Free WAEC Math objective Past Questions and Answers (+PDF)

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See the standard 50 WAEC objective Math questions with answers and explanation or download 3 YEARS PDF at the bottom of this post for offline study.

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WAEC modular arithmetic

1. If {x: 2 ≤ x ≤ 18; x ⋹ integer} and 7 + x = 4 (mod 9), find the highest value of x.

A. 2
B. 5
C. 15
D. 18

WAEC number base

2. The sum of 110112, 111112 and 100002 is 10m10n02, find the values of m and n.

A. m = 0, n = 0
B. m = 1, n = 0
C. m = 0, n = 1
D. m = 1, n = 1

WAEC financial arithmetic

3. A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to ₦1.00, how much did the engine cost in naira?

A. ₦250,000.00
B. ₦200,000.00
C. ₦150,000.00
D. ₦100,000.00

WAEC indices

4. Find the value of x.

A. 1
B. ½
C. -½
D. -1

WAEC sequence and series

5. Find the 7th term of the sequence: 2, 5, 10, 17, 26 ...

A. 37
B. 48
C. 50
D. 63

WAEC logarithm

6. Given that logx64 = 3, evaluate xlog28.

A. 6
B. 9
C. 12
D. 24

WAEC indices

7. If 2n = y, find 2(2+n/3)

A. 4y1/3
B. 4y-3
C. 2y1/3
D. 2y-3

WAEC factorization

8. Factorize completely: 6ax – 12by – 9ay + 8bx.

A. (2a – 3b)(4x + 3y)
B. (3a + 4b)(2x + 3y)
C. (3a – 4b)(2x + 3y)
D. (2a + 3b)(4x – 3y)

WAEC quadratic equation

9. Find the equation whose roots are ¾ and -4

A. 4x2 – 13x + 12 = 0
B. 4x2 – 13x - 12 = 0
C. 4x2 + 13x - 12 = 0
D. 4x2 + 13x + 12 = 0

WAEC fractional arithmetic

10. If m = 4, n = 9 and r = 16, evaluate:

A. 1⁵⁄₁₆
B. 1¹⁄₁₆
C. ¹⁄₁₆
D. -37/48

WAEC quadratic equation

11. Adding 42 to a given positive number gives the same result as squaring the number. Find the number.

A. 14
B. 13
C. 7
D. 6

WAEC graphical representation

12. Ada draws the graph of y = x2 – x – 2 and y = 2x – 1 on the same axes. Which of these equations is she solving?

A. x2 – x – 30 = 0
B. x2 – 3x – 1 = 0
C. x2 – 3x – 3 = 0
D. x2 + 3x – 1 = 0

WAEC volumes

13. The volume of a cone of height 3cm is 38½ cm3. Find the radius of its base.     [Take π = 22/7]

A. 3.0 cm
B. 3.5 cm
C. 4.0 cm
D. 4.5 cm

WAEC circles

14. A sector of a circle with radius 6 cm subtends an angle of 60⁰ at the centre. Calculate its perimeter in terms of π.

A. 2(π + 6) cm
B. 2(π + 3) cm
C. 2(π + 2) cm
D. (π + 12) cm

WAEC volumes

15. The dimensions of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take π = 22/7]

A. 14 m
B. 7 m
C. 3½ m
D. 1¾ cm

WAEC circles

16. In the diagram, O is the centre of the circle. If PQ//RS and ∠ONS = 140⁰, find the size of ∠POM.

A. 40⁰
B. 50⁰
C. 60⁰
D. 80⁰

17. In the diagram, PTR is a tangent to the circle centre O. If angle TON = 108⁰, calculate the size of angle PTN.

A. 132⁰
B. 126⁰
C. 108⁰
D. 102⁰

WAEC angles

18. In the diagram above, PQ//RT, QR//SU, ∠PQR = 48⁰ and ∠RTS = x. Find the value of x.

A. 134⁰
B. 132⁰
C. 96⁰
D. 48⁰

In the diagram below, O is the centre of the circle. RT is a diameter, ∠PQT = 33⁰ and ∠TQS = 76⁰. Use this information to answer questions 19 and 20.

19. Calculate the value of angle PTR.

A. 73⁰
B. 67⁰
C. 57⁰
D. 37⁰

20. Find the size of angle PRS.

A. 76⁰
B. 71⁰
C. 38⁰
D. 33⁰

WAEC graphical representation

The table below shows some values for a linear graph. Use it to answer questions 21–22.

21. Find the gradient of the line.

A. 1
B. 2
C. 3
D. 4

22. What is the value of y when x = 2?

A. 5
B. 7
C. 9
D. 11

WAEC trigonometry

23. Given that tan⁡x = ⅔ where 0⁰ ≤ x ≤ 90⁰, find the value of 2sinx.

WAEC triangles and polygon

24. PQRS is a square. If X is the midpoint of PQ, calculate, correct to the nearest degree, ∠ZPX.

A. 53⁰
B. 55⁰
C. 63⁰
D. 65⁰

WAEC angle of elevation

25. The angle of elevation of an aircraft from a point K on the horizontal ground is 30⁰. If the aircraft is 800m above the ground, how far is it from K?

A. 400.00 m
B. 692.82 m
C. 923.76 m
D. 1,600.00 m

WAEC statistics

26. The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 72 students.

A. 32⁰
B. 45⁰
C. 60⁰
D. 75⁰

27. The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 53, 54, 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Find the third quartile.

A. 62
B. 63
C. 64
D. 65

28. The table shows the distribution of scores of some students in a test. Calculate the mean score.

A. 5.6
B. 6.2
C. 6.6
D. 7.0

WAEC probability

29. The probability that Kebba, Ebou and Omar will hit a target are 2/3, 3/4 and 4/5 respectively. Find the probability that only Kebba will hit the target.

A. 2/5
B. 7/60
C. 1/30
D. 1/60

WAEC triangles and polygon

30. In the diagram, VW//YZ, /WX/ = 6cm, /XY/ = 16cm, /YZ/ = 20cm and /ZX/ = 12cm. Calculate /VX/.

A. 3 cm
B. 4 cm
C. 6 cm
D. 8 cm

WAEC word problem

31. Tom will 25 years old in n years’ time. If he/she is 5 years younger than Bade, find Bade’s present age.

A. (30 – n) years
B. (20 – n) years
C. (25 – n) years
D. (30 + n) years

WAEC surds

32. (√2 + √3)/√3 is simplified as m + n√6, find the value of (m + n).

A. ⅓
B. ⅔
C. 1⅓
D. 1⅔

WAEC angles

33. In the diagram, QT and QR are straight lines, ∠ROS = (3n - 20⁰), ∠POT = 2m, ∠SOT = n, ∠POL = m and ∠QOL is a right angle. Find the value of n.

A. 35⁰
B. 40⁰
C. 55⁰
D. 60⁰

WAEC subject of a formula

34. Make k the subject of the relation:

WAEC statistics

35. Which of the following is used to determine the mode of a group of data?

A. Bar chart
B. Frequency polygon
C. Ogive
D. Histogram

WAEC plane shapes

36. The area of a rhombus is 110 cm2. If the diagonals are 20 cm and (2x + 1) cm long, find the value of x.

A. 5.0
B. 4.0
C. 3.0
D. 2.5

WAEC algebraic fractions

37. Simplify:

WAEC linear inequalities

38. Illustrate graphically the solution of:

WAEC fractional arithmetic

39. A farmer uses 2/5 of his land to grow cassava, 1/3 of the remainder for yam and the rest for maize. Find the part of the land used for maize.

A. 2/15
B. 2/5
C. 2/3
D. 4/5

WAEC variation

40. The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of the petrol is consumed on a distance of 15km, how far will the vehicle go on 9 litres of petrol?

A. 22½ km
B. 30 km
C. 33¾ km
D. 45 km

WAEC profit and loss

41. A trader bought 100 oranges at 5 for ₦40.00 and sold them at 20 for ₦120.00. Find the profit or loss percent.

A. 20% profit
B. 20% loss
C. 25% profit
D. 25% loss

WAEC sets

42. Describe the shaded portion in the diagram.

A. P’ ⋂ Q ⋂ R’
B. (P ⋂ R)’ ⋂ Q
C. P’ ⋂ Q ⋂ R
D. (P ⋃ Q)’ ⋂ R

WAEC simultaneous equation

43. Find the value of p if ¼p + 3q = 10 and 2p - ⅓q = 7

A. 4
B. 3
C. -3
D. -4

WAEC statistics

44. Calculate the mean deviation of 5, 3, 0, 7, 2, 1.

A. 0.0
B. 2.0
C. 2.5
D. 3.0

WAEC plane shapes

45. In the diagram above, the shaded part is a carpet laid in a room with dimensions 3.5m by 2.2m leaving a margin of 0.5m round it. Find the area of the margin.

A. 4.7 m2
B. 4.9 m2
C. 5.7 m2
D. 5.9 m2

WAEC triangles and polygon

46. Two angles of a pentagon are in the ratio 2:3. The others are 60⁰ each. Calculate the smaller of the two angles.

A. 72⁰
B. 100⁰
C. 120⁰
D. 144⁰

WAEC probability

47. A letter is selected from the letters of the English alphabet. What is the probability that the letters selected is from the word MATHEMATICS?

A. 9/13
B. 11/26
C. 4/13
D. 1/26

WAEC circles

48. In a circle radius r cm, a chord 16√3 cm long is 10 cm from the centre of the circle. Find, correct to the nearest cm, the value of r.

A. 22 cm
B. 17 cm
C. 16 cm
D. 15 cm

WAEC logical reasoning

49. Consider the following statements:

X: Locally manufactured tyres are attractive
Y: Many locally manufactured tyres do not last long

Denoting locally manufactured tyres by M, attractive tyres by R and long-lasting tyres by L, which of these Venn diagrams illustrates the statement?

WAEC triangles and polygon

50. In the diagram, OX bisects ∠YXZ and OZ bisects ∠YZX. If ∠XYZ = 68⁰, calculate the value of ∠XOZ.

A. 68⁰
B. 72⁰
C. 112⁰
D. 124⁰

• This past questions were extracted from the official WAEC 2015 Math paper 1.

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