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ตัวอย่างข้อสอบ Las 8คณิตศาสตร์ม.4

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Text of ตัวอย่างข้อสอบ Las 8คณิตศาสตร์ม.4

  • 1. LAS 4

2. ~2~ 80 1. .A = 1, 2, 3, ... , 100 .B = 0, - 1, - 2, .... C =x | x Q. D ={ x|x R x > 0 }2. . 1 1,2,3 . 2 123 ,, . 3 1,2,3 . 0 3. A = 1,2,3 A . 1, 2,3 . 2,3,1 . 3, 1,2 . 1,3,24. . A A = . A 24 . . 3. ~3~5. 1) 0 2) 3) 4) . 1 4 4 . 1 4 3 . 1 4 2 . 1 4 1 6. A = { 2, 4, 6, 8, 10 } P(A) . 5. 10 . 16. 327. A = {1 , 2 , 3 , 4 , ...} B = {{1},{2}, 5, 6 , 7 , 8 , ...} A B . 2 . 4 . 5 . 68. A B 4. ~4~(1) (A B) A(2) (A B) B = (3) A= A(4) A (AB) = A B. (1) (4) 4 . (1) (4) 3 . (1) (4) 2 . (1) (4) 3 9. U = {1,2,3,4,5,6} , A = {1,2,3,4} , B = {2,3,4} C= {1,2}. A B C = {1,2,3,4}. C = {2,3,4,5}.A B C 2.B-A=10. A - B = 1,2,4, B - A = 3,5 AB= 1,2,3,4,5,6,7 AB . 0,1,4,6,7. 0,1,3,5,7. 1,2,3,4,7. 1,2,4,5,6 5. ~5~11. AB = 2, 3 BC = 4 AC = AB = 2 34 5 8AC = 1, 2, 3, 4, 5, 9 5 B C . 9. 1 4 9. 1 2 3 4. 3 4 5 8 912. .AB/. B A. A/B. (AB) A13. . AB A . B A AB .A B A. BAB A B 6. ~6~14. C BA U. (A B) C. A (B C). A B C . (A B) (A C)15. 4 8 3 2 . 6 . 8 . 9 . 11 7. ~7~16. 25 5 7 4 . 4 . 9 . 13 . 15 17.. 4 300 150 200 110 . 40. 60. 90. 13018. 4 150 70 50 8. ~8~ 20 . 10 . 20 . 30 . 4019. 65 37 31 42 . 12 . 14 . 15 . 19 20. 3 35 24 9. ~9~ 26 32 8 7 9 . 17 . 19 . 21 . 24 21. A , B C AB, AC, BC , ABC ABC 8, 9, 10, 3 45 A (BC) , B (AC) C (AB) . 24 . 23 . 22 . 2122. 5 2 4 8y 32 3 , 9 , x , 81 , 243 x + y . 16. 27. 34. 43 10. ~ 10 ~ 23. 1 + 3 + 5 + ... + 199 . 7,500 . 9,950 . 10,000 . 20,50024. (1) 1. 2. 5 5 (2) 1. 2. . (1) (2). (1) . (2) . (1) (2)25. 11. ~ 11 ~ 1. 2. . . . . 26. . 1. 2. . 1. 2. . 1. 2. . 1. 2. 27. 12. ~ 12 ~. . . . 28. 1. 2. . . .. 29. 13. ~ 13 ~. 1. 2. . 1. 2. . 1. 2. . 1. 2. 30. (1) (2) (3) (4) . (1) (2). (1) (3). (1) , (2) (3). (1) , (2) , (3) (4) 14. ~ 14 ~31. 1. 2. . 1 2 . 1 2 . 1 2 . 1 2 32. . . . . 33. . . . . 34. . 0 . 2 15. ~ 15 ~ . 1 . 2 335. a b . a < b a < b2 . a < b a2 < b . a < b a < ab . a < b a 2 < b236. . . . . 37. a b . a b b a . a b a ba . baba a . b b38. 1) 2) 3) 16. ~ 16 ~. 1, 2 3 . 1, 3 2 . 2, 3 1 . 1, 3 2 39. a, b (1) a < b a 2 b2 (2) a < b < 0 ab a 2 . (1) (2) . (1) (2) . (1) (2) . (1) (2)40. a,b,c . a b a c b c . a c a b c b a b . a b c c . a c a c c b41. a, b, c d . a < b c < d a - c < b - d. a < b c < d ac < bd. a < b c-a > c-b. a < b a n < bn42. a, b, c . a + c = b + c a = b 17. ~ 17 ~. ac = bc a = b. a < b ac < bc. a < b ac > bc43. a, b (1) a < b a 2 b2(2) a < b < 0 ab a 2 . (1) (2) . (1) (2) . (1) (2) . (1) (2)44. a, b c . a b ac bc . a b 1 1 a b . a2 b2 a b . a 3 b3 a b45. 3x 2 + 16x - 35 > 0 5 . , 7, 3 5 . , 7, 35 . , 7 ,3 5 . , 7 ,3 46. a b x 2 3x 20 0 a 3 b 3 . 53 18. ~ 18 ~. 87. 95. 10747. 2x 2x - 5 2x + 5 . 10 . 15 . 20 . 25 48. . . . .49. 3 + -1 - - 4 - 5 . -2. 3. 4. 5 19. ~ 19 ~50. 4X = 6 . ( 2 , 10 ). (10 , 2 ). ( 2 , 10 ).( 2 , 10 )51. .a = ax = a .x = a-a < x < a .x > ax < -a x > a . x a x -a x > a52. (a, b) 2 x 3 3 x 2 b a . 11. 12. 13. 1453. A = 0, 1, -2 , B = 1, 2 y =x AB . 1, 1 , 2, -2 , 3, -3r = . r = 1, 1 , -2, 2 . r = -1, 1 , 2, -2 , 3, 3 . r = 1, 1 , 2, -254. r = 3, 5 , -1, 0 , 4, -3 , 6, 1 . Dr =3, -1, 7, 4, 6 R r = 3, -1, 7, 4, 6 . Dr = 5, 0, -3, -1 20. ~ 20 ~ 3, -1, 4, 6Rr =. Dr = 3, -1, 4, 6R r = 5, 0, -3, -1. Dr = 3, -1, 4, 6 R r = 5, 0, -3, -1, 755. x,y | y =r =3x + 8 . D = y | y R r + R = x | x R r+. Dr = x | x RR r = y | y R. Dr = x | x R x 0R r = y | y R.Dr = x | x RR r = y | y R y 3 56. U = { 1 , 2 , 3 , 4 } R = { (x , y) U Ux < y } . 4. 6 . 5. 757. . . 21. ~ 21 ~ ..58. 1 . y 5x 22 +1. y 3x 2 11. y x 1 22.y x2 159. y 2x 12 2. . (-1 , -2). y y 2. x 60. . y1 15x2 22. ~ 22 ~ 1 . y 2 x 2 3 2 . y3 x 22 2 . y4 10 x2 361. r = { (x , y ) | y = x2 } . { (0 ,0) , (1,2) , (2,4) , (3,6) , (4,8) }. { (0,0) , (1,1) , (2,4) , (3,9) , (4,16) }. { (0,0) , (1,1) , (2,4) , (3,9) }.{ (1,1) , (2,4) , (3,9)}62. y ax 2 a 0 ax 2 bx c 0 bx c . . . . 23. ~ 23 ~63. y 2x 3 22 . 2,2 . 3,2 . 2,2 . 3,264. . y1 15x21 2y2 x 3 .2y 3 x 2 22 . . y4 10 x 3 265. xy2 x + y2 = 10 . 5 . 15 . 25 . 3566. y x 2 6x 5 .. . 24. ~ 24 ~ .67. f x x 32 31) 3,32) . 1) 2) . 1) 2) . 1) 2) . 1) 2) 68. C t V(t) v t 0.8c 0.9 t 1 900,000 3 . 399,360 . 496,660 . 566,390 . 583,200 69. 4000 x f x 40001.3 10 x 6760 . 10 25. ~ 25 ~ . 20 . 25 . 30 70. t S st 3t 2 15t . 2.5 . 3.5 . 5.5. 7.5 71. y 960 x 3x2 y x . 100 . 140 . 120 . 16072. y 0 . 5 x 1 26. ~ 26 ~ . x 5 x 1. 5 x 1. x 5 x 173. f t = 0.5 5t f t t 12.5 . 0.5 . 1.0 . 1.5 . 2.0 74.. x 1 5 0 . . 2 . . 75. . x 12 1 0 . 7x 22 0 . x 42 4 . x 72 376. c 3 . f x x c D f R . f x x c R 3 f, . f x x c R f 3, . f x x c 2 R f 2, 77. -2 x - 5 - 1= 0 2 . -5 -1 27. ~ 27 ~. -5 1. 5 -1. 78. 5,000 () 1,000 15.00 1,000 22.002,000 2,000 32.003,000 3,000 55.005,000 3,000 4,000 . . . 13 . 105 79. 2 28. ~ 28 ~. 6. 5. 3. 280. . . y 2x x 1 .y 2 x 1 .y 2 .y 0.2x. 29. ~ 29 ~ LAS 4 1 21 41 612 22 42 62 3 23 43 634 24 44 64 5 25 45 656 26 46 667 27 47 678 28 48 689 29 49 6910 30 50 70 11 31 51 7112 32 52 7213 33 53 7314 34 54 7415 35 55 7516 36 56 7617 37 57 7718 38 58 7819 39 59 7920 40 60 80

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