Mathematics Past Questions | WAEC, NECO, GCE

150 WAEC, NECO Mathematics Past Questions and answers

Access WAEC, NECO, GCE Mathematics past questions and answers, with 150 objectives, 10 theory questions with complete solutions, and 5 theory questions.

Table of Contents

Introduction
WAEC, NECO Mathematics Past Questions (150 OBJs)
Mathematics Past Questions on theory and Answers (10 Solved)
Mathematics Theory Questions Without Answers (5 Unsolved)
Conclusion

WAEC, NECO, GCE Mathematics Past Questions (1–150) objectives

1. Simplify: 3/4÷2/3
A. 9/8
B. 8/9
C. 6/7
D. 3/5
Answer: A

2. Evaluate: 3²×3³
A. 243
B. 27
C. 243
D. 243
Answer: A

3. Express 0.45 as a fraction in its simplest form.
A. 9/20
B. 45/100
C. 5/11
D. 4/9
Answer: A

4. The LCM of 12, 18 and 30 is
A. 180
B. 90
C. 60
D. 120
Answer: B

5. Solve: If x−3=7x – 3 = 7, find x.
A. 4
B. 5
C. 10
D. 9
Answer: C

6. Factorize: x²−9
A. (x+3)(x−3)
B. (x−9)(x+1)
C. (x−1)²
D. (x+9)(x−1)
Answer: A

7. If x=3x = 3, evaluate 2x²−4x+1
A. 5
B. 7
C. 3
D. 1
Answer: A

8. Solve: 2/x=4
A. 1/2
B. 8
C. 1/4
D. 1/8
Answer: B

9. Find the simple interest on ₦2000 for 2 years at 5% per annum.
A. ₦200
B. ₦100
C. ₦400
D. ₦500
Answer: A

WAEC Mathematics Past Questions

10. Find the value of log⁡10/1000
A. 2
B. 3
C. 4
D. 1
Answer: B

11. If a man spends 25% of his salary, what percentage remains?
A. 75%
B. 85%
C. 65%
D. 50%
Answer: A

12. Solve the inequality: 2x− 5 < 7
A. x<6
B. x>6
C. x<1
D. x>1
Answer: A

13. Convert 1101₂ to decimal.
A. 13
B. 12
C. 11
D. 14
Answer: A

14. What is the square root of 144?
A. 11
B. 13
C. 12
D. 10
Answer: C

15. A regular polygon has 8 sides. What is the sum of its interior angles?
A. 1080°
B. 900°
C. 720°
D. 1020°
Answer: A

16. Find the next number in the sequence: 2, 4, 8, 16, __
A. 18
B. 20
C. 32
D. 24
Answer: C

17. If ∠A=30∘\angle A = 30^\circ in a right-angled triangle, find ∠B\angle B.
A. 45°
B. 60°
C. 90°
D. 30°
Answer: B

18. The mode of 3, 3, 4, 5, 6 is
A. 4
B. 3
C. 6
D. 5
Answer: B

19. What is the median of: 2, 5, 7, 10, 12?
A. 5
B. 7
C. 10
D. 12
Answer: B

20. Convert 120° to radians.
A. 2π/3
B. π/2
C. 3π/2
D. 3π/4
Answer: A

21. What is the value of sin 30°?
A. 1
B. 1/2
C. 0
D. √3/2
Answer: B

22. Evaluate: 2x+5=15
A. x = 5
B. x = 6
C. x = 4
D. x = 7
Answer: A

23. If the radius of a circle is 7 cm, find its area.
A. 154 cm²
B. 144 cm²
C. 147 cm²
D. 150 cm²
Answer: A

24. The volume of a cube of side 5 cm is
A. 125 cm³
B. 100 cm³
C. 150 cm³
D. 200 cm³
Answer: A

25. What is the slope of the line passing through (2, 3) and (4, 7)?
A. 1
B. 2
C. 3
D. 4
Answer: B

26. Which of these numbers is a prime number?
A. 9
B. 15
C. 7
D. 21
Answer: C

27. What is the 5th term of the A.P: 3, 6, 9…?
A. 12
B. 15
C. 18
D. 21
Answer: B

28. Find the value of (x−2)² when x=4
A. 2
B. 4
C. 8
D. 16
Answer: B

29. Convert 3.75 to a fraction.
A. 15/4
B. 17/4
C. 19/4
D. 13/4
Answer: A

WAEC Mathematics Past Questions

30. How many degrees are in a straight angle?
A. 90°
B. 45°
C. 180°
D. 360°
Answer: C

31. If 3 mangoes cost ₦150, what is the cost of 5 mangoes?
A. ₦200
B. ₦250
C. ₦300
D. ₦100
Answer: B

32. A set with no element is called
A. finite set
B. null set
C. empty set
D. both B and C
Answer: D

33. Find the next in the sequence: 81, 27, 9, 3, __
A. 2
B. 1
C. 0
D. 4
Answer: B

34. What is the solution to x² = 49
A. x = 7
B. x = –7
C. x = ±7
D. x = 14
Answer: C

35. The area of a triangle with base 10 cm and height 5 cm is
A. 25 cm²
B. 50 cm²
C. 30 cm²
D. 35 cm²
Answer: A

36. Solve: 4x−3=5x−6
A. x = 3
B. x = –3
C. x = 6
D. x = –6
Answer: C

37. If the mean of 2, 4, 6, 8, x is 6, find x.
A. 10
B. 12
C. 6
D. 8
Answer: A

38. Express 25% as a decimal.
A. 0.5
B. 0.25
C. 0.75
D. 0.20
Answer: B

39. Which of the following has no square root?
A. 25
B. 16
C. 8
D. 36
Answer: C

40. What is the cube root of 64?
A. 4
B. 8
C. 6
D. 2
Answer: A

41. In a class of 40 students, 22 are girls. What percentage are boys?
A. 55%
B. 45%
C. 40%
D. 50%
Answer: B

42. A fair die is thrown once. What is the probability of getting an odd number?
A. 1/6
B. 3/6
C. 1/2
D. 2/3
Answer: C

43. Simplify: √49+√25
A. 12
B. 11
C. 13
D. 14
Answer: C

44. If x = -2, evaluate x² + 4x+4
A. 0
B. 4
C. 8
D. 16
Answer: A

45. The perimeter of a square of side 9 cm is
A. 18 cm
B. 36 cm
C. 27 cm
D. 81 cm
Answer: B

46. Solve: 2(x+3)=12
A. x = 3
B. x = 6
C. x = –3
D. x = –6
Answer: A

47. What is the additive inverse of –8?
A. –8
B. 8
C. 0
D. 1
Answer: B

48. The sum of the angles in a triangle is
A. 180°
B. 360°
C. 90°
D. 270°
Answer: A

49. Convert 0.75 to percentage.
A. 65%
B. 75%
C. 80%
D. 70%
Answer: B

50. If y varies directly as x and y = 10 when x = 2, find y when x = 5.
A. 25
B. 10
C. 15
D. 20
Answer: D

WAEC, NECO, GCE Mathematics Past Questions (51–150) Objectives

51. Solve: 3x+7=2x+10
A. x = 1
B. x = 2
C. x = 3
D. x = 4
Answer: C

52. Find the HCF of 24, 36 and 60.
A. 6
B. 12
C. 18
D. 24
Answer: B

53. A circle has a circumference of 44 cm. What is its diameter? (Take π=22/7)
A. 14 cm
B. 10 cm
C. 21 cm
D. 28 cm
Answer: A

54. The third term of a geometric progression is 16 and the common ratio is 2. What is the first term?
A. 2
B. 4
C. 1
D. 8
Answer: B

55. If 2x – 3 > 5, find x.
A. x > 4
B. x < 4
C. x = 4
D. x = 5
Answer: A

56. Find the solution to x²−5x+6=0
A. x = 2 or 3
B. x = 1 or 6
C. x = –2 or –3
D. x = 3 or 4
Answer: A

57. Find the 6th term of the arithmetic sequence 2, 5, 8,…
A. 17
B. 20
C. 15
D. 18
Answer: A

58. The number of diagonals in a hexagon is
A. 9
B. 12
C. 15
D. 18
Answer: B

59. What is the gradient of a line parallel to y = 3x + 4
A. 3
B. 4
C. –3
D. –4
Answer: A

60. A pie chart angle is 72°. What percentage of the total data does it represent?
A. 10%
B. 15%
C. 20%
D. 25%
Answer: C

WAEC Mathematics Past Questions

61. Simplify: (2x)²
A. 4x
B. 2x
C. 4x^2
D. 2x^2
Answer: C

62. Find the value of x in the equation X/2=6
A. 3
B. 6
C. 12
D. 2
Answer: C

63. If 6 workers complete a job in 10 days, how long will 3 workers take?
A. 15
B. 20
C. 5
D. 30
Answer: B

64. Find the volume of a cylinder of radius 7 cm and height 10 cm. Use π=22/7
A. 1540 cm³
B. 1200 cm³
C. 1400 cm³
D. 1600 cm³
Answer: A

65. Find the value of xx in 2/3 = 4/x
A. 6
B. 5
C. 8
D. 7
Answer: C

66. Simplify 2x−3(x−2)
A. −x+6
B. x−6
C. 2x−3x+6
D. −x−6
Answer: A

67. Which of these is a quadratic equation?
A. X²+2x+1=0
B. 2x+1=0
C. X³+1=0
D. 3x−2=0
Answer: A

68. Find the difference between the highest and lowest prime numbers less than 20.
A. 15
B. 16
C. 17
D. 18
Answer: C

69. What is the 10th multiple of 3?
A. 30
B. 33
C. 36
D. 27
Answer: B

70. A cone has a radius 3 cm and height 4 cm. Find its volume. (Use π = 3.15)
A. 37.68 cm³
B. 50.24 cm³
C. 56.52 cm³
D. 45.12 cm³
Answer: A

71. If y = 2x + 1, find y when x = 4
A. 9
B. 8
C. 6
D. 10
Answer: A

72. What is the probability of getting a head when a coin is tossed?
A. 0
B. 0.5
C. 1
D. 0.25
Answer: B

73. The bearing of B from A is 045°. What is the bearing of A from B?
A. 225°
B. 180°
C. 045°
D. 315°
Answer: D

74. What is the mean of 3, 5, 7, 9, 11?
A. 6
B. 7
C. 8
D. 9
Answer: B

75. Find the perimeter of a rectangle of length 12 cm and breadth 8 cm.
A. 40 cm
B. 20 cm
C. 60 cm
D. 48 cm
Answer: A

76. How many even numbers between 1 and 20?
A. 10
B. 9
C. 8
D. 11
Answer: A

77. Find the value of 2³ + 3²
A. 17
B. 15
C. 18
D. 19
Answer: D

78. Factorize: X²+5x+6
A. (x+2)(x+3)
B. (x+1)(x+6)
C. (x+3)²
D. (x+1)(x+5)
Answer: A

79. What is the sum of the exterior angles of any polygon?
A. 180°
B. 360°
C. 540°
D. Depends on the sides
Answer: B

80. Which of the following is not a rational number?
A. 0
B. 1/2
C. √2
D. 5
Answer: C

WAEC Mathematics Past Questions

81. Find the median of 3, 7, 9, 15, 21
A. 7
B. 9
C. 15
D. 21
Answer: B

82. Express 1 hour 30 minutes in seconds.
A. 3600 s
B. 4500 s
C. 5400 s
D. 7200 s
Answer: C

83. If 5 pencils cost ₦75, what is the cost of one?
A. ₦10
B. ₦15
C. ₦20
D. ₦25
Answer: B

84. The probability of an impossible event is
A. 1
B. 0.5
C. 0
D. –1
Answer: C

85. A triangle with two equal sides is
A. Scalene
B. Isosceles
C. Right
D. Equilateral
Answer: B

86. What is 20% of 80?
A. 16
B. 20
C. 8
D. 10
Answer: A

87. A line that cuts a circle at two points is called
A. Radius
B. Diameter
C. Chord
D. Secant
Answer: D

88. The square of 0.2 is
A. 0.4
B. 0.04
C. 0.02
D. 0.2
Answer: B

89. Simplify 3/4+2/3
A. 17/12
B. 5/7
C. 7/12
D. 11/12
Answer: A

90. If x = 2 and y = 3, evaluate xy+y
A. 9
B. 6
C. 8
D. 7
Answer: A

91. Solve: x+1/X = 5, find x when x > 0
A. 2
B. 3
C. 1
D. 5
Answer: A

92. A student scored 60 out of 80. What is the percentage?
A. 75%
B. 70%
C. 80%
D. 60%
Answer: A

93. Find the area of a trapezium with bases 8 cm, 12 cm and height 5 cm.
A. 50 cm²
B. 60 cm²
C. 40 cm²
D. 70 cm²
Answer: A

94. The result of 10010^0 is
A. 10
B. 1
C. 0
D. Undefined
Answer: B

95. The additive identity is
A. 1
B. 0
C. –1
D. Any number
Answer: B

96. Find the product of the square roots of 49 and 16
A. 28
B. 14
C. 32
D. 56
Answer: A

97. Simplify: 5x − 2x + 4
A. 3x + 4
B. 7x + 4
C. 2x + 4
D. 4x + 4
Answer: A

98. If x : y = 2 : 3, find y when x = 10
A. 12
B. 15
C. 14
D. 16
Answer: B

99. A shopkeeper gives a discount of 20% on ₦500. What is the selling price?
A. ₦400
B. ₦300
C. ₦450
D. ₦350
Answer: A

100. Solve: 5/x = 10/6
A. x = 3
B. x = 2
C. x = 6
D. x = 5
Answer: C

Mathematics Past Questions and answers for WAEC, NECO, GCE

Section A (objectives)

Solve: 2x + 3 = 9
A. 2
B. 4
C. 3
D. 5
Answer: C
The LCM of 6, 8, and 12 is
A. 24
B. 48
C. 12
D. 36
Answer: A
Solve: x2=25
A. 25
B. 0
C. ±5
D. 5
Answer: C
What is the gradient of the line y=3x−7y = 3x – 7?
A. -7
B. 3
C. -3
D. 7
Answer: B
Convert 0.75 to a fraction
A. ¼
B. ⅕
C. ¾
D. ⅜
Answer: C
Find the area of a triangle with base 10 cm and height 6 cm
A. 30 cm²
B. 60 cm²
C. 16 cm²
D. 36 cm²
Answer: A
What is the mode of the set: 2, 4, 4, 5, 6?
A. 2
B. 4
C. 5
D. 6
Answer: B
Find the median of 3, 7, 9, 11, 13
A. 7
B. 9
C. 11
D. 13
Answer: B
If 1x = 2, find x
A. 1
B. 2
C. 0.5
D. 3
Answer: B
Simplify: (x+2)² (x + 2)
A. x²+2
B. x2+4x+4
C. x2+2x+4
D. x2+6x+4
Answer: B
Solve: 3x=2x+5
A. x = 0
B. x = 5
C. x = -5
D. x = 10
Answer: B
Convert 1101 in base 2 to base 10
A. 13
B. 15
C. 12
D. 14
Answer: A
Solve: 2×3 = 4
A. x = 4
B. x = 6
C. x = 5
D. x = 3
Answer: B
What is the probability of getting an odd number when a die is thrown once?
A. ⅓
B. ½
C. 1⁄6
D. ⅔
Answer: B
Find the simple interest on ₦5,000 at 6% for 2 years
A. ₦600
B. ₦300
C. ₦500
D. ₦100
Answer: A
The value of log⁡101000
A. 3
B. 2
C. 4
D. 1
Answer: A
Evaluate: 32−22
A. 3
B. 5
C. 9
D. 1
Answer: B
If x=−2x = -2, evaluate x2+3x
A. -4
B. 2
C. 10
D. -6
Answer: A
A straight line cuts the y-axis at (0, -4). What is the y-intercept?
A. 4
B. -4
C. 0
D. 1
Answer: B
Expand: (x−1)(x+1)
A.x 4 −2x 2 +1
B. x2+2x+1
C. x2−2x+1
D. X²+1
Answer: A
Solve: 5x+2=3x+8
A. x = 1
B. x = 2
C. x = 3
D. x = 6
Answer: C
Find the value of 49
A. 6
B. 7
C. 8
D. 9
Answer: B
A car travels 120 km in 3 hours. What is its average speed?
A. 50 km/h
B. 40 km/h
C. 60 km/h
D. 80 km/h
Answer: B
In a triangle, the sum of interior angles is
A. 90°
B. 180°
C. 360°
D. 270°
Answer: B
Convert 150° to radians
A. 2.62
B. 2.00
C. 1.57
D. 3.14
Answer: A
Find the next number in the sequence: 2, 4, 8, 16, ___
A. 20
B. 30
C. 32
D. 64
Answer: C
A polygon with 5 sides is called a
A. Hexagon
B. Pentagon
C. Quadrilateral
D. Octagon
Answer: B
Expand: (x−2)²
A. x2−2x+4
B. x2−2x+2
C. X²−4x+4
D. x2+4x+4
Answer: C
Solve: x2+x−6=0
A. x = -2 or 3
B. x = 1 or 6
C. x = 2 or 3
D. x = -1 or 6
Answer: A
A number is divisible by 9 if the sum of its digits is divisible by
A. 2
B. 5
C. 9
D. 6
Answer: C
Find the square root of 144
A. 14
B. 12
C. 13
D. 15
Answer: B
If y=2x+1y = 2x + 1, find y when x = 3
A. 5
B. 6
C. 7
D. 8
Answer: C
What is 20% of 250?
A. 50
B. 25
C. 20
D. 40
Answer: A
Convert 1.25 to a fraction
A. 5/4
B. 4/5
C. 3/2
D. 1/2
Answer: A
If a number is multiplied by 0, the result is
A. 0
B. 1
C. The number itself
D. Undefined
Answer: A
How many sides does a hexagon have?
A. 5
B. 6
C. 7
D. 8
Answer: B
Solve: 4x−7=9
A. x = 5
B. x = 3
C. x = 4
D. x = 2
Answer: C
Find the perimeter of a square with side 6 cm
A. 24 cm
B. 12 cm
C. 36 cm
D. 18 cm
Answer: A
Solve: 2(x−1)=8
A. x = 4
B. x = 3
C. x = 5
D. x = 2
Answer: C
What is the HCF of 12 and 18?
A. 6
B. 3
C. 2
D. 12
Answer: A
Convert 0.2 to percentage
A. 10%
B. 20%
C. 2%
D. 200%
Answer: B
What is the mean of 2, 4, 6, 8?
A. 6
B. 5
C. 4
D. 3
Answer: B
What is the cube of 3?
A. 6
B. 9
C. 27
D. 81
Answer: C
Which of the following is a prime number?
A. 12
B. 11
C. 10
D. 15
Answer: B
Convert 45 minutes to hours
A. 1.25
B. 0.75
C. 0.5
D. 1.5
Answer: B
Solve: 2x+5=11
A. x = 3
B. x = 4
C. x = 5
D. x = 6
Answer: A
Simplify: 3/4+1/2
A. 3/2
B. 1/4
C. 5/4
D. 7/4
Answer: C
Find the next odd number after 21
A. 24
B. 23
C. 22
D. 25
Answer: B
What is the square of -5?
A. -25
B. 25
C. 5
D. 0
Answer: B
Simplify: 2x−3+4x+5 option A. 6x+2. B. 6x−2. C. 2x+8 D. 4x+8

10 WAEC, NECO Mathematics past Questions and Answers

Section B (Theory)

Question 1:
Factorize completely: x2−9x+20
Answer:
We look for two numbers whose product is 20 and whose sum is -9.
Those numbers are -4 and -5.
So, x2−9x+20=(x−4)(x−5)

Question 2:
Solve the equation: 2x+3=3x−2
Answer: 2x+3=3x−2⇒3+2=3x−2x⇒5=x2x + 3 = 3x – 2

So, x = 5

Question 3:
Find the sum of the interior angles of a hexagon.
Answer:
Sum of interior angles of an n-sided polygon = (n−2)×180°(n – 2)(6−2)×180°=4×180°=720°(6 – 2)

Question 4:
Solve for x: x2−5x=0
Answer:
Factor: x(x−5)=0⇒x=0 or x=5x(x – 5) = 0

Question 5:
Find the simple interest on ₦8,000 for 3 years at 5% per annum.
Answer:
Simple Interest = P×R×T100 =8000×5×3100=120000100=₦1,200

Question 6:
Convert 0.625 to a fraction in its simplest form.
Answer:
0.625 = 6251000=58

Question 7:
A man bought a television for ₦80,000 and sold it at a profit of 15%. Find the selling price.
Answer:
Profit = 15% of ₦80,000 = 15100×80000=₦12,000
Selling price = 80,000 + 12,000 = ₦92,000

Question 8:
Solve: 1x+1/2=1
Answer: 1x=1−1/2=1/2⇒x=2

Question 9:
If the radius of a circle is 7 cm, find its area. (Take π = 22/7)
Answer:
Area = πr2=22/7×7×7=154 cm2

Question 10:
Find the mean of the numbers: 10, 20, 30, 40, 50
Answer:
Mean = 10+20+30+40+50/5=150/5=30

5 WAEC, NECO Mathematics Past Questions

Section C (Theory 2)

Question 1:
A trader bought 100 mangoes at ₦20 each. 10 of the mangoes got spoiled and the rest were sold at ₦30 each.
(a) Calculate the total cost and total revenue.
(b) What is the profit or loss?

Question 2:
A ladder 10 meters long leans against a vertical wall such that it makes an angle of 60° with the ground.
Calculate:
(a) The height of the wall the ladder reaches.
(b) The distance between the foot of the ladder and the wall.
(Take cos⁡60°=0.5\cos 60° = 0.5, sin⁡60°=0.866\sin 60° = 0.866)

Question 3:
Given that y=3×2−4x+7y = 3
(a) Find the value of y when x=−2x = -2
(b) Find the gradient of the curve at x=1x = 1

Question 4:
Solve the inequality: 2x−3<5x+6≤8x−1

Give your answer in set notation.

Question 5:
The table below shows the marks scored by students in a test:

Marks	10	20	30	40	50
No. of Students	3	7	10	5	5

(a) Calculate the mean mark.
(b) Find the modal class.
(c) Represent the data using a bar chart.

Mathematics Past Questions | WAEC, NECO, GCE

10 WAEC, NECO Mathematics past Questions and Answers

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