2025 WAEC GCE General Mathematics (Core) Paper 1/2 Objective and Essay Questions and Answers

2025 WAEC GCE General Mathematics (Core) Paper 1/2 Objective and Essay Questions and Answers

GENERAL MATHEMATICS (CORE) PAPER 1 – OBJECTIVE

60 Questions and Answers

Instruction: Answer all the questions. Choose the option that best answers each question.

1. Evaluate: $7+3\times 4$.

A. 40
B. 19
C. 28
D. 34
Answer: B

2. Express 0.008 in standard form.

A. 8×10−28 \times 10^{-2}8×10−2
B. 8×10−38 \times 10^{-3}8×10−3
C. 8×10−48 \times 10^{-4}8×10−4
D. 8×10−18 \times 10^{-1}8×10−1
Answer: C

3. Find the LCM of 12 and 18.

A. 36
B. 24
C. 18
D. 48
Answer: A

4. Simplify: 34÷18\frac{3}{4} \div \frac{1}{8}43​÷81​.

A. 2
B. 6
C. 8
D. 10
Answer: B

5. Convert 130°F to °C.

A. 45°C
B. 54°C
C. 60°C
D. 72°C
Answer: B

6. Find √144.

A. 10
B. 11
C. 12
D. 14
Answer: C

7. If y = 2x – 5, find y when x = 6.

A. 2
B. 5
C. 7
D. 12
Answer: D

8. Evaluate: 2−32^{-3}2−3.

A. ⅛
B. 8
C. ¼
D. –⅛
Answer: A

9. Convert 0.45 to a percentage.

A. 0.45%
B. 4.5%
C. 45%
D. 450%
Answer: C

10. Solve: $3x=27$.

A. 3
B. 6
C. 9
D. 12
Answer: C

11. The reciprocal of 0.2 is…

A. 2
B. 5
C. 10
D. 20
Answer: B

12. If a = 4, b = 3, evaluate a2−b2a^2 – b^2a2−b2.

A. 7
B. 13
C. 16
D. 25
Answer: A

13. Simplify: (x2)3(x^2)^3(x2)3.

A. x5x^5x5
B. x6x^6x6
C. x3x^3x3
D. x9x^9x9
Answer: B

2025 WAEC GCE General Mathematics (Core) Paper 1/2 Objective and Essay Questions and Answers

14. Convert 5 km to metres.

A. 50 m
B. 500 m
C. 5000 m
D. 50,000 m
Answer: C

15. What is the simple interest on ₦20,000 at 10% for 2 years?

A. ₦2,000
B. ₦3,000
C. ₦4,000
D. ₦5,000
Answer: C

16. The mode of 2, 4, 4, 6, 8 is…

A. 2
B. 4
C. 6
D. 8
Answer: B

17. Express 3 hours 30 minutes in minutes.

A. 180
B. 200
C. 210
D. 230
Answer: C

18. Evaluate: 56+13\frac{5}{6} + \frac{1}{3}65​+31​.

A. ½
B. ⅔
C. 1
D. 1½
Answer: C

19. The additive inverse of –7 is…

A. –7
B. 0
C. 7
D. –1
Answer: C

20. Convert 260° into radians.

A. 13π9\frac{13\pi}{9}913π​
B. 11π6\frac{11\pi}{6}611π​
C. 26π9\frac{26\pi}{9}926π​
D. 11π9\frac{11\pi}{9}911π​
Answer: D

21. Find the median of 3, 7, 9, 2, 5.

A. 3
B. 5
C. 7
D. 9
Answer: B

22. Evaluate: log₁₀100.

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

23. Rationalize 13\frac{1}{\sqrt{3}}3​1​.

A. 33\frac{\sqrt{3}}{3}33​​
B. 333\sqrt{3}33​
C. 3\sqrt{3}3​
D. 13\frac{1}{3}31​
Answer: A

24. A triangle with sides 5 cm, 5 cm, 8 cm is…

A. Scalene
B. Isosceles
C. Equilateral
D. Right-angled
Answer: B

25. If P = {1,2,3} and Q = {2,3,4}, find $P\cap Q$.

A. {1}
B. {2,3}
C. {1,2,3,4}
D. {3,4}
Answer: B

26. The sum of interior angles of a pentagon is…

A. 360°
B. 450°
C. 540°
D. 720°
Answer: C

27. Find the area of a circle of radius 7 cm.

A. 22 cm²
B. 49π cm²
C. 14π cm²
D. 154 cm²
Answer: D

28. Expand: (x + 2)(x – 3).

A. x2−x−6x^2 – x – 6x2−x−6
B. x2+x−6x^2 + x – 6x2+x−6
C. x2−5x−6x^2 – 5x – 6x2−5x−6
D. x2−x+6x^2 – x + 6x2−x+6
Answer: A

29. If a map scale is 1:50,000, 1 cm represents…

A. 50 m
B. 500 m
C. 5 km
D. 50 km
Answer: B

2025 WAEC GCE General Mathematics (Core) Paper 1/2 Objective and Essay Questions and Answers

30. The next term in the sequence: 3, 6, 12, 24… is

A. 30
B. 36
C. 48
D. 60
Answer: C

31. Find the gradient of the line through (2,3) and (6,11).

A. 1
B. 2
C. 3
D. 8
Answer: B

32. Which is a prime number?

A. 21
B. 39
C. 41
D. 49
Answer: C

33. Write 0.72 as a fraction in simplest form.

A. 18/25
B. 36/50
C. 72/100
D. 7/10
Answer: A

34. If 5 pencils cost ₦150, what is the cost of 8 pencils?

A. ₦180
B. ₦200
C. ₦240
D. ₦300
Answer: C

35. Find the missing angle:

A straight line = 180°. One angle is 130°.
A. 40°
B. 50°
C. 60°
D. 70°
Answer: A

36. Value of π is approximately…

A. 3.0
B. 3.14
C. 3.4
D. 22
Answer: B

37. Simplify: 4x−1x\frac{4}{x} – \frac{1}{x}x4​−x1​.

A. x4\frac{x}{4}4x​
B. 3x\frac{3}{x}x3​
C. 43x\frac{4}{3x}3x4​
D. 13x\frac{1}{3x}3x1​
Answer: B

38. Convert 250° to the nearest radian.

A. 3.2 rad
B. 4.36 rad
C. 5.20 rad
D. 4.08 rad
Answer: B

39. The mean of 5, 7, 8, 10 is…

A. 5
B. 8
C. 7.5
D. 10
Answer: C

2025 WAEC GCE General Mathematics (Core) Paper 1/2 Objective and Essay Questions and Answers

40. Solve: $x-4=12$.

A. 16
B. 8
C. 12
D. 20
Answer: A

41. A box contains 5 red and 3 blue balls. Probability of picking a red ball is…

A. ⅓
B. ⅝
C. ¾
D. ½
Answer: B

42. Factorize: x2−9x^2 – 9x2−9.

A. (x – 3)(x + 3)
B. (x – 9)(x + 1)
C. (x – 1)(x + 9)
D. (x – 3)^2
Answer: A

43. Solve: $\log x=2$.

A. x = 20
B. x = 100
C. x = 200
D. x = 1000
Answer: B

44. A straight angle is…

A. 45°
B. 90°
C. 180°
D. 360°
Answer: C

45. The volume of a cube of side 4 cm is…

A. 16 cm³
B. 32 cm³
C. 48 cm³
D. 64 cm³
Answer: D

46. Approximate 5.678 to the nearest whole number.

A. 5
B. 6
C. 7
D. 8
Answer: B

47. If x : y = 3 : 5, then y/x is…

A. 1/2
B. 3/5
C. 5/3
D. 2/5
Answer: C

48. Convert 3.5 hours to seconds.

A. 3600
B. 7200
C. 10,800
D. 12,600
Answer: C

49. The bearing of East is…

A. 045°
B. 090°
C. 180°
D. 270°
Answer: B

50. Solve for x: $2(x–3)=12$.

A. 3
B. 6
C. 9
D. 12
Answer: B

51. If a = 2, b = –3, find ab.

A. –6
B. 6
C. –1
D. 1
Answer: A

52. Simplify: 50\sqrt{50}50​.

A. 525\sqrt{2}52​
B. 25225\sqrt{2}252​
C. 252\sqrt{5}25​
D. 10210\sqrt{2}102​
Answer: A

53. What is the coefficient of x in 7x – 3?

A. –3
B. 0
C. 3
D. 7
Answer: D

54. A regular hexagon has how many lines of symmetry?

A. 6
B. 3
C. 12
D. 8
Answer: A

55. The solution of $x+5=0$ is…

A. –5
B. 5
C. 10
D. –10
Answer: A

2025 WAEC GCE General Mathematics (Core) Paper 1/2 Objective and Essay Questions and Answers

56. Convert 96° to radians.

A. 6π5\frac{6\pi}{5}56π​
B. 8π15\frac{8\pi}{15}158π​
C. 16π15\frac{16\pi}{15}1516π​
D. 48π5\frac{48\pi}{5}548π​
Answer: B

57. If a box contains 40 apples and 8 are bad, what percentage is good?

A. 20%
B. 80%
C. 75%
D. 10%
Answer: B

58. Find the perimeter of a rectangle of length 12 cm and breadth 5 cm.

A. 17 cm
B. 24 cm
C. 30 cm
D. 34 cm
Answer: D

59. Solve: $4x+1=21$.

A. 4
B. 5
C. 6
D. 7
Answer: C

60. The gradient of a horizontal line is…

A. 0
B. 1
C. Undefined
D. Infinite
Answer: A

2025 WAEC GCE General Mathematics (Core) Paper 1/2 Objective and Essay Questions and Answers

GENERAL MATHEMATICS (CORE) PAPER 2 – ESSAY

9 Questions with Full Answers

1. Simplify completely:

3xx2−4−2x+2\frac{3x}{x^2 – 4} – \frac{2}{x + 2}x2−43x​−x+22​

Solution

=3x(x−2)(x+2)−2(x−2)(x+2)(x−2)= \frac{3x}{(x-2)(x+2)} – \frac{2(x-2)}{(x+2)(x-2)}=(x−2)(x+2)3x​−(x+2)(x−2)2(x−2)​ =3x−2x+4(x−2)(x+2)= \frac{3x – 2x + 4}{(x-2)(x+2)}=(x−2)(x+2)3x−2x+4​ =x+4×2−4= \frac{x + 4}{x^2 – 4}=x2−4x+4​

2. A trader bought goods for ₦84,000 and sold at a 25% profit. Find the selling price.

Solution

Profit = 25% of 84,000
= 0.25 × 84,000 = ₦21,000

Selling price = 84,000 + 21,000 = ₦105,000

3. Solve the simultaneous equations:

$$2x+y=11$$ $$x-y=1$$

Solution

Add the equations:
3x = 12 → x = 4
Substitute: y = 11 – 2(4) = 3
Solution: x = 4, y = 3

4. The lengths of sides of a triangle are 7 cm, 9 cm, and 12 cm. Find the area using Heron’s formula.

Solution

Semi-perimeter:

s=7+9+122=14s = \frac{7 + 9 + 12}{2} = 14s=27+9+12​=14

Area:

s(s−a)(s−b)(s−c)\sqrt{s(s-a)(s-b)(s-c)}s(s−a)(s−b)(s−c)​ =14(14−7)(14−9)(14−12)= \sqrt{14(14-7)(14-9)(14-12)}=14(14−7)(14−9)(14−12)​ =14×7×5×2= \sqrt{14 × 7 × 5 × 2}=14×7×5×2​ =980=31.3 cm2= \sqrt{980} = 31.3\ \text{cm}^2=980​=31.3 cm2

5. A cylinder has radius 7 cm and height 10 cm. Find its volume.

Solution

V=πr2h=π(72)(10)V = \pi r^2h = \pi(7^2)(10)V=πr2h=π(72)(10) =490π=1539.4 cm3= 490\pi = 1539.4\ \text{cm}^3=490π=1539.4 cm3

6. Find the mean of the following scores:

5, 8, 9, 12, 6, 10, 15.

Solution

Sum = 65
Number = 7
Mean = 65 ÷ 7 = 9.29

7. Expand and simplify:

$$(2x-3)(x+5)$$

Solution

$$=2x(x+5)-3(x+5)$$ =2×2+10x−3x−15= 2x^2 + 10x – 3x – 15=2x2+10x−3x−15 =2×2+7x−15= 2x^2 + 7x – 15=2x2+7x−15

8. The distance between two towns on a map is 5 cm. If the scale is 1:50,000, find the actual distance in km.

Solution

1 cm = 50,000 cm = 0.5 km
So 5 cm = 5 × 0.5 = 2.5 km

9. Find the equation of the line passing through (1, 4) and (5, 12).

Solution

Gradient:

m=12−45−1=2m = \frac{12-4}{5-1} = 2m=5−112−4​=2

Equation:

$$y-4=2(x-1)$$ $$y=2x+2$$