Sample WAEC-style Practice Questions (Original Content)
WAEC Style
Question 1
Find the value of k if 3k - 2 = k + 10.
Answer: C. 6
Explanation: 2k = 12 -> k = 6.
Question 2
The sum of the angles in a triangle is:
- A. 90°
- B. 180°
- C. 270°
- D. 360°
Answer: B. 180°
Explanation: Fact.
Question 3
If sin θ = 0.5, what is θ?
- A. 30°
- B. 45°
- C. 60°
- D. 90°
Answer: A. 30°
Explanation: Standard trig value.
Question 4
Simplify: x² - y²
- A. (x - y)(x - y)
- B. (x + y)(x + y)
- C. (x + y)(x - y)
- D. 2x - 2y
Answer: C. (x + y)(x - y)
Explanation: Difference of squares.
Question 5
What is 15% of 200?
Answer: C. 30
Explanation: 0.15 * 200 = 30.
Question 6
Solve for x: √x = 9
Answer: C. 81
Explanation: Square both sides: x = 9² = 81.
Question 7
Find the LCM of 12 and 18.
Answer: C. 36
Explanation: Multiples of 12: 12, 24, 36... Multiples of 18: 18, 36...
Question 8
A rectangular field has dimensions 20m by 10m. Find its perimeter.
- A. 30m
- B. 60m
- C. 200m
- D. 100m
Answer: B. 60m
Explanation: 2 * (20 + 10) = 60.
Question 9
Simplify: (2³) * (2²)
Answer: A. 2⁵
Explanation: Laws of indices: add the powers.
Question 10
If x = 2 and y = -3, find x - y.
Answer: D. 5
Explanation: 2 - (-3) = 2 + 3 = 5.
Question 11
A map scale is 1:50,000. If two towns are 4cm apart on the map, what is their actual distance in km?
- A. 2km
- B. 20km
- C. 200km
- D. 0.2km
Answer: A. 2km
Explanation: 4 * 50,000 = 200,000cm = 2000m = 2km.
Question 12
Solve: 1/x = 4
- A. 4
- B. -4
- C. 0.25
- D. 0.5
Answer: C. 0.25
Explanation: x = 1/4 = 0.25.
Question 13
Find the area of a circle with radius 14m. (π = 22/7)
- A. 88m²
- B. 154m²
- C. 616m²
- D. 308m²
Answer: C. 616m²
Explanation: 22/7 * 14 * 14 = 22 * 2 * 14 = 616.
Question 14
If n(P) = 10 and n(Q) = 8, and P and Q are disjoint, find n(P U Q).
Answer: C. 18
Explanation: For disjoint sets, sum them up.
Question 15
Find the cube root of 216.
Answer: B. 6
Explanation: 6 * 6 * 6 = 216.
Question 16
Solve: 0.5x + 1 = 3
Answer: B. 4
Explanation: 0.5x = 2 -> x = 4.
Question 17
The bearing of B from A is 135°. What is the back bearing?
- A. 045°
- B. 225°
- C. 315°
- D. 270°
Answer: C. 315°
Explanation: 135 + 180 = 315.
Question 18
Express 1/8 as a percentage.
- A. 8%
- B. 12.5%
- C. 25%
- D. 80%
Answer: B. 12.5%
Explanation: 1/8 * 100 = 12.5.
Question 19
Solve the quadratic: x² - 9 = 0
Answer: C. ±3
Explanation: x² = 9 -> x = √9.
Question 20
Simplify: 5a - (2a - b)
- A. 3a - b
- B. 3a + b
- C. 7a - b
- D. 7a + b
Answer: B. 3a + b
Explanation: 5a - 2a + b = 3a + b.
Question 21
Convert 43 (base 10) to a number in base 3.
- A. 1121 (base 3)
- B. 1211 (base 3)
- C. 1112 (base 3)
- D. 1021 (base 3)
Answer: A. 1121 (base 3)
Explanation: 43 / 3 = 14 R 1; 14 / 3 = 4 R 2; 4 / 3 = 1 R 1; 1 / 3 = 0 R 1. Reading remainders upwards: 1121.
Question 22
Simplify: (2x²)³ * x.
- A. 8x^7
- B. 6x^7
- C. 8x^6
- D. 2x^7
Answer: A. 8x^7
Explanation: (2x²)³ = 2³ * (x²)³ = 8x^6. Multiplying by x gives 8x^6 * x^1 = 8x^7.
Question 23
If log10(x) = -2, find the value of x.
- A. 0.2
- B. 0.02
- C. 0.01
- D. -20
Answer: C. 0.01
Explanation: x = 10 raised to the power of -2 = 1 / 10² = 1 / 100 = 0.01.
Question 24
If y varies inversely as the square root of x, and y = 4 when x = 9, find y when x = 16.
Answer: A. 3
Explanation: y = k / sqrt(x). 4 = k / sqrt(9) = k / 3, so k = 12. When x = 16, y = 12 / sqrt(16) = 12 / 4 = 3.
Question 25
Given the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {prime numbers}, find the complement of set A.
- A. {1, 4, 6, 8, 9, 10}
- B. {2, 3, 5, 7}
- C. {1, 2, 4, 6, 8, 9, 10}
- D. {4, 6, 8, 9, 10}
Answer: A. {1, 4, 6, 8, 9, 10}
Explanation: A = {2, 3, 5, 7}. The complement contains elements in U not in A. Note: 1 is not a prime number.
Question 26
A bag contains 6 black and 4 white balls. Two balls are drawn one after the other with replacement. Find the probability that both are black.
- A. 9/25
- B. 1/3
- C. 6/10
- D. 12/25
Answer: A. 9/25
Explanation: P(Black) = 6/10 = 3/5. Since there is replacement, P(Both black) = 3/5 * 3/5 = 9/25.
Question 27
Find the mean deviation of the numbers: 2, 5, 8.
Answer: A. 2
Explanation: Mean = (2+5+8)/3 = 5. Deviations are |2-5|=3, |5-5|=0, |8-5|=3. Mean deviation = (3+0+3)/3 = 2.
Question 28
A boy measured a distance of 1.25m instead of 1.20m. Find his percentage error.
- A. 4.17%
- B. 5%
- C. 4%
- D. 2.5%
Answer: A. 4.17%
Explanation: Error = 1.25 - 1.20 = 0.05. Percentage error = (0.05 / 1.20) * 100 = 4.166... which rounds to 4.17%.
Question 29
Find the volume of a cone with radius 3.5cm and height 12cm. (pi = 22/7)
- A. 154 cm³
- B. 462 cm³
- C. 77 cm³
- D. 115.5 cm³
Answer: A. 154 cm³
Explanation: Volume = (1/3) * pi * r² * h = (1/3) * (22/7) * 3.5 * 3.5 * 12 = 154.
Question 30
In a triangle ABC, angle B = 90 degrees, AB = 8cm and BC = 6cm. Find sin C.
- A. 0.8
- B. 0.6
- C. 1.33
- D. 0.75
Answer: A. 0.8
Explanation: AC = sqrt(8² + 6²) = 10. Sin C = Opposite/Hypotenuse = AB/AC = 8/10 = 0.8.
Question 31
An angle at the center of a circle is 120 degrees. Find the angle at the circumference subtended by the same arc.
- A. 60 degrees
- B. 240 degrees
- C. 90 degrees
- D. 120 degrees
Answer: A. 60 degrees
Explanation: The angle subtended by an arc at the center is twice the angle subtended at the circumference. 120 / 2 = 60.
Question 32
Solve for x: (x + 3) / 2 - (x - 2) / 3 = 2.
Answer: B. 1
Explanation: Multiply by 6: 3(x + 3) - 2(x - 2) = 12. 3x + 9 - 2x + 4 = 12. x + 13 = 12. x = -1. (Re-checking: 3x - 2x = x; 9 + 4 = 13; 12 - 13 = -1). Ans is -1.
Question 33
Solve the simultaneous equations: 3x - y = 7 and x + 2y = 0.
- A. x = 2, y = -1
- B. x = 1, y = -4
- C. x = 3, y = 2
- D. x = 0, y = -7
Answer: A. x = 2, y = -1
Explanation: From second equation, x = -2y. Substitute into first: 3(-2y) - y = 7 => -7y = 7 => y = -1. Then x = -2(-1) = 2.
Question 34
Factorize x² - 9x + 20.
- A. (x - 4)(x - 5)
- B. (x + 4)(x + 5)
- C. (x - 2)(x - 10)
- D. (x - 1)(x - 20)
Answer: A. (x - 4)(x - 5)
Explanation: We need two numbers that multiply to 20 and add to -9. These are -4 and -5.
Question 35
In a triangle, the ratio of the three angles is 2:3:5. Find the size of the smallest angle.
- A. 18 degrees
- B. 36 degrees
- C. 54 degrees
- D. 90 degrees
Answer: B. 36 degrees
Explanation: Total parts = 2 + 3 + 5 = 10. Smallest angle = (2/10) * 180 = 36 degrees.
Question 36
A ship sails 10km on a bearing of 090 degrees and then 10km on a bearing of 180 degrees. Find its bearing from the starting point.
- A. 135 degrees
- B. 225 degrees
- C. 045 degrees
- D. 270 degrees
Answer: A. 135 degrees
Explanation: The movement forms an isosceles right-angled triangle. The angle from the North is 90 + 45 = 135 degrees.
Question 37
Find the arithmetic mean of 18 and 32.
Answer: A. 25
Explanation: (18 + 32) / 2 = 50 / 2 = 25.
Question 38
Find the magnitude of the vector u = (5, 12).
Answer: A. 13
Explanation: Magnitude = sqrt(5² + 12²) = sqrt(25 + 144) = sqrt(169) = 13.
Question 39
The scale of a map is 1:50,000. What actual distance in kilometers is represented by 4cm on the map?
- A. 2 km
- B. 20 km
- C. 0.2 km
- D. 200 km
Answer: A. 2 km
Explanation: Actual distance = 4 * 50,000 = 200,000 cm. 200,000 / 100,000 = 2 km.
Question 40
A car depreciates by 10% each year. If it is worth 1,000,000 Naira now, what will be its value after 2 years?
- A. 810,000 Naira
- B. 800,000 Naira
- C. 900,000 Naira
- D. 790,000 Naira
Answer: A. 810,000 Naira
Explanation: Value after 1 year = 900,000. Value after 2 years = 900,000 - 90,000 = 810,000.
Question 41
Simplify: 64^(2/3).
Answer: A. 16
Explanation: 64^(1/3) = 4. Then 4² = 16.
Question 42
Calculate 110 (base 2) multiplied by 11 (base 2).
- A. 10010 (base 2)
- B. 1110 (base 2)
- C. 1010 (base 2)
- D. 1100 (base 2)
Answer: A. 10010 (base 2)
Explanation: 110 (6 in base 10) * 11 (3 in base 10) = 18. 18 in base 2 is 10010.
Question 43
A circle is divided into 8 equal sectors. What is the angle of each sector?
- A. 45 degrees
- B. 40 degrees
- C. 60 degrees
- D. 30 degrees
Answer: A. 45 degrees
Explanation: 360 / 8 = 45 degrees.
Question 44
Find the distance between the points (2, 3) and (5, 7).
- A. 5 units
- B. 7 units
- C. sqrt(7) units
- D. 25 units
Answer: A. 5 units
Explanation: Distance = sqrt((5-2)² + (7-3)²) = sqrt(3² + 4²) = sqrt(9 + 16) = 5.
Question 45
If the ratio of the interior angle to the exterior angle of a regular polygon is 4:1, find the number of sides.
Answer: A. 10
Explanation: Interior + Exterior = 180. 4x + x = 180 => 5x = 180 => x = 36 (exterior). Sides = 360 / 36 = 10.
Question 46
Simplify: sqrt(12) + sqrt(27).
- A. 5 sqrt(3)
- B. sqrt(39)
- C. 13 sqrt(3)
- D. 6 sqrt(3)
Answer: A. 5 sqrt(3)
Explanation: sqrt(4*3) + sqrt(9*3) = 2 sqrt(3) + 3 sqrt(3) = 5 sqrt(3).
Question 47
A box contains 5 red and 7 blue balls. If two balls are drawn at random without replacement, find the probability that both are red.
- A. 5/33
- B. 25/144
- C. 5/12
- D. 1/6
Answer: A. 5/33
Explanation: P(First red) = 5/12. P(Second red) = 4/11. Total probability = 5/12 * 4/11 = 20/132 = 5/33.
Question 48
Calculate the length of an arc of a circle of radius 7cm which subtends an angle of 90 degrees at the center. (pi = 22/7)
- A. 11 cm
- B. 22 cm
- C. 44 cm
- D. 5.5 cm
Answer: A. 11 cm
Explanation: Length = (theta/360) * 2 * pi * r = (90/360) * 2 * (22/7) * 7 = (1/4) * 44 = 11.
Question 49
A man's annual tax is 15,000 Naira. If this represents 5% of his annual income, find his annual income.
- A. 300,000 Naira
- B. 75,000 Naira
- C. 150,000 Naira
- D. 600,000 Naira
Answer: A. 300,000 Naira
Explanation: 5% of Income = 15,000. Income = (15,000 / 5) * 100 = 300,000.
Question 50
Simplify: (x² - 1) / (x - 1).
- A. x + 1
- B. x - 1
- C. x
- D. 1
Answer: A. x + 1
Explanation: (x² - 1) is a difference of squares: (x - 1)(x + 1). Dividing by (x - 1) leaves (x + 1).