1. This document contains 20 multiple choice questions about mathematics. 2. The questions cover topics like algebra, equations, inequalities, and coordinate geometry. 3. The correct answers to the questions are not provided, as the purpose is to assess mathematical knowledge.

1. 1
F ก F
1.
2
( 2 8 18 32)+ + + F F ก F F
[O-net ʾก ก 2548]
1. 60
2. 60 2
3. 100 2
4. 200

2. 2
2.
65
33
2
32 2
27
(64)
−
+ F F ก F F
[O-net ʾก ก 2548]
1.
13
24
−
2.
5
6
−
3.
2
3
4.
19
24

3. 3
3. ก F a,b ˈ F F ก
[O-net ʾก ก 2548]
1. F a b< F F
2 2
a b<
2. F 0a b< < F F
2
ab a<
3. F a b< F F a b<
4. F
2 2
a b< F F a b<

4. 4
4. F sin 65x = ° F ก F F ˈ
[O-net ʾก ก 2548]
1.
2
1
x
x x
x
< <
+
2.
2
2
1 1
x x
x
x x
< <
+ +
3.
2
2
2
1
x
x x
x
< <
+
4.
2
2
2
1
x
x x
x
< <
+

5. 5
5. ก F I ˈ
1 1 2
{ | }
1 3
x
A x I
x
− −
= ∈ ≤
−
ก A F ก F F
[O-net ʾก ก 2548]
1. 4
2. 5
3. 6
4. 7

6. 6
6.
1 1
2 2
2 2
− − − F F ก F F
[O-net ʾก ก 2549]
1.
3 2
2 2
−
2.
2 3
2 2
−
3.
5 3 2
2 2
−
4.
3 2 5
2 2
−

7. 7
7.
2 2 3 3
(1 2) (2 8) (1 2) (2 8)− + + − F F ก F F
[O-net ʾก ก 2549]
1. 32−
2. 24−
3. 32 16 2− −
4. 24 16 2− −

8. 8
8. F 5x ≤ F F F ก
[O-net ʾก ก 2549]
1.
2
25x ≤
2. 5x ≤
3. 25x x ≤
4.
2
( ) 25x x− ≤

9. 9
9. F
1
2
x = − ˈ ก ก
2
3 1 0ax x+ − = F ก ก ก ก
F F ก F F
[O-net ʾก ก 2549]
1. 5−
2.
1
5
−
3.
1
5
4. 5

10. 10
10. m F ก
2
4 0x mx− + = ก ˈ ˈ
F
[O-net ʾก ก 2549]
1. ( 5,5)−
2. ( , 4) [3, )−∞ − ∪ ∞
3. ( ,0) [5, )−∞ ∪ ∞
4. ( , 3) [4, )−∞ − ∪ ∞

11. 11
11.
25 2
( )
6 15
− F F ก F F
[O-net ʾก ก 2550]
1.
3
10
2.
7
10
3. 5 2−
4. 6 2−

12. 12
12. 43
( 18 2 125 3 4)+ − − F F ก F F
[O-net ʾก ก 2550]
1. 1000−
2. 1000
3. 2 5 5 2−
4. 5 2 2 5−

13. 13
13. ก 1 2 1
1 2
x
− ≤ + ≤
−
F F
[O-net ʾก ก 2550]
1. [ 2 1,1]−
2. [ 2 1,2]−
3. [3 2 2,1]−
4. [3 2 2,2]−

14. 14
14. ก F F ˈ กก F 2
[O-net ʾก ก 2550]
1.
2
( 2) 1 0x − + =
2.
2 2
( 2) ( 1) 0x x+ − =
3.
2 2
( 1) ( 2) 0x x− + =
4.
2 2
( 1)( 2) 0x x− + =

15. 15
15. ก ก ก
3
2x x x− = F ก F F
[O-net ʾก ก 2550]
1. 0
2. 3
3. 3 1−
4. 3 1+

16. 16
16. F F
(ก) ก F กก F 0
( ) ก F กก F 0
F F ก F
[O-net ʾก ก 2551]
1. (ก) ก ( ) ก
2. (ก) ก ( )
3. (ก) ( ) ก
4. (ก) ( )

17. 17
17. F
1
2
2 8 2 2
( 2)
32
 
+ − +
 
 
 
F ก F F
[O-net ʾก ก 2551]
1. 1−
2. 1
3. 3
4. 5

18. 18
18. ก F F ก F F 3 3 5 1.732
2.236
F F
(ก) 2.235 1.731 5 3 2.237 1.733+ ≤ + ≤ +
( ) 2.235 1.731 5 3 2.237 1.733− ≤ − ≤ −
F F ก F
[O-net ʾก ก 2551]
1. (ก) ก ( ) ก
2. (ก) ก ( )
3. (ก) ( ) ก
4. (ก) ( )

19. 19
19. F F
(ก) ก F ก ก ก F F a
b 0b a a b+ = = +
( ) ก F ก ก F F a b
1ba ab= =
F F ก F
[O-net ʾก ก 2551]
1. (ก) ก ( ) ก
2. (ก) ก ( )
3. (ก) ( ) ก
4. (ก) ( )

20. 20
20. F a b ˈ ก ก F ก
F c d ˈ ก ก F ก
F F
(ก) a-b ˈ ก
( ) c-d ˈ ก
F F ก F
[O-net ʾก ก 2551]
1. (ก) ก ( ) ก
2. (ก) ก ( )
3. (ก) ( ) ก
4. (ก) ( )

21. 21
21. ก 7 6x − = F F ˈ
[O-net ʾก ก 2551]
1. ก F F 10 15
2. ก ก F F ก 14
3. ก กก F 2
4. ก F F F F ก F 3

22. 22
22. F F
ก. ˈ F F ˈ ก
. ˈ F F ˈ ก
F ก F
[O-net ʾก ก 2552]
1. F ก
2. F ก F
3. F F
4. F ก

23. 23
23. ก F s,t,u v ˈ s t< u v<
F F
ก. s u t v− < −
. s v t u− < −
F ก F
[O-net ʾก ก 2552]
1. F ก F
2. F ก F
3. F F
4. F ก F

24. 24
24. ก 2 5 1x− = F F
[O-net ʾก ก 2552]
1. ( 10, 5)− −
2. ( 6, 4)− −
3. ( 4,5)−
4. ( 3,6)−

25. 25
25. F
3
4
ˈ ก
2
4 6 0x bx+ − = b ˈ F ก
ก F ก F
[O-net ʾก ก 2552]
1. 2−
2.
1
2
−
3.
1
2
4. 2

26. 26
26.
2
( 4 3 5 2 3 5 5 2 4 3 3 5 )− − − + − F ก F
[O-net ʾก ก 2552]
1. 0
2. 180
3. 192
4. 200

27. 27
27. ก F a ˈ ก n ˈ F ก
F F
ก. ( )nn
a a=
.
n n
a a=
F ก F
[O-net ʾก ก 2552]
1. F ก F
2. F ก F
3. F F
4. F ก F

28. 28
28. F
2
( 3 1)−
− ˈ F F
[O-net ʾก ก 2553]
1. ˈ ก F ก F 1.8
2. ˈ ก กก F 1.8
3. ˈ ก F ก F 1.8
4. ˈ ก กก F 1.8

29. 29
29. F F
ก. F a b ˈ a b< F
3 3
a b<
. F a , b c ˈ ac bc= F a b=
F F ก F
[O-net ʾก ก 2553]
1. ก ก ก
2. ก ก
3. ก ก
4. ก

30. 30
30. ก F a,b c ˈ
3
0a b c >
F F
ก. 0ac >
. 0bc >
F F ก F
[O-net ʾก ก 2553]
1. ก ก ก
2. ก ก
3. ก ก
4. ก

31. 31
31. F ก
2 2
( 1)(2 6 ) 0x x x c+ − + = ก ˈ 1 ก F
c F F F
[O-net ʾก ก 2553]
1. (0,3)
2. (3,6)
3. (6,9)
4. (9,12)

32. 32
32. F
2 3
2 3
x
+
=
−
2 3
2 3
y
−
=
+
F
2 2
4x xy y− + F ก
F
[O-net ʾก ก 2553]

33. 33
33. F a,b,c d ˈ
2 3
( 1) ( ) 4x ax b cx dx− + = + + ก x
F a+b+c+d F ก F
[O-net ʾก ก 2553]

34. 34
34. F
2
( 2) 25p − = 2
( 1) 81q + = F F ก ˈ F
2p q− F ก F
[O-net ʾก ก 2553]

35. 35
35. F F ʽ ( , )a b ˈ ก
1 6 3 17x x− + − < 2x >
F a b+ F ก F
[O-net ʾก ก 2553]

36. 36
36. F
6 3
6 3
x
+
=
−
6 3
6 3
y
−
=
+
F F
2 2
4x xy y− +
F F ก
[Entrance ก . ʾ 2520]
ก. -2
. -4
. -6
. 30
. 34

37. 37
37. F y ก ก
2 2 5 2 3 2 5 7 2y y y y− + − + + + − = F F ก F y
ก F
[Entrance ก . ʾ 2520]
ก. 2 5 35y + =
. 3 2 14y + =
. 4 3 39y + =
. 2 5 35y − =
. 2 7 1y − =

38. 38
38. ก
2
11 2
12 5 8
x
≤ + F ก
[Entrance ก . ʾ 2520]
ก. 5 3 2 11x< + <
. 17 3 2 20x≤ + <
. 7 2 3 11x< + <
. 11 2 3 13x≤ + <
. F F ก

39. 39
39. ก
2
4 13 4 1x x− + < F กF
[Entrance ก . ʾ 2520]
ก. (1,3)
.
1
( ,3)
4
.
1
{ ,3}
4
. {1,3}
. F F ก

40. 40
40. (2 3)− (2 3)+ ˈ ก ก
[Entrance ก . ʾ 2521]
ก.
2
2 0x x+ − =
.
2
2 3 0x x+ − =
.
2
2 0x x− − =
.
2
2 3 1 0x x+ + =
.
2
4 1 0x x− + =

41. 41
41. F x F ก
3 1
1
x
x
x
−
< −
−
[Entrance ก . ʾ 2521]
ก. 3x > 1x <
. 3 1x− < <
. 1x <
. 3x < −
. F F ก

42. 42
42. x F F F ก 16 11 5x x x− + − = + ˈ
[Entrance ก . ʾ 2521]
ก.
16
3
−
. 20
. 27
. 31
. F F ก

43. 43
43. F 10 100x< < 1 5y< <
(1) 2 100
x
y
< < (2)
2
1 1
10 4
y
x
< <
(3)
2
11 125x y< + < (4) 9 95x y< − <
F ก F
[Entrance ก . ʾ 2523]
ก. F (1) F
. F (4) F
. F (2),(3) F ก
. F (1),(3) F ก
. F (3),(4) F ก

44. 44
44. a b ˈ F ก F
[Entrance ก . ʾ 2523]
ก. F a ˈ F
2
a ˈ F
. F 0a ≥ F
2
a a≥
. F
n n
a b= ก F n F a=b
. F a ˈ ก b ˈ ก F ab ˈ ก
. ก ก F

45. 45
45. ก F x,y,z ˈ 3 ( )x y xy x y= + +△ F F
ก F
[Entrance ก . ʾ 2524]
ก. x y△ ˈ ก
. x y y x≠△ △
. ( ) ( )x y z z y x=△ △ △ △
. F a x a x=△
. F F ก

46. 46
46. ก F x,y,z ˈ F F ก F
[Entrance ก . ʾ 2524]
ก. F 2x y− ˈ F F ก F 1 F
1
( 1)
2
y x≥ −
. F x y< 0z ≠ F xz yz yz< ≤
.
2 2 2
x y x y+ < +
. ก
2
5 4x x− > F (5, )∞
. F ,a b ˈ 0a > x b a− ≤ F b a x a b− ≤ ≤ +

47. 47
47. ก F x,y,z ˈ F ก x y z< < F ก
x,y,z F ก F 57 F F x ก F ก ก F
F ก F
[Entrance ก . ʾ 2524]
ก. 19
. 11
. 13
. 17
. 15

48. 48
48. ก F I ˈ * ˈ ก
* 2a b a b= + + ,a b I∈ ˈ F 4 F *
[Entrance ก . ʾ 2524]
ก. 0
. -2
. -4
. -6
. -8

49. 49
49. F F ˈ
[Entrance ก . ʾ 2525]
ก. F a ˈ ก F a ˈ ก
. { | 2 ,A x x n n= = ˈ } ʽ Fก F ˈ F
. F a b ˈ F 0ax b+ =
. F a c< b d< a,b,c,d ˈ F a bi c di+ < +
2
1i = −
. ก
2
3 4 0z z− + =
F F ก

50. 50
50. F S ˈ F ˈ F ก F △ F
ˈ
b
a b a=△ a,b ˈ F ˈ F S F
(1) ก ก F ˈ 1 (2) F F ก ˈ 0 (3) ก F
[Entrance ก . ʾ 2525]
ก. F (1) F ก
. F (2) F ก
. F (3) F ก
. F (1) (2) F ก
. F (1),(2),(3) F

51. 51
51. F x F ก ก
( 1)( 5)
0
( 1)
x x
x
+ −
<
− ˈ ก F
[Entrance ก . ʾ 2525]
ก.
2
6 5 0x x− + >
. 2 1 1x − >
. 1 2x< <
. 1x < − 1 4x< <
.
2
1 0x − <

52. 52
52.
3 2
5
1 1
x
x
−
>
+ −
[Entrance ก . ʾ 2526]
ก.
1
( 6, 2) (0, )
4
− − ∪
.
1
( 6, 2) ( 1, )
4
− − ∪ −
.
1
( 6, 1) (0, )
4
− − ∪
. ( 6, 1) ( 1, )− − ∪ − ∞

53. 53
53. F F
[Entrance ก . ʾ 2526]
ก. F , 0a b > a b≠ F 2
a b
b a
+ <
. F , 0a b > a b≠ F 2 2
1 1a b
b a a b
+ > +
. F
2 2
1a b+ = 2 2
1c d+ = F 1ac bd+ ≤
. ก ก ก ˈ ก F

54. 54
54.
3 2
4
2
x
x
−
<
+
[Entrance ก . ʾ 2526]
ก.
11 5 5
( , ) ( , )
2 6 6
− − ∪ − ∞
.
5
( , 11) ( , )
6
−∞ − ∪ − ∞
.
11 5
( , ) ( , )
2 6
−∞ − ∪ − ∞
.
3 5
( , ) ( , )
2 6
−∞ − ∪ − ∞

55. 55
55. ,x y x y x y+ ≤ + F M F
3 2
2 3 4x x x M− + − ≤ ก x [ ]3,2−
[Entrance ก . ʾ 2526]
ก. 4
. 4−
. 2
. 58

56. 56
56. ก F F ก
[Entrance ก . ʾ 2526]
ก. 1 2x x+ − =
. 12 2x x+ + =
. 4 8 2x x− + − =
. 3 3x x− = −

57. 57
57.
( 32 243) ( 72 27)
( 12 3 8) ( 75 48)
− + +
+ − −
F ก F F
[Entrance ก . ʾ 2527]
ก.
2
( 3 2)
3
−
.
2 3
( 3 2)
3
−
.
2
( 2 6)
3
−
.
2
( 6 2)
3
−

58. 58
58. F F F
[Entrance ก . ʾ 2528]
ก. F x ˈ ก F F x F F 9x <
. F a ˈ F ˈ F F p q , 0p q ≠
p
a
q
=
. F a ˈ F ˈ ก F a F F
. F a ˈ F
n n
a a= 2,4,6,...n =

59. 59
59. ก
1 2 1
22
x
x
+
<
+
[Entrance ก . ʾ 2528]
ก. { }| 2x x > −
. { }| 0x x >
. { }| 0x x ≥
.
1
| 0
2
x x
 
− ≤ ≤ 
 

60. 60
60. ก
2 55
( 2) (2 3) 2 1 3x x x+ − + − + = F F
[Entrance ก . ʾ 2528]
ก. [ ]10,300−
. [ ]400,600
. [ ]64, 32− −
. [ ]250,350

61. 61
61. F F
(1) F F { | , , 0n
A x x a a R a= = ∈ > n ˈ } F A
ʽ ก
(2) F F { | ,A x x ab a= = ˈ ก b ˈ ก } F
A ˈ ก
(3) F F A ˈ ก * A *x y xy= −
,x y A∈ F A ก ก F F * ˈ -1
(4) F F A ˈ ก ก ∆ A
( )x y y x y∆ = − ,x y A∈ F ∆ ก
F F ก
[Entrance ก . ʾ 2529]
ก. F (1) F (3) ˈ
. F (1) F (4) ˈ
. F (2) F (4) ˈ
. F (2) F (3) ˈ

62. 62
62. F A ˈ ก
4 2
2 1x x
≥
− +
F F ก
[Entrance ก . ʾ 2529]
ก. A = ∅
. ( 2,10]A ⊂ −
. { 1, 2} (2, )A = − ∪ ∞
. F F ก

63. 63
63. F F ก
[Entrance ก . ʾ 2530]
ก. ก ก ก ก ก F F ก F F
. ก ก ก ก ก F ก ก F
. ก ,a b R∈ ก F * (2 )(2 )a b
a b = R ก F *
F ก ก F
. ก a ก b a b+ ˈ ก

64. 64
64. F A ˈ ก 4 3 1x x− + − = F A F ก F
[Entrance ก . ʾ 2530]
ก. {3, 4}
.
7 1
{ | }
2 2
x R x∈ − ≤
. ( , 4)−∞
. [3, )∞

65. 65
65. F A ˈ ก
2
3 5 2 0x x+ + <
B ˈ ก
2 1
0
3
x
x
+
≥
−
F ( ) 'A B∪ F
[Entrance ก . ʾ 2530]
ก. ∅
.
2
[ 1, )
3
− −
.
1
( ,3]
2
−
.
2 1
( , 1] [ , ) [3, )
3 2
−∞ − ∪ − − ∪ ∞

66. 66
66. F , ,x y z ˈ F F ก
[Entrance ก . ʾ 2530]
ก. F x y< F xz yz< xz yz>
. F 1 x y< ≤ n ˈ F ( 1) ( 1)n n
x y− ≤ −
.
2 2
2( ) ( )
2 ( ) 2
2
x y x y
xy x y xy
+ + −
≤ ≤ + −
. F 1 2x − < F
3
3
1 1
2 2
2 2
x
< < −

67. 67
67. ก F R ˈ
{ | 5 2}
{ | 2 5}
A x R x x
B x R x
= ∈ + − ≤
= ∈ − <
F F ก
[Entrance ก . ʾ 2531]
ก. { | 3 7}A B x R x∪ = ∈ − < <
.
1
{ | 3 }
16
A B x R x∩ = ∈ − < ≤
. { | 7}A B x R x− = ∈ >
.
1
{ | 3 }
16
B A x R x− = ∈ − < <

68. 68
68. F
2 2
{ | 2 6 11 2 3 5 25}S x U x x x x= ∈ − + + − + =
F ก ก S F F ก F F
[Entrance ก . ʾ 2531]
ก. 3
. 4
. 5
. 6

69. 69
69. ก F * 8, ,a b a b a b I= + − ∀ ∈ I =
F F F ก
[Entrance ก . ʾ 2531]
ก. (2 *3)* 4 2 *(3* 4)≠
. ก ก F “*” I 8
. F a “*” I a−
. “*” F ก

70. 70
70. , ,a b c F F F F
“ F a bc< F F a b< a c< ” F ˈ
[Entrance ก . ʾ 2532]
ก. 1, 4, 1a b c= = =
. 1, 2, 0a b c= − = − =
. 1, 1, 1a b c= = − = −
. 1, 1, 2a b c= − = − = −

71. 71
71. F F ก
[Entrance ก . ʾ 2532]
ก. ก 0a ≠ ก b ab ˈ ก
. F ,a b ˈ ก ก F
b
a ˈ ก
. ก ,a b a b≠ − a b+ ˈ ก
. F ,a b ˈ ก
1
b
a
≠ F ab ˈ ก

72. 72
72. ก F
1
{ | 0}
2
x
A x R
x
−
= ∈ ≤
−
{ |1 3}B x R x= ∈ ≤ ≤
R ˈ 'A B∪ F F
[Entrance ก . ʾ 2532]
ก. [ 3, 1] [1,3]− − ∪
. [ , 2] [2, ]−∞ − ∪ ∞
. [ 3,3]−
. ( , )−∞ ∞

73. 73
73. F ก F ( , )a b ( , )c d F ก F F F
[Entrance ก . ʾ 2533]
ก. F a c< b d< F c b<
. F a c< d b< F c b<
. F a c> b c< F d a<
. F a c> b d< F b c>

74. 74
74. ,A B
{( ) | , }A B a b a A b B+ = + ∈ ∈
F { | 2 1 3 2}A x x x= + − − =
1 1
2 4
{ | 6 0}B x x x= − − =
F A B+ F F
[Entrance ก . ʾ 2533]
ก. {97}
. {85,93}
. {20, 28}
. {20, 28,85,93}

75. 75
75. x ก F ก ก
2
22 4
2
3
x
x
−
≥ ˈ ก
F
[Entrance ก . ʾ 2533]
ก. [ 1,0.5)−
. [0.5,1)
. [1,1.5)
. [1.5, 2)

76. 76
76. F a ˈ F F
2
4 3x x a− + ≤ ก F x
4 11 5x − ≤ F a F ก ก F
[Entrance ก . ʾ 2533]
ก.
2
5 6 0x x− + =
.
2
2 3 0x x+ − =
.
2
3 2 0x x− + =
.
2
5 4 0x x+ + =

77. 77
77. ก F a b ˈ F F a x b< < F F F
[Entrance ก . ʾ 2534]
ก. 0x a+ >
. 0x b+ <
.
1 1
x b
<
.
1 1
x a
<

78. 78
78. x ˈ ก 15 22 2 105x− = − F
F ก F
[Entrance ก . ʾ 2534]

79. 79
79. F R ˈ
2
{ | 3 2 0}A x R x x= ∈ + − >
{ | 3 2 4}B x R x= ∈ − ≤
F F
1 2
(1) [ , )
2 3
1 2
(2) ' ( , ) ( , )
2 3
B A
A B
− = −
∪ = −∞ − ∪ ∞
F F
[Entrance ก . ʾ 2535]
ก. (1) ก (2) ก
. (1) ก (2)
. (1) (2) ก
. (1) (2)

80. 80
80. F F F ก
[Entrance ก . ʾ 2535]
ก.
1x
xy
y
−
= x y ˈ
. F xy zy> F x z> ,x y z ˈ
. F 0x > 0y > F
n n nx y xy= n ˈ ก
.
n n
x x= x ˈ n ˈ

81. 81
81. F R ˈ
3 2
{ | 6 9 1k R x x x k∈ − + + < ก [0,3]}x ∈ F F
[Entrance ก . ʾ 2535]
ก.
1
( , )
2
∞
. (1, )∞
.
31
( , )
8
∞
. (5, )∞

82. 82
82. ก ก ก
1 1
2
1 6
x x
x x
−
+ =
−
F F
[Entrance ก . ʾ 2535]

83. 83
83. F a b ˈ ก a b< 2 2
3( ) 10a b ab+ = F
3
a b
a b
+ 
 
− 
F F ก F
[Entrance ก . ʾ 2536]
ก. -2
. -4
. -6
. -8

84. 84
84. F p ˈ ก ,m n ˈ F 3x +
3 2
x mx nx p+ + + 1x − 3 2
x mx nx p+ + + 4
F m n F ก F
[Entrance ก . ʾ 2537]
ก. 4, 4m n= = −
. 2, 2m n= = −
. 4, 4m n= − =
. 2, 2m n= − =

85. 85
85. F , ,m x y z ˈ F F F F 0
x
z
y
> > F F F
ˈ
[Entrance ก . ʾ 2538]
ก.
1y
x z
<
. x yz>
.
my
mz
x
<
.
mx
mz
y
>

86. 86
86. ก F S ˈ ก
1
2
2
x
x
−
>
+
a ˈ F
F S F
2
1a + F ก F F
[Entrance ก . ʾ 2538]
ก. 2
. 5
. 10
. 26

87. 87
87. F a ˈ F x a− 3 2
2 5 2x x x+ − − 4 F
ก F a F ก ก F F ก F F
[Entrance ก . ʾ 2538]
ก. -6
. -2
. 2
. 6

88. 88
88. ก F ก F { |x x ˈ F F 0 100 100}x− ≤ ≤
F { |A x= . . . x ก 21 ˈ 3 } ก A F ก F F
[Entrance ก . ʾ 2538]
ก. 29
. 34
. 68
. 58

89. 89
89. F x y ˈ ก 80 200x< < x pq= p
q ˈ p q≠ F x y ˈ F . . .
x y F ก 15015 F ก F y F
ก F F ก F
[Entrance ก . ʾ 2538]

90. 90
90. ก F A ˈ ก
3
0
2
x
x
−
≥
+
B ˈ ก
1
1
2 2
x
− ≤
( ) 'A B− F ก F F
[Entrance ก . ʾ 2540]
ก. ( , 2) ( 1, )−∞ − ∪ − ∞
. ( , 2) [ 1, )−∞ − ∪ − ∞
. ( , 2] ( 1, )−∞ − ∪ − ∞
. ( , 2] [ 1, )−∞ − ∪ − ∞

91. 91
91. F 1 500 F 3 5 F ก F F
[Entrance ก . ʾ 2540]
ก. 167
. 200
. 233
. 266

92. 92
92. F n ˈ ก . . . n 42 F ก 6
F 0 0 042 ,0nq r r n= + < <
0 1 1 02 ,0n r r r r= + < <
0 12r r=
0 0 1, ,q r r ˈ F . . . n 42 F F ก F
[Entrance ก . ʾ 2540]

93. 93
93.
1
2
2
x
x
−
>
− F F F
[Entrance ก . ʾ 2541]
ก. ∅
. (2,3)
. ( 1,2) (2,7)− ∪
.
5
( ,2) (2,3)
3
∪

94. 94
94. F ,a b ˈ ก a b< , 5 a 3 b F
,a b ˈ F . . . ,a b F ก 165 F a b
F ก F F
[Entrance ก . ʾ 2541]
ก. 1
. 2
. 3
. 4

95. 95
95. ก 210 ก
[Entrance 1 , 2541]
ก. 14
. 15
. 16
. 17

96. 96
96. ก F A B ˈ ก
2
3
0
2
x
x
−
≥
+
2
2 2x− ≤
F ˈ B A−
[Entrance 1 , 2541]
ก. { 1.6,1,6}−
. { 1.7,1,7}−
. { 1.8,1,8}−
. { 1.8,1,7}−

97. 97
97. a b F ( , )a b = . . . a b F
{1,2,3,...,400}A = ก { | ( ,40) 5}x A x∈ = F F ก F
F
[Entrance 1 , 2542]
ก. 30
. 40
. 60
. 80

98. 98
98. F { | 2 4}A x x= − < 2 1
{ |15 8 1 0}B x x x− −
= − + > F
A B∩ F F
[Entrance 1 , 2542]
ก. ( 2,3) (5,6)− ∪
. (0,3) (5,6)∪
. (0,3) (3,5) (5,6)∪ ∪
. ( 2,0) (0,3) (5,6)− ∪ ∪

99. 99
99. F {0,1,2,...,7}S = *a b = กก ab F
6 ก ,a b S∈ F F
(1) *1x x= ก x S∈
(2) {4* | } {0,2,4}x x S∈ =
F F ˈ
[Entrance 1 , 2542]
ก. (1) (2) ก
. (1) ก F (2)
. (1) F (2) ก
. (1) (2)

100. 100
100. F , ,x y z ˈ ก F ก ก F ก F y ˈ
ก F F F 3 x y z+ + ˈ ก F y F F
[Entrance 1 , 2543]

101. 101
101. ก F 1x + 1x − ˈ ก
3 2
( ) 3p x x x ax b= + − + ,a b ˈ F F กก ( )p x
F x a b− − F ก F F
[Entrance 1 , 2544]
ก. 15
. 17
. 19
. 21

102. 102
102. ก F { | 1 2A x x= − <
1 1
}
1 2x
>
+
2
{ | 2 0}B x x x= + < A B∩ F F F
[Entrance 1 , 2544]
ก. ( 1,0)−
. [ 1,0)−
. (0,1)
. (0,1]

103. 103
103. ก F
3 2
( ) 2P x x ax bx= + + + a b ˈ F
1x − 3x + F ( )P x F 5 2a b+ F F ก F
[Entrance 1 , 2544]
ก. -11
. -1
. 1
. 9

104. 104
104. ก F A ˈ ก
2
12 0x x+ − <
B ˈ ก 3 1x− <
A B∩ ˈ F F
[Entrance 1 , 2545]
ก. ( 5, 3)− −
. ( 3, 1)− −
. (1,3)
. (3,5)

105. 105
105. F S ˈ ก
3 2
2
1
x
x
−
≥
−
F F
(1) ( 1,0] (1, )S = − ∪ ∞
(2) [ ( 2) ]x x S x S∃ ∈ ∧ + ∉
F F ก
[Entrance 1 , 2545]
ก. (1) ก (2) ก
. (1) ก (2)
. (1) (2) ก
. (1) (2)

106. 106
106. ก F A ˈ ก 1x x> −
B ˈ ก
5
0
( 1)( 3)
x
x x
−
≥
+ +
F A B− F ( , )a b F a b+ F F ก F
[Entrance 1 , 2546]

107. 107
107. ก F I
{ | 1 1 1 1 50}S x x x= − − − + <i
ก S I∩ F ก F F
[Entrance 1 , 2546]
ก. 13
. 14
. 15
. 16

108. 108
108. ก F
3 2
( ) 4f x x kx mx= + + + k m ˈ F F 2x −
ˈ ก ( )f x 1x + ( )f x F 3 F F
F k m+ F ก F
[Entrance 1 , 2546]

109. 109
109. F F
(1) F ,a b c ˈ | (2 )a b c− 2
| ( )a b c+ F | 3a c
(2) F
2
2 2
{ | 1}
2
x x
A x R
x
− +
= ∈ <
−
3 2
{ | 2 0}B x R x x= ∈ − <
F A B=
F F ก
[Entrance 1 , 2546]
ก. (1) ก (2) ก
. (1) ก (2)
. (1) (2) ก
. (1) (2)

110. 110
110. F S ˈ ก
3 2
0
1 1
x
x
−
≥
− −
{ | 0x x > }x S≠ ˈ F F
[Entrance 1- ʾ 2547]
ก. [0,1]
.
1 3
[ , ]
4 2
.
1
[ ,2]
2
.
3
[ ,3]
4

111. 111
111. F a b ˈ F
2
x ax b+ + 3 2
3 5 7x x x− + +
F ก 10 F F a b+ F ก F F
[Entrance 1- ʾ 2547]
ก. 1
. 2
. 3
. 4

112. 112
112. ก F m ˈ ก n ˈ F m 777
910 F n F m n− F ก F
[Entrance 1- ʾ 2547]

113. 113
113. F F F
[Entrance 1- ʾ 2547]
ก. F , ,a b n ˈ ก |n a |n b F F F n . . .
,a b F
. F , ,a b n ˈ ก |a n |b n F F F . . . ,a b
n F
. F , ,a m n ˈ ก |a mn F F F |a m |a n
. F d c ˈ . . . . . . ก ,m n F F F
dc mn=

114. 114
114. ˈ ก
2
6
5 1
x
x
−
− ≤ ≤ F ก F F
[Entrance 1- ʾ 2547]
ก. 8
. 9
. 10
. 11

115. 115
115. F a ˈ F ก b ˈ ก
F F ก
[A-net ก F ʾ 2549]
1. a b ˈ F
2. a b+ ˈ
3. . . . a b F ก . . . a 2b
4. . . . a b F ก . . . a 2b

116. 116
116. ก F I ˈ
F
2
{ | 2 9 26 0S x I x x= ∈ − − ≤ 1 2 3}x− ≥ F
ก ก S F ก F
[A-net ก F ʾ 2549]

117. 117
117. F x ˈ ก F 9,12 15 x
F 11 x 7 F x F F ก F
[A-net ก F ʾ 2549]

118. 118
118. ก F { | (2 1)( 1) 2}A x x x= + − <
2
{ |16 9 0}B x x= − >
A B∩ ˈ F F F
[A-net ก F ʾ 2550]
1.
2 7
( , )
3 3
−
2.
5
( 1, )
3
−
3.
4 5
( , )
3 4
−
4.
5
( ,1)
3
−

119. 119
119. ก F n ˈ ก F F F 7 F F ก 4
F 9 11 F ก ( 2)n − F n
[A-net ก F ʾ 2550]

120. 120
120. F ก
2
2 ( 2)x x x+ − < − F ( , )a b F a b+
F F ก F
[A-net ก F ʾ 2550]

121. 121
121. ก F A ˈ ก
2 2
2 4 3x x x x+ − ≤ − +
{1}B A= − F a ˈ ก B 0a b− ≥ ก b B∈ F
F F
ก.
4
3
a ˈ F
.
5
a
ˈ F
F F ก
[A-net ก F ʾ 2551]
1. ก. ก . ก
2. ก. ก .
3. ก. . ก
4. ก. .

122. 122
122. ก F n ˈ F ก F n 551 731
r F ก n 1093 2r + F
1r
n
−
F F ก F
F
[A-net ก F ʾ 2551]
1.
1
17
2.
1
18
3.
1
19
4.
1
20

123. 123
123. ก F
2
{ | 2 3 0}A x x x= + − < { | 1 2 }B x x x= + ≥
F ( , )A B a b− = F 3 a b+ F F
[A-net ก F ʾ 2551]

124. 124
124. F
3 2
( ) 10P x x ax bx= + + + ,a b ˈ
2
( ) 9Q x x= + F ( )Q x ( )P x 1 F ( ) ( )P a P b+ F F
[A-net ก F ʾ 2551]

125. 125
125. ก F
3
{ | 1}S x x= = F F F ก S
[PAT1 ʾ 2552]
1.
3
{ | 1}x x =
2.
2
{ | 1}x x =
3.
3
{ | 1}x x = −
4.
4
{ | }x x x=

126. 126
126. ก F S ˈ ก
3 2
2 7 7 2 0x x x− + − =
ก ก S F ก F F
[PAT1 ʾ 2552]
1. 2.1
2. 2.2
3. 3.3
4. 3.5

127. 127
127. ก F { | 1 3 }A x x x= − ≤ − a ˈ ก F ก A
F a F F F
[PAT1 ʾ 2552]
1. (0,0.5]
2. (0.5,1]
3. (1,1.5]
4. (1.5,2]

128. 128
128. ก F n ˈ r ˈ กก
2
n F 11
F F ˈ F r F F
[PAT1 ʾ 2552]
1. 1
2. 3
3. 5
4. 7

129. 129
129. ก F ( )P x ( )Q x ˈ ก 2551 F ก
( ) ( )P n Q n= 1,2,...,2551n = (2552) (2552) 1P Q= +
F (0) (0)P Q− F ก F F
[PAT1 ʾ 2552]
1. 0
2. 1
3. -1
4. F F F F

130. 130
130. ก F A ˈ ก
(2 1)( 1)
0
2
x x
x
+ −
≥
−
B ˈ ก
2
2 7 3 0x x− + <
F [ , )A B c d∩ = F 6c d− F ก F F
[PAT1 ก ก ʾ 2552]
1. 4
2. 5
3. 6
4. 7

131. 131
131. ก F
2 2
{ | ( 1)( 3) 15}A x x x= − − ≤
F a ˈ ก F F A b ˈ ก F ก A F
2
( )b a− F ก F F
[PAT1 ก ก ʾ 2552]
1. 24
2. 16
3. 8
4. 4

132. 132
132. ก F S ˈ ก
4 2
2
13 36
0
5 6
x x
x x
− +
≥
+ +
F a ˈ F F (2, )S ∩ ∞ b ˈ F ก
b S∉ F
2 2
a b− F ก F F
[PAT1 ก ก ʾ 2552]
1. -9
2. -5
3. 5
4. 9

133. 133
133. F F 100 999 F 2 F F 3 F
F ก F F
[PAT1 ก ก ʾ 2552]
1. 250
2. 283
3. 300
4. 303

134. 134
134. ก F A ˈ ก
3 2
27 27 0x x x+ − − =
B ˈ ก
3 2
(1 3) (36 3) 36 0x x x+ − − + − =
A B∩ ˈ F F F
[PAT1 ʾ 2552]
1. [ 3 5, 0.9]− −
2. [ 1.1,0]−
3. [0,3 5]
4. [1,5 3]

135. 135
135. ก F 2 2
2
{ | }
3 2 1
x x
S x
x x x
+
= ≥
− + −
F F F ˈ S
[PAT1 ʾ 2552]
1. ( , 3)−∞ −
2. ( 1,0.5)−
3. ( 0.5,2)−
4. (1, )∞

136. 136
136. ก F A ˈ F ก F
ก. 1 A∈
. F x A∈ F
1
A
x
∈
. x A∉ ก F 2x A∈
F F ˈ ก A
[PAT1 ʾ 2552]
1.
1
2
2.
1
8
3.
1
16
4.
1
32

137. 137
137. F a ˈ . . . 403 465 b ˈ . . . 431 465
F a b− F F
[PAT1 ʾ 2552]

138. 138
138. ก F
1 2 1
(0,1) ( ,2) ( ,3) ... ( , )
2 3
n
n
I n
n
−
= ∩ ∩ ∩ ∩ n
ˈ F n F F
2551 2553
( , ]
2554 2552
nI ⊆ F ก F F
[PAT1 ʾ 2552]
1. 2554
2. 2552
3. 1277
4. 1276

139. 139
139. ก F
2
{ | 6 9 4}A x R x x= ∈ − + ≤
R F F ก F
[PAT1 ʾ 2553]
1. ' { | 3 4}A x R x= ∈ − >
2. ' ( 1, )A ⊂ − ∞
3. { | 7}A x R x= ∈ ≤
4. { | 2 3 7}A x R x⊂ ∈ − <

140. 140
140. F N ก F
b
a b a∗ = ,a b N∈
F F , ,a b c N∈
ก. a b b a∗ = ∗
. ( ) ( )a b c a b c∗ ∗ = ∗ ∗
. ( ) ( ) ( )a b c a b a c∗ + = ∗ + ∗
. ( ) ( ) ( )a b c a c b c+ ∗ = ∗ + ∗
F F ก F
[PAT1 ʾ 2553]
1. ก 2 F . .
2. ก 2 F . .
3. ก 1 F .
4. ก. . . . ก F

141. 141
141. F { | 3 1 1 7 1}S x R x x x= ∈ + + − = +
R F ก ก S F ก F
[PAT1 ʾ 2553]

142. 142
142. F R
F
1 2
{ | 1}
3
x
A x R
x x
− −
= ∈ >
+ −
F [0,1)A ∩ F ก F F
[PAT1 ก ก ʾ 2553]
1.
1 2
{ | }
3 3
x x< <
2.
1
{ | 1}
3
x x< <
3.
2
{ | 1}
3
x x< <
4.
2 3
{ | }
3 2
x x< <

143. 143
143. F R
F { | 1 3 1 7 1}S x R x x x= ∈ + + − = −
{ | 3 1, }T y R y x x S= ∈ = + ∈
F ก ก T F ก F
[PAT1 ก ก ʾ 2553]

144. 144
144. a b ˈ ก
ก F a b⊗ ˈ F
(ก) 4a a a⊗ = +
( ) a b b a⊗ = ⊗
( )
( )a a b a b
a b b
⊗ + +
=
⊗
F (8 5) 100⊗ ⊗ F ก F
[PAT1 ก ก ʾ 2553]

145. 145
145. F N
ก F a b a b∗ = + ,a b N∈
F F
ก. ( ) ( )a b c a b c∗ ∗ = ∗ ∗ , ,a b c N∈
. ( ) ( ) ( )a b c a b a c∗ + = ∗ + ∗ , ,a b c N∈
F F ก F
[PAT1 ʾ 2553]
1. ก. ก . ก
2. ก. ก F .
3. ก. F . ก
4. ก. .

146. 146
146. F N
,a b N∈
,
,
,
a a b
a b a a b
b a b
>

⊗ = =
 <
,
,
,
b a b
a b a a b
a a b
>

∆ = =
 <
F F , ,a b c N∈
ก. a b b a⊗ = ⊗
. ( ) ( )a b c a b c⊗ ⊗ = ⊗ ⊗
. ( ) ( ) ( )a b c a b a c∆ ⊗ = ∆ ⊗ ∆
F F ก F
[PAT1 ʾ 2553]
1. ก 1 F F ก.
2. ก 2 F F ก. F .
3. ก 2 F F ก. F .
4. ก 3 F F ก. . .

147. 147
147. a b ˈ ก
a b∗ a kb= ก k
F ,x y z ˈ ก F F F ˈ
[PAT1 ʾ 2553]
1. F x y∗ y z∗ F ( )x y z+ ∗
2. F x y∗ x z∗ F ( )x yz∗
3. F x y∗ x z∗ F ( )x y z∗ +
4. F x y∗ F y x∗

148. 148
148. F R
F
2 2
{ | 2 2 9 2 3 15}A x R x x x x= ∈ − + − − + =
F ก ก ก A F ก F
[PAT1 ʾ 2553]

149. 149
149. ก F ,x y z ˈ ก F ก ก
1 1
2, 32, 81xyz x y
z x
= + = + =
1 p
z
y q
+ =
p q ˈ ก . . . p q F ก 1
F F p q− F ก F F
[PAT1 ʾ 2554]
1. 3,925
2. 4,832
3. 4,951
4. 5,182

150. 150
150. ก F I
F
4 2 2
5 2
2 75
( )
270
x x a x
f x
x b x
− + −
=
+ −
,a b I∈
F {( , ) | (30) 0}A a b I I f= ∈ × =
2 2
{( , ) | 2 3}B a b I I a ab b= ∈ × − + <
F ก A B∩ F ก F
[PAT1 ʾ 2554]

151. 151
151. F d ˈ ก กก F 1 3456, 2561 1308
F d F ก r F d r+ F ก F
[PAT1 ʾ 2554]

152. 152
152. ก F , ,a b c ˈ
2 2
x y ax by cxy∗ = + + ,x y
F 1 2 3, 2 3 4∗ = ∗ = 0d >
x d x∗ = ก x
F F 2 3 4a b c d+ + + F ก F
[PAT1 ʾ 2554]

153. 153
153. ก F ( 1)( 1) 1x y x y∗ = + + −
F F
[PAT1 ʾ 2554]
1. ( 1) ( 1) ( ) 1x x x x− ∗ + = ∗ −
2. ( 2) ( ) ( 2)x y x y x∗ + = ∗ + ∗
3. ( 2) ( ) 2x y x y∗ ∗ = ∗ ∗
4. ( ) ( 1)( )x x y x x y x∗ ∗ = + ∗ +

154. 154
154. F A F ก ก
3 1 2 2 3 1x x x− − > +
B ก
2
( 2)( 1) 0x x x+ + <
F F F ก F
[PAT1 ʾ 2555]
1. A B− ก 5
2. A B A∪ =
3. A B∩ ก 1
4. ( ) ( )A B B A B− ∪ − =

155. 155
155.
b
a b a∗ = a b ˈ ก
F ,a b c ˈ ก F F F ก F
[PAT1 ʾ 2555]
1. ( ) ( )a b c a c b∗ ∗ = ∗ ∗
2. ( ) ( )a b c a bc∗ ∗ = ∗
3. ( ) ( )a b c a b c∗ ∗ = ∗ ∗
4. ( ) ( ) ( )a b c a c b c+ ∗ = ∗ + ∗

156. 156
156. ก F 7 4 3 , 2 2 2 2...a b= + =
2 3c = + F F ก F
[PAT1 ʾ 2555]
1.
1 1 1
c a b
> >
2.
1 1 1
c b a
> >
3.
1 1 1
b a c
> >
4.
1 1 1
b c a
> >

157. 157
157. F a b ˈ F
5
4ax bx+ + F
2
( 1)x −
F a b− F ก F
[PAT1 ʾ 2555]

158. 158
158. F
5 4 3 2
( )f x x ax bx cx dx e= + + + + + , , , ,a b c d e
ˈ F ก ( )y f x= ก ก 3 2y x= + 1,0,1,2x = −
F F (3) ( 2)f f− − F ก F
[PAT1 ʾ 2555]

159. 159
159. F d ˈ ก กก F 1 1059 , 1417 2312
F d F F ก r F F d r+ F ก F
[PAT1 ʾ 2555]

160. 160
160. ก F ab ˈ ก , {1,2,...,9}a b∈
a F ก F b
F (310 ) (465 ) 2790ab ba× − × = F a b+ F ก F
[PAT1 ʾ 2555]

161. 161
161. ก S ˈ ( , , , , , )a b c d e f
, , , , , {0,1,2,...,9}a b c d e f ∈ F ก
3 2 2
4 , 2 7b
a c d− = − = 3 2
1e f− = −
ก S F ก F
[PAT1 ʾ 2555]

162. 162
162. ก F I
F { | 2 7 9}A x I x= ∈ + ≤ 2
{ | 1 1}B x I x x= ∈ − − >
F F
(ก) ก A B∩ F ก 7
( ) A B− ˈ F
F F ก F
[PAT1 ʾ 2555]
1. (ก) ก ( ) ก
2. (ก) ก F ( )
3. (ก) F ( ) ก
4. (ก) ( )

163. 163
163. F 0,1,2,3 4 4× F ( F 1 )
a b 2
3 0
c d 1
2 0 1 3
F F 0,1,2 3
F ก F 0,1,2 3
F F
(ก) F a c< F b d<
( ) F a b> F c d<
( ) F b d< F c d<
( ) a b c d+ = +
F F F ก F
[PAT1 ʾ 2555]
1. (ก)-( ) ก 1 F
2. (ก)-( ) ก 2 F
3. (ก)-( ) ก 3 F
4. (ก)-( ) ก ก F

164. 164
164. F A ˈ ก
3 2 2 3 1 3 10 6 3 1 14x x x x+ + + + + + + =
F B ˈ ก
ก ก A B∪ F ก F
[PAT1 ʾ 2555]

165. 165
165. ก F {1,2,3,..., }A k= k ˈ ก
F {( , ) | 0 7}B a b A A b a= ∈ × < − ≤
F k F ก F F ก B F ก 714
[PAT1 ʾ 2555]

166. 166
166. F x ก abc y ก cba
, , {1,2,3,...,9}a b c ∈ , ,a b c ก F ก
F S ˈ x x y− F ก F
ก ก S F ก F
[PAT1 ʾ 2555]

167. 167
167. ก F R F
{ | 2 5 7}A x R x x= ∈ − + ≤ 2
{ | 12 }B x R x x= ∈ < +
F F
(ก) { |1 4}A B x R x∩ ⊂ ∈ ≤ <
( ) A B− ˈ ก (finite set)
F F ก F
[PAT1 ʾ 2556]
1. (ก) ก ( ) ก
2. (ก) ก F ( )
3. (ก) F ( ) ก
4. (ก) ( )

168. 168
168. ก F
33 3
7 5 , 5 7 , 5 7A B C= = = 3
7 5D =
F F ก F
[PAT1 ʾ 2556]
1. D C A B> > >
2. A C B D> > >
3. A B D C> > >
4. C A D B> > >

169. 169
169. ก F , ,a b c d ˈ ก
2 , 5 , 6a b b c c d< < < 100d <
F a F ก F ก F
[PAT1 ʾ 2556]

170. 170
170. ก F , , {1,2,3,...,9}a b c ∈ 3 ก abc F ก
F ก ก abc ab ba ac ca bc cb= + + + + +
( abc 3 ก , , , , ,ab ba ac ca bc cb 2 ก)
[PAT1 ʾ 2556]

171. 171
171. x y ˈ ก ก F x y∗ ˈ ก
F
(1) ( ) ( )x xy x x y∗ = ∗
(2) (1 ) 1x x x∗ ∗ = ∗
(3) 1 1 1∗ =
F 2 (5 (5 6))∗ ∗ ∗ F ก F
[PAT1 ʾ 2556]

172. 172
172. F R F
2 2
{ | 3 4 3 2}A x R x x x x= ∈ + − + > +
F A ˈ F F
[PAT1 ʾ 2557]
1. ( ,2) (3,4)−∞ ∪
2. ( ,0) (3, )−∞ ∪ ∞
3. ( , 1) (4, )−∞ − ∪ ∞
4. ( 1, )− ∞

173. 173
173. ก F a b ˈ ก a b<
ก x a x b b a− − − = − F ก F F
[PAT1 ʾ 2557]
1. { }b
2. ( , ]a b
3. [ , )b ∞
4. ( , )
2
a b+
∞

174. 174
174. F , , , ,a b c d e ˈ ก 5 4 3 2a b c d e= = = =
2 3 4 5a b c d e+ + + + ˈ ก F F F
4 3 4a b c d e+ + + + F ก F F
[PAT1 ʾ 2557]
1. 52
2. 120
3. 262
4. 312

175. 175
175. F ʽ F ˈ 10 ก ABCDEFGHIJ
(ก) , , , , , , , , , {0,1, 2,...,9}A B C D E F G H I J ∈
, , , , , , , , ,A B C D E F G H I J ˈ ก F ก
( ) , , ,A B C D ˈ ก A B C D> > >
( ) , ,E F G ˈ F ก E F G> >
( ) H I J> > 15H I J+ + =
F C F I+ + F ก F F
[PAT1 ʾ 2557]
1. 10
2. 13
3. 15
4. 17

176. 176
176. F x ˈ ก ˈ ก
2 2
14 3 9 5 1x x x x+ − − + − = F F
1 2
2 1
4 12 9
3 2
x x
x x
− −
− −
− +
−
F ก F
[PAT1 ʾ 2557]

177. 177
177. F A ก 2 2 2 4x x x− + + = − F
A ˈ F F
[PAT1 ʾ 2557]
1. ( 4,0)−
2. ( 1,1)−
3. (0, 4)
4. ( 3, 2)−

178. 178
178. F A x F ก ก
2 2
4 3
1
4 8 7 4 10 7
x x
x x x x
+ =
− + − +
F B x F ก ก
2 2
2 4x x x− + >
F F
(ก) A B⊂
( ) ก F A B∩ F ก 2
F F ก F
[PAT1 ʾ 2557]
1. (ก) ก ( ) ก
2. (ก) ก F ( )
3. (ก) F ( ) ก
4. (ก) ( )

179. 179
179. ก F ,a b c ˈ ก a b< F F
(ก)
2 3 4 2 3
3 2 3 3 2
a b c a b
a b c a b
+ + +
>
+ + +
( )
3 2 3 2
2 3 2 3
a b c a b
a b c a b
+ + +
>
+ + +
F F ก F
[PAT1 ʾ 2557]
1. (ก) ก ( ) ก
2. (ก) ก F ( )
3. (ก) F ( ) ก
4. (ก) ( )

180. 180
180. F ก ก ก ABCDEF
, , , , , {0,1, 2,...,9}A B C D E F ∈
14A B+ = 0C D D E E F− > − > − >
F F ก
[PAT1 ʾ 2557]

181. 181
181. F A 2 2 2 2
a b c d+ + +
, , ,a b c d ˈ ก
(ก) a b d= +
( ) ( ) ( )a b c d b a c d+ + + = −
( ) 2 ( 1)cd a c+ = −
F M F ก A m F F A F F M m−
F ก F
[PAT1 ʾ 2557]

182. 182
182. F a b ˈ ก
aRb a F b
F F
(ก) F xRy yRz F ( )xR y z+ ก ก ,x y
z
( ) F wRx yRz F ( ) ( )wy R xz ก ก
, ,w x y z
F F ก F
[PAT1 ก ʾ 2557]
1. (ก) ก ( ) ก
2. (ก) ก F ( )
3. (ก) F ( ) ก
4. (ก) ( )

183. 183
183. F , , ,a b c d x ˈ ก
F F
(ก) F
a c
b d
< F
a x c x
b d
+ +
<
( )
a a x
b b x
+
<
+
F F ก F
[PAT1 ก ʾ 2557]
1. (ก) ก ( ) ก
2. (ก) ก F ( )
3. (ก) F ( ) ก
4. (ก) ( )

184. 184
184. ก F , ,A B C D ˈ ก F ก
,B C D D A C B= + = + − 2A C B= −
F F ก F
[PAT1 ก ʾ 2557]
1. D A C B< < <
2. A D C B< < <
3. D C A B< < <
4. C A D B< < <

185. 185
185. F S ก
2
3 2 6 2 4 4 10 3x x x x+ − − + − = −
F ก ก S F ก
a
b
. . . a b F ก 1
F a b+ F ก F
[PAT1 ก ʾ 2557]