3. 2555 ( 7 55) . Sila Sookrasamee 1 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ x 3 7 3 2 0 , 3 7 0 2 3 x x x x = = = = 3 1. 3 : | 3 2 | | 3 7 |
0 3 2 (3 7) 0 4 2 x x x x x x< + 2. 3 7 7 : | 3 2 | | 3 7 | 0 (3
2 ) (3 7) 0 2 2 2 3 3 x x x x x x x < + < 3. 7 7 : | 3 2 | |
3 7 | 0 2 3 (3 7) 0 4 4 3 3 x x x x x x x 2. 3. x union [2,4] [ , ]
[2,4] 2 4 6a b a b= + = + = 6 ... 2 n 720 = 10800 4 3 2 1080 8 1350
8 25 54 8 25 2 27 2 3 5= = = = 2 4 4 2 720 9 80 9 16 5 3 2 5 2 3 5=
= = = 3 2 2 3 5 3 15 3 225 675n = = = = 675 ( ) 2 22 2 1 2 1 22
2tan 2 2 2 2 sec (2tan 2) 1 tan (2tan 2) 1 1 1 1 8 9 1 tan 1 21 2 =
+ = + = + = + = + = 9
4. 2555 ( 7 55) . Sila Sookrasamee 2 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ = 4 3 = 8 2 3 dy x dx = 2 4 8 8 73 3 2 (2) 2 (2) 1 2 3 3 x y + =
= = + = (2,1) 2 2 2 2 8 3 10| | | 4(2) 3(1) 10 | 3 54 3 ax by c d a
b ++ + + = = = = + + 3 2 2 2 2 1 3 2 2 3 3 4 3 3 3 4 3 3 3 4 3 3 9
0 (3 3 3)(3 3) 0 3 3,3 3 3 ,3 x x x x x x x x x + = + = + = = = = 1
3 , 2 2 x = 1 3 2 2 2 + = 33log 2 log 23 31 33 3log 2 log 2 log( 27
10 27 3 3 2 8 2) 1 log10x x x x x x x+ = + = + = + = + = + == =
2
5. 2555 ( 7 55) . Sila Sookrasamee 3 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ r+1 = ( ) ( ) ( ) ( ) 10 10 10 1 10 2 2 2 2 3 3 3 10 2 20 5 4 3
102 2 2 10 .. 10 10 102 10 9 8 7 2 20 5 0 4 2 16 3360 4 24 r r r r
r r x x x x rx x x x x r r r rx + = + + + = = = = = 5 0 x 3360 3360
5 x % 86% 4 2 % 540 344 90% 90 6 540 344 2 98% 4 2 2 x x x + = = =
+ = = + 98% = 4 3 = 8 2 3 dy x dx = 2 4 8 8 73 3 2 (2) 2 (2) 1 2 3
3 x y + = = = + = (2,1) 2 2 2 2 8 3 10| | | 4(2) 3(1) 10 | 3 54 3
ax by c d a b ++ + + = = = = + + 3 2 2 2 2 3 2 00 0 6 | 2 | (12 6 )
6 2 | 6(4) 2(8) 8x x dx x x dx x x = = = =
6. 2555 ( 7 55) . Sila Sookrasamee 4 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ ( ) 3 2 3 2 3 2 3 2 ( ) 1 ( 1)( 2)( 3) ( 6 11 6) ( ) ( 6 11 6) 1
1 (4) 0 4 6 4 11 4 6 1 (64 96 44 6) 1 6 1 6 1 1 24 ( ) ( 6 11 6) 1
(5) (125 150 55 6) 1 1 3 6 6 6 p x A x x x A x x x p x A x x x p A
A A A p x x x x p = = + = + + = = + + = + + = + = = + + = + + = + =
1 2 3 1 3 1 2 4 2 2 z z i + = + = Im( ) 0Z > 3 1 5 1 2 2 6 z i =
+ = 8 40 2 1 3 1 1 6 6 3 2 2 z i = = + = + 5.
7. 2555 ( 7 55) . Sila Sookrasamee 5 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 5 ... 2 a,b 5 , 5a k b l= = 1575 25 25 25 125 125 63 5 5 ( 5)( 5)
25ab a b kl k l kl k l k l= = = = ( 5)( 5) 63 25 88 11 8 16, 13 80,
65k l k l a b = + = = = = = = 25 25 80 65 25 80 25 65 1575ab a b ok
= = 80 65 15a b = = 1 23 4 | | | || | sin 1 5sin 5sin 3 sin cos 1
sin 5 5 u v u v = = = = = = = cos
8. 2555 ( 7 55) . Sila Sookrasamee 6 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 2 2 2 24 (2 ) ( ) 2 . . . 2 | | | || | cos | | 2(1) 1(5) 5 2 4 25
19 5 u v u v u v u v v v u u v v + = = = = + = 2 2 2 2 2 2 2 2 2 2
2 9 72 16 32 16 9( 8 16) 16( 2 1) 16 9 16 16 1 16 144 16 ( 4) ( 1)
9( 4) 16( 1) 144 1 4 3 x x y y x x y y x y x y = + + + = + = + + +
= = H=Hyperbola (4,-1) X a=4, b=3 2 2 2 2 4 3 5c a b= + = + = E H
5a = (4,-1) E: 2 2 2 2 2 2 2 2 ( 4) ( 1) ( 4) ( 1) 1 5 x y x y a b
b + + + = + = E 2 2 2 2 2 2 2 2 1 1 5 1 4 5 5 55 c a b a b b e e a
a a a = = = = = = = 2 2 24 4 5 20 5 5 b a= = = E: 2 2 ( 4) ( 1) 1
25 20 x y + + = 3
9. 2555 ( 7 55) . Sila Sookrasamee 7 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 2 2 2 2 2 2 2 cos2 3cos2 (2cos 1) 3(2cos 1) (4cos 1) 6cos 3)
10cos 4 1 2 10cos 2 0 cos cos 2 cos 55 cos cos[180 ( )] cos( ) cos
cos sin sin A B A B B B B B B A B C A B A B A B A B = + = + = + = =
= = = = + = + = + 2 1 5 2 5 1 2 2 3 5 5 5 5 55 = + = + 3
10. 2555 ( 7 55) . Sila Sookrasamee 8 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 2 1 2 24 2 2 4 (4 4 4 ) (4 8 2 ) 12 6 2 1 2 1 1 1 3 2 2 2 1 2 | |
1 1 1 ( 4 3 4) ( 6 4 2) 3 3 2 2 2 4c a b a b c b c a b c x a AX B y
b z A b c c = = + + = + == = = = + + + = + + = x column A 1 2 1 1 2
2 2 4 ( 2 2 2 ) 6 3 | | 4 3 3 2 a b c a c b c a b c b b c x A + + +
+ = = += = 5
11. 2555 ( 7 55) . Sila Sookrasamee 9 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 1 1 1 0 0 1 0 1 0 | | | | | | 0 0 1 AX B AX I A X A X X = = = = =
= 1 1 1 1 1 1 0 2 3 2 15 0 ( 10 15 0) 8 | | | | | | 8 5 5 1 X A X X
= = + + + + = = = = 2 2 2 1 1 1 1 11 2 4 2 2 22 1 1 1 1 1 1 2 2 2 2
2 log ( 1) 2log ( 2) log (9 3) log ( 1) log ( 2) log (9 3) ( 1)( 2)
1 log ( 1) log ( 2) log (9 3) log 0 log 9 3 2 x x x x x x x x x x x
x + + + = + + + + + = + + + = = ( 1)( 2) 1 9 3 x x x + + 2 2( 1)(
2) 1 3 2 9 3 6 5 ( 1)( 5) 0 9 3 x x x x x x x x x x + + + + + = 1 (
,1] [5, )S = log y 0y > 1 0, 2 0, 9 3 0x x x+ > + > > 1
3 x > 1 1 ( ,1] [5, ) 3 S= 1 2 {1,5,6,7,8,9,10}S S = 7 3
13. 2555 ( 7 55) . Sila Sookrasamee 11 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 1. 1 1 1 1 ( 3) ( 3) n n i i i i X X X X n n= = = + += 2. = _ max
_ min max min max min max min _ max _ min max min max min max min (
3) ( 3) ( 3) ( 3) 6 new new new new X X X X X X X X X X X X X X X X
+ + = = < + + + + + + + 3. 1 1 1 1 ( 3) 3 3 n n new i i i i X X
X X n n= = = + = + = + 4. 5. 2 2 2 2 1 1 1 1 [( 3) ( 3)] ( ) n n
new i i i i S X X X X S n n= = + += = S 2.
14. 2555 ( 7 55) . Sila Sookrasamee 12 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 117.8 0.44 (1) 126.7 1.34 (2) 126.7 117.8 1.78 (2) (1) 8.9 (2) 5
126.7 1.34 5 120 1.78 X S X S S S X = = = = = = = 125 125 125 120 1
5 X S = = =Z 0.3413 0.5 0.3413 0.8413 84.13%+ = = 1
15. 2555 ( 7 55) . Sila Sookrasamee 13 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ Y 2 2 2 ( ) 4 ( ) ( 3) 4 ( 9)x h p y k x p y = = = (1,5) 2 1 (1
3) 4 (5 9) 4 4 ( 4) 4 p p p = = = = 2 ( 3) ( 9)x y = 2 6y x x= + 0y
= 0,6x = x 6 6 2 3 2 6 3 2 00 0 1 1 ( 6 ) 3 | 6 3(6 ) 36 3 3 ydx x
x dx x x= + = + = + = 4.
16. 2555 ( 7 55) . Sila Sookrasamee 14 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 2 2 ( ) 2 ( ( ) ( ) (2) 2 2 (2) 2 (2) 4 ( 1) 4 (0) 4 d d f x cx g
x cx g x dx dx d d f c g c g c c c dx dx = + = + = + = C ( )f x x=1
2 ( ) 2 ( ( ) ( ) d d f x cx g x cx g x dx dx = + 2 (2) 2 2 (2) 2
(2) 4 ( 1) 4 (0) 4 d d f c g c g c c c dx dx = + = + = 2 12 (1) (
(1) 1) (1) 2(1) 10 ( 1)4 12 1 2 4 f c g c c= + = + = + = = = (2) 4
4(2) 8 d f c dx = = = 1 40 1 (1 3 5 .. 39) 2(2 4 6 .. 40)n n a = =
+ + + + + + + + + 1 39 2 40 20 2 20 2 2 + + = + = x 20 20 40 21 400
840 1240= + = + = 4
17. 2555 ( 7 55) . Sila Sookrasamee 15 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 2 2 2 2 2 2 2 2 2 3 5 7 [(2 ) ( 1)][(3 ) ( 1)][(5 ) ( 1)][(7 ) (
1)] A I A I A I A I a a a a a a a a = + + + + 1 2 4 6 48= = 5 1 1 1
2 2 2 2 2 1 1 1 2 2 2 2 3 2 2 2 1 1 2, 1 2 2 1 3 3 3 3 ( 3) 3 2 4 2
3 1 1 2 2 4 4(2 3) 2 3 ... 2 4(2 3) 2 1 1 1 4 33 2 3 1 2 n i i a a
b a c a b a c a b r r a a r r r = = = = = = = = = = = = = + = + + +
= = = = = = = + 2
18. 2555 ( 7 55) . Sila Sookrasamee 16 18 Boonchuay
Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath
/ 2 2 2 2 2 2 2 2 ( ), '( ) 1. ( 1), 2 1 ( 1), 2 1 1 1 2. , , ( 1)
( 1) ( 1) ( 1) 3. ( 1), 2 1 ( 1), 2 1 4. ( 1) ( ), ' , 3 2 ( 1), (
) '(0 ) ' 3 2 1 1 1 0 0 (0 ) 1 1 1 0 0 5. , 2 , 2 x x oo f x f x x
x x x x x x x x x x x x x x x f x f x f x x x x x x x x x x x f x x
x = + = + = + += + = = = + + + + + += + = + += + = = = = '(0 )f +
'(0 )f 3 1 -1 0x = 3