Casio FX-9750G User manual

Program Library
1 Prime Factor Analysis
2 Greatest Common Measure
3t-Test Value
4 Circle and Tangents
5 Rotating a Figure
Before using the Program Library
• Be sure to check how many bytes of unused memory is remain-
ing before attempting to perform any programming.
• This Program Library is divided into two sections: a numeric cal-
culation section and a graphics section. Programs in the numeric
calculation section produce results only, while graphics programs
use the entire display area for graphing. Also note that calcula-
tions within graphics programs do not use the multiplication sign
(×) wherever it can be dropped (i.e. in front of open parenthesis).
Chapter
21

376
PROGRAM SHEET
Program for Prime Factor Analysis
Description
Produces prime factors of arbitrary positive integers
For 1 < m< 1010
Prime numbers are produced from the lowest value first. “END” is displayed at the end
of the program.
(Overview)
mis divided by 2 and by all successive odd numbers (d= 3, 5, 7, 9, 11, 13, ....) to check
for divisibility.
Where dis a prime factor, mi= mi–1/dis assumed, and division is repeated until
mi+ 1 <d.
Example [1]
119 = 7 ×17
[2]
440730 = 2 ×3 ×3 ×5 ×59 ×83
[3]
262701 = 3 ×3 ×17 ×17 ×101
Preparation and operation
• Store the program written on the next page.
• Execute the program as shown below.
Step Key operation Display Step Key operation Display
No. 1

377
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P
Lbl
Lbl
Lbl
Lbl
Lbl
Goto
Lbl
Lbl
Lbl
Lbl
Lbl
R
0
1
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6
5
6
7
8
9
M
:
:
:
:
:
:
:
:
:
:
:
"
2
Frac
B
B
A
B
A
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F
M
^
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A
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^
^
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A
"
A
A
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A
N
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⇒
→
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2
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B
B
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:
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:
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8
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–
→
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0
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4
=
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0
2
A
⇒
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0
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:
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3
1
1
÷
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:
⇒
:
B
7
A
B
C
D
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P
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R
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U
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mi
d
mi +1
Goto
3
)
:
9
→
=
Goto
:
B
0
5
:
⇒
:
No. 1
Line Program
File
name
Memory Contents

378
PROGRAM SHEET
Program for Greatest Common Measure
Description
Euclidean general division is used to determine the greatest common measure for two interers
aand b.
For |a|, |b| < 109, positive values are taken as < 1010
(Overview)
n0=max (|a|, |b|)
n1= min (|a|, |b|)
nk–2
nk= nk–2 – ––– nk–1
nk–1
k= 2, 3....
If nk= 0, then the greatest common measure (c) will be nk–1.
Example [1] [2] [3]
When a= 238 a= 23345 a= 522952
b= 374 b= 9135 b= 3208137866
↓↓ ↓
c= 34 c= 1015 c= 998
Preparation and operation
• Store the program written on the next page.
• Execute the program as shown below.
Step Key operation Display Step Key operation Display
No. 2

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C
Lbl
Abs
B
A
Lbl
C
B
Lbl
M
1
A
<
→
2
=
→
3
N
:
→
A
C
:
0
A
:
"
A
⇒
:
( – )
⇒
:
B
F
A
:
Goto
B
(
Goto
C
^
A
"
Abs
2
→
lnt
3
→
Goto
C
?
B
:
A
(
:
B
1
T
→
→
:
A
:
:
:
→
B
2
A
B
C
÷
Goto
"
B
)
:
B
:
×
"
B
?
–
→
A
A
B
C
D
E
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a, n0
b, n1
nk
B
)
:
→C:
No. 2
Line Program
File
name
Memory Contents

380
PROGRAM SHEET
t =(x – m)
xn–1
n
Program for t-Test Value
Description
The mean (sample mean) and sample standard deviation can be used to obtain a t-test value.
x: mean of xdata
xσn–1 : sample standard deviation of xdata
n: number of data items
m: hypothetical population standard deviation (normally repre-
sented by µ , but mis used here because of variable name
limitations)
Example To determine whether the population standard deviation for sample data 55, 54, 51,
55, 53, 53, 54, 52, is 53.
Perform a t-test with a level of significance of 5%.
Preparation and operation
• Store the program written on the next page.
• Execute the program as shown below.
No. 3
Step Key operation Display Step Key operation Display
The above operation produces a t-test value of t(53) = 0.7533708035. According to the t-distribution
table in the next page, a level of significance of 5% and a degree of freedom of 7 (n– 1 = 8 – 1 = 7)
produce a two-sided t-test value of approximately 2.365. Since the calculated t-test value is lower
than the table value, the hypothesis that population mean mequals 53 is accepted.

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240
∞
0.2
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.341
1.325
1.316
1.310
1.306
1.303
1.301
1.299
1.296
1.292
1.289
1.285
1.282
0.1
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.753
1.725
1.708
1.697
1.690
1.684
1.679
1.676
1.671
1.664
1.658
1.651
1.645
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.131
2.086
2.060
2.042
2.030
2.021
2.014
2.009
2.000
1.990
1.980
1.970
1.960
63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
2.947
2.845
2.787
2.750
2.724
2.704
2.690
2.678
2.660
2.639
2.617
2.596
2.576
0.05 0.01
1
2
3
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7
T
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5
l-Var
Lbl
(
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Goto
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4
List
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x
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T
3
_
A
B
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mt
,53,
P (Probability)
Degree
of Freedom
No. 3
Line Program
•t-distribution table
The values in the top row of the table show the probability (two-sided
probability) that the absolute value of tis greater than the table values
for a given degree of freedom.
Memory Contents
File
name
M:aM
T:aT

382
PROGRAM SHEET
Program for Circle and Tangents
Description
Formula for circle:
x2+ y2= r2
Formula for tangent line passing
through point A (x', y'):
y– y' = m(x– x')
*mrepresents the slope of the
tangent line
With this program, slope mand intercept b(= y' – mx') are obtained for lines drawn from point
A (x', y') and are tangent to a circle with a radius ofr. The trace function is used to read out the
coordinates at the points of tangency, and factor zoom is used to enlarge the graph.
Example
To determine mand bfor the following values:
r= 1
x'= 3
y'= 2
Notes
• The point plotted for A cannot be moved. Even if it is moved on the graph, the calculation is
performed using the original value.
• An error (Ma ERROR) occurs when r= x'.
• Be sure to always perform a trace operation whenever you select trace and the message
TRACE is on the display.
Preparation and operation
• Store the program written on the next page.
• Execute the program as shown below.
No. 4
0X
YA(x',y')
r
A
B
C
D
E
F
G
H
I
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Q
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Memory Contents

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T
Prog
"
R
Prog
"
X
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Plot
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Lbl
Graph Y=
"
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No. 4
Line Program
File
name

384
View
Window
35
36
37
38
39
40
41
42
43
44
1
2
1
2
Prog
S
Graph Y=
Goto
Lbl
Graph Y=
Prog
:
Lbl
"
W
1
C
Graph Y=
Graph Y=
"
=
N
3
9
M
"
Goto
3
E
I
(–)
,
I
(–)
C
2
(
_
_
(
W
6
_
N
N
6
1
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⇒
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3
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D
W
,
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–
x2
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=
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B
C
(–)
⇒
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3
Goto
R
.
9
C
1
_
L
,
E
3
"
.
No. 4
Line Program
File
name
File
name

385
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4
5
Program for Circle and Tangents No. 4
Step Key Operation Display

386
Program for Circle and Tangents No. 4
Step Key Operation Display
6
7
8
9
10

387
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Program for Circle and Tangents No. 4
Step Key Operation Display

388
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17
18
Program for Circle and Tangents No. 4
Step Key Operation Display

389
A
B
C
D
E
F
G
x1
y1
x2
y2
x3
y3
x'1
y'1
x'2
y'2
x'3
y'3
H
I
J
K
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N
O
P
Q
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Y
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0X
Y
B(x2, y2)
A(x1, y1)
C(x3, y3)
PROGRAM SHEET
Program for Rotating a Figure
Description
Formula for coordinate transforma-
tion:(x, y) →(x', y')
x' = xcos θ – ysin θ
y' = xsin θ + ycos θ
Graphing of rotation of any geometric figure by θ degrees.
Example
To rotate by 45°the triangle defined by pointsA (2, 0.5), B (6, 0.5), and C (5, 1.5)
Notes
• Use the cursor keys to move the pointer around the display.
• To interrupt program execution, press Awhile the graphic screen is on the display.
• The triangle cannot be drawn if the result of the coordinate transformation operation exceeds
View Window parameters.
Preparation and operation
• Store the program written on the next page.
• Execute the program as shown below.
No. 5
Memory Contents

390
No. 5
Line Program
File
name
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R
.
"
X
"
Plot
X
"
X
"
Plot
X
"
X
"
Plot
X
Lbl
Line
"
A
A
Plot
C
C
Plot
E
E
Plot
Plot
Cls
O
(–)
4
(
1
Y
A
→
(
2
Y
C
→
(
3
Y
E
→
1
:
A
cos
sin
G
cos
sin
I
cos
sin
K
G
:
T
0
,
X
=
1
,
A
X
=
2
,
C
X
=
3
,
E
_
Plot
N
Q
Q
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Q
Q
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Q
Q
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.
1
1
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:
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,
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Y
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→
Y
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→
Y
→
?
→
B
E
sin
cos
sin
cos
Line
sin
cos
Line
Line
D
1
_
1
A
→
B
2
C
→
D
3
E
→
F
:
:
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Q
Q
Q
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Q
Q
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:
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F
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→
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Plot
2
Plot
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_
_
_
_
_
,
.

_
_
_
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_
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G
H
I
J
K
L
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,
C
→
1
,
Q
,
D
_
(–)
:
0
Line
F
View
Window
: Goto 1
.8,5
^

391
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2
3
4
5
Program for Rotating a Figure No. 5
Step Key Operation Display

392
6
7
8
9
10
Program for Rotating a Figure No. 5
Step Key Operation Display
(Locate the pointer at X = 5)
Continue, repeating from step 8.