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WAEC Mathematics Expo

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WAEC Mathematics questions and answers for 2023/2024 are here. Are you a WAEC candidate?  If your answer is yes, this post will show you the WAEC Mathematics answers and the tricks you need to excel in your WAEC exam.

WAEC questions are set and compiled by the West African Senior School Certificate Examination Board (WASSCE). Make sure you follow the instructions as provided by WAEC

WAEC Mathematics Essay and Objective 2023(EXPO/RUNZ)

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2023/2024 WAEC Mathematics Questions and Answers

Symbols used:

^ means raise to power
/ division

SQRT means square root

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 colors?

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 a 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

Are the WAEC objective questions difficult? Let’s quickly move to the Solutions of 2023/2024 WAEC Mathematics Questions

Solutions to WAEC Mathematics Questions

1.A

The two zeros before 3 are not counted since they are not between whole numbers

2. A

0.064^(-1/3) = 5/2

3.  y+1/2 – 2y-1/3 = 4

Multiply through by 6

3y + 3 – 4y + 2 = 24

Collecting like terms

Implies:

y =-19

Answer: A

4. D

5. B

6. U = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

T = (2, 3, 5, 7)

M = (1, 3, 5, 7, 5)

(T’ n M’) = the numbers in the union set U but not in T and M

(T’ n M’) = (4, 6, 8, 10)

Answer: A

7. Log9 base 3 – log 8 base 2 / log 9 base 3

Log3^2 base 3 – log2^3 base 2 / log 3^2

2log3 base 3 – 3log2 base 2 / 2log3 base 3

Log3 base 3 = 1

Log 2 base = 1

Reason: Log to its own base is 1

This implies:

2 -3 /2 = -1/2

Answer: D

8. Convert both sides to base ten

2xy^1 + 3Xy^0 = 1×2^3 + 1×2^2 + 1x 2^1 + 1×2^0

2y +3 = 8 + 4 + 2 + 2 + 1

2y + 3 = 15

2y = 15-3

Y = 12/2 = 6

Answer: C

9. 6, p, 14

First term a = 6, third term = 14

Number of terms of A.P = a + (n-1)d

T3 =14 = a + 2d

6 + 2d = 14

Common difference d = 14

P = second term

T2 = a + d = 6 + 4 = 10

Answer: B

10. 4 SQRT(7) – 15 SQRT(2) + 6 SQRT(2)

4 SRT(7) – 9 SRT(2)

Answer: C

11. m/n = 2/1

m = 2n

3(2n)^2 – 2n^2 / 2n^2 +2n^2

12n^2 – 2n^2 / 4n^2 + 2n^2 = 10n^2/6n^2

= 5/3

Answer:  B

12. H = kp / y^2 where k = constant, H = 1, p = 8, y = 2

k = Hy^2 /p =  4×1/8 = ½

H = p/2y^2

Answer: C

13. Factorizing:

(4x^2 -6x)(-10x +15)

2x(2x – 3)-5(2x – 3)

2x-5 = 0 or 2x-3 = 0

X = 5/2 or x = 3/2

Answer: B

14. C

15. B

16. 15 percent profit = 115 = 6,900 naira

Let the percent  Bala sold the article at 6600 naira = x

115 = 6,900

X = 6600

Cross multiplying

6900x = 759000

X = 110 percent

The percentage profit if he had sold it at 6600 naira = 110 – 100

= 10 percent

Answer: B

17. 3p = 4q

9p = 8q – 12

p = 4q/3

8q – 12 -(36q/3)

24q – 36 – 36q

-12q = 36

q = -3

3p = -12

p = -4, pq = -3x-4 = 12

Answer: A

18. (0.25)^y = 32

(1/4)^y = 32

2^-2 = 2^5

-2y = 5

y = -5/2

Answer: A

19. C

20. (x-7)(x+2)/ (x+7)(x+2) = (x-7) / (x+7)

Answer: A

21. 3p – 1/p^2 -p

It will be undefined when the denominator p^2 – p = 0

therefore, p = 1 would make it zero

Answer: A

22. Given:

T.S.A = 165 cm^2

D = 7 cm

h = ?

pi = 22/7

T.S.A = 2pirh + 2pir^2

165 -2x(22/7)x3.5^2 = 2x(22/7) x3.5h

165 – 77 = 22h,

h = 88/22

h = 4.0 cm

Answer: C

Are you enjoying the Solutions to WAEC Mathematics Questions? Let’s continue.

23. 2^a = SQRT(64)

2^a = 8

2^a = 2^3

a = 3

but b/a = 3

therefore, b = 3a = 3×3 = 9

a^2 + b^2 = 3^2 + 9^2 = 90

Answer: C

24. Angle XYZ = 180 – (90+52)

180-142 = 38 degrees

From sin rule,

XZ/sin38 = 32/sin52

XZ = 25 cm

Answer: B

26. tita = 72

r = 3.5

pi = 22/7

arc length = 2pir(tita/360)

arc length = 2x( 22/7 )x3.5x(72/360) = 4.4 cm

Answer: C

27. 2lb = (a+b)h

2lb = ah + bh

2lb- bh = ah

b(2l-h) = ah

b = ah/2l-h

Answer: A

28. agent commission = 8 percent

percentage received by eric = 100 – 8 = 92

let the selling price be x

92x/100 = 117760

x = 11776000/92

x = 128000.00 dollars

Answer: B

1. arc length = 2pir(tita/360)

22 = 2×22/7x15xtita/360

tita = 55440/660

tita = 84 degrees

Answer: B

30. l = 15

width = x

if its sides are doubled,

l = 30

width = 2x

area = 30* 2x = 60x cm^2

These questions and solutions are waec practice questions to get you prepared for your 2023/2024 WAEC Mathematics Questions.

If you have questions, use the comment box and you will be attended to as soon as possible. Goodluck.