สอบ 7 วิชา

1. 1 Bio 7 55 By Prachatip Phollarp Note: 1. 4 2. 3 3. 4 4. 4 5. 1 6. 3 7. 5 8. 5 9. 4 10. 2 11. 3 12. 1 13. 3 14. 1 15. 3 16. 4 17. 4 18. 5 19. 2 20. 5 21. 2 22. 1 23. 5 24. 5 25. 4 26. 3 27. 5 28. 2 29. 1 30. 1 31. 4 32. 5 33. 3 34. 4 35. 4 36. 3 37. 1 38. 4 39. 4 40. 2 41. 1 42. 3 43. 2 44. 4 45. 5 46. 4 47. 2 48. 1 49. 3 50. 1 51. 2 52. 1 53. 3 54. 2 55. 2 56. 5 57. 2 58. 1 59. 4 60. 3 61. 1 62. 4 63. 2 64. 3 65. 3 66. 2 67. 3 68. 1 69. 3 70. 5 71. 3 72. 2 73. 2 74. 4 75. 3 76. 3 77. 1 78. 5 79. 3 80. 5 81. 4 82. 3 83. 2 84. 2 85. 5 86. 2 87. 2 88. 2 89. 3 90. 5 91. 2 92. 2 93. 3 94. 4 95. 4 96. 3 97. 4 98. 2 99. 2 100. 3

2. 7 ( 2554 : 2555)

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

12. 2555 ( 7 55) . Sila Sookrasamee 10 18 Boonchuay Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath / 7 6 7 2 6 5,6 7 6 7 1 2 5 4,5,6 7 5 - 7 2 2 4 3,4,5,6 7 4 - 7 3 2 3 2,3,4,5,6 7 3 - 7 4 2 2 1,2,3,4,5,6 7 2 - 7 5 2 1 1,2,3,4,5,6 7 1 - 7 6 1 7 6 2 1 64= = 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

19. 2555 ( 7 55) . Sila Sookrasamee 17 18 Boonchuay Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath / 7 1 3 4 1 7= + = ( 7 2,4,6,1,3,5,7 2,4,6,7,15,31 ) 10 3, 5,7,.. 7 10 8 87+ = 1 8 2 17+ = 3 4 17 71= + = 2, 4 87 2 89+ = 87 4 91+ = 88,89 ,88,89,90 91 88, 3+4x89, 90, 3+4x91 17(71) 17(71) 70,17,72,74 85,89, 91 70 70,72, 74 1 2 91, ,..,a a a 74a 4

20. 2555 ( 7 55) . Sila Sookrasamee 18 18 Boonchuay Pataralertsiri ( , ,) http://www.facebook.com/groups/HighSchoolMath / 4 a,b,c,d 3 =3x3x3x3 = 81 0M ad bc= = 3 1,0,1ad bc= = 1ad bc= = -1,1 1,-1 2 2 2 4= = 0ad bc= = 0,0 0,-1 0,1 -1,0 1,0 5 5 5 25 = 1ad bc= = 1,1 -1,-1 2 2 2 4= = 3 0M ad bc= = 4 25 4 33+ + = 0M ad bc= 81 33 48 = M inverse 0M ad bc= 48 81 4.

21. 7 ( 2554 : 2555)

22. http://www.facebook.com/groups/HighSchoolMath/ 7 1 5 2 1 3 1 4 1 5 4 6 3 7 5 8 2 9 3 10 4 11 5 12 5 13 5 14 1 15 4 16 1 17 1 18 4 19 5 20 5 21 4 22 4 23 3 24 2 25 2 26 2 27 3 28 1 29 3 30 3 31 3,5 32 4 33 4 34 3 35 2 36 4 37 1 38 4 39 2 40 1 41 2 42 1 43 3 44 2 45 5 46 3 47 1 48 2 49 3 50 5

23. 7 ( 2554 : 2555)

สอบ 7 วิชา

Documents