosub AVERAGE

Display of line

K≠

(n-int(M/2))

N

End

LOOP1

LOOP2

LOOP3

Enter unit for calculating average.

Returns to entry of no. of divisions if the number
of divisions more than no. of data.

Range for graph set.

I = 0, K = int (M/2)

First calculation. Jumps to subroutine.

Jumps to subroutine.
Number of calculation times of moving sum judged.

Repeated until calculation of no. of divisions performed.

Subroutine
Setting of counter

Subroutine
Calculation of
moving sum

Subroutine
Calculation of
average

X = K, Y = H
Jumps to

subroutine.
Jumps to

subroutine.

Jumps to
subroutine.

Line displayed.

Judgment of end.

COUNT

I = I + 1, J = I, S = 0

Return

MOVINGSUM

Calculation of moving sum

Return

AVERAGE

Calculation of moving average

Return

PROGRAMME LIST

(STAT MODE)

Title : MVIN AVG

Label MAIN
Print "Input DIVISION
Input D
D M
1_Stats L1
If M≥n Goto MAIN
Rem RANGE
(xmax-xmin)/10 Yscl
0 Xmin
n Xmax
1 Xscl
xmin Ymin
xmax Ymax
0 I
int (M/2) K
Gosub COUNT
Label LOOP1
Gosub MOVINGSUM
If M≥J Goto LOOP1
Gosub AVERAGE
Label LOOP2
K X
H Y
Gosub COUNT
Label LOOP3
Gosub MOVINGSUM
If (I+M)>J Goto LOOP3
Gosub AVERAGE
Line (X, Y, K, H)
If K≠(n-int (M/2))
Wait
End
Label COUNT
I+1 I
I J
0 S
Return
Label MOVINGSUM
S+L1(J) S
J+1 J
Return
Label AVERAGE
S/M H
K+1 K
Return

Goto LOOP2

16

EL-9650/9600c/9450/9400 Graphing Calculator

Parameters

name of parameter
H
I
J
K
M

content
moving average
counter
counter
counter
number of divisions

name of parameter
S
X
Y
Yscl
B

content

moving sum

starting point (x)

starting point (y)

scale of y-axis

input of number of divisions

Exercise

Find the moving average every three months (number of divisions: 3) from the follo wing
table of monthly sales.

Month
Sales[$]

Jan.
300

Feb.

326

Mar.

323

Apr.

344

May.

300

Jun.
401

Jul.

398

On the graph, Xmax = 8, Ymin = 300, and Ymax = 450.
Set up condition: decimal point in Float Pt Mode.

Enter statistical data into L1.

1

2nd F

SET UP

* *

CL1C

Key Operation

STAT

ENTER

A

*

(When using EL-9650/9600c)

Aug.

450

DisplayStep

Specify the programme mode.

2

Select the title MVIN AVG.

Enter the number of divisions(3).

3

0

03623

ENTER

43

ENTER

93

ENTER

2nd F

ENTER

3

ENTER

23

4

ENTER

04

8

ENTER

PRGM

A

*

3

1

ENTER

003

ENTER

054

17

EL-9650/9600c/9450/9400 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.)

Start

Graph plot

I = I + 1

Setting of

coordinates

of line

Display of line

Y

(I + 1) < n

End

FLOWCHART

Enter statistical data using
statistics feature before
executing program.

Graph plotted using

DRAWLOOP

N

automatic scaling.

Counter

Data as coordinates
(starting point and
finishing point).

Line drawn between
set coordinates.

Whether or not lines of no.
of data drawn judged.
Repeated until lines drawn
by the no. of data.

PROGRAMME LIST

Title : XY GRAPH

ClrG
Rem DRAWING SD
2 -Stats L1,L2
Rem RANGE
xmin Xmin
xmax Xmax
ymin Ymin
ymax Ymax
(Xmax-Xmin) / 10 Xscl
(Ymax-Ymin) / 10 Yscl
Rem BROKEN LINE
0 I
Label DRAWLOOP
I+1 I
L1(I) X
L2(I) Y
L1(I+1) Z
L2(I+1) W
Line(X,Y,Z,W)
If (I+1) <n Goto DRAWLOOP
Wait
End

(STAT MODE)

Name of parameter
I
X
Z

Content
counter
x of line starting point
x of line finishing point

PARAMETERS

Name of parameter
Y
W

Content

y of line starting point
y of line finishing point

*n = number of statistical data

18

EL-9650/9600c/9450/9400 Graphing Calculator

Exercise

The following table shows examined water vapour pressure. Draw a graph
of this data.

Temperature [˚C]
Pressure [mmHg]04.581109.2052017.5323031.8264055.3395092.55860149.4770223.7980355.2990525.90

Set up condition: decimal point in Float Pt Mode.
*

Enter statistical data into

1

L1 and L2.

2

2nd F

SET UP

CL1C

*

Key Operation

A

*

ENTER

0

01

ENTER

01

ENTER

STAT

…

0

(Other numbers not shown)

100

760.00

DisplayStep

(When using EL-9650/9600c)

3

Specify the programme mode.

4

Select the title XY GRAPH.

(Drawing of graph)

•

4

…

2nd F

67

PRGM

85

0

A

1

ENTER

*

ENTER

19

EL-9650/9600c/9450/9400 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 X
starting point X

1. K0 = Hf (Xn , Yn), R1 = (1/2) (K0-2Q0), Y

2. Q1 = Q0 + 3R1- (1/2)K
K1 = Hf (Xn + H/2, Y

3. Q2 = Q1 + 3R2 - (1 - 1/2) K
K2 = Hf (Xn + H/2, Y

4. Q3 = Q2 + 3R3- (1 + 1/2) K
K3 = Hf (X
Q4 = Q3 + 3R4 - (1/2)K

n + 1 and Yn - 1 from Xn and Yn. Input Qo = 0 at the

0.

(1)

= Yn +R

1

0

(1)

), R2 = (1 - 1/2) (K1-Q1), Y

(2)

), R3 = (1 + 1/2) (K2 -Q2),Y

(3)

n+1

, Y

), R4 = (1/6) (K3-2Q3), Y

3

1

2

n+1

= Y

(2)=Y(1)

(3)

(3)

+ R

= Y

+ R

2

(2)

+ R

3

4

Y

Y

3

Y

2

Y

1

0

h

h

X1X2X

X

3

Start

Entry of data

Initial setting

MAIN

Gosub

Calculation of step 1.

Gosub

Calculation of step 2.

Gosub

Calculation of step 3.

Gosub

Calculation of step 4.

Z <= I

Y

S = I

O = J

Z ≠ I
Y

Processing

in case of
inequality

SUB1

Display of result

Processing for

next calculation

Enter Data.

Initial coordinates (X, Y), step
of x (H), and interval of solutions (T)

Data for calculation set.
Calculation executed.

Jumps to subroutine.

Jumps to subroutine.

Jumps to subroutine.

Jumps to subroutine.

Judgment of calculation end

N

If calculation result of I smaller
than value of increase of I,
calculation repeated again.

N

SUB2

Prior processing for next calculation
Z = Z + T, S = X, O = J

FLOWCHART

Following calculation
performed when calculation
result of x not equal to the
value of increase of X.

(Z - S) (J - O)

P =

H

+ O,

M = Z
N = P

Subroutine

FORMULA

Subroutine for

calculating

built-in function

Return

PROGRAMME LIST

Title : RUNGE

Rem INITIAL
Print " Input X0
Input X
Print " Input Y0
Input Y
X I
Y J
Print " Input H
Input H
Print " Input T
Input T

-1

1+√(2

) A

-1

1- √(2

) B
I+T Z
O Q
I S
Label MAIN
Rem 1
Gosub

FORMULA
H F K
(K-2 Q) /2 R
J+R J
Q+3 R-K/2 Q

I+H/2 I
Rem 2
Gosub
H F K
B (K-Q) R
J+R J
Q+3 R-B K Q
Rem 3
Gosub
H F K
A (K-Q) R
J+R J
Q+3 R - A K Q
I+H/2 I
Rem 4
Gosub
H F K
(K - 2 Q) /6 R
J+R J
Q+3 R - K/2 Q
If Z≤I Goto
I S
J O

Subroutine for calculating
built-in function

f = -I J

(Another equation can be used.)

(REAL MODE)

Goto MAIN
Label NEXT

FORMULA

If Z≠I Goto
I M
J N
Label SUB1
ClrT
Print "XN=

FORMULA

Print M
Print "YN=
Print N
Wait
Z+T Z
I S
J O

FORMULA

Goto MAIN
Label SUB2
(Z-S) (J-O) /H+O
Z M
P N

NEXT

Goto SUB1
Label

-I J F
Return

SUB2

P

FORMULA

20

EL-9650/9600c/9450/9400 Graphing Calculator

PARAMETERS

Name of parameter
A
B
F
H
K
O
P
Q
R

Content
value of 1+ (1/2)
value of 1- (1/2)
f (I,J)
step
calculating working area
value of Yn-1
increase of J
value of Qn
value of Rn

Name of parameter
S
T
I
J
Z
X
Y
M
N

Content
value of Xn-1
interval
Xn
Yn
value of increase of X
input of X
input of Y
indicates Xn
indicates Yn

0

0

Exercise

Initial settings: Y = 10 when X = 0. F ind 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.

Specify the programme mode.

1

Select the title RUNGE.

2nd F

SET UP

* * * *

1C

CL2B

Key Operation

2nd F

PRGM

(When using EL-9650/9600c)

A

*

...

.

DisplayStep

Enter the values of X0, Y0,

2

H and T.

3

(Display of X1)
(Display of Y1)

4

(Display of X2)
(Display of Y2)

5

(Display of X3)
(Display of Y3)

Similar operation is performed
hereafter.

ENTER

00•
00•

ENTER

ENTER

ENTER

0

10

1
3

ENTER

ENTER

ENTER

21

A

EL-9650/9600c/9450/9400 Graphing Calculator

nalysing 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

Factor
Error
Total

Sum of squares (S)
SA = [A] - [X]
S

E

= [AS] - [A]

S

T

= [AS] - [X]

Degree of freedom (θ)

θA = A - 1
θ

E

= A (N- 1)

θ

T

= AN - 1

Variance (V)
VA = SA ÷ θ
VE = SE ÷ θ

Variance ratio (F)

A

FA = VA ÷ V

E

E

[X] = (Σ Σ Xij)2 ÷ AN
[A] = Σi (Σj Xij)
[AS] = Σi Σj (Xij)

2

÷ N

2

A : number of levels
N: repeated frequency
X: number of data

FLOWCHART PROGRAMME LIST

Start

LOOP2

Entry of number of levels

and repeat frequency

Declaration of one

variable statistic

Entry of data

Accumulation of data

Accumulation of

square of data

K = K + 1

Y

(N+1)>K

Display of ΣX

(sum of levels)

Accumulation

of (ΣX)

S = S + 1

Y

(A+1)>S

Calculation of X,Y and Z

Calculation and display

of sum of squares

Calculation and display

of degree of freedom

Calculation and display

of variance

LOOP1

Judgment of repeated frequency.

N

2

Repeated frequency corresponding
to no. of levels judged.

N

Title : VARIANCE

Rem INPUT

Enter no. of levels and repeated
frequency.

One variable statistic
(Stat X) declared.

Data and square of data
accumulated.

ΣX (sum of levels) displayed.
ΣX obtained with

statistics feature.
Square of ΣX accumulated.

X, Y and Z calculated.
Sum of squares (E, M, P)

calculated and displayed.
Sum of degree of freedom

(Q, R, D) calculated and
displayed.

Print "Input LEVEL
Input L
L A
Print "Input TIMES
Input T
T N
0 W
0 B
0 C
1 S
Label LOOP2
N dim(L1)
1 K
Label LOOP1
ClrT
S L
K T
Print "Input DATA
Print "LEVEL
Print L
Print "TIME
Print T
Input I
I L1(K)
B+I B

2

C+I
K+1 K
If (N+1)>K Goto LOOP1
1_Stats L1
Σx J
Print "Σx=
Print J
Wait
W+(Σx)
S+1 S
If (A+1)>S Goto LOOP2
Rem CALCULATE

2

B

/A/N X

Variance (V, U) calculated and displayed.

C

2

W

(STAT MODE)

W/N Y
C Z
Rem SUM OF SQUARES
Y-X E
Z-Y M
Z-X P
Print "SUM OF SQUARES
Print E
Print "ERROR SUM OF SQUARES
Print M
Wait
Print "TOTAL SUM OF SQUARES
Print P
Wait
Rem DEGREES OF FREEDOM
A-1 Q
A (N-1) R
A N-1 D
Print "DEGREES OF FREEDOM
Print Q
Print "

DEGREES OF FREEDOM
Print R
Wait
Print "

SUM OF DEGREES OF FREEDOM
Print D
Wait
Rem VARIANCE
E/Q V
M/R U
Print "VARIANCE
Print V
Print "VARIANCE OF ERRORS
Print U
Wait
Rem VARIANCE RATIO
V/U F
Print "VARIANCE RATIO
Print F
End

ABOUT ERRORS

Calculation and display

of variance ratio

End

22

Variance ratio (F) calculated and displayed.

EL-9650/9600c/9450/9400 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
repeated frequency
loop 2 counter

2

/ a/ n

(ΣΣ xi)

2

Σi Σj (xij)
variance ratio factor
sum of squares factor
sum of squares error
sum of squares total

Name of parameter
V
U
Y
Q
R
D
T
L
W
B
C

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.

Content
variance factor
variance error

2

Σi (Σ jxij)
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)
total sum of squares (all data)

/ n

Increase mouse weight (grams/day)

Hormone

(grams/mouse)

10
20
30

10
882
923
933

20
891
915
939

30
864
923
925

40
888
912
940

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.

*

Specify the programme mode.

1

Select the title VARIANCE.

Enter the number of levels and

2

the repeated frequency.

2nd F

SET UP

CL1C

*

Key Operation

(When using EL-9650/9600c)

2nd F

PRGM

A

*

ENTER

53

50
885
930
932

DisplayStep

3

ENTER

23

EL-9650/9600c/9450/9400 Graphing Calculator

Enter the statistical data

4

in level 1.

(Display of total of hormone 10 g)

Enter the statistical data

5

in level 2.

(Display of total of hormone 20 g)

Enter the statistical data

6

in level 3.

(Display of total of hormone 30 g)

7

(Display of sum of squares)
(Display of error sum of squares)

Key Operation

2

88

ENTER

88

ENTER

ENTER

19

ENTER

39

ENTER

39

ENTER

39

ENTER

ENTER

68

4

8

ENTER

5

0

9

2

29

ENTER

19

ENTER

39

ENTER

49

ENTER

3

2

3

0

ENTER

ENTER

ENTER

ENTER

ENTER

DisplayStep

(When using EL-9650/9600c)

198

588

329

529

8

9

10

11

12

ENTER

(Display of sum of squares)

ENTER

(Display of degrees of freedom)
(Display of degrees of freedom about errors)

ENTER

(Display of sum of degrees of freedom)

ENTER

(Display of variance)
(Display of variance of errors)

ENTER

(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

EL-9650/9600c/9450/9400 Graphing Calculator

Calculating Parabolic Motion

Display on a graph the altitude change and the horizontal distance over a period of time

0

when an object is thrown at initial velocity V
distance and altitude after t seconds. Specify the angle in Deg.

and angle θ, and find the horizontal

Calculation

•

•

X = V0

cos θ

Initial velocity V0 [m/s]
Angle θ [˚ ]
Gravitational acceleration g = 9.8 [m/s
Time T [s]

Entry of initial velocity

Calculation and

display from

released angle 45ß

Entry of released angle

Y

θ≤ 0 or θ> 90

Calculation and

display of values

for entered angle

Range setting

LOOP1

Calculation and

plotting of graph

D = (D + T/100)

Y

D ≤ T

Entry of time

T Y = V

FLOWCHART PROGRAMME LIST(REAL MODE)

Start

THETA

N

TX

N

•

•

2

]

T - 1 gT

0

sin θ

Enter velocity when thrown.
Highest altitude, throwing

distance (horizontal distance),
and time (duration of flight) in
case of released angle 45˚
calculated and displayed.

Angle for throwing entered.

Entered angle less than or equal
to 0˚ or larger than 90˚?

Highest altitude, throwing distance
(horizontal distance), and time
(duration of flight) for entered angle
calculated and displayed.

Range of graph set based on
values for released angle 45˚.

Graph (parabola) calculated
and plotted.

Elapsed time counted.
Calculation and plotting repeated

until D (time elapsed) reaches
T (duration of flight).

2

2

y

0

V

θ

Title : PARABOLA

Print "V0 (M/S),θ,T(S)
Print "Input V0
Input V
2 V sin 45/9.8 A

2

/9.8 B

V

2

/19.6 C

V
Print "HMAX=
Print C
Print "LMAX=
Print B
Print "TMAX=
Print A
Wait
Label THETA
Input θ
If θ ≤ 0 Goto THETA
If θ > 90 Goto THETA

2

(sin θ)2/19.6 H

V

2

sin (2θ)/9.8 L

V
2 V sin θ/9.8 T
Print "H=
Print H
Print "L=
Print L
Print "T=
Print T
Wait
C/10 Yscl
B/10 Xscl

x

0 Xmin
0 Ymin
B Xmax
C Ymax
0 D
Label LOOP1
V cos θ D X
V sin θ D-(0.5 9.8 D
Pnt0N(X,Y)
D+(T/100) D
If D≤T Goto LOOP1
Wait
Label TX
Print "Input TX
Input Z
If Z≤0 Goto THETA
If Z>T Goto THETA
V cos θ Z X
V sin θ Z-(0.5 9.8 Z
Print "X=
Print X
Print "Y=
Print Y
Wait
Line(0,Y,X,Y)
Line(X,0,X,Y)
Wait
Goto TX
0000

2

) Y

2

) Y

Z ≤ 0 or Z > T

N

Calculation and

display of distance

and altitude after time Z.

Display of graph

Entered time less than or equal

Y

to 0 or more than T?

Altitude and distance after entered
time elapses from throwing
calculated and displayed.

Returns to entry of time.

25

EL-9650/9600c/9450/9400 Graphing Calculator

PARAMETERS

Name of parameter
H
L
T
X
Y
D
Yscl

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

Content
highest altitude
horizontal distance
time
distance (after time Z)
altitude (after time Z)
time elapsed
scale of y-coordinate

SET UP

B

Name of parameter
Xscl
Z
V

θ

C
B
A

1C

CL1

Content
scale of x-coordinate
input of time period
initial velocity (V
angle (released angle)
highest altitude when released at 90˚
horizontal distance when released at 45˚
time period when released at 45˚

0

)

Specify the programme mode.

1

Select the title PARABOLA.

Enter the value of the initial velocity.

2

3

Enter the angle value.

4

(Display of highest altitude)
(Display of horizontal distance)
(Display of time until dropping of object)

5

(Display of graph of parabola)

Key Operation

2nd F

PRGM

5

ENTER

ENTER

2

ENTER

52

ENTER

DisplayStep

(When using EL-9650/9600c)

A

*

6

Enter the value of time period Z.

7

(Display of distance after Z seconds)
(Display of altitude after Z seconds)

8

26

(Altitude and distance after Z seconds are
displayed on the parabola graph.)

ENTER

ENTER

3

ENTER

Key pad for the SHARP EL-9650/9600c Calculator

Graphing keys
Power supply ON/OFF key
Alphabet specification key
Secondary function specification key
Display screen

Cursor movement keys
Clear/Quit key
Variable enter key
Calculation execute key
Communication port for peripheral devices

Key pad for the SHARP EL-9450/9400 Calculator

Graphing keys
Power supply ON/OFF key
Alphabet specification key
Secondary function specification key
Display screen

Cursor movement keys
Clear/Quit key
Variable enter key
Calculation execute key
Communication port for peripheral devices

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-9650/9600c and 9450/9400 graphing calculator, including the necessary procedures
and definitions as outlined 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,
specifying whether you have created the problem for the EL-9650/9600c or the EL-9450/9400. If your
contribution is chosen, your name will be included in the next edition of The EL-9650/9600c/9450/9400
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: Fax:
E-mail:

* You are making this sheet for the ( EL-9650/9600c, EL-9450/9400).

SUBJECT: Write either a title or about the subject matter.

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INTRODUCTION and CALCULATION:

Write a brief explanation of the subject, and the formula with definitions, including a diagram if relevant.

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SHARP Graphing Calculator

PARAMETERS:

Define the parameters used in the programme.

PROGRAMME LIST:

List the procedure of data to be entered.

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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

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before solving the problem.

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SHARP CORPORATION Osaka, Japan

Fax:

SHARP Graphing Calculator

SHARP CORPORATION OSAKA, JAPAN