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2025 WAEC Mathematics Essay & OBJ Answers [3rd June]
Get Free Live 2025 WAEC May/June General Mathematics (Maths) Essay (Theory) and Objectives Questions and Answers for School Candidates Free of Charge | WAEC May/June Free EXPO Room (3rd June, 2025).
WAEC May/June 2025 FREE ANSWER ROOM [School Candidates]

Tuesday, 3rd June 2025
General Mathematics/Mathematics (Core) 2 (Essay) – 09:30am – 12:00pm
General Mathematics/Mathematics (Core) 1 (Objective) – 3:00pm – 4:30pm
 

2025 WAEC GENERAL MATHEMATICS OBJECTIVES (OBJ) ANSWERS

1. The volume of a cone of height 18 cm is 8,316 cm³. Find the base radius.
✅ A. 21 cm

2. A square has diagonal length of 10 cm. Find the perimeter of the square.
✅ C. 20√2 cm

3. The height of 4 orange seedlings are 2 cm, 5 cm, 7 cm, and 10 cm. Calculate the variance.
✅ C. 8.5

4. Two towns X and Y are located at (-2, -5) and (3, 7). Find the distance between them.
✅ C. 13 units

5. Given that (xᵐy⁴)/x³, find the value of m.
✅ C. 3

6. Solve: 1/3(k – 4) – 1/2(k + 1) = 1/6
✅ D. k = 12

7. In a class of 42 students, 21 offer History and 28 offer Government. If each student offers at least one subject, find the probability that a student selected at random offers Government only.
✅ C. 1/2

8. Which of the following correctly represents the statement: “The sun is shining if and only if the weather is warm”?
✅ D. q ⇔ p

9. The bearing of I from G is 064°. What is the bearing of G from I?
✅ C. 244°

10. Ajoke will be 31 years in x years. If Ajoke is 6 years older than Chioma, find an expression for Chioma’s age.
✅ A. 25 – x

11. Simplify √200 – √72
✅ B. 4√2

12. Simplify: (2 1/5 ÷ 1 1/2) × (12 – 1 3/4)
✅ B. 15 3/4

13. Given that x + y = 1 and x + 3y = 5, find x² + 4xy + 3y².
✅ B. 5

14. Write 0.0364891 in three significant figures and express in standard form.
✅ D. 3.65 × 10⁻²

15. Radius and height of a circular cylinder are 8 cm and 14 cm. Find its curved surface area. (π = 22/7)
✅ C. 352 cm²

16. Interior angle of a regular polygon is 150°. How many sides has the polygon?
✅ C. 12

17. Solve: d² – 4d – 96 = 0
✅ C. d = –8, 12

18. Interior angles of a triangle are in the ratio 2:5:8. Find the difference between the smallest and largest angles.
✅ D. 72°

19. Interior angles of a hexagon are: 107°, 2x°, 150°, 95°, (2x – 15)°, and 123°. Find x.
✅ B. 65

20. Two ball bearings have volumes 1.6 cm³ and 5.4 cm³. Find the ratio of their surface areas.
✅ A. 4:9

21. Given that 2t = 14, find t.
✅ C. 7

22. Two consecutive odd integers such that the sum of 5 times the smaller and 3 times the bigger is 222. Find the smaller.
✅ C. 27

23. Kwakye, Sabina, and Owusu shared $12,000. Kwakye got 20%. The rest was shared 5:3 between Sabina and Owusu. How much did Sabina get?
✅ C. $6,000.00

24. The third and ninth terms of an AP are 9 and 27 respectively. Find the fifth term.
✅ C. 3

25. If 2log₅x = 4, find x.
✅ A. 25

26. A cylinder and a cone have the same volume. If the height of the cone is 24 cm, find the height of the cylinder.
✅ B. 8 cm

27. P varies inversely as the square of Q. If P = 5 when Q = 6, find Q when P = 1.8
✅ B. 10

28. Factorize: 3 – 2x – x²
✅ D. (x + 3)(1 – x)

29. Make r the subject of the relation: 1/p = b/r + c/t
✅ A. r = pct / pb

30. In ∆PQR, QR = 2 cm, ∠PRQ = 60°, ∠PQR = 90°. Find |PR|
✅ B. 4 cm

31. A sector of radius 21 cm subtends 120° at the center. Find the arc length. (π = 22/7)
✅ B. 22 cm

32. Town population increases by 2% yearly. After 2 years, it becomes 83,232. Find original population to the nearest thousand.
✅ B. 81,000

33. A profit of 8% was made on $500. At what price should it be sold to make a 16% profit?
✅ C. $573.04

34. M = {x: 2 ≤ x ≤ 6}, N = {x: 4 ≤ x ≤ 8}. Find M' ∩ N' (complement and intersection).
✅ B. {1, 8, 9}

35. Given sin(x – 46°) = cos(62°), find x.
✅ C. 74

36. Given that log₄16 = logᵧ36, find the value of y.
✅ C. 6

37. In the diagram, ∠PMQ = 34° and ∠NQM = 28°. Find ∠QTN.
✅ D. 118°

38. Find ∠MPN.
✅ A. 62°

39. For what value of x is (3x + 2)/(2x + 1) undefined?
✅ B. –½

40. In the diagram, ∠QRS = (5x)° and ∠QOS = (6x + 24)°. Find ∠QPS.
✅ A. 75°

41. In the diagram, ∠STR = 37° and ∠QRT = 39°. Find ∠SPR.
✅ C. 84°

42. John sold an article for ₦105,000 at a loss of 4%. What was the cost price?
✅ A. ₦109,375.00

43. In the diagram, ∠RST = 45° and ∠ZTU = 20°. Find the angle marked x.
✅ C. 45°

44. Find the angle marked p.
✅ B. 25°

45. What is the gradient of the line 7y – 5x = 35?
✅ A. 7/5

46. From the Venn diagram provided, what valid conclusion can be drawn?
✅ B. Some of my friends are smart.

47. Given age data: [13, 14, 15, 16] and number of students: [3, 14, 13, 8], find the average age to the nearest whole number.
✅ B. 15

48. Find the median age.
✅ B. 15

49. Angle of elevation from base Q is 36°, and wall is 12 m away. Find ladder length PQ.
✅ A. 9 m

50. A fair dice is thrown once. Find the probability of getting an odd number or a prime number.
✅ D. 5/6.


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