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
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