50 Objective Questions, 5 Theory Questions, and Full Solutions
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• WAEC 2026/2027 Mathematics Likely Questions and Answers
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• WAEC Mathematics Syllabus Topics and Practice Questions 2026/2027
• WAEC 2027 Mathematics Calculation and Theory Solutions
Introduction
Mathematics is one of the two compulsory subjects every WAEC 2026/2027 candidate must sit, regardless of their track. Scoring an A (70 and above) in WAEC Mathematics is absolutely possible when you understand the pattern of questions and practice consistently. Many students fear Mathematics unnecessarily. The truth is that WAEC Maths follows a predictable pattern year after year, and the student who works through enough past questions will recognise that pattern.
WAEC Mathematics covers Number and Numeration, Algebra, Geometry, Mensuration, Trigonometry, Statistics, and Probability. Paper 1 is the multiple-choice section. Paper 2 requires you to show full working for each solution. Showing your steps matters enormously in Paper 2, even if your final answer has a small error.
This guide gives you 50 likely objective questions and 5 full theory questions with step-by-step solutions. Work through every question. Understand every step. Then test yourself under timed conditions until the methods become automatic.
50 Likely WAEC 2026/2027 WAEC 2026/2027 Mathematics Objective Questions
Each question includes four options. The correct answer is marked with ✅. Study the reasoning behind each correct choice, not just the answer itself.
Q1. Simplify: 3x + 2y – x + 4y
A. 2x + 6y ✅
B. 4x + 6y
C. 2x + 2y
D. 4x + 2y
Q2. Find the value of x if 2x – 5 = 11
A. 3
B. 6
C. 8 ✅
D. 16
Q3. What is 15% of 200?
A. 25
B. 30 ✅
C. 35
D. 45
Q4. Express 0.0045 in standard form
A. 4.5 × 10⁻²
B. 4.5 × 10⁻³ ✅
C. 45 × 10⁻⁴
D. 4.5 × 10³
Q5. The area of a circle with radius 7 cm is (take π = 22/7):
A. 44 cm²
B. 154 cm² ✅
C. 22 cm²
D. 616 cm²
Q6. Find the HCF of 24 and 36
A. 6
B. 12 ✅
C. 18
D. 72
Q7. If the angles of a triangle are in the ratio 2:3:5, find the largest angle.
A. 36°
B. 54°
C. 90° ✅
D. 72°
Q8. Solve: x² – 5x + 6 = 0
A. x = 1 or 6
B. x = 2 or 3 ✅
C. x = -2 or -3
D. x = 3 or 4
Q9. A trader buys goods for ₦500 and sells for ₦625. What is the percentage profit?
A. 20%
B. 25% ✅
C. 30%
D. 15%
Q10. Find the gradient of the line passing through (2, 3) and (4, 7).
A. 1
B. 2 ✅
C. 3
D. 4
Q11. What is the LCM of 6, 8, and 12?
A. 12
B. 24 ✅
C. 48
D. 96
Q12. Evaluate: log₁₀ 1000
A. 2
B. 3 ✅
C. 10
D. 100
Q13. A bag contains 4 red and 6 blue balls. What is the probability of picking a red ball?
A. 2/5 ✅
B. 3/5
C. 1/4
D. 4/7
Q14. The sum of interior angles of a pentagon is:
A. 360°
B. 540° ✅
C. 720°
D. 900°
Q15. If y varies directly as x and y = 12 when x = 3, find y when x = 7.
A. 21
B. 28 ✅
C. 36
D. 42
Q16. Find the mean of: 4, 7, 3, 8, 9, 5
A. 5
B. 6 ✅
C. 7
D. 8
Q17. Simplify: (3²)³
A. 3⁵
B. 3⁶ ✅
C. 9⁶
D. 3⁹
Q18. A car travels 240 km in 3 hours. What is its average speed?
A. 60 km/h
B. 80 km/h ✅
C. 70 km/h
D. 100 km/h
Q19. Find the value of sin 30°
A. 1
B. √3/2
C. 1/2 ✅
D. 0
Q20. What is the volume of a cylinder with radius 3.5 cm and height 10 cm? (π = 22/7)
A. 385 cm³ ✅
B. 440 cm³
C. 220 cm³
D. 770 cm³
Q21. If P = {2, 4, 6, 8} and Q = {4, 8, 12}, find P ∩ Q.
A. {2, 4, 6, 8, 12}
B. {4, 8} ✅
C. {6, 12}
D. {2, 6}
Q22. The simple interest on ₦8,000 at 5% per annum for 3 years is:
A. ₦800
B. ₦1,000
C. ₦1,200 ✅
D. ₦1,500
Q23. Factorize completely: 6x² – 9x
A. 3x(2x – 3) ✅
B. 2x(3x – 4)
C. 3(2x² – 3x)
D. 6x(x – 1)
Q24. Find the median of: 2, 5, 7, 3, 9
A. 3
B. 5 ✅
C. 7
D. 9
Q25. Convert 110₂ to base 10
A. 5
B. 6 ✅
C. 7
D. 4
Q26. If 3x + 2 = 5x – 4, find x.
A. 1
B. 2
C. 3 ✅
D. 6
Q27. A cone has base radius 6 cm and height 8 cm. Find its volume. (π = 22/7)
A. 301.7 cm³ ✅
B. 452.4 cm³
C. 150.9 cm³
D. 200 cm³
Q28. The bearing of B from A is 070°. What is the bearing of A from B?
A. 110°
B. 250° ✅
C. 290°
D. 070°
Q29. Evaluate: 2⁵ ÷ 2²
A. 4
B. 8 ✅
C. 16
D. 2
Q30. Find x: log x = 2 (base 10)
A. 20
B. 100 ✅
C. 1000
D. 10
Q31. The circumference of a circle is 44 cm. Find its radius. (π = 22/7)
A. 5 cm
B. 7 cm ✅
C. 14 cm
D. 11 cm
Q32. If a:b = 3:4 and b:c = 2:5, find a:c.
A. 3:10 ✅
B. 6:5
C. 3:5
D. 6:20
Q33. What is the value of tan 45°?
A. 0
B. 1 ✅
C. √2
D. 1/2
Q34. A square has perimeter 48 cm. Find its area.
A. 100 cm²
B. 144 cm² ✅
C. 192 cm²
D. 48 cm²
Q35. Find the compound interest on ₦5,000 at 10% per annum for 2 years.
A. ₦950
B. ₦1,000
C. ₦1,050 ✅
D. ₦1,100
Q36. Simplify: (2x³y²)³
A. 6x⁹y⁶
B. 8x⁹y⁶ ✅
C. 2x⁶y⁵
D. 4x⁹y⁶
Q37. In a right-angled triangle, the side opposite the right angle is called the:
A. Base
B. Adjacent
C. Hypotenuse ✅
D. Altitude
Q38. Find the range of: 3, 7, 1, 9, 4, 12
A. 9
B. 11 ✅
C. 12
D. 8
Q39. What is 3/4 expressed as a percentage?
A. 34%
B. 60%
C. 75% ✅
D. 80%
Q40. Find the nth term of the sequence 5, 8, 11, 14…
A. 3n + 2 ✅
B. 3n + 1
C. 2n + 3
D. 5n
Q41. The angles on a straight line add up to:
A. 90°
B. 270°
C. 180° ✅
D. 360°
Q42. Simplify: (1/2 + 1/3) × 12
A. 5
B. 10 ✅
C. 6
D. 4
Q43. If the cost of 5 pens is ₦75, find the cost of 8 pens.
A. ₦100
B. ₦112
C. ₦120 ✅
D. ₦150
Q44. In a pie chart, a sector representing 25% of the data has an angle of:
A. 25°
B. 45°
C. 90° ✅
D. 75°
Q45. Find x if 5x/3 = 10.
A. 2
B. 4
C. 6 ✅
D. 8
Q46. The exterior angle of a regular hexagon is:
A. 45°
B. 60° ✅
C. 72°
D. 90°
Q47. Solve: 2(x – 3) = 14
A. 5
B. 8
C. 10 ✅
D. 14
Q48. A man is 40 years old and his son is 10. In how many years will the man be three times his son’s age?
A. 5 years ✅
B. 10 years
C. 15 years
D. 20 years
Q49. Find the gradient of the line 3y – 6x = 9.
A. -6
B. 2 ✅
C. 3
D. 9
Q50. The mode of the data 2, 3, 3, 4, 4, 4, 5 is:
A. 3
B. 2
C. 4 ✅
D. 5
5 Likely WAEC 2026/2027 WAEC 2026/2027 Mathematics Theory Questions with Model Answers
Theory questions require organized, well-explained answers. Use the model answers below as a guide for structure, depth, and language. Practise writing your own answers and comparing them to the models.
Theory Question 1
(a) Factorize completely: 2x² + 5x – 3(b) Find the roots of the equation 2x² + 5x – 3 = 0(c) A rectangular field is 15 m long and 8 m wide. Find (i) its perimeter and (ii) its area.
MODEL ANSWER:
(a) Factorize 2x² + 5x – 3
We look for two numbers whose product is 2 × (-3) = -6 and whose sum is 5.
The numbers are 6 and -1.
2x² + 6x – x – 3
= 2x(x + 3) – 1(x + 3)
= (2x – 1)(x + 3) ✓
(b) Roots of 2x² + 5x – 3 = 0
From (a): (2x – 1)(x + 3) = 0
Either 2x – 1 = 0 → x = 1/2
Or x + 3 = 0 → x = -3
∴ x = 1/2 or x = -3 ✓
(c) (i) Perimeter = 2(length + width) = 2(15 + 8) = 2 × 23 = 46 m ✓
(ii) Area = length × width = 15 × 8 = 120 m² ✓
Theory Question 2
The table below shows the marks scored by 30 students in a test:Mark: 1-10, 11-20, 21-30, 31-40, 41-50Frequency: 3, 7, 10, 6, 4(a) Draw a frequency distribution table showing class boundaries, class midpoints, and cumulative frequency.(b) Calculate the mean mark.(c) What is the modal class?
MODEL ANSWER:
(a) Frequency Distribution Table:
Class | Midpoint (x) | Frequency (f) | fx | Cumulative Freq
1-10 | 5.5 | 3 | 16.5 | 3
11-20 | 15.5 | 7 | 108.5 | 10
21-30 | 25.5 | 10 | 255 | 20
31-40 | 35.5 | 6 | 213 | 26
41-50 | 45.5 | 4 | 182 | 30
Total: Σf = 30, Σfx = 775
(b) Mean = Σfx / Σf = 775 / 30 = 25.83 (to 2 decimal places) ✓
(c) The modal class is 21-30, because it has the highest frequency of 10. ✓
Theory Question 3
A ladder 10 m long leans against a vertical wall. The foot of the ladder is 6 m from the base of the wall.(a) How high up the wall does the ladder reach? Leave your answer in surd form and also as a decimal.(b) Find the angle the ladder makes with the ground, correct to the nearest degree.
MODEL ANSWER:
(a) Using Pythagoras’ theorem: h² + 6² = 10²
h² = 100 – 36 = 64
h = √64 = 8 m ✓
(In surd form: h = √64 = 8. Since 64 is a perfect square, the surd simplifies to 8 m exactly.)
(b) The angle θ the ladder makes with the ground:
sin θ = opposite/hypotenuse = 8/10 = 0.8
θ = sin⁻¹(0.8)
θ ≈ 53° (to the nearest degree) ✓
Theory Question 4
(a) A man invests ₦20,000 at 8% per annum compound interest. Calculate the amount at the end of 3 years.(b) A shop sells a television set marked at ₦45,000 with a 15% discount. Find the selling price.
MODEL ANSWER:
(a) Compound Interest Formula: A = P(1 + r/100)^n
P = ₦20,000, r = 8%, n = 3 years
A = 20,000 × (1 + 8/100)³
A = 20,000 × (1.08)³
A = 20,000 × 1.259712
A = ₦25,194.24 ✓
(b) Discount = 15% of ₦45,000 = 0.15 × 45,000 = ₦6,750
Selling price = ₦45,000 – ₦6,750 = ₦38,250 ✓
Theory Question 5
The coordinates of triangle ABC are A(1, 2), B(4, 2), and C(4, 6).(a) Draw the triangle on graph paper.(b) Find the length of BC.(c) Find the length of AC.(d) Find the area of triangle ABC.
MODEL ANSWER:
(a) Plot A(1,2), B(4,2), C(4,6) and connect them. [Diagram to be drawn on graph paper]
(b) BC is a vertical line from B(4,2) to C(4,6).
Length of BC = 6 – 2 = 4 units ✓
(c) AC connects A(1,2) and C(4,6).
Using the distance formula: AC = √[(4-1)² + (6-2)²]
= √[3² + 4²] = √[9 + 16] = √25 = 5 units ✓
(d) AB is horizontal: length = 4 – 1 = 3 units
BC is vertical: length = 4 units
Since angle B = 90° (AB is horizontal, BC is vertical):
Area = (1/2) × base × height = (1/2) × 3 × 4 = 6 square units ✓
Study Tips: How to Score A in WAEC WAEC 2026/2027 Mathematics 2026/2027
Tip 1: Show all working in Paper 2. WAEC awards marks for correct steps, even if the final answer is wrong.
Tip 2: Know the formula for area, volume, perimeter, and surface area of all shapes on the syllabus.
Tip 3: Practice statistics questions (mean, median, mode, cumulative frequency) as they appear in almost every exam.
Tip 4: Spend at least 30 minutes per day solving past questions under timed conditions.
Tip 5: If you are stuck on a question, move on and come back. Do not waste time on one question when others are waiting.
Frequently Asked Questions
Q: Is WAEC Mathematics the same for all students in 2026/2027?
A: Yes. The WAEC Mathematics examination is the same for all students, whether they are in the Science, Arts, or Commercial track. Every WAEC candidate must sit Mathematics as a compulsory subject.
Q: How is WAEC Mathematics Paper 2 marked?
A: In Paper 2, WAEC examiners award marks for each correct step shown. Even if your final answer is wrong, you can earn partial marks for correct working. Always show every calculation step clearly.
Q: What are the most important topics in WAEC Mathematics 2026/2027?
A: Algebra (equations and factorization), Statistics (mean, median, frequency tables), Mensuration (areas and volumes), Number and Numeration (fractions, percentages, ratios), and Trigonometry appear in almost every WAEC Mathematics examination.
