2026 WAEC GCE GENERAL MATHEMATICS

Questions and Answers | Objective and Essay Exam Guide

Set by the Examiner — Original Model Practice Paper

Prepare confidently for the 2026 WAEC GCE General Mathematics examination with this original practice guide. This exam guide contains 60 carefully worked objective questions covering number bases, indices, logarithms, surds, sets, probability, equations, ratio and percentage, financial arithmetic, sequences, mensuration, geometry, trigonometry, statistics and coordinate geometry, alongside 5 detailed essay questions with fully worked step-by-step solutions and a complete marking guide. Designed strictly to reflect the current WAEC GCE General Mathematics syllabus format and standard, this is an original practice resource for self-study and revision and is not an actual past or leaked WAEC question paper.

Instructions to Candidates

1. This paper consists of two sections: Section A (Objective) and Section B (Essay).

2. Section A contains 60 objective questions. Answer ALL questions in this section.

3. Section B contains 5 essay questions. Answer as instructed by your teacher or invigilator (typically 4 out of 5).

4. Calculators are not to be used unless otherwise permitted; show all workings clearly.

5. Time allowed: 2 hours 40 minutes (practice paper — adjust to your own revision schedule).

6. This is an original practice examination created strictly for revision purposes based on the general structure of the WAEC GCE General Mathematics syllabus. It does not reproduce, predict, or represent any actual WAEC question paper.

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SECTION A: OBJECTIVE TEST (60 Questions)

1. Convert 101101 (base 2) to base 10.

(A) 43

(B) 45

(C) 47

(D) 53

2. Convert 2A (base 16) to base 10.

(A) 40

(B) 41

(C) 42

(D) 44

3. Convert 37 (base 10) to base 2.

(A) 100101

(B) 100111

(C) 101001

(D) 110001

4. Add 23 (base 5) and 14 (base 5), leaving your answer in base 5.

(A) 41

(B) 42

(C) 43

(D) 44

5. Simplify 2^3 x 2^4.

(A) 2^7

(B) 2^12

(C) 4^7

(D) 2^1

6. Evaluate 3^0.

(A) 0

(B) 1

(C) 3

(D) 9

7. Simplify (2^5) / (2^2).

(A) 2^2

(B) 2^3

(C) 2^7

(D) 2^10

8. Evaluate 4^(1/2).

(A) 1

(B) 2

(C) 4

(D) 8

9. Simplify (3^2)^3.

(A) 3^5

(B) 3^6

(C) 9^3

(D) 3^9

10. If log 2 = 0.3010, find log 8.

(A) 0.3010

(B) 0.6020

(C) 0.9030

(D) 1.2040

11. Evaluate log 2 8 (log to base 2 of 8).

(A) 2

(B) 3

(C) 4

(D) 8

12. Simplify log 20 – log 2 (base 10).

(A) 0

(B) 1

(C) 2

(D) 10

13. Evaluate log 3 27 (log to base 3 of 27).

(A) 2

(B) 3

(C) 9

(D) 27

14. Simplify √50.

(A) 5√2

(B) 10√2

(C) 2√5

(D) 25√2

15. Simplify √18 + √8.

(A) 3√2

(B) 5√2

(C) 26

(D) 4√2

16. Rationalize 1/√3.

(A) √3

(B) √3/3

(C) 1/3

(D) 3√3

17. If A = {1,2,3,4} and B = {3,4,5,6}, find A ∩ B.

(A) {1,2}

(B) {3,4}

(C) {5,6}

(D) {1,2,3,4,5,6}

18. If A = {1,2,3,4} and B = {3,4,5,6}, find A ∪ B.

(A) {3,4}

(B) {1,2,5,6}

(C) {1,2,3,4,5,6}

(D) {1,2,3,4}

19. If n(A) = 10, n(B) = 8 and n(A ∩ B) = 3, find n(A ∪ B).

(A) 11

(B) 13

(C) 15

(D) 18

20. If U = {1,2,…,10} and A = {2,4,6,8,10}, find A’ (the complement of A in U).

(A) {1,3,5,7,9}

(B) {2,4,6,8,10}

(C) {1,2,3,4,5}

(D) {}

21. A bag contains 4 red balls and 6 blue balls. Find the probability of picking a red ball at random.

(A) 2/5

(B) 3/5

(C) 1/2

(D) 4/10 only, not simplified

22. A fair die is rolled once. Find the probability of obtaining a number greater than 4.

(A) 1/6

(B) 1/3

(C) 1/2

(D) 2/3

23. A coin is tossed twice. Find the probability of obtaining two heads.

(A) 1/2

(B) 1/3

(C) 1/4

(D) 1/8

24. Solve for x: 2x + 3 = 11.

(A) 3

(B) 4

(C) 5

(D) 7

25. Solve for x: 3x – 5 = 16.

(A) 5

(B) 6

(C) 7

(D) 9

26. Find the roots of x^2 – 4 = 0.

(A) x = 0 only

(B) x = 2 only

(C) x = ±2

(D) x = ±4

27. Find the roots of x^2 + 2x – 8 = 0.

(A) x = 2 or x = -4

(B) x = -2 or x = 4

(C) x = 2 or x = 4

(D) x = -2 or x = -4

28. Solve the simultaneous equations x + y = 7 and x – y = 3.

(A) x = 4, y = 3

(B) x = 5, y = 2

(C) x = 6, y = 1

(D) x = 3, y = 4

29. Solve the simultaneous equations 2x + y = 10 and x – y = 2.

(A) x = 3, y = 4

(B) x = 4, y = 2

(C) x = 5, y = 0

(D) x = 2, y = 6

30. Solve the simultaneous equations x + 2y = 8 and 2x – y = 1.

(A) x = 2, y = 3

(B) x = 3, y = 2

(C) x = 1, y = 3

(D) x = 4, y = 2

31. Simplify the ratio 15:20 to its lowest terms.

(A) 2:3

(B) 3:4

(C) 4:5

(D) 3:5

32. Share N240 between two people in the ratio 3:5. Find the larger share.

(A) 90

(B) 120

(C) 150

(D) 160

33. Express 3/4 as a percentage.

(A) 34%

(B) 43%

(C) 75%

(D) 80%

34. Find 20% of 150.

(A) 20

(B) 25

(C) 30

(D) 35

35. A number is increased by 25% to become 100. Find the original number.

(A) 70

(B) 75

(C) 80

(D) 90

36. Find the simple interest on N5,000 at 10% per annum for 2 years.

(A) 500

(B) 1,000

(C) 1,500

(D) 2,000

37. Find the total amount due after 2 years for a simple interest loan of N5,000 at 10% per annum.

(A) 5,500

(B) 5,800

(C) 6,000

(D) 6,500

38. A trader buys an item for N800 and sells it for N1,000. Find the percentage profit.

(A) 20%

(B) 25%

(C) 30%

(D) 40%

39. An item bought at N600 is sold at a profit of 20%. Find the selling price.

(A) 620

(B) 660

(C) 700

(D) 720

40. An item is sold for N900 at a loss of 20% of the cost price. Find the cost price.

(A) 1,000

(B) 1,080

(C) 1,125

(D) 1,150

41. Find the 10th term of an Arithmetic Progression (AP) whose first term is 3 and common difference is 4.

(A) 35

(B) 37

(C) 39

(D) 43

42. Find the sum of the first 10 terms of an AP whose first term is 2 and common difference is 3.

(A) 145

(B) 150

(C) 155

(D) 160

43. Find the common ratio of the Geometric Progression (GP) 2, 6, 18, 54, …

(A) 2

(B) 3

(C) 4

(D) 6

44. Find the 5th term of a GP whose first term is 2 and common ratio is 3.

(A) 54

(B) 108

(C) 162

(D) 486

45. Find the area of a rectangle of length 8 cm and width 5 cm.

(A) 13 cm^2

(B) 26 cm^2

(C) 40 cm^2

(D) 45 cm^2

46. Find the perimeter of a rectangle of length 8 cm and width 5 cm.

(A) 13 cm

(B) 26 cm

(C) 40 cm

(D) 45 cm

47. Find the area of a circle of radius 7 cm. (Take pi = 22/7)

(A) 44 cm^2

(B) 77 cm^2

(C) 154 cm^2

(D) 308 cm^2

48. Find the circumference of a circle of radius 7 cm. (Take pi = 22/7)

(A) 22 cm

(B) 44 cm

(C) 88 cm

(D) 154 cm

49. Find the volume of a cuboid with length 4 cm, width 3 cm and height 5 cm.

(A) 12 cm^3

(B) 20 cm^3

(C) 60 cm^3

(D) 60 cm^2

50. Find the sum of the interior angles of a hexagon.

(A) 360 degrees

(B) 540 degrees

(C) 720 degrees

(D) 900 degrees

51. The angles of a triangle are x, 2x and 90 degrees. Find the value of x.

(A) 20 degrees

(B) 30 degrees

(C) 45 degrees

(D) 60 degrees

52. The angle at the circumference of a circle is 35 degrees. Find the angle at the centre subtended by the same arc.

(A) 17.5 degrees

(B) 35 degrees

(C) 70 degrees

(D) 140 degrees

53. Find the exterior angle of a regular octagon.

(A) 30 degrees

(B) 40 degrees

(C) 45 degrees

(D) 60 degrees

54. Evaluate sin 30 degrees.

(A) 0

(B) 0.5

(C) 0.707

(D) 1

55. Evaluate cos 60 degrees.

(A) 0

(B) 0.5

(C) 0.866

(D) 1

56. Evaluate tan 45 degrees.

(A) 0

(B) 0.5

(C) 1

(D) 1.5

57. In a right-angled triangle, the side opposite an angle is 3 cm and the hypotenuse is 5 cm. Find the sine of the angle.

(A) 0.4

(B) 0.6

(C) 0.75

(D) 0.8

58. Find the mean of the numbers 2, 4, 6, 8 and 10.

(A) 5

(B) 6

(C) 7

(D) 8

59. Find the median of the numbers 3, 7, 5, 9, 2.

(A) 3

(B) 5

(C) 7

(D) 9

60. Find the distance between the points (0,0) and (3,4) on the Cartesian plane.

(A) 3

(B) 4

(C) 5

(D) 7

SECTION A: ANSWER KEY

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	B	11	B	21	A	31	B	41	C	51	B
2	C	12	B	22	B	32	C	42	C	52	C
3	A	13	B	23	C	33	C	43	B	53	C
4	B	14	A	24	B	34	C	44	C	54	B
5	A	15	B	25	C	35	C	45	C	55	B
6	B	16	B	26	C	36	B	46	B	56	C
7	B	17	B	27	A	37	C	47	C	57	B
8	B	18	C	28	B	38	B	48	B	58	B
9	B	19	C	29	B	39	D	49	C	59	B
10	C	20	A	30	A	40	C	50	C	60	C

SECTION B: ESSAY QUESTIONS AND MODEL ANSWERS

Question 1: Quadratic Equations

(a) Solve the equation x^2 – 3x – 10 = 0 by factorization. (8 marks)

(b) A rectangle has a length that is 3 cm more than its width. If the area of the rectangle is 40 cm^2, find its width and length. (12 marks)

Model Answer / Marking Guide:

(a) x^2 – 3x – 10 = 0. We need two numbers that multiply to give -10 and add to give -3: these are -5 and 2.

• x^2 – 5x + 2x – 10 = 0
• x(x – 5) + 2(x – 5) = 0
• (x – 5)(x + 2) = 0
• x = 5 or x = -2

(b) Let the width be w cm, so the length is (w + 3) cm. Area = w(w + 3) = 40, giving w^2 + 3w – 40 = 0. Factorizing: (w + 8)(w – 5) = 0, so w = 5 or w = -8. Since width cannot be negative, w = 5 cm. Length = w + 3 = 8 cm.

Allocation: (a) correct factorization method (4 marks), correct roots (4 marks); (b) correct equation set up (4 marks), correct factorization/solution (4 marks), correct width and length with rejection of the negative value (4 marks).

Question 2: Simultaneous Linear Equations

The cost of 3 pens and 2 books is N850, while the cost of 5 pens and 4 books is N1,550. If a pen costs N x and a book costs N y:

(a) Write down two equations connecting x and y. (4 marks)

(b) Solve the equations simultaneously to find the cost of one pen and one book. (16 marks)

Model Answer / Marking Guide:

(a) 3x + 2y = 850 …(i); 5x + 4y = 1550 …(ii)

(b) Multiply equation (i) by 2: 6x + 4y = 1700 …(iii). Subtract equation (ii) from (iii): (6x + 4y) – (5x + 4y) = 1700 – 1550, giving x = 150.

Substitute x = 150 into equation (i): 3(150) + 2y = 850, so 450 + 2y = 850, 2y = 400, y = 200.

Therefore, a pen costs N150 and a book costs N200.

Allocation: Correct equations (2 marks each = 4 marks); correct method of elimination or substitution (6 marks); correct value of x (5 marks); correct value of y (5 marks).

Question 3: Mensuration

A cylindrical water tank has a radius of 7 m and a height of 10 m. (Take pi = 22/7)

(a) Find the volume of the tank. (10 marks)

(b) Find the total surface area of the tank. (10 marks)

Model Answer / Marking Guide:

(a) Volume of a cylinder = pi x r^2 x h = 22/7 x 7^2 x 10 = 22/7 x 49 x 10 = 22 x 7 x 10 = 1,540 m^3.

(b) Total surface area of a closed cylinder = 2 x pi x r x (r + h) = 2 x 22/7 x 7 x (7 + 10) = 2 x 22 x 17 = 748 m^2.

Allocation: (a) correct formula (3 marks), correct substitution and working (4 marks), correct final answer with unit (3 marks); (b) correct formula (3 marks), correct substitution and working (4 marks), correct final answer with unit (3 marks).

Question 4: Statistics

The scores obtained by 10 students in a mathematics test are: 4, 6, 7, 5, 8, 6, 9, 5, 6, 4.

(a) Construct a frequency table for the scores. (6 marks)

(b) Find the mean score. (7 marks)

(c) Find the mode of the scores. (3 marks)

(d) Find the median of the scores. (4 marks)

Model Answer / Marking Guide:

(a) Frequency table: Score 4 occurs 2 times; Score 5 occurs 2 times; Score 6 occurs 3 times; Score 7 occurs 1 time; Score 8 occurs 1 time; Score 9 occurs 1 time. (Total frequency = 10)

(b) Mean = sum of scores / number of students = (4+6+7+5+8+6+9+5+6+4) / 10 = 60 / 10 = 6.

(c) The mode is the score that occurs most frequently, which is 6 (occurring 3 times).

(d) Arranging the scores in order: 4, 4, 5, 5, 6, 6, 6, 7, 8, 9. With 10 values, the median is the average of the 5th and 6th values: (6 + 6) / 2 = 6.

Allocation: Correct and complete frequency table (6 marks); correct mean with clear working (7 marks); correct mode (3 marks); correct arrangement and median (4 marks).

Question 5: Trigonometry

A ladder 10 m long leans against a vertical wall so that it makes an angle of 60 degrees with the ground.

(a) Find the height reached by the ladder on the wall, correct to 2 decimal places. (10 marks)

(b) Find the distance of the foot of the ladder from the base of the wall, correct to 2 decimal places. (10 marks)

Model Answer / Marking Guide:

(a) The height on the wall is opposite the 60 degree angle, and the ladder is the hypotenuse. Using sine: height = 10 x sin 60 degrees = 10 x 0.8660 = 8.66 m (to 2 decimal places).

(b) The distance from the base of the wall is adjacent to the 60 degree angle. Using cosine: distance = 10 x cos 60 degrees = 10 x 0.5 = 5.00 m.

Allocation: (a) correct identification of sine ratio (3 marks), correct substitution (3 marks), correct final answer (4 marks); (b) correct identification of cosine ratio (3 marks), correct substitution (3 marks), correct final answer (4 marks).

OVERALL MARKING GUIDE SUMMARY

Section	Content	Marks
Section A	60 Objective (Multiple Choice) Questions at 1 mark each	60
Section B	5 Essay Questions at 20 marks each (answer any 4, or as specified by the examiner)	80 (max obtainable if all attempted, subject to instructions)
Total	Combined Theory and Objective Paper	100 (typical scaled total)

Disclaimer: This is a 100% original practice examination prepared strictly in line with the general structure and scope of the current WAEC GCE General Mathematics syllabus. It is intended solely for revision and self-assessment purposes. It does not reproduce, predict, or claim to represent any actual past or upcoming WAEC GCE examination paper.

Continue visiting EDUJECTS.com for verified examination updates, revision guides, past question analysis, and study materials throughout the 2026 examination season.

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