Sample WAEC-style Practice Questions (Original Content)
WAEC Style
Question 1
Convert 231 (base 4) to a number in base 10.
Answer: B. 45
Explanation: (2 x 4²) + (3 x 4¹) + (1 x 4⁰) = (2 x 16) + (3 x 4) + (1 x 1) = 32 + 12 + 1 = 45.
Question 2
Simplify the expression: (3x - 4)(x + 2)
- A. 3x² - 8
- B. 3x² + 2x - 8
- C. 3x² - 2x - 8
- D. 3x² + 10x - 8
Answer: B. 3x² + 2x - 8
Explanation: 3x(x) + 3x(2) - 4(x) - 4(2) = 3x² + 6x - 4x - 8 = 3x² + 2x - 8.
Question 3
If n(A) = 15, n(B) = 12 and n(A ∪ B) = 20, find n(A ∩ B).
Answer: A. 7
Explanation: n(A ∪ B) = n(A) + n(B) - n(A ∩ B). So, 20 = 15 + 12 - x. 20 = 27 - x. x = 7.
Question 4
What is the sum of the exterior angles of a regular pentagon?
- A. 180°
- B. 360°
- C. 540°
- D. 720°
Answer: B. 360°
Explanation: The sum of exterior angles of any convex polygon is always 360°.
Question 5
If x varies directly as y, and x = 15 when y = 5, find x when y = 8.
Answer: C. 24
Explanation: x = ky. 15 = k(5) so k = 3. When y = 8, x = 3(8) = 24.
Question 6
Find the median of the following set of scores: 2, 10, 5, 3, 8, 1.
Answer: B. 4
Explanation: Arrange in order: 1, 2, 3, 5, 8, 10. The middle numbers are 3 and 5. (3+5)/2 = 4.
Question 7
Evaluate: 8^(2/3)
Answer: B. 4
Explanation: Cube root of 8 is 2. 2 squared (2²) = 4.
Question 8
Solve for x: log(base 4) 8 + log(base 4) 2 = x
Answer: A. 2
Explanation: log 8 + log 2 = log(8 x 2) = log(base 4) 16. Since 4² = 16, x = 2.
Question 9
Calculate the volume of a cone with radius 7cm and height 3cm. (Take π = 22/7)
- A. 462 cm³
- B. 154 cm³
- C. 77 cm³
- D. 231 cm³
Answer: B. 154 cm³
Explanation: V = (1/3)πr²h = (1/3) x (22/7) x 7 x 7 x 3 = 22 x 7 = 154.
Question 10
In a right-angled triangle, tan θ = 3/4. Find sin θ.
- A. 3/5
- B. 4/5
- C. 5/3
- D. 1/2
Answer: A. 3/5
Explanation: Opposite = 3, Adjacent = 4. Hypotenuse = √(3² + 4²) = 5. Sin θ = Opp/Hyp = 3/5.
Question 11
Increase 400 by 15%.
- A. 415
- B. 445
- C. 460
- D. 500
Answer: C. 460
Explanation: 15% of 400 = 0.15 x 400 = 60. 400 + 60 = 460.
Question 12
Solve the linear equation: 5x - 3 = 2x + 9
Answer: C. 4
Explanation: 5x - 2x = 9 + 3 -> 3x = 12 -> x = 4.
Question 13
Two fair dice are rolled once. What is the probability of getting a total sum of 12?
- A. 1/6
- B. 1/12
- C. 1/36
- D. 1/18
Answer: C. 1/36
Explanation: Total outcomes = 6 x 6 = 36. Only one outcome gives 12 (6,6). Probability = 1/36.
Question 14
The angle at the center of a circle is 120°. What is the angle at the circumference subtended by the same arc?
- A. 240°
- B. 120°
- C. 90°
- D. 60°
Answer: D. 60°
Explanation: The angle at the center is twice the angle at the circumference. 120 / 2 = 60.
Question 15
Rationalize the denominator: 2 / √2
Answer: B. √2
Explanation: (2 / √2) x (√2 / √2) = 2√2 / 2 = √2.
Question 16
If y = x² + 3, find the gradient (dy/dx) of the curve at x = 3.
Answer: B. 6
Explanation: dy/dx = 2x. At x = 3, 2(3) = 6.
Question 17
Add the binary numbers: 111 + 101
- A. 1100
- B. 1010
- C. 1111
- D. 1001
Answer: A. 1100
Explanation: In base 10, 7 + 5 = 12. 12 in binary is 1100.
Question 18
Find the total amount on N1,000 borrowed at 10% simple interest for 2 years.
- A. N1,100
- B. N1,200
- C. N200
- D. N1,020
Answer: B. N1,200
Explanation: Interest = (1000 x 10 x 2) / 100 = 200. Amount = Principal + Interest = 1000 + 200 = 1200.
Question 19
Solve the inequality: -2x < 6
- A. x < -3
- B. x > -3
- C. x < 3
- D. x > 3
Answer: B. x > -3
Explanation: When dividing an inequality by a negative number, the sign reverses. 6 / -2 = -3, so x > -3.
Question 20
Find the distance between the origin (0,0) and the point (3,4).
- A. 5 units
- B. 7 units
- C. 25 units
- D. 1 unit
Answer: A. 5 units
Explanation: Distance = √(3² + 4²) = √(9 + 16) = √25 = 5.
Question 21
Find the 10th term of the Arithmetic Progression (A.P.): 2, 5, 8, 11...
Answer: B. 29
Explanation: a = 2, d = 3. T10 = a + 9d = 2 + 9(3) = 2 + 27 = 29.
Question 22
Solve the inequality: 3(x - 2) < 2x + 5.
- A. x < 11
- B. x > 11
- C. x < 1
- D. x > -1
Answer: A. x < 11
Explanation: 3x - 6 < 2x + 5 becomes 3x - 2x < 5 + 6, so x < 11.
Question 23
Calculate the area of a circle whose diameter is 14cm. (Take pi = 22/7)
- A. 44 cm²
- B. 154 cm²
- C. 616 cm²
- D. 77 cm²
Answer: B. 154 cm²
Explanation: radius r = 7. Area = pi * r² = (22/7) * 7 * 7 = 154.
Question 24
Factorize completely: x² - 5x + 6.
- A. (x-1)(x-6)
- B. (x-2)(x-3)
- C. (x+2)(x+3)
- D. (x-5)(x+1)
Answer: B. (x-2)(x-3)
Explanation: We need two numbers that multiply to 6 and add to -5. These are -2 and -3.
Question 25
Find the value of x if 2^(x+1) = 32.
Answer: B. 4
Explanation: 2^(x+1) = 2^5. Therefore, x + 1 = 5, which means x = 4.
Question 26
A bag contains 5 red and 3 blue balls. If a ball is picked at random, what is the probability it is blue?
- A. 5/8
- B. 3/8
- C. 3/5
- D. 1/2
Answer: B. 3/8
Explanation: Probability = (Number of blue balls) / (Total balls) = 3 / (5 + 3) = 3/8.
Question 27
Calculate the simple interest on 400 Naira for 3 years at 5% per annum.
- A. 20 Naira
- B. 60 Naira
- C. 120 Naira
- D. 460 Naira
Answer: B. 60 Naira
Explanation: Interest = (Principal * Rate * Time) / 100 = (400 * 5 * 3) / 100 = 60.
Question 28
If cos(theta) = 0.8, find tan(theta) where theta is an acute angle.
- A. 0.6
- B. 0.75
- C. 1.33
- D. 0.5
Answer: B. 0.75
Explanation: If cos = 4/5, then adjacent = 4 and hypotenuse = 5. Opposite = √(5² - 4²) = 3. tan = 3/4 = 0.75.
Question 29
Find the mean of the following set of numbers: 10, 12, 14, 16, 18.
Answer: B. 14
Explanation: (10 + 12 + 14 + 16 + 18) / 5 = 70 / 5 = 14.
Question 30
What is the three-figure bearing of North-West?
- A. 045°
- B. 135°
- C. 225°
- D. 315°
Answer: D. 315°
Explanation: North is 000°, West is 270°. North-West is halfway between West and North: 270 + 45 = 315.
Question 31
Calculate the volume of a cylinder with radius 3cm and height 7cm. (Take pi = 22/7)
- A. 198 cm³
- B. 66 cm³
- C. 132 cm³
- D. 44 cm³
Answer: A. 198 cm³
Explanation: Volume = pi * r² * h = (22/7) * 3² * 7 = 22 * 9 = 198.
Question 32
Solve for y in the equation: 2y/3 - 4 = 2.
Answer: C. 9
Explanation: 2y/3 = 6. Multiplying by 3 gives 2y = 18. Thus y = 9.
Question 33
What is the sum of interior angles of a pentagon (5-sided polygon)?
- A. 360°
- B. 540°
- C. 720°
- D. 900°
Answer: B. 540°
Explanation: Sum = (n - 2) * 180 = (5 - 2) * 180 = 3 * 180 = 540.
Question 34
Simplify: √(72) + √(50) - √(8).
- A. 9√(2)
- B. 11√(2)
- C. 13√(2)
- D. 15√(2)
Answer: A. 9√(2)
Explanation: 6√(2) + 5√(2) - 2√(2) = (6 + 5 - 2)√(2) = 9√(2).
Question 35
Find the gradient (slope) of the line joining points (2, 3) and (5, 9).
Answer: A. 2
Explanation: Gradient m = (y2 - y1) / (x2 - x1) = (9 - 3) / (5 - 2) = 6 / 3 = 2.
Question 36
In a right-angled triangle, the hypotenuse is 13cm and one side is 5cm. Find the third side.
- A. 8 cm
- B. 10 cm
- C. 12 cm
- D. 15 cm
Answer: C. 12 cm
Explanation: Using Pythagoras: Side = √(13² - 5²) = √(169 - 25) = √144 = 12.
Question 37
Express 0.0000457 in scientific notation.
- A. 4.57 x 10^-5
- B. 4.57 x 10^-4
- C. 45.7 x 10^-6
- D. 0.457 x 10^-4
Answer: A. 4.57 x 10^-5
Explanation: The decimal moves 5 places to the right to sit after the first non-zero digit.
Question 38
Convert 25 (base 10) to a binary number (base 2).
- A. 11001
- B. 10110
- C. 11101
- D. 10101
Answer: A. 11001
Explanation: 25 divided by 2 gives remainders: 1, 0, 0, 1, 1 (read backwards).
Question 39
Find the median of the following set: 5, 3, 8, 10, 2, 6, 7.
Answer: B. 6
Explanation: Sort the data: 2, 3, 5, 6, 7, 8, 10. The middle value is 6.
Question 40
If Universal set U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, find A' (the complement of A).
- A. {1, 3, 5}
- B. {1, 2, 3}
- C. {4, 5, 6}
- D. { }
Answer: A. {1, 3, 5}
Explanation: The complement contains all elements in U that are not in A.
Question 41
The angle of elevation of the top of a tower from a point 20m away on the ground is 30°. Find the height of the tower.
- A. 20√(3) m
- B. 20/√(3) m
- C. 10 m
- D. 40 m
Answer: B. 20/√(3) m
Explanation: tan(30) = height/20. Height = 20 * tan(30) = 20 * (1/√3).
Question 42
Solve for x: x/2 + x/3 = 5.
Answer: B. 6
Explanation: Multiply through by 6: 3x + 2x = 30. 5x = 30, so x = 6.
Question 43
A car travels 240km in 3 hours. Find its speed in meters per second (m/s).
- A. 80 m/s
- B. 22.2 m/s
- C. 40 m/s
- D. 13.3 m/s
Answer: B. 22.2 m/s
Explanation: Speed = 80 km/h. Convert to m/s: (80 * 1000) / 3600 = 22.22...
Question 44
What is the mode of the following data: 2, 4, 4, 5, 7, 7, 7, 9?
Answer: C. 7
Explanation: The mode is the number that appears most frequently. 7 appears three times.
Question 45
Simplify: log2(16) - log2(4).
Answer: A. 2
Explanation: log2(16/4) = log2(4) = 2.
Question 46
If the ratio of the areas of two similar triangles is 16:25, what is the ratio of their corresponding sides?
- A. 4:5
- B. 2:5
- C. 16:25
- D. 256:625
Answer: A. 4:5
Explanation: The ratio of sides is the square root of the ratio of areas: √16 : √25 = 4 : 5.
Question 47
Find the values of x such that (x + 2)² = 49.
- A. 5 or -9
- B. 7 or -7
- C. 5 only
- D. 9 or -5
Answer: A. 5 or -9
Explanation: x + 2 = 7 or x + 2 = -7. This gives x = 5 or x = -9.
Question 48
The probability of an event happening is 0.35. What is the probability of the event NOT happening?
- A. 0.35
- B. 0.55
- C. 0.65
- D. 0.75
Answer: C. 0.65
Explanation: Probability of NOT happening = 1 - 0.35 = 0.65.
Question 49
Find the sum of the first 5 terms of the Geometric Progression (G.P.): 3, 6, 12...
Answer: C. 93
Explanation: a = 3, r = 2. Sum = a(r^n - 1) / (r - 1) = 3(2^5 - 1) / (2 - 1) = 3(31) = 93.
Question 50
Find the value of x if the angles of a triangle are 2x, 3x, and 40°.
- A. 20°
- B. 28°
- C. 30°
- D. 35°
Answer: B. 28°
Explanation: 2x + 3x + 40 = 180. 5x = 140. x = 28.