1

1 O-Net

1.

+

+

1. 0 2. 1 3. 2 4. 3 2. ,

1. -5 2. -6 3. -7 4. -8 3.

+

1.

2. 25 + 82 3. 3 + 72 4. 5 + 82 4. 2x 3 = 23 x 1. 6.5 2. 7.5 3. 8.5 4. 9.5 5. 1. 63 37 2. b = b b 3.

4. x x

2

6. . 0.000125 = 0.05 . 0.343 = 0.07 . 9 . 0.008a 0.2 |a| 1. . 2. . 3. . . 4. . . 7. 0.216 + 0.729

+ 0.0025

1. 0.75 2. 0.15 3. -0.65 4. -0.75 8. 6, 9, 12 15 4 1. 94 2. 184 3. 364 4. 544 9. 5 4 6 5 8 7 1. 240 2. 140 3. 120 4. 119 10. ... 220 385 ... 1. 7 2. 11 3. 28 4. 55 11. 3 84, 98, 126 1. 6 2. 7 3. 12 4. 14

3

12. a = 4, b = 6 , c = 12 d = 1 1. ()

= 4

2. (ac + bd) cd = 1 3. (bc + ad) + (ab cd) = 18 4.

= 1

13. a b = abab

a b 4 (6 3) 1. -2 2. -12 3. 24 4. 72 14. A = (12) + [(18) (6)] B = (14) (71) C = [261 (9)] 8 A, B, C 1. A, B, C 2. B, C, A 3. A, C, B

4. B, A, C 15. 1. |12| + |9| + |21| = |29| + |7| + |6| 2. [(85)] + |17| + |39| < |28| + |47| + [(56)] 3. |43| + |34| + |62| > [(74)] + |23| + |62| 4. |8| |10| + |9| = |17| + 2|3| (4) 16. -68 17 1. 4 2. -4 3. 3 4. -3 17. a = 1, b = 2 c = 3 1.

2. ()

3. 3(ab c) 4. (a + b)(a c)

4

18. 512 8 343 7 3 8 2 7 1. 15 2. 12 3. 9 4. 6 19. 2 : 3 : 4 1. 20o, 60o, 100o 2. 40o, 60o, 80o 3. 20o, 40o, 120o 4. 30o, 70o, 80o 20. 1. 6.25% 1 : 15 2. 16 40 40 3. 8 : 25 30 % 4. 15% 60 7 120 21. 84 20% 350 1. 21 2. 25 3. 30 4. 34 22. 45 600 18 27 13 1. 20% 2. 3. 15% 4. 20%

5

23. 18 2 : 5 7 : 4 1. 30 2. 45 3. 54 4. 63 24. 6,420 7% 1. 240 2. 380 3. 420 4. 448 25. 80 10% 25% 72 1. 48.6 2. 31.4 3. 23.4 4. 18.0 26. 441 225 1. 2 : 1 2. 3 : 2 3. 5 : 3 4. 7 : 5 27. 16 21 2 50 1. 3 2. 4 3. 5 4. 6

6

28. 175 1. 16 2. 28 3. 55 4. 70 29. 243 1. 4 2. 10 3. 16 4. 20 30. 35 63

1. 50.5 2. 62.4 3. 69.3 4. 75.2 31. 750 760 1. 10 2. 35 3. 50 4. 66 32. 90 1 20 1. 100 2. 110 3. 120 4. 130

7

33. ABCD E DC ABCE 36 AB= 12, DE = 4 ABED 1. 16 2. 18 3. 24 4. 36 34. 110 1. 47 2. 52 3. 63 4. 74 35. 3.5 4

1. 2,829 2. 3,150 3. 4,400 4. 4,950 36. 4 4 1. 2 2. 3 3. 4 4. 5 37. 10 44

1. 6 2. 7 3. 12 4. 14 38. 84

1. 28 2. 48 3. 66 4. 84

8

39. 2 18 1. 12 2. 14 3. 16 4. 18 40. 6 14 1. 440 2. 528 3. 748 4. 880 41. 7 20

1. 1,640 2. 1,540 3. 1,400 4. 1,060 42. 6 8 12 1. 288 2. 348 3. 420 4. 576 43. 5 1. 5 2. 15 3. 125 4. 145

9

44. 18 4 1.40

1. 11,008 2. 24,640 3. 26,420 4. 64,240 45. 5 49.14 1. 80.90 2. 81.90 3. 91.80 4. 91.90 46. 10 13 1 20 1. 5 2. 10 3. 12 4. 24 47. 24 16 ( 3.14) 1. 753.6 2. 754 3. 754.6 4. 755 48. 12 5 8 4 50 1. 12,500 2. 12,800 3. 15,600 4. 21,500

10

49. POQ ROS X, Y Z 1. 10, 14 15 2. 10, 15 14 3. 14, 10 15 4. 15, 14 10 50.

1.

2.

3.

4. 51. ABC PQR 1. ABC PQR 2. 3 A P B R C Q 3. ABC PQR 4. 1. 3

11

52. ABCD DAF = BAE 1. ADF ABE (- - ) 2. AEF 3. CEF 4. 1., 2. 3. 53. BAE = BDC, AEB = DCB = DCB AE = DC 1. AEB DCB(- - ) 2. AB = BD 3. BE = BC 4. 1., 2. 3. 54.

1. ABC EFG 2. ACB = EFG 3. ABC = EGF 4. 2. 3. 55. 11:00 . 18 3.5 175 1. 7 2. 8 3. 9 4. 10 56. 1 80 14.5 1. 19.33 2. 20.43 3. 21.55 4. 23.64

12

57. 6.5 2.5 1. 5 2. 6 3. 6.7 4. 7 58. 1. 2. 3. 4. 59. PQRS A B PQ RS PS = PB, RA = RQ PR . PRB RPA - - . PSR RQP - - 1. . . 2. . . 3. . . 4. . . 60. ABC ABC A(1, 2), B(3, 0), C(5,1) X 3 Y 8 ABC 1. A(4, 10)B(6, 8) C(2, 8) 2. A(4, 10)B(6, 8) C(2, 9) 3. A(3, 10)B(6, 8) C(2, 9) 4. A(3, 10)B(5, 8) C(2, 9) 61. X 2

Y 5 1. A(1, 4) A(3, 4) 2. B(4, 3) B(4, 2) 3. C(2, 5) C(4, 0) 4. 1

13

62. . MN ABC . A A . ABC ABC 1. . 2. . 3. . . 4. . . 63. 1. BB CC 2. AA// CC 3. ABC ABC 4. 1.- 3. 64. ABC ABC O 1. ABC O 90 2. ABC O 180 3. ABC O 270 4. ABC O 90

14

65. PQR P(2, 1), Q(1, 4) R(3, 3) 1. X P(2, 1) 2. X 3 Y 2 P (5, 1) 3. X 3 Y2 Q (4, 2) 4. X 3 Y 2 R (6, 0) 66. = 3 1. 3 = 9 2.

= 3 2

3.

= 2 4. 5 + = 8 67. 1. 3(x 1) = 9 2.

x + 8 = 1

3.

= 2 4.

+

=

68. x + 1 2x 6 32 1. 9 2. 10 3. 11 4. 12 69.

80 1. 120 2. 240 3. 320 4. 360

15

70. 18 1. 38 2. 40 3. 42 4. 46 71. 60 25

280 14,000 1. 200 2. 80 3. 60 4. 40 72. 2 57 3 : 4 35 25% 1. 32 25 2. 31 26 3. 30 27 4. 29 28 73. 1. x = 3 4x = 13 2. x = y x + 6 = y + 6 3. x = 7 x + 1 = 6 4. x m = y mxy = 1 74. 3x ky + 5 = 0 (1, 3) k + 1 1.

2.

3. 1

4. 1

75. 3x 2y = 6 5x 3y = 10 1. (0, 2) 2. (2, 0) 3. (0, -2) 4. (-2, 0)

16

76. 2x 5 = 3y 17 y = 3x + 3 11(X + Y) 1. 50 2. 55 3. 60 4. 70 77. x 2y = 5 kx + y = 5 (1, 3) k 1. -7 2. -8 3. -9 4. -10 78. x + y = 20 x y = 10 1. (10, 20) 2. (15, 5) 3. (5, 15) 4. (20, 10) 79. 50 120 1. 10 40 2. 40 10 3. 20 30 4. 30 20 80. 2 4 5 4 6 3 2 3 1. 4 2. 5 3. 6 4. 7 81. 2 4 750 1 3 600 1. 125 2. 200 3. 225 4. 315

17

82. 10 -36 1. 35 2. 67 3. 73 4. 84 83. 10 60 1. x < 2 2. x < 2 3. x > 2 4. x > 2 84. 10 5 150 900 10 1. 15 2. 20 3. 25 4. 30 85. X 90 20 1. 106 2. 107 3. 108 4. 109 86. 200 50 1. 250 2. 250 3. 250 4. 250 87. 40 136 1. 137 2. 170 3. 173 4. 175

18

88. ()

102 66 72

240 1. 153 2. 99 3. 98 4. 45 89.

4 : 1

1. 100 2. 150 3. 200 4. 250 90.

1. 2 : 1 : 3 2. 2 : 9 : 6 3. 6 : 2 : 9 4. 3 : 1 : 2

19

91. ()

30 39 4 40 49 5 50 59 12 60 69 10 70 79 a 80 89 7

67.25 1. 65 2. 70 3. 75 4. 80 92. A ; 7, 2, 5, 13, 18, 21 B ; 4, 6, 7, 8, 9, 9, 10, 7, 6, 7 A+B 1. 12 2. 15 3. 16 4. 17 93. 3 2 : 1 : 3 50, 80 75 1. 67.50 2. 71.35 3. 76.50 4. 77.17 94. 40 12.5 10 12.65 1. 12 2. 14 3. 16 4. 18

20

95. 5 1, 2, 3, 4 5 2 . 2 . 3 . 4 1. . . 2. . . 3. . . 4. 2. 3. 96. 5 3, 5, 6, 7 8 2 1. 2. 3. 4. 1. 2. 3. 97. 8 12 16 1 1.

2.

3.

4.

98. 15 8 1.

2.

3.

4.

21

99. 200 3 1, 2, 3 1.

2.

3.

4.

100. 3 4 2 1 1.

2.

3.

4.

22

2 O-Net 2552

1 : 25 : 3

1.

37 1. 1 2. 5 3. 7 4. 8 2. 1. 2. 0 3. 4. 3.

0.5

8 1. 18 2. 20 3. 22 4. 24 4. : 5 : 3 : 4 : 7 50 40 1. 84 2. 80 3. 60 4. 48

23

5. 3

+

+

1. 1 2. 2 3. 3 4. 4 6. a 170 94 5 4 a + 5 1. 2 2. 3 3. 4 4. 5 7. 21 1. 4,400 2. 4,410 3. 4,420 4. 4,430 8. ABCD AB CD 8 P Q AD BC ABCD 40 P Q 1. 3 2. 4 3. 5 4. 6

24

9. 1. 582 2. 682 3. 762 4. 772 10. 4 36 3 60, 90, A A 1. 150 2. 160 3. 180 4. 200 11. 2.4 3.2 1. 4.0 2. 4.5 3. 5.6 4. 6.7 12. X X 1. 12 2. 13 3. 14 4. 15 13. ACE BCD C AB DE AB = 2 ., AC = 1.5 .,DE = 4 ., DC = AB, BC = X . EC = Y . X + Y 1. 3.0 2. 3.5 3. 4.0 4. 4.5

36 90

60 A

25

14. AB = 6 AC = 10 DE = 3 ABC = CDE = 90 AD 1. 8 2. 7 3. 6 4. 5 15. 1, 1, 2, 1, 2, 3, 1, 2, 3, 4,... 19 1. 1 2. 2 3. 3 4. 4 16. 1. 2. 3. 4.

26

17. ABC XY A (3, 3), B (5, 9), C (10, 5) ABC 1. 19 2. 21 3. 23 4. 33 18. 1. a a > 2. a, b, c a > c a > 3. x x > 4 x > 2 4. y y > 1 y > 1 19. X + Y = 2 X Y = 8 1. 2X + Y = 5 2. X 2Y = 7 3. 3X + 2Y =11 4. 2X 3Y = 19 20. 4 1 3 1 6 1 1 1 1. 2 2. 3 3. 4 4. 5 21. 200 2553 1. 134 2. 88 3. 84 4. 78

27

22. 2 2 3 1 3 3 1 4 3 2 4 3 3 2 2 4 3 1 2 1 1. 4 2. 3 3. 2 4. 1 23. 60 5 44 65 1. 35 2. 37 3. 38 4. 39 24. 6 5 1. 13 2. 12 3. 11 4. 10

28

25. 5 1, 2, 3, 4, 5 2 2 1. 0.1 2. 0.2 3. 0.3 4. 0.4 2: 5 : 5 26 30 1 9 1. 10 2. 11 3. 12 4. 13 5. 15 6. 16 7. 18 8. 19 9. 20 26. 6 27. ABC AB= 30 BC = 18 AC 28. 40, 48 52 29. ABC B BC = 103 COS A =

AC

30. 1 1 2 3 3 6 4 10 55

29

2 O-Net 2553

1 : 4 15 1. 64 10 16 1. 256 2. 160 3. 25.6 4. 16.0 2. A 36 54 B 36 54 (A B) 6 1. 1 2. 3 3. 4 4. 4 3. 1. 2 2. 3 3. 4 4. 5 4. 7 1. 30 2. 27 3. 21 4. 18

30

5. 1 3

1. 2. 3. 4. 6. 3 6 1. 46 7 2. 43 46 3. 39 43 4. 6 39

31

7. 40 60 6 7 60 1. 9 2. 10 3. 11 4. 12 8. 4 2554 17 2553 1. 2. 3. 4. 9. 7 14

1. 3: 5 2. 3 : 7 3. 3 : 10 4. 3 : 14 10. (1, 2), (2, 3), (3, 4), (4, 6), (5, 10), (6, 16), (7, 26), (8, y) y (8, y) 1. 42 2. 39 3. 36 4. 34 11. 1 2 10 30 1. 10 2. 20 3. 30 4. 40

32

12. 6 45 40, 41, 45, 49, 50, A 6 1. 2. 3. 4. 13. 3 2 1.

2.

3.

4.

14. 3 150 () 1 10 a 11 20 43 21 30 34 31 40 31 41 50 2a 10 1.

2.

3.

4.

15.

ABCD 36 AF AE DAB 3 BE 1. 3 2. 23 3. 33 4. 43

33

2 : 5 : 4 16. 4, 6, a a

17. 3 3 1 1 18. 2 2 3 19 2 3 3 19. 2 1 2 20. 1 2 3 4 + 1 = 5 5 = 25 2 3 4 5 + 1 = 11 11 = 121 3 4 5 6 + 1 = 19 19 = 361 4 5 6 7 + 1 = 29 29 = 841 24 25 26 27 + 1 = A A A

34

1 O-Net

1. 2 1

1 + 2+

1

2 + 3+

1

3 + 4

=

+

+

=

+

+

= 2 1 + 3 2 + 4 3 = 1 + 4 = 1 + 2 = 1

2. 4 ,

=

=

= 8 3. 1

+

=

+

=

+

=

+

=

3 +

=

+

= 3 +

=

35

4. 2 2x 3 = 23

2x 3

= 23

2x 3 = 4(3) 2x 3 = 12 2x = 12 + 3 2x = 15

x =

= 7.5

5. 2 1., 3 4. 2. b = |b| b

6. 3 . . . 9 9 . 0.008a 0.2a

7. 2 0.216 = 0.6 0.6 0.6 = 0.6 0.729 = 0.9 0.9 0.9 = 0.9

=

=

= 0.4

0.0025 = 0.05 0.05 = 0.05

0.216 + 0.729

+

0.0025

0.6 + (0.9) (0.4) + 0.05 = 0.15

36

8. 2 ... 6, 9, 12 15

3) 6 9 12 15 2) 2 3 4 5 1 3 2 5 ... = 3 2 3 2 5 = 180 6 , 9 , 12 15 4 180 + 4= 184

9. 4 1 1 5, 6 8 ... 5, 6 8 1 ... 5 , 6 8 2) 5 6 8 5 3 4

... 2534= 120 120-1 = 119

10. 3 220 385 ... ... 5 ) 220 385 11) 44 77 4 7

... 5 11 = 55 ... 5 11 4 7 = 1,540 ... ...

= 28

11. 4 3 84 , 98, 126 ... 2 ) 84 98 126 7) 42 49 63 6 7 9

... 2 x 7 = 14 14

37

12. 2 a = 4, b = 6, c = 2 d = 1

1. ()

=

= 4

2. ()()()()()

=

= 1

3. [(6)2 + (4)(1)] + [(4)(6) (2)(1)] = (12 + 4) + (24 + 2) = 8 + 26 = 18

4. ()()()

=

= 1

13. 2 a b =

6 3 =

=

= 6

4 (6 3) =

=

= 12 14. 2 A = (12) + [(18) (6)] = 96

B = (14) (71) = 994 C = [261 (9)] 8 = 232 994,-232, 96

15. 1 1. |12| + |9| + |21| = |29| + |7| + |6|

2. [(85)] + |17| + |39| < |28| + |47| + [(56)]

3. |43| + |34| + |62| > [(74)] + |23| + |62|

4. |8| |10| + |9| = |17| + 2|3| (4)

16. 2 = 68

= 17

=

= 4

38

17. 4 a = 1, b = 2 c = 3

1.

= ()()

=

= 3

2. ()

= ()()()

= 3

3. 3(ab c) = 3[(1)(2) 3] 3(5) = 15 4. (a + b)(a c) = [(1) + 2][1 3] (1)(4) = 4

18. 1 512 = 8 343 = 7

3 8 2 7 = 3(3) + 2(3) = 15

19. 2 2: 3 : 4 9

180

=

2 = 40

=

3 = 60

=

4 = 80

39

20. 2 1. 6.25% .

=

= 1: 16

2. ..

=

3.

=

= 32%

4. 15% 60

=

x =

= 9

=

=

100 y = 7.5 15% 60 7.5 120

21. 2 20% 120 100 84

= 70

1 = 70 1 14 14 1 350

= 25

25 350 22. 4 45 600 27 18

486 18 13 234 486 + 234 = 720 (720 600) = 120 600 120 100

100 = 20

20 %

40

23. 4 : = 7x 4x

18 : = 2 5 : = 5 2 7x 18 : 4x 18 = 5 2

=

14x 36 = 20x 90 6x = 54 x = 9 (79) = 63

24. 3 = + 7% x 6420 = x +

6420 =

x = ,

= 6,000

=

6,000 = 420 25. 3 80 10%

100 90 80

80 = 72

100 75 72

72 = 54

80 72 54 80 54 72

72 = 48.6

(72 - 48.6) = 23.4

41

26. 4 = R = 441

= r = 225

=

=

=

R r = 7 5

27. 4 1 2

16 (16 2) = 32

21 (21 2) = 42

2(32 + 42) = 148

2 = 148 + 148 = 296

1 50

= 5.92

6

28. 4 175

=

7 7 = 77

= 175 77 = 98

=

=

= 28

1 = 2.5

28 =28 2.5= 70

42

29. 2 =

243 =

=

= 16

= 4

1 = 2.5

4 = 2.5 4 = 10

30. 3 = 2r 63

= 2

63 = 6,930

100 = 1

,

= 69.30

31. 4 1 = 0.9

760 760 0.9 = 684

750 684 = 66

32. 3 60 90

20 30

1 20

= 90 + 30 = 120

120

43

33. 3 =

=

= 3

AD = 3

ABED =

=

3 (4 + 12)

= 24

34. 3 3

. = 10 2 = 20

. = 6 18 = 108

. = 10 6 = 60

= 20 + 108 + 60 = 188

1 = 4

=

= 47

(110 47) = 63

44

35. 4

r = .

= 4

1 = 2.5

1 = 90

=

=

.

2.5 4 90

= 4,950

36. 1

= h

=

r

= rh

r13 = rh

(2) = 2 h

= h

= h

h = 2

45

37. 4

44 2r = 44 ( r ) 2(

)r = 44

r =

= 7 2r = 14

38. 3

D D D =

84

= 264 264

= 66

39. 1 = 2 rh = 2 13 r

2h2 h = h h = 18 h = 18 h = 12 12

40. 2 =

rh =

6 6 14

= 528

46

41. 2

v = rh r h v =

7 7 10 = 1,540

= 1,540

42. 1

= =

6 8 12 = 288

= 288 43. 3

= = 5 5 5 = 125 = 125

47

44. 2

(R) 9 (r) 5 (h) 140 v = Rh rh v = h(R r) =

140(9 5)

= 24,640 45. 2 = v

v = =

49.14 5

= 81.9 81.9

48

46. 3

= 4

= 4(

)

()

= 13 5

= 144

= 12

= 4

10 12 = 240

1 20

240

= 12

49

47. 2

1 r r = 16 + 12 = 400 = 20 (12)(20) = 240 753.6 ( 3.14) 754 1

48. 3 =

(5 + 8) 4 12 = 13 24 = 312 50 312 50 = 15,600

49. 2

POQ ROS PO RO,

OQ OS PQ RS PO = RO = 15 ,

OQ = OS = 14 , PQ = RS = 10 , X = 10 , Y = 15 Z = 14

50. 2 2. --

50

51. 4 1.

2.

3. ABC PQ

52. 4 DAF = BAE ( )

AD = AB ( )

ADF = ABE ( )

ADF ABE ( -- )

AF = AE DF = BE (ADF ABE)

DC = BC ()

CF = CE (DC DF = BC BE) 53. 4 BAE = BDC ( )

AE = DC ( )

AEB = DCB ( )

AEB DCB ( -- )

54. 4 1. ABC EGF (--)

2. ACB = AGF

3. ABC = EFG

51

55. 3

x ABC ~ DEF

= .

.

x = .18.

x = 9 9

56. 1 ABC AC = AB + BC 1 = 0.8 + AB 1 0.64 = AB AB = 0.36 AB = (0.6) AB = 0.6 ABC ~ AED

=

.

= ..

x = ..

.

x = 19.33

52

57. 2

x

x = 6.5 2.5

= 42.25 6.25

= 36 X = 6

6

58. 1

59. 3

PRB RPA --

PSR RQP --

60. 2 ABC X Y X

Y 2 X 3 Y

8 X Y

A (-4 , 10 )

B (-6 , 8 )

C (2 , 9 )

53

61. 3 X Y X

Y X 2 Y 5 X Y

1. Y 2. 2 X 8 3. X 2 Y 5 4.

62. 2 . MN ABC . A A . ABC ABC

63. 4 1.

2. CC AA// CC 3. ABC ABC

64. 2 180 O O A O A AO = AO B O B BO = BO C O C CO = CO ABC ABC O 180

54

65. 4 X X

1. 2. 3 4. ( 3, -2 ) R ( 6, 1 )

66. 2

= 3h 2 h = 3

3(3) 2

8 7

67. 2 1. 3(x 1) = 9 x 1 = 3 x = 4 2.

x + 8 = 1

x = 7 x = 7 5

2

x = 2

x = 17.5 3.

= 2

2x + 3 = 8 2x = 5 x =

4.

+

=

6

3x + 5 = 2 3x = 3 x = 1

55

68. 2 32

(x + 1) + (x + 1) + (2x 6) = 32 4x 4 = 32 4x = 36 X = 9 x 1 = 9 + 1 = 10

69. 3 1

1

=

= 5

12

1 (

+

) = 1 (

) = 1

=

=

80

80

1 80 1

= 80 4 320

70. 3 2x 2x + 2 2 2x = 4x 18 4x (2x + 2) = 18 2x 2 = 18 2x = 20 x = 10 20 22 = 20 + 22 = 42

56

71. 2 x 25x

280 x 60(280 x) 25x + 60(280 x) 14,000 25x + 60(280 x) = 14,000 25x + 16,800 60x = 14,000 35x = 2,800 x = 80 80

72. 1 = x = 57 x 3: 4 =

[35 (3 + 4)]

= 196 3x + 4(57 x) = 196 3x + 228 4x = 196 x = 32 = 32 57 32 = 25

73 2 1. x = 3 4x = 4(3) = 12 2. x = y x + 6 = y + 6 3. x = 7 x + 1 = 7 + 1 x + 1 = 8 4. x m = y m x m + m = y m + m x = y xy = yy = y

57

74. 3 3x ky + 5 = 0 (1, 3)

x = 1 y = 3 3x ky + 5 = 0

3(1) k(3) + 5 = 0 3(1) + 3k + 5 = 0 3k + 2 = 0 3k = 2 k =

k k + 1 =

+ 1

=

+ 1

=

+

= 139

= 14

9

75 2 3x 2y = 6 (1)

5x 3y = 10 (2)

5 (1) 15x 10y = 30 (3) 3 (2) 15x 9y = 30 (4)

(3) - (4) y = 0 y = 0 y (1) 3x 2(0) = 6 3(x) = 6 x = 2 (2, 0)

58

76. 3 2x 5 = 3y (1)

2x 3y = 5 17 y = 3x + 3 3x + y = 14 (2) 3 (2) 9x + 3y = 42 (3) (3) + (1) 11x = 47 x =

x (2) 3

+ y = 14

y = 14

y =

=

11(x + y) = 11

+

=

()

= 60

77. 2 (1, 3) x 2y = 5 kx + y = 5 (1)k + (3) = 5 k = 5 + 3 k = 8 k = 8

78. 2 x + y = 20 (1) x y = 10 (2) (1) + (2) 2 x = 30 x = 15 x (1) 15 + y = 20 y = 5 (15, 5)

59

79. 1 x 2x

y 4y 50 x + y = 50 (1) 120 2x + 4y = 120 (2) 2 (1) 2x + 2y = 100 (3) (2) (3) 2y = 20 y = 10 y (1) x + 10= 50 x= 40 40 10

80. 3 1 1 x 1 1 y 5 2 4 (5 2 x) + (5 4 y) = 10x + 20y (1) 3 4 6 (3 4 x) + (3 6 y) = 12x + 18y (2)

(1) = (2) 10x + 20y = 12x + 18y 2y = 2x x = y

y (1) 10x + 20x = 30x 1 2 4 2x + 4y (3) y = x (3) 2x + 4y = 5x 2 3 30 =

= 6

6

60

81. 3 x 1

y 1 2 4 750 2y + 4x = 750 (1) 1 3 600 y + 3x = 600 (2) 2 (2) 2y + 6x = 1200 (3) (3) (1) 2x = 450 x = 225 225

82. 3 x y 10 x + y = 10 (1) -36 36 + (10x + y) = 10y + x (2) 36 + 10x + y 10y x = 0 9x 9y = 36 (3) 9(1) 9x + 9y = 90 (4) (3) + (4) 18x = 126 x =

x = 7 x = 7 (1) 7 + y = 10 y = 3 73

83. 2 x 10 5(x + 10) 60 5(x + 10) < 60 x + 10 <

x + 10 < 12 x < 12 10 x < 2

61

84. 4 10 = x

5 = y = 150 x + y = 150 (1) = 900 10x+5y = 900 (2) 5 (1) 5x + 5y = 750 (3) (2)-(3) 5x = 150 x = 30 10 30

85. 4 x 90 x 90 20 x 95 < 20 x < 20 + 90 x < 110 109

86. 3 x 200 x 200 200 50

x 200 > 50 x > 50 + 200 x > 250 250

62

87. 4 x

40 x 40 136 x 40 < 136 x < 136 + 40 x < 176 175

88. 3

()

102 102

240 100

= 42.5

42.5 3.6

= 153

66 66

240 100

= 27.5

27.5 3.6

= 99

72 78

240 100

= 30

30 3.6

= 108

89. 3 30% 4 : 1 24% 6% = 24%

100 (30 + 25 + 15 + 24 ) = 6% 6% 80 15%

80 15

6= 200

63

90. 3 100%

= 100 30 10 15 = 45% : : 30 : 10 : 45 6 : 2 : 9

91. 4 (x) (f) f(x) 30 39 4 34.5 138 40 49 5 44.5 222.5 50 -59 12 54.5 65.4 60 69 10 64.5 64.5 70 79 a 74.5 74.5a 80 - 89 7 84.5 591.5

x = ()

67.25 = .

67.25(38 + a) = 2251 + 74.5a 74.5a 67.25a = 2555.5 2251 7.25a = 314.5

a = ..

a = 42 N = 38 + a

= 38 + 42 = 80

64

92. 4 7 , 2 , 5 , 13 , 18 , 21

2 , 5 , 7 , 13 , 18 , 21

=

=

= 3.5

=

= 10 a = 10 4 , 6 , 7 , 8 , 9 , 9 , 10 , 7 , 6 , 7 7 B = 7 A + B = 10 + 7 = 17

93. 1 w = 2 w = 1 w = 3 x = 50 x = 80 x = 75 =

=2(50) + 1(80) + 3(75)

2 + 1 + 3

=100 + 80 + 225

6

=405

6 = 67.5

67.5 94. 3 = 40 12.5 = 500

= 40 12.65 = 506 506 500 = 6

6 + 10 = 16 95. 4 . 2 3, 1 5, 2

4 3 5 . 3 1 2, 1 5, 2 4 4 5 . 4 1 3

65

3 5 96. 3 1. 3 8 5 8

2. 3 5 3 7 3.

97. 3 16 = 8 + 12 x 16 = 20 x x = 4

=

=

98. 4 15 S = {0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15} n(S) = 16 8 E = {8 9 10 11 12 13 14 15 16} n(E) = 9 P(E) = ()

()

P(E) =

66

99. 1 3 1, 2, 3 200

S = {1 , 2 , 3 , 12 , 13 , 21 , 23 , 31 , 32 , 123 , 132 , 213 , 231 , 312 , 321} n(s) = 15 200 E = {213 , 231 , 312 , 321}

P(E) =n(E)

n(S)

P(E) =4

15

100. 4 3 4 2

S = , , , , , , , , n(S) = 9 1 E = { , } n(E) = 2

P(E) = ()()

P(E) =

67

2 O-Net 2552 1. 1 2. 3 3. 2 4. 1 5. 3 6. 2 7. 2 8. 3 9. 2 10. 1 11. 1 12. 3 13. 3 14. 3 15. 4 16. 4 17. 1 18. 4 19. 4 20. 2 21. 4 22. 2 23. 2 24. 4 25. 1 26. 5 27. 4 28. 7 29. 9 30. 1

2 O-Net 2553 1. 2 2. 1 3. 3 4. 3 5. 4 6. 2 7. 4 8. 4 9. 4 10. 1 11. 1 12. 4 13. 2 14. 3 15. 2 16. 7 17. 6 18. 5 19. 11 20. 649