เฉลยข้อสอบ PAT 1 2558 ชุดที่ 1
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Transcript of เฉลยข้อสอบ PAT 1 2558 ชุดที่ 1
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- 1 - PAT 1 2558 www.focus-physics.com
PAT 1 (.. 58)
71 (PAT 1)
1 1 30 6
1. [ / PAT1 .. 2558 ]
R {x R |1 x 2}
P(x) 23x 4x 4 0 Q(x) 2 2x | x 4 |
() x[P(x)] x[P(x) Q(x)]
() x[Q(x)] x[P(x)]
1. () () 2. () ()
3. () () 4. () ()
2. [ / PAT1 .. 2558 ]
p,q r
() p (q r)
(p q) (p r)
() p (q r)
[( p q) r] (p r)
1. () () 2. () ()
3. () () 4. () ()
3. [ / PAT1 .. 2558 ]
A x 2x 6 x x 1 x 3
A
1. ( 1,2) 2. (0,3) 3. (1,4) 4. (2,5)
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- 2 - PAT 1 2558 www.focus-physics.com
4. [ / PAT1 .. 2558 ]
R S S
2 2f {(x, y) R R | y |1 x | y 4} 4g {(x, y) R R | y 1 x }
A f B g
() A B () (A B) (B A)
1. () () 2. () ()
3. () () 4. () ()
5. [ / PAT1 .. 2558 ]
a 0 a 1 a | x | 1 1x
1. 1( , )a
2. 1( 1, )1 a
3. 1(1, )a
4. 1( , )1 a
6. [ / PAT1 .. 2558 ]
a, b c a b c 0
a o135 b
b o105 c
c o120 a
a 5 b c
1. 10 2 61 3
2. 10 3 6
1 3
3. 10 4 6
1 3
4. 10 5 6
1 3
7. [ / PAT1 .. 2558 ]
A 2 2m nlog 4x 4x 1 log (6x 11x 4) 4
m 3x 4 n 2x 1 2B {8x | x A}
B
8. [ / PAT1 .. 2558 ]
na nb 1 2 n1 2 b
a a ... a n 1
b b ... b 2n 1
n 1,2,3,... 100100
2b
a
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- 3 - PAT 1 2558 www.focus-physics.com
9. [ / PAT1 .. 2558 ]
S 2x 3 3x 2 x 3 2 x 1 2 2 x
a b S 25b 58a
1. 2 {x R |1 x 2}
P x : 23x 4x 4 0
3x 2 x 2 0
22
3
2
( , 2)3
2
(1, 2) ( , 2)3
x P x
Q x : 2 2x x 4
2 2
2 2x x 4
2 2
2 2x x 4 0
2 2 2 2x x 4 x x 4 0
22x 4 4 0
24 2 x 2 0
8 x 2 x 2 0
2 2
, 2 2,
1, 2 , 2 2,
2 1 22
x Q x
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- 4 - PAT 1 2558 www.focus-physics.com
.
P x x P x Q x
T T T
T T T
. .
x Q x P x
T T T .
2. 1 . p q r p q p r
p q r p q p r
p q p r T T T . . p (q r) p q r
p q r p r T q r T r
F q r T
T T T
.
3. 2
2x 6 x x 1 x 3
2x 6 x x 1
26 x x 1 x 3
2x 1 6 x x
26 x x x 2
2 2x 2x 1 6 x x
2 26 x x x 4x 4
2 2x 2x 1 6 x x
2 26 x x x 4x 4
22x 3x 5 0
20 2x 3x 2 2x 5 x 1 0 2x 1 x 2 0
1 5
2
2 1
2
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- 5 - PAT 1 2558 www.focus-physics.com
26 x x 0
26 x x 0
2 x 3 x 0
x 2 x 3 0
2 3
2 1 1
2
5
2
3
2x 6 x x 1 x 3 1 5( , )2 2
0, 3
4. 3
A 2 2f x, y R R y 1 x y 4 2 2y 1 x y 4
2
2
4 y1 x
y
1 x 0 2
2
4 y0
y
2
2
y 40
y
2
y 2 y 20
y
2 0 0 2
fA R 2,2 0
B 4g x x, y R R y 1 x 41 x 0
21 x 21 x 0
21 x 0
1 x 1 x 0
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- 6 - PAT 1 2558 www.focus-physics.com
x 1 x 1 0
1 1
gB D 1,1
. B , 1 1, 1 A 1 B A B .
. A B A B B A . 5. 4
2
0
x 0x 0
ax 11
x
ax 11 0
x
ax x 10
x
1
,0 ,a 1
ax 11
x
ax 11 0
x
ax x 10
x
a 1 x 10
x
1
a 10
1
a 1
0
10,a 1
1
2
3
1x 0 0,
a 1
1
,a 1
1
,0 , x 0a 1
1
,a 1
1 1, ,
a 1 1 a
a 1 x 10
x
4
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- 7 - PAT 1 2558 www.focus-physics.com
6. 4
v
u
v
u
v
u
u
v 180u v
u
v
u
v
v
a o135 b
b o105 c
c o120 a
c
ab
120105
135
75 60
45
a b c 0 () ABC
sin e sin 75 sin 60 sin 45a b c
a 5
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- 8 - PAT 1 2558 www.focus-physics.com
sin60 sin60b a 5
sin75 sin75
sin 45 sin 45c a 5
sin75 sin75
75
15
3 1
3 1
2 2
sin60 sin 45b c 5 5sin75 sin75
sin 60 sin 455
sin75 sin75
sin 60 sin 455sin75
3 / 2 2 / 2
53 1 2 2
3 / 2 / 2
5 23 1 / 2
3 25 23 1
10 5 63 1
7. 4.5
2 2
m nlog 4x 4x 1 log (6x 11x 4) 4
2
m nlog 2x 1 log 3x 4 2x 1 4
1
2
2
2x 13x 4
log 2x 1 log 3x 4 2x 1 4
2
2
2x 1 2x 13x 4log 2x 1 log 3x 4 log 2x 1 4
2
2x 13x 4log 2x 1 log 3x 4 1 4
2x 13x 42log 2x 1 log 3x 4 3
3x 4log 2x 1 A
1
2A 3A
22A 3A 1 0
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- 9 - PAT 1 2558 www.focus-physics.com
2A 1 A 1 0
1
A ,12
3x 41
log 2x 12
3x 4log 2x 1 1
1
22x 1 3x 4 1
2x 1 3x 4
24x 4x 1 3x 4 x 3 log 24x x 3 0
4x 3 x 1 0
3
x , 14
x 1 log
3
A4
2B {8x | x A}
23 9
B 8( ) 8 4.54 16
B 4.5 8. 3.97 n 199 100
1 2 3 4 5 3a a a a a 5 a ( n 5 )
1 3 5 7 9 5 5 25
3 41 2 3 4 5 6a a
a a a a a a 62
( n 6 )
5 71 3 5 7 9 11 6 362
1 2 n1 2 b
a a ... a n 1
b b ... b 2n 1
1 2 3 199
1 2 3 199
a a a ... a 199 1
b b b ... b 2 199 1
1 2 3 199
1 2 3 199
a a a ... a 199 1
b b b ... b 2 199 1
100100
199a 200
199b 397
100100
a 200
b 397 100
100
2b 397 3972 3.97
a 200 100
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- 10 - PAT 1 2558 www.focus-physics.com
9. 112
2x 3 3x 2 x 3 2 x 1 2 2 x
2x 3 3 3x 2 x 2 x 1 2 2 x 0 ------
x 1 a , 2 x b
23x 2 x x 1 2 x ab
2 23 x x 1 2 2 x a 2b
2x 3 3x 2 x 3 2 x 1 2 2 x
23 x 3 3x 2 x 2 x 1 2 2 x 0
2 2a 2b 3ab 2a 2b 0
2 2a 2b 3ab 2a 2b 0
a 2b a b 2 a b 0
a 2b 2 a b 0
a b 0, a 2b 2 0 a b 0
x 1 2 x
2 2
x 1 2 x
x 1 2 x
3x
2
3
x2
x 1 2 x
a 2b 2 0
x 1 2 2 x 2 0
x 1 2 2 2 x
2 2
x 1 2 2 2 x
x 1 4 x 1 4 4 2 x
5x 5 4 x 1 0
5 x 1 4 x 1 0
2
5 x 1 4 x 1 0
x 1 5 x 1 4 0 5 x 1 4 0
x 1 0
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- 11 - PAT 1 2558 www.focus-physics.com
x 1
x 1 x 1 2 2 2 x
3
S , 12
3a , b 1
2
3
25b 58a 25 1 58( ) 1122
