If you are a candidate seeking WAEC Mathematics Questions and Answers for 2023, you have arrived at the right place as we will break them down for you. We will go further to show you how WAEC Mathematics questions are set and the best way to answer for full marks.

The West African Senior School Certificate Examination (WASSCE) is organized by WAEC in West African countries. The exam boasts millions of candidates each year due to its importance and over 15 subjects are sat for in the exams including Mathematics. That being said, let’s go through the questions and answers for the subject at hand.

## WAEC Mathematics Questions and Answers 2022/2023

Paper 1 – Objectives

1. Express, correct to three significant figures, 0.003597.
A. 0.359
B. 0.004
C. 0.00360
D. 0.00359

2. Evaluate: (0.064)^-1/3
A. 5/2
B. 2/5
C. -2/5
D. -5/2

3. Solve: y+1/2 – 2y-1/3 = 4
A. y = 19
B. y = -19
C. y = -29
D. y = 29

4. Simplify, and correct to three significant figures, (27.63)^2 – (12.37)^2
A. 614
B. 612
C. 611
D. 610

5. If 7 + y = 4 (mod 8), find the least value of y, 10<=y<=30
A. 11
B. 13
C. 19
D. 21

6. If T = (prime numbers) and
M = (odd numbers) are subsets of
U = (x: 0<x<=10, and x is an integer), find (T’ n M’).
A. (4, 6, 8, 10)
B. (1, 4, 6, 8, 10)
C. (1, 2, 4, 6, 8, 10)
D. (1, 2, 3, 5, 7, 8, 9)

7. Evaluate: log9 base 3 – log8 base 2 /log9 base 3
A. -1/3
B. 1/2
C. 1/3
D. -1/2

8. If 23y = 1111two, find the value of y.
A. 4
B. 5
C. 6
D. 7

9. If 6, P and 14 are consecutive terms in an Arithmetic Progression (A.P), find the value of P.
A. 9
B. 10
C. 6
D. 8

10. Evaluate: 2 (SQRT 28) – 3 (SQRT 50) + (SQRT 50)
A. 4 (SQRT 7) – 21 (SQRT 2)
B. 4 (SQRT 7) – 11 (SQRT 2)
C. 4 (SQRT 7) – 9 (SQRT 2)
D. 4 (SQRT 7) + (SQRT 2)

11. If m : n = 2 : 1, evaluate 3m^2 – 2n^2 /m^2 + mn
A. 4/3
B. 5/3
C. 3/4
D. 3/5

12. H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y
A. H = p /4y^2
B. H = 2p / y^2
C. H = p / 2 y^2
D. H = p / y^2

13. Solve 4x^2 – 16x + 15
A. X = 1 (1/2) or X = -2 (1/2)
B. X = 1 (1/2) or X = 2 (1/2)
C. X = 1 (1/2) or X = -1 (1/2)
D. X = -1 (1/2) or X = -2 (1/2)

14. Evaluate 0.42 divided by 2.5 /0.5 x 2.05, leaving the answer in standard form.
A. 1.639 x 10^2
B. 1.639 x 10^1
C. 1.639 x 10^-1
D. 1.639 x 10^-2

15. Simplify: log6 – 3log3 + 2/3log27.
A. 3log 2
B. Log2
C. Log3
D. 2log3

16. Bala sold an article for 6,900.00 naira and made a profit of 15 percent. Calculate his percentage profit if he had sold for 6600.00.
A. 5 percent
B. 10 percent
C. 12 percent
D. 13 percent

17. If 3p = 4q and 9p = 8q-12, find the value of pq.
A. 12
B. 7
C. -7
D. -12

18. If (0.25)^y = 32, find the value of y.
A. y = -5/2
B. y = -3/2
B. y = 3/2
D. y = 5/2

19. There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?
A. 3/4
B. 1/3
C. 2/3
D. 1/4

20. Simplify: x^2 – 5x – 14 / x^2 – 9x + 14
A. X – 7 /x + 7
B. X + 7 /x – 7
C. X – 2 /x + 4
D. X + 2 /x – 2

21. Which of these values would make 3p – 1 /p^2 – p undefined?
A. 1
B. 1/3
C. -1/3
D. -1

22. The total surface area of a solid cylinder is 165 cm2. If the base diameter is 7 cm, calculate its height. (Take pi = 22/7)
A. 7.5 cm
B. 4.5 cm
C. 4.0 cm
D. 2.0 cm

23. If 2^a = SQRT(64) and b/a = 3, evaluate a^2 + b^2.
A. 250
B. 160
C. 90
D. 48

24. In triangle XYZ, line XZ = 32 cm, angle YXZ = 52 degrees and XZY = 90 degrees. Find, correct to the nearest centimeter, line XZ.
A. 31 cm
B. 25 cm
C. 20 cm
D. 13 cm

25. If log 2 base x = 0.3, evaluate log 8 base x.
A. 2.4
B. 1.2
C. 0.9
D. 0.6

26. An arc subtends an angle of 72 degrees at the center of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. (Take pi = 22/7)
A. 6.6 cm
B. 8.8 cm
C. 4.4 cm
D. 2.2 cm

27. Make b the subject of the relation
lb = 1/2(a+b)h
A. ah /2l – h
B. 2l – h/al
C. al/2l – h
D. al/2 – h

29. Eric sold his house through an agent who charged 8 percent commission on the selling price. If Eric received 117,760.00 dollars after the sale, what was the selling price of the house?
A. 130,000.00 dollars
B. 128,000.00 dollars
C. 125,000.000 dollars
D. 120,000.00 dollars

29. Find the angle which an arc of length 22 cm subtends at the centre of a circle of radius 15 cm. (take pi = 22/7)
A. 70 degrees
B. 84 degrees
C. 96 degrees
D. 156 degrees

30. A rectangular board has a length of 15 cm and width x cm. If its sides are doubled, find its new area.
A. 60x cm squared
B. 45x cm squared
C. 30x cm squared
D. 15x cm squared

31. In the diagram, POS and ROT are straight lines. OPQR is a parallelogram, line OS = line OT and angle OST = 50 degrees. Calculate the value of angle OPQ.
A. 100 degrees
B. 120 degrees
C.140 degrees
D. 160 degrees

32. Factorize completely: (2x + 2y)(x-y) + (2x – 2y)(x + y)
A. 4(x – y)(x + y)
B. 4(x – y)
C. 2(x – y) (x + y)
D. 2(x – y)

33. The interior angles of a polygon are 3x, 2x, 4x, 3x and 6x. Find the size of the smallest angle of the polygon.
A. 80 degrees
B. 60 degrees
C. 40 degrees
D. 30 degrees

34. A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?
A. 2/3
B. 3/5
C. 7/20
D. 12/25

35. Find the equation of a straight line passing through the points (1, -5) and having gradient of ¾.
A. 3x + 4y – 23 = 0
B. 3x + 4y + 23 = 0
C. 3x – 4y + 23 = 0
D. 3x – 4y – 23 = 0

36. The foot of a ladder is 6 m from the base of an electric pole. The top of the ladder rest against the pole at a point 8 m above the ground. How long is the ladder?
A. 14 m
B. 12 m
C. 10 m
D. 7 m

37. If tan x = 3/4, 0<x<90,
evaluate cos x/2sin x
A. 8/3
B. 3/2
C. 4/3
D. 2/3

38. From the top of a vertical cliff 20 m high, a boat at sea can be sighted 75 m away and on the same horizontal position as the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
A. 56 degrees
B. 75 degrees
C. 16 degrees
D. 15 degrees

39. In the diagram, O is the centre of the circle of radius 18 cm. If angle ZXY = 70 degrees, calculate the length of arc ZY. (Take pi = 22/7)
A. 11 cm
B. 22 cm
C. 44 cm
D. 80 cm

In the diagram, RT is tangent to the circle at R, angle PQR = 70 degrees, angle QRT = 52 degrees, angle QSR = y and angle PRQ = x. Use the diagram to answer questions 40 and 41

40. Find the value of y.
A. 70 degrees
B. 60 degree
C. 52 degree
D. 18 degree

41. Calculate the value of x
A. 70 degrees
B. 58 degrees
C. 55 degrees
D. 48 degrees

42. Calculate the variance of 2, 4, 7, 8, 9
A. 7.2
B. 6.8
C. 3.5
D. 2.6

43. The fourth term of an Arithmetic Progression (A.P.) is 37 and the first term is -20. Find the common difference.
A. 63
B. 57
C. 19
D. 17

In the diagram, PQ is parallel to RS, angle QFG = 105 degrees and angle FEG = 50 degrees. Use the diagram to answer questions 44 and 45.

44. Find the value of m
A. 130 degrees
B. 105 degrees
C. 75 degrees
D. 55 degrees

45. Find the values of n
A. 40 degrees
B. 55 degrees
C. 75 degrees
D. 130 degrees

46. A box contains 5 red, 6 green and 7 yellow pencils of the same size. What is the probability of picking a green pencil at random?
A. 1/6
B. 1/4
C. 1/3
D. 1/2

47. The pie chart represents fruits on display in a grocery shop. If there are 60 oranges on display, how many apples are there?
A. 90
B. 80
C. 70
D. 40

The following are scores obtained by some students in a test.
8 18 10 14 18 11 13 14 17 15 8 16 13
Use this information to answer questions 48 to 50

48. Find the mode of the distribution
A. 18
B. 14
C. 13
D. 8

49. Find the median score.
A. 14.5
B. 14.0
C. 13.5
D. 13.0

50. How many students scored above the mean score?
A. 10
B. 9
C. 8
D. 7

### Paper 2 – Theory

1. (a) Solve: 7x + 4 < (4x + 3).
(b) Salem, Sunday and Shaka shared a sum of N 1,100.00. For every N2.00 that Salem gets, Sunday gets fifty kobo and for every N 4.00 Sunday gets, Shaka gets N 2.00. Find Shaka’s share.

2. (a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.
(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.

3. (a) A boy 1.2 m tall, stands 6 m away from the foot of a vertical lamp pole 4.2 m long. If the lamp is at the tip of the pole, represent this information in a diagram.
(b) Calculate the:
(i) length of the shadow of the boy cast by the lamp;
(ii) angle of elevation of the lamp from the boy, correct to the nearest degree.

4. (a) The present ages of a father and his son are in the ratio 10 : 3. If the son is 15 years old now, in how many years will the ratio of their ages be 2 : 1?
b) The arithmetic mean of x, y and z is 6 while that of x, y, z, t, u, v and w is 9. Calculate the arithmetic mean of t, u, v, and w.

5. point H is 20m away from the foot of a tower on the same horizontal ground. From point H, the angle of elevation of point (P) on the tower and the top (T) of the tower are 30o and 50o respectively. Calculate, and correct 3 significant figures:
(a) /PT/;
(b) The distance between H and the top of the tower;
(c) The position of H if the angle of depression of H from the top of the tower is to be 40°.

DISCLAIMER! These are not real WAEC GCE Mathematics questions but likely repeated questions over the years to help candidates understand the nature of their examinations. Ensure to take note of every question provided on this page.