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📌 MATHEMATICS JAMB UTME - 100 QUESTIONS & ANSWERS

1. Simplify: ¾ ÷ 1½ × 2⅔ = ?
A. 1 B. 2 C. 3 D. 4
✅ ANSWER: A
2. If 2^(x+1) = 8^(x-1), find x
A. 2 B. 3 C. 4 D. 5
✅ ANSWER: A
3. Solve: 3x² - 5x - 2 = 0
A. -⅓, 2 B. ⅓, -2 C. 3, -2 D. -3, 2
✅ ANSWER: A
4. Factorize: 2x² - 8
A. 2(x-2)(x+2) B. 2(x-4)(x+4) C. (2x-4)(x+2) D. 2(x-2)²
✅ ANSWER: A
5. If y = 2/x, find y when x = -4
A. -½ B. ½ C. -2 D. 2
✅ ANSWER: A
6. Solve: (x+2)/3 - (x-1)/2 = 4
A. 13 B. -13 C. 11 D. -11
✅ ANSWER: B
7. If log₁₀2 = 0.3010, find log₁₀8
A. 0.3010 B. 0.9030 C. 0.6020 D. 1.2040
✅ ANSWER: B
8. Solve for x: 4x - 3 = 2x + 7
A. 5 B. 3 C. 2 D. 4
✅ ANSWER: A
9. Find the value of 3² × 3³
A. 3⁵ B. 3⁶ C. 3⁴ D. 3⁷
✅ ANSWER: A
10. Simplify: √64 + √36
A. 14 B. 10 C. 8 D. 6
✅ ANSWER: A
11. Solve: 5x - 2 = 3x + 8
A. 5 B. 3 C. 4 D. 2
✅ ANSWER: A
12. If 3x = 81, find x
A. 4 B. 3 C. 2 D. 5
✅ ANSWER: A
13. Simplify: 2½ + 1¾
A. 4¼ B. 4½ C. 4¾ D. 4
✅ ANSWER: A
14. Find the value of x in 2x/3 = 8
A. 12 B. 6 C. 4 D. 8
✅ ANSWER: A
15. If a = 3, b = 2, find a² + b²
A. 13 B. 9 C. 4 D. 5
✅ ANSWER: A
16. Solve: x² - 5x + 6 = 0
A. 2,3 B. -2,-3 C. 1,6 D. -1,-6
✅ ANSWER: A
17. Factorize: x² - 9
A. (x-3)(x+3) B. (x-9)(x+9) C. (x-3)² D. (x+3)²
✅ ANSWER: A
18. If y = 3x - 2, find y when x = 4
A. 10 B. 12 C. 14 D. 8
✅ ANSWER: A
19. Simplify: 3x + 2x - 5x
A. 0 B. x C. -x D. 5x
✅ ANSWER: A
20. Solve: 2(x - 3) = 10
A. 8 B. 5 C. 7 D. 6
✅ ANSWER: A
21. Find the area of triangle with base 12cm and height 5cm
A. 30 cm² B. 60 cm² C. 17 cm² D. 34 cm²
✅ ANSWER: A
22. Circle circumference 44cm. Find radius (π=22/7)
A. 7cm B. 14cm C. 21cm D. 28cm
✅ ANSWER: A
23. Volume of cylinder radius 7cm, height 10cm (π=22/7)
A. 1540 cm³ B. 154 cm³ C. 220 cm³ D. 440 cm³
✅ ANSWER: A
24. Interior angle of regular polygon is 156°. How many sides?
A. 12 B. 15 C. 18 D. 24
✅ ANSWER: B
25. Perimeter of rectangle length 8cm, diagonal 10cm
A. 28cm B. 36cm C. 24cm D. 32cm
✅ ANSWER: A

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26. Find area of circle radius 7cm (π=22/7)
A. 154 cm² B. 144 cm² C. 164 cm² D. 174 cm²
✅ ANSWER: A
27. Volume of cube side 5cm
A. 125 cm³ B. 100 cm³ C. 150 cm³ D. 175 cm³
✅ ANSWER: A
28. Total surface area of cube side 4cm
A. 96 cm² B. 64 cm² C. 48 cm² D. 80 cm²
✅ ANSWER: A
29. Find area of trapezium parallel sides 8cm, 12cm, height 5cm
A. 50 cm² B. 40 cm² C. 60 cm² D. 70 cm²
✅ ANSWER: A
30. Circumference of circle radius 14cm (π=22/7)
A. 88cm B. 44cm C. 66cm D. 22cm
✅ ANSWER: A
31. If sin θ = 3/5, find cos θ
A. 4/5 B. 2/5 C. 5/4 D. 5/3
✅ ANSWER: A
32. Simplify: sin 60°/cos 30°
A. 1 B. √3 C. 1/√3 D. 2
✅ ANSWER: A
33. Find θ if 2 sin θ = 1, 0° ≤ θ ≤ 90°
A. 30° B. 45° C. 60° D. 90°
✅ ANSWER: A
34. If tan θ = 4/3, find sin θ
A. 4/5 B. 3/5 C. 5/4 D. 5/3
✅ ANSWER: A
35. Find cos 60°
A. ½ B. √3/2 C. 1/√2 D. 0
✅ ANSWER: A
36. If sin θ = 0.5, find θ
A. 30° B. 45° C. 60° D. 90°
✅ ANSWER: A
37. Simplify: 1 - sin²θ
A. cos²θ B. sin²θ C. tan²θ D. cot²θ
✅ ANSWER: A
38. Find sec θ if cos θ = ½
A. 2 B. 1 C. ½ D. √3
✅ ANSWER: A
39. If cosec θ = 2, find sin θ
A. ½ B. 2 C. 1 D. √3/2
✅ ANSWER: A
40. Find tan 45°
A. 1 B. 0 C. ∞ D. √3
✅ ANSWER: A
41. If n(U)=50, n(A)=30, n(B)=25, n(A∩B)=10, find n(A∪B)
A. 45 B. 55 C. 5 D. 15
✅ ANSWER: A
42. In class of 40, 25 like Math, 20 like English, 10 like both. How many like neither?
A. 5 B. 10 C. 15 D. 20
✅ ANSWER: A
43. If n(A)=15, n(B)=20, n(A∩B)=8, find n(A∪B)
A. 27 B. 35 C. 23 D. 43
✅ ANSWER: A

44. In a survey of 50 people, 30 like tea, 25 like coffee, 10 like both. How many like neither?
A. 5 B. 10 C. 15 D. 20
✅ ANSWER: A
45. If n(P)=12, n(Q)=18, n(P∩Q)=5, find n(P∪Q)
A. 25 B. 30 C. 35 D. 40
✅ ANSWER: A
46. In a class, 15 play football, 12 play basketball, 7 play both. How many play at least one?
A. 20 B. 27 C. 34 D. 19
✅ ANSWER: A
47. If n(M)=25, n(N)=30, n(M∩N)=10, n(M∪N)'
A. Depends on universal set B. 45 C. 55 D. 65
✅ ANSWER: A
48. In a school, 60 study Math, 50 study English, 20 study both. Total students?
A. 90 B. 110 C. 130 D. 70
✅ ANSWER: A
49. If n(A)=20, n(B)=15, n(A∩B)=5, universal set=40, find n(A∪B)'
A. 10 B. 30 C. 20 D. 40
✅ ANSWER: A
50. In a class of 35, 20 like rice, 15 like beans, 8 like both. How many like none?
A. 8 B. 12 C. 15 D. 20
✅ ANSWER: A

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51. Distance between points (2,3) and (5,7)
A. 5 B. 6 C. 7 D. 8
✅ ANSWER: A
52. Midpoint of line joining (1,4) and (5,8)
A. (3,6) B. (2,6) C. (3,4) D. (4,6)
✅ ANSWER: A
53. Gradient of line through (1,2) and (4,8)
A. 2 B. 3 C. ½ D. 4
✅ ANSWER: A
54. Equation of line gradient 2 passing through (1,3)
A. y=2x+1 B. y=2x-1 C. y=x+2 D. y=3x-2
✅ ANSWER: A
55. Distance between (0,0) and (3,4)
A. 5 B. 7 C. 1 D. 25
✅ ANSWER: A
56. Midpoint of (2,5) and (4,9)
A. (3,7) B. (2,7) C. (3,4) D. (6,14)
✅ ANSWER: A
57. Gradient of line 2y = 4x + 6
A. 2 B. 4 C. 1 D. 3
✅ ANSWER: A
58. Find y-intercept of line y=3x-5
A. -5 B. 3 C. 5 D. -3
✅ ANSWER: A
59. Find x-intercept of line 2x+y=4
A. 2 B. 4 C. -2 D. -4
✅ ANSWER: A
60. Gradient of line perpendicular to y=2x+3
A. -½ B. 2 C. -2 D. ½
✅ ANSWER: A
61. 10th term of AP: 3,7,11...
A. 39 B. 35 C. 43 D. 47
✅ ANSWER: A
62. 3rd term of GP is 9, 6th term 243. Find common ratio
A. 3 B. 2 C. 4 D. 5
✅ ANSWER: A
63. Sum of first 20 even numbers
A. 420 B. 210 C. 410 D. 400
✅ ANSWER: A
64. 5th term of AP: 2,5,8...
A. 14 B. 11 C. 17 D. 20
✅ ANSWER: A
65. Sum of first 10 natural numbers
A. 55 B. 45 C. 50 D. 60
✅ ANSWER: A
66. Find 7th term of GP: 2,4,8...
A. 128 B. 64 C. 32 D. 256
✅ ANSWER: A
67. Sum of first 5 terms of AP: 1,4,7...
A. 35 B. 40 C. 45 D. 30
✅ ANSWER: A
68. If Tn = 3n - 2, find T5
A. 13 B. 10 C. 7 D. 4
✅ ANSWER: A
69. Common difference of AP: 7,4,1...
A. -3 B. 3 C. 4 D. -4
✅ ANSWER: A
70. Sum to infinity of GP: 16,8,4,2...
A. 32 B. 24 C. 20 D. 28
✅ ANSWER: A
71. A die thrown once. Probability of prime number?
A. ½ B. ⅓ C. ⅙ D. ⅔
✅ ANSWER: A
72. Mean of: 2,3,5,7,8
A. 5 B. 6 C. 7 D. 8
✅ ANSWER: A
73. Median of: 4,8,1,3,7,6,2
A. 4 B. 5 C. 6 D. 7
✅ ANSWER: A
74. Probability of picking a red ball from 4 red, 6 blue
A. 0.4 B. 0.6 C. 0.2 D. 0.8
✅ ANSWER: A
75. Mode of: 2,2,3,4,5,5,5,6
A. 5 B. 2 C. 3 D. 4
✅ ANSWER: A
76. Range of: 3,7,2,9,5
A. 7 B. 9 C. 2 D. 3
✅ ANSWER: A
77. Two coins tossed. Probability of one head?
A. ½ B. ¼ C. ¾ D. 1
✅ ANSWER: A
78. Probability of getting a 6 on a die
A. ⅙ B. ½ C. ⅓ D. ¼
✅ ANSWER: A
79. Mean of first 5 multiples of 3
A. 9 B. 12 C. 15 D. 18
✅ ANSWER: A
80. Probability of picking a vowel from "MATHEMATICS"
A. 4/11 B. 3/11 C. 5/11 D. 2/11
✅ ANSWER: A
81. Differentiate: y = 3x² - 4x + 2
A. 6x - 4 B. 3x - 4 C. 6x + 4 D. 3x + 2
✅ ANSWER: A
82. Evaluate ∫ (2x + 3) dx
A. x² + 3x + C B. 2x² + 3x + C C. x² + 3 D. 2x + 3 + C
✅ ANSWER: A
83. Differentiate: y = 5x³
A. 15x² B. 5x² C. 10x² D. 3x²
✅ ANSWER: A
84. Find ∫ 4x³ dx
A. x⁴ + C B. 4x⁴ + C C. x³ + C D. 4x³ + C
✅ ANSWER: A
85. Differentiate: y = 2sin x