Sample WAEC-style Practice Questions (Original Content)
WAEC Style
Question 1
Find the value of x if 2x + 7 = 15 - 2x.
Answer: A. 2
Explanation: 2x + 2x = 15 - 7 -> 4x = 8 -> x = 2.
Question 2
A circle has a circumference of 44cm. Find its radius. (Take π = 22/7)
- A. 3.5cm
- B. 7cm
- C. 14cm
- D. 21cm
Answer: B. 7cm
Explanation: C = 2πr -> 44 = 2 * (22/7) * r -> 44 = (44/7)r -> r = 7.
Question 3
Calculate the gradient of the line joining (1, 2) and (3, 10).
Answer: C. 4
Explanation: m = (10 - 2) / (3 - 1) = 8 / 2 = 4.
Question 4
If y varies inversely as x, and y = 4 when x = 3, find y when x = 2.
Answer: A. 6
Explanation: y = k/x -> 4 = k/3 -> k = 12. New y = 12/2 = 6.
Question 5
Factorize: 3x² - 12
- A. 3(x - 2)(x + 2)
- B. (3x - 4)(x + 3)
- C. 3(x - 4)²
- D. 3(x + 2)²
Answer: A. 3(x - 2)(x + 2)
Explanation: 3(x² - 4). This is a difference of squares: 3(x - 2)(x + 2).
Question 6
Convert 123 (base 10) to binary.
- A. 1111011
- B. 1101111
- C. 1011011
- D. 1111111
Answer: A. 1111011
Explanation: Successive division of 123 by 2 gives remainders 1, 1, 0, 1, 1, 1, 1.
Question 7
Solve: log 2 + log x = log 10
Answer: B. 5
Explanation: log(2x) = log 10 -> 2x = 10 -> x = 5.
Question 8
Find the 15th term of an AP whose first term is 2 and common difference is 4.
Answer: A. 58
Explanation: T15 = a + 14d = 2 + 14(4) = 2 + 56 = 58.
Question 9
A die is rolled. What is the probability of getting a prime number?
- A. 1/6
- B. 1/3
- C. 1/2
- D. 2/3
Answer: C. 1/2
Explanation: Prime numbers are {2, 3, 5}. Probability = 3/6 = 1/2.
Question 10
What is the value of (0.2)³?
- A. 0.6
- B. 0.06
- C. 0.008
- D. 0.08
Answer: C. 0.008
Explanation: 0.2 * 0.2 * 0.2 = 0.008.
Question 11
Find the simple interest on N40,000 for 6 months at 4% per annum.
- A. N1,600
- B. N800
- C. N400
- D. N9,600
Answer: B. N800
Explanation: Interest = (40000 * 4 * 0.5) / 100 = 800.
Question 12
Solve the inequality: 10 - 3x > 1
- A. x > 3
- B. x < 3
- C. x > -3
- D. x < -3
Answer: B. x < 3
Explanation: -3x > -9. Divide by -3 and flip sign: x < 3.
Question 13
Calculate the volume of a sphere with diameter 6cm. (Take π = 3.14)
- A. 113.04 cm³
- B. 904.32 cm³
- C. 37.68 cm³
- D. 18.84 cm³
Answer: A. 113.04 cm³
Explanation: r = 3. Vol = 4/3 * 3.14 * 3³ = 4 * 3.14 * 9 = 113.04.
Question 14
The interior angle of a regular polygon is 120°. Find the number of sides.
Answer: B. 6
Explanation: Ext angle = 180 - 120 = 60. Sides = 360 / 60 = 6.
Question 15
Simplify: (√2 + √3)²
- A. 5
- B. 5 + 2√6
- C. 5 + √6
- D. 13
Answer: B. 5 + 2√6
Explanation: (√2)² + 2(√2)(√3) + (√3)² = 2 + 2√6 + 3 = 5 + 2√6.
Question 16
Find the median of: 15, 12, 18, 10, 22, 14, 16
Answer: B. 15
Explanation: Ordered: 10, 12, 14, 15, 16, 18, 22. Middle is 15.
Question 17
A ladder 10m long leans against a wall. If the foot of the ladder is 6m from the wall, how high up the wall does it reach?
- A. 4m
- B. 8m
- C. 16m
- D. 64m
Answer: B. 8m
Explanation: h = √(10² - 6²) = √(100 - 36) = √64 = 8.
Question 18
Express 42% as a fraction in its simplest form.
- A. 42/100
- B. 21/50
- C. 7/15
- D. 21/25
Answer: B. 21/50
Explanation: 42/100. Divide by 2 = 21/50.
Question 19
Solve: 3x - 5 = 7
Answer: A. 4
Explanation: 3x = 12 -> x = 4.
Question 20
What is the mode of the following data: 2, 3, 3, 4, 5, 5, 5, 6?
Answer: C. 5
Explanation: 5 occurs most frequently.
Question 21
A man's salary was increased from 20,000 Naira to 25,000 Naira. Calculate the percentage increase.
- A. 20%
- B. 25%
- C. 5%
- D. 15%
Answer: B. 25%
Explanation: Increase = 5,000. Percentage Increase = (5,000 / 20,000) * 100 = 25%.
Question 22
Simplify the expression: (x^5 * x^3) / x^4.
- A. x^2
- B. x^4
- C. x^15
- D. x^12
Answer: B. x^4
Explanation: x^(5+3) / x^4 = x^8 / x^4 = x^(8-4) = x^4.
Question 23
If P = {1, 2, 3, 4, 5, 6} and Q = {2, 4, 6, 8, 10}, find the number of elements in (P union Q).
Answer: C. 8
Explanation: P union Q = {1, 2, 3, 4, 5, 6, 8, 10}. There are 8 unique elements.
Question 24
Find the value of x in the triangle where the angles are 3x, 4x, and 2x.
- A. 10 degrees
- B. 20 degrees
- C. 30 degrees
- D. 40 degrees
Answer: B. 20 degrees
Explanation: 3x + 4x + 2x = 180. 9x = 180. x = 20.
Question 25
What is the sum of the interior angles of a regular hexagon (6-sided polygon)?
- A. 360 degrees
- B. 540 degrees
- C. 720 degrees
- D. 900 degrees
Answer: C. 720 degrees
Explanation: Sum = (n - 2) * 180 = (6 - 2) * 180 = 4 * 180 = 720.
Question 26
How many years will it take for 500 Naira to earn 150 Naira simple interest at 6% per annum?
- A. 3 years
- B. 4 years
- C. 5 years
- D. 6 years
Answer: C. 5 years
Explanation: Time = (100 * Interest) / (Principal * Rate) = (100 * 150) / (500 * 6) = 15000 / 3000 = 5.
Question 27
Rationalize the denominator of: 10 / sqrt(5).
- A. 2
- B. 2 sqrt(5)
- C. 5 sqrt(2)
- D. sqrt(10)
Answer: B. 2 sqrt(5)
Explanation: (10 * sqrt(5)) / (sqrt(5) * sqrt(5)) = 10 sqrt(5) / 5 = 2 sqrt(5).
Question 28
A number is chosen at random from the set {1, 2, 3, ..., 10}. What is the probability that it is a prime number?
- A. 1/2
- B. 2/5
- C. 3/10
- D. 3/5
Answer: B. 2/5
Explanation: Prime numbers are {2, 3, 5, 7}. Probability = 4 / 10 = 2/5.
Question 29
Find the area of a sector of a circle with radius 6cm and angle 70 degrees at the center. (pi = 22/7)
- A. 22 cm²
- B. 44 cm²
- C. 11 cm²
- D. 33 cm²
Answer: A. 22 cm²
Explanation: Area = (70/360) * (22/7) * 6 * 6 = (1/36 * 10) * (22/7 * 7) is not right. Let's re-calculate: (70/360) * (22/7) * 36 = 70/10 * 22/7 = 7 * 22/7 = 22.
Question 30
Solve for x: (2/3)x - 5 = 7.
Answer: C. 18
Explanation: (2/3)x = 12. x = (12 * 3) / 2 = 36 / 2 = 18.
Question 31
Calculate the gradient of the line passing through points A(4, 5) and B(2, 1).
Answer: A. 2
Explanation: Gradient = (1 - 5) / (2 - 4) = -4 / -2 = 2.
Question 32
If y varies inversely as x, and y = 10 when x = 2, find y when x = 5.
Answer: B. 4
Explanation: y * x = k. 10 * 2 = 20. So y * 5 = 20, which means y = 4.
Question 33
If the bearing of P from Q is 060 degrees, what is the bearing of Q from P?
- A. 120 degrees
- B. 240 degrees
- C. 300 degrees
- D. 060 degrees
Answer: B. 240 degrees
Explanation: Reciprocal bearing = 60 + 180 = 240.
Question 34
Calculate the volume of a sphere with radius 3cm. (Take pi = 22/7)
- A. 113.14 cm³
- B. 37.71 cm³
- C. 154 cm³
- D. 88 cm³
Answer: A. 113.14 cm³
Explanation: Volume = (4/3) * pi * r³ = (4/3) * (22/7) * 27 = 4 * (22/7) * 9 = 792 / 7 = 113.14.
Question 35
Factorize completely: 4a² - 9b².
- A. (2a - 3b)(2a - 3b)
- B. (2a + 3b)(2a + 3b)
- C. (2a - 3b)(2a + 3b)
- D. (4a - 9b)(a + b)
Answer: C. (2a - 3b)(2a + 3b)
Explanation: This is a difference of two squares: (2a)² - (3b)².
Question 36
In a right-angled triangle, if the opposite side is 3 and the hypotenuse is 6, what is the angle theta?
- A. 30 degrees
- B. 45 degrees
- C. 60 degrees
- D. 90 degrees
Answer: A. 30 degrees
Explanation: sin theta = 3 / 6 = 0.5. theta = arcsin(0.5) = 30 degrees.
Question 37
A car is sold for 2,400 Naira at a profit of 20%. Find the cost price.
- A. 1,920 Naira
- B. 2,000 Naira
- C. 2,100 Naira
- D. 1,800 Naira
Answer: B. 2,000 Naira
Explanation: 120% = 2,400. 100% = (2,400 / 120) * 100 = 20 * 100 = 2,000.
Question 38
Find the roots of the equation x² - x - 12 = 0.
- A. 4 and -3
- B. -4 and 3
- C. 6 and -2
- D. -6 and 2
Answer: A. 4 and -3
Explanation: (x - 4)(x + 3) = 0 gives x = 4 or x = -3.
Question 39
Simplify: log10(500) - log10(5).
Answer: B. 2
Explanation: log(a) - log(b) = log(a / b). log10(500 / 5) = log10(100) = 2.
Question 40
Express 0.0000048 in standard form.
- A. 4.8 * 10^-6
- B. 4.8 * 10^-5
- C. 4.8 * 10^6
- D. 0.48 * 10^-5
Answer: A. 4.8 * 10^-6
Explanation: Move the decimal 6 places to the right.
Question 41
Find the median of the following set of numbers: 4, 12, 7, 10, 8, 15, 2.
Answer: C. 8
Explanation: Arranged set: 2, 4, 7, 8, 10, 12, 15. The middle number is 8.
Question 42
If the exterior angle of a regular polygon is 40 degrees, how many sides does it have?
Answer: B. 9
Explanation: Number of sides = 360 / exterior angle = 360 / 40 = 9.
Question 43
If the sides of two similar triangles are in the ratio 2:3, what is the ratio of their areas?
- A. 2:3
- B. 4:6
- C. 4:9
- D. 8:27
Answer: C. 4:9
Explanation: Area ratio is the square of the side ratio. 2²:3² = 4:9.
Question 44
Evaluate 1011 (base 2) + 110 (base 2).
- A. 10001 (base 2)
- B. 10101 (base 2)
- C. 1111 (base 2)
- D. 1001 (base 2)
Answer: A. 10001 (base 2)
Explanation: 11 + 6 = 17 in base 10. 17 in base 2 is 10001.
Question 45
Calculate the total surface area of a closed cylinder with radius 7cm and height 3cm. (pi = 22/7)
- A. 132 cm²
- B. 308 cm²
- C. 440 cm²
- D. 154 cm²
Answer: C. 440 cm²
Explanation: Area = 2 * pi * r * (r + h) = 2 * (22/7) * 7 * (7 + 3) = 44 * 10 = 440.
Question 46
Solve the inequality: 3x + 4 is greater than or equal to 13.
- A. x is greater than or equal to 3
- B. x is less than or equal to 3
- C. x is greater than 3
- D. x is less than 3
Answer: A. x is greater than or equal to 3
Explanation: 3x is greater than or equal to 9. x is greater than or equal to 3.
Question 47
A ladder 13m long leans against a wall. If the foot of the ladder is 5m from the wall, how high up the wall does it reach?
- A. 8m
- B. 10m
- C. 12m
- D. 11m
Answer: C. 12m
Explanation: Height = sqrt(13² - 5²) = sqrt(169 - 25) = sqrt(144) = 12.
Question 48
What is 35% of 200?
Answer: A. 70
Explanation: 0.35 * 200 = 70.
Question 49
In a Geometric Progression (GP), the first term is 2 and the third term is 18. Find the positive common ratio.
Answer: B. 3
Explanation: a * r² = 18. 2 * r² = 18. r² = 9. r = 3.
Question 50
Solve the simultaneous equations: x + y = 10, x - y = 4.
- A. x=6, y=4
- B. x=7, y=3
- C. x=5, y=5
- D. x=8, y=2
Answer: B. x=7, y=3
Explanation: Add both equations: 2x = 14, so x = 7. Subtracting x from 10 gives y = 3.