50
(K) ( 60%) ......
1. 32 ..... 32 ..... 100
(P)
1) 32 ..... 32 ..... 100 ......
2)
(A) 32 ..... 32 ..... 100 ......
1) . .
2)
3)
อา Mimi
10 2564
ทิ
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12 2564 8.30-10.10 . 1-2
1.
40 -
1. r
1.1
1.2
ะ1.3
1.4 r
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1.6
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52
2. ( 60%) ......
40 ..... 40 ..... 100
(K)
1.
(P)
1) 40 ..... 40 ..... 100 ......
2)
(A) 40 ..... 40 ..... 100 ......
1) .
2)
3)
ชา 2564
12
ตุฑัฅิ
53
22
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9 2564 11.50-13.30 . 5-6
2.
39 -
3. /
3.1
3.2 /
3.3 /
3.4 /
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3.6
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54
4. ( 60%) ......
39 ..... 39 ..... 100
(K)
1.
(P)
1) 39 ..... 39 ..... 100 ......
2)
(A) 39 ..... 39 ..... 100 ......
1) .
2)
3)
Shi Mimi
9 2564
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12 2564 13.30-15.10 . 7-8
36 -
/
_
r
r
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r
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56
(K) ( 60%) ......
1. 36 ..... 36 ..... 100
(P)
1) 36 ..... 36 ..... 100 ......
2)
(A) 36 ..... 36 ..... 100 ......
1) .
2)
3)
ภM
12 2564
ตุ่ฬิ
57
31102 2 3 4
1 2
pattern)
ON LINE
AB
1.
1.2 r Dr
r
4.1
Dr x x, y r
2 Rr y x, y r Rr
r
r
r
3
:
:
1.
2.
3.
4.
5.
:
1.
4
58
5
3
3
3
3
6. 3 33
- 33
3 3. power point
4. +
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: 6 classdojo
7.
.4 2.
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. (2548).
: .
.:
(2548). 4 2. :
. (2548)
2 4( 4) :
.
7.
google meet kb404 / kb406 / kb407 / kb409
rr
rr
1.
r AB
r
r r Dr
r Rr
Dr Rr r
Dr x x, y r
Rr y x, y r
2. 1
1 r (1, 4),(2, 5),(4, 8),(7,10) 1
r (1, 4),(2, 5),(4, 8),(7,10)
Dr 1, 2, 4, 7
Rr 4, 5, 8,10
3.
4. 1
60
r
r
5. 2
2 A 1, 2, 3, 4, 5 r (x, y) A A y x2
r (x, y) A A y x2
r
(1,1),(2, 4),(3, 9),(4,16),(5, 25)
r 1, 2, 3, 4, 5
Dr 1, 4, 9,16, 25
Rr
6. 2
7. 3
3 A 4, 3, 2, 1, 0,1, 2, 3, 4 , B 0,1, 2, 3, 4, 5
r (x, y) B A x y 5 r
r (x, y) B A x y 5
r (1, 4),(2, 3),(3, 2),(4,1),(5, 0)
Dr 1, 2, 3, 4, 5
Rr 0,1, 2, 3, 4
8. 3
9. 2 3
r
r
10. 4
4 (x, y) R R y x 5
1) r (x, y) R R y 2x 8
2) r
61
1) y x 5 x y
xx R x
Dr R
y R
y x5 yy R
Rr
2) y 2x 8 x y
xx R R x
Dr
y 2x 8 y
yy R R
Rr
11. 2
12. 4
Dr R Rr R
r (x, y) R R y ax b, a 0
13. 5
5 r (x, y) y = 1
1+ x
y= 1 x= 1 y
1+ x x
x
Dr x R x 1 R1
y= 1
1+ x
xy
y(1 x) 1
y xy 1
xy 1 y
x 1y
y
x 1 1
y
y y=0
Rr y R y 0 R0 2
14. 5
15.
y x xy
62
x y yx
16. 6
6 r (x, y) R R y 2x 7
3x 5
y 2x 7
3x 5
x= 5
x 3 y
Dr x Rx 5 R5
3 3
y 2x 7
3x 5
xy
y(3x 5) 2x 7
3xy 5y
3xy 2x 2x 7
x(3y 2)
5y 7
x
5y 7
R2
3 5y 7
3y 2
y x= 2 x
y Ry 2 3
Rr 3
17. 6
18. 5
r {(x, y) R R y ax b , a, b, c, d }
cx d
Dr x R x d R d Rr y Ry a Ra
c c c c
3.
4. 3( )
63
8
3 1. 3 -3
2. 57
3
-
-
-
-
64
(Domain) (Range)
r (1, 2),(2, 4),(3, 6),(4, 8) Dr
Rr
1, 2, 3, 4 r
2, 4, 6, 8 r
r AB
r
r r
r
Dr Rr r
Dr x x, y r
Rr y x, y r
1 r (1, 4),(2, 5),(4, 8),(7,10)
2 A 1, 2, 3, 4, 5 r
r
r
r (x, y) A A y x2
3 A 4, 3, 2, 1, 0,1, 2, 3, 4 , B 0,1, 2, 3, 4, 5
(x, y) B A x y 5
r r
r 65
r ..
..
4 (x, y) R R y x 5
1) r (x, y) R R y 2x 8
2) r
r (x, y) R R y ax b, a 0 Dr R Rr R
5 r (x, y) y = 1
1+ x
y x xy
x y xx
66
6 r (x, y) R R y 2x 7
3x 5
r {(x, y) R R y ax b , a, b, c, d }
cx d
Dr x R x d R d Rr y Ry a R a
c c c c
7 r (x, y) R R y 4 x2
67
8 r (x, y) R R x 2 y 3 4
.
9
68
10
11
.
xX
yY
69
3
.................... ......... ..... .........
1) r (1, 2),(2, 3),(3, 4),(4, 5) A 1, 2, 3 B 2, 3, 4
2) r (1, 4),(3, 6),(5, 8),(7, 9)
3) r (x, y) A B y x 1
4) r (x, y) y 3x 2
r (x, y) xy x 3y 1 0
6) r (x, y) y x 2
x1
7) r (x, y) y x 3
x5
70
1) r (1, 2),(2, 3),(3, 4),(4, 5)
Dr 1, 2, 3, 4,
Rr 2, 3, 4, 5
2) r (1, 4),(3, 6),(5, 8),(7, 9)
Dr 1, 3, 5, 7
Rr 4, 6, 8, 9
3) r (x, y) A B y x 1 A 1, 2, 3 B 2, 3, 4
r (x, y) A B y x 1 y
r (1, 2),(2, 3),(3, 4)
Dr 1, 2, 3
Rr 2, 3, 4
4) r (x, y) y 3x 2 x
1) y
y 3x 2
x
Dr x x R
2) x y
x y2
3
y x
Rr x x R
r (x, y) xy x 3y 1 0
1) y x
xy x 3y 1 0
xy 3y x 1
y x1
x
x3
x3 y
Dr x x 3
71
2) x y
xy x 3y 1 0
xy x 3y 1
x 3y 1
y
y1
Rr y y 1 y1 x
x1 y
6) r (x, y) y x 2 x
x
x1 y
1) y
y x2
x1
x
Dr x x 1
2) x y
y x2
x1
yx y x 2
yx x 2 y y1
x 2y
y1
y
Rr y y 1
7) r (x, y) y 2x 3
3x 5
1) y x
y 2x 3
3x 5
5
x x 3
Dr xx 5
3
72
2) x y
y 2x 3
3x 5
y(3x 5) 2x 3
3xy 5y 2x 3
3xy 2x 5y 3
x(3y 2) 5y 3
x 5y 3
3y 2
y y 2 x
3
Rr yy 2
3
73
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2 31102 4/4
2 2564
16-17 2564 8.30-9.20/10.10-11.00 . 1/3
39 6
ะ.
.
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r
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74
( 60%) ......
(K) 33 ..... 33 ..... 100
......
(P) ......
1)
2)
(A) 33 ..... 33 ..... 100
1)
2) 33 ..... 33 100
3) .
ภi Mimi
17 2564
75
32
2 31102 4/6
2 2564
19 2564 8.30 - 10.10 . 1 - 2
1
40 5
1.
1.1 ะ
1.2
1.3 ะ
1.4
................................................................................................................................ ...........
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1.5 /
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1.6
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76
( 60%) ......
(K) 35 ..... 35 ..... 100
......
(P) ......
1)
2)
(A) 35 ..... 35 ..... 100
1)
2) 35 ..... 35 . 100
3) .
ก ฒุ
19 2564
ตั
77
32
2 31102 4/6
2 2564
19 2564 8.30 - 10.10 . 1 - 2
40 5
ะ
.
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/
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78
( 60%) ......
(K) 35 ..... 35 ..... 100
......
(P) ......
1)
2)
(A) 35 ..... 35 ..... 100
1)
2) 35 ..... 35 . 100
3) .
ภi ตi
19 2564
ฅั
79
32
2 31102 4/6
2 2564
19 2564 8.30 - 10.10 . 1 - 2
39 4
n
ะ
r
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/
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....................................................................................... ....................................................
80
( 60%) ......
(K) 35 ..... 35 ..... 100
......
(P) ......
1)
2)
(A) 35 ..... 35 ..... 100
1)
2) 35 ..... 35 . 100
3) .
ภi ต
16 2564
ฅ้
4 81
4
31102 2
1 ON LINE
1. Dr
1.2 Rr
mathematical model)
4.1
2
r AB
rr
rr
Dr x x, y r
Rr y x, y r
3
:
:
1.
2.
3.
4.
5.
:
1.
4
82
5
4
4
4
4
6. 4 44
- 44
4 3. power point
4. +
5. google classroom
6 classdojo
7.
83
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:
: .
. (2537). .:
. (2548).
(2548). 4 2. :
. (2548)
2 4( 4) :
.
7.
google meet kb404 / kb406 / kb407 / kb409
r r
rr
1. 1
1 r (x, y) R R y 4 x2
y 4 x2
xy
4 x2 0
x2 4 0
(x 2)(x 2) 0
2 x2
Dr x R 2 x 2
2, 2
y 4 x2
xy
84
y2 4 x2 y0
x2 4 y2 y0
x 4 y2 y0
yx y0
4 y2 0 y0
y2 4 0 y0
y0
(y 2)(y 2) 0
2 y2 1
Rr y R 0 y 2
0, 2
2. 2
2 r (x, y) R R x 2 y 3 4
Dr 2, 6
x2 y3 4
y3 4 x2
y3 0
4 x2 0
x2 4
4 x2 4
2x6
Dr x R 2 x 6
x2 y3 4
x2 4 y3
x2 0
4 y3 0
y3 4
4 y3 4
1y7
85
Rr yR1 x 7 Rr 1, 7
3. 3 2
4.
3
x ry
r 3
Dr x x R
Rr y y R
5.
6. 4
4
86
x ry
r 1
Dr x x R 4
Rr y R y 1
7.
8. 5
5
Dr x x R
Rr y y 4
5.
6. 4( )
87
8
4 1. 4 - 4
2. 60 %
4
-
-
-
-
88
4
(Domain) (Range)
r (1, 2),(2, 4),(3, 6),(4, 8) r Dr
r Rr
1, 2, 3, 4 r
2, 4, 6, 8 r
r AB
r
r
Dr Rr r
Dr x x, y r
Rr y x, y r
1 r (1, 4),(2, 5),(4, 8),(7,10)
2 A 1, 2, 3, 4, 5 r
r
r
r (x, y) y x2, x A
89
3 A 4, 3, 2, 1, 0,1, 2, 3, 4 , B 0,1, 2, 3, 4, 5
r (x, y) B A x y 5 r
r
r
4 (x, y) R R y x 5
3) r (x, y) R R y 2x 8
4) r
r (x, y) R R y ax b, a 0 Dr R Rr R
90
5 r (x, y) y = 1
1+ x
y x xy
x y xx
6 r (x, y) R R y 2x 7
3x 5
r {(x, y) R R y ax b , a, b, c, d }
cx d
Dr x R x d R d Rr y Ry a Ra
c c c c
91
7 r (x, y) R R y 4 x2
8 r (x, y) R R x 2 y 3 4
92
9
10
93
11
xX
yY
94
4
.................... ......... ..... .........
1.
1) r (x, y) y x 2
............................................................................................................................. .................................................
..............................................................................................................................................................................
............................................................................................................................. .................................................
............................................................................................................................. .................................................
..............................................................................................................................................................................
............................................................................................................................. .................................................
............................................................................................................................. .................................................
.......................................................................................................................................................................... ....
2) r (x, y) y x2 1
............................................................................................. .................................................................................
............................................................................................................................. .................................................
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.................................................................................. ............................................................................................
............................................................................................................................. .................................................
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............................................................................................................................. .................................................
3) r (x, y) y 9 x2
............................................................................................................................. .................................................
....................................................................................................................................................... .......................
........................................................................................................... ...................................................................
............................................................................................................................. .................................................
........................................................................................................................................... ...................................
95
4) r (x, y) y 5x2 9
..............................................................................................................................................................................
............................................................................................................................. .................................................
............................................................................................................................. .................................................
............................................................................................................................................................................. .
............................................................................................................................. .................................................
............................................................................................................................. .................................................
................................................................................................................................................................. .............
...................................................................................................................... ........................................................
1) r (x, y) y x 2
.......................................................................................... ....................................................................................
............................................................................................................................. .................................................
............................................................................................................................. .................................................
..............................................................................................................................................................................
............................................................................................................................. .................................................
............................................................................................................................. .................................................
..............................................................................................................................................................................
............................................................................................................................. .................................................
............................................................................................................................. .................................................
..............................................................................................................................................................................
2) r (x, y) y x2 1
....................................................................................................... .......................................................................
............................................................................................................................. .................................................
....................................................................................................................................... .......................................
............................................................................................ ..................................................................................
............................................................................................................................. .................................................
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96
4
1. x2
1) r (x, y) y
1) y x
y x2 y
x
x2 0
x2
Dr x x 2
2) x y
y x2
y2 x 2
x 2 y2 x
y
y x2 y0
Rr y y 0
2) r (x, y) y x2 1
1) y x
y x2 1
xy
x2 1 0
(x 1)(x 1) 0
x1 x1
Dr x x 1 x1
2x y
y x2 1
y2 x2 1
x2 y2 1
97
x y2 1 x
y y0
y x2 1 x
Rr y y 0
y0
3) r (x, y) y 9 x2
1) y x
y 9 x2
xy
9 x2 0
x2 9 0
(x 3)(x 3) 0
3x3
Dr x 3 x 3
2x y
y 9 x2
y2 9 x2
x2 9 y2
x 9 y2
yx
9 y2 0
y2 9 0
(y 3)(y 3) 0
3y3
y
y 9 x2
Rr y 0 y 3
98
4) r (x, y) y 5x2 9
1) y x
y 5x2 9
x y
Dr x x R y0
2x y
y 5x2 9
y2 5x2 9
x2 y2 9
5
x y2 9
5
yx
y2 9 0
5
y2 9 0
(y 3)(y 3) 0
y3 y3
y 5x2 9
Rr y y 3
1) r (x, y) y x 2
r (x, y) y x 2
99
x r y
2) r r
Dr x x R
Rr y y R
(x, y) y x2 1
r (x, y) y x2 1
x r
y xx R r 1
yy 1
Dr
Rr
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