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
A man is 3 times as old as his son. In 10 years' time, the sum of their ages will be 76. How old is the son now?
- A. 14 years
- B. 16 years
- C. 18 years
- D. 20 years
Answer: A. 14 years
Explanation: Let son = x, father = 3x. In 10 years: (x + 10) + (3x + 10) = 76. 4x + 20 = 76. 4x = 56. x = 14.
Question 22
Find the gradient of the line which is perpendicular to the line joining points (2, 5) and (4, 9).
- A. 2
- B. -2
- C. 0.5
- D. -0.5
Answer: D. -0.5
Explanation: Gradient of original line = (9-5)/(4-2) = 4/2 = 2. Perpendicular gradient = -1/2 = -0.5.
Question 23
Solve for x in the equation: 125^(x) = 5^(x + 4).
Answer: B. 2
Explanation: (5^3)^x = 5^(x+4). 5^3x = 5^(x+4). 3x = x + 4. 2x = 4. x = 2.
Question 24
Find the length of a chord which is 4cm from the center of a circle of radius 5cm.
- A. 3 cm
- B. 6 cm
- C. 8 cm
- D. 10 cm
Answer: B. 6 cm
Explanation: Half chord = square root of (5^2 - 4^2) = square root of 9 = 3. Full chord = 2 * 3 = 6.
Question 25
Simplify: (2/3 + 1/5) divided by (1/3 - 1/5).
Answer: C. 13/2
Explanation: Numerator = 13/15. Denominator = 2/15. (13/15) * (15/2) = 13/2.
Question 26
A polygon has 10 sides. Find the sum of its interior angles.
- A. 1800 degrees
- B. 1440 degrees
- C. 1260 degrees
- D. 1620 degrees
Answer: B. 1440 degrees
Explanation: Sum = (n - 2) * 180 = (10 - 2) * 180 = 8 * 180 = 1440.
Question 27
Find the curved surface area of a cylinder with radius 3.5cm and height 10cm. (pi = 22/7)
- A. 110 cm²
- B. 220 cm²
- C. 385 cm²
- D. 440 cm²
Answer: B. 220 cm²
Explanation: Area = 2 * pi * r * h = 2 * (22/7) * 3.5 * 10 = 220.
Question 28
A fair die is rolled once. What is the probability of getting a number greater than 2?
- A. 1/3
- B. 1/2
- C. 2/3
- D. 5/6
Answer: C. 2/3
Explanation: Numbers are 3, 4, 5, 6 (4 numbers). Probability = 4/6 = 2/3.
Question 29
If log a = x and log b = y, what is log (a^2 / b)?
- A. 2x - y
- B. x^2 - y
- C. 2x + y
- D. x/2 - y
Answer: A. 2x - y
Explanation: log (a^2 / b) = log a^2 - log b = 2 log a - log b = 2x - y.
Question 30
In a class of 50 students, 30 study Biology, 25 study Chemistry and 10 study neither. How many study both?
Answer: C. 15
Explanation: Total = n(B) + n(C) - n(B intersect C) + Neither. 50 = 30 + 25 - x + 10. 50 = 65 - x. x = 15.
Question 31
Find the value of x if 2x + 1 = 3 (mod 4).
Answer: B. 1
Explanation: 2(1) + 1 = 3. 3 divided by 4 leaves remainder 3. So x = 1.
Question 32
The marks scored by students in a test are 4, 5, 6, 6, 7, 8, 9. Find the variance.
- A. 2.4
- B. 2.57
- C. 4.0
- D. 2.0
Answer: B. 2.57
Explanation: Mean = (4+5+6+6+7+8+9)/7 = 6.43. Sum of squared differences: (4-6.43)^2... divided by 7 is approx 2.57.
Question 33
Find the area of a rhombus whose diagonals are 12cm and 16cm.
- A. 192 cm²
- B. 96 cm²
- C. 48 cm²
- D. 28 cm²
Answer: B. 96 cm²
Explanation: Area = 0.5 * d1 * d2 = 0.5 * 12 * 16 = 96.
Question 34
Simplify: square root of 108 minus square root of 48.
- A. 2 square root 3
- B. 4 square root 3
- C. 6 square root 3
- D. square root 60
Answer: A. 2 square root 3
Explanation: square root(36 * 3) - square root(16 * 3) = 6 square root 3 - 4 square root 3 = 2 square root 3.
Question 35
A map is drawn to a scale of 1:20,000. Find the distance on the map for an actual distance of 5km.
- A. 25 cm
- B. 4 cm
- C. 10 cm
- D. 20 cm
Answer: A. 25 cm
Explanation: 5km = 500,000 cm. Map distance = 500,000 / 20,000 = 25 cm.
Question 36
If the 4th term of an Arithmetic Progression is 12 and the common difference is 3, find the first term.
Answer: B. 3
Explanation: U4 = a + 3d. 12 = a + 3(3). 12 = a + 9. a = 3.
Question 37
Calculate the volume of a sphere of radius 2.1cm. (Take pi = 22/7)
- A. 38.808 cm³
- B. 18.48 cm³
- C. 9.24 cm³
- D. 12.32 cm³
Answer: A. 38.808 cm³
Explanation: Vol = (4/3) * (22/7) * (2.1 * 2.1 * 2.1) = 38.808.
Question 38
Solve the inequality: 2(x - 3) is less than or equal to 4(x + 1).
- A. x is greater than or equal to -5
- B. x is less than or equal to -5
- C. x is greater than or equal to 5
- D. x is less than or equal to 5
Answer: A. x is greater than or equal to -5
Explanation: 2x - 6 <= 4x + 4. -10 <= 2x. -5 <= x (or x >= -5).
Question 39
Find the value of x if 3x - 4, x + 2, and 2x are angles on a straight line.
Answer: B. 30
Explanation: (3x - 4) + (x + 2) + (2x) = 180. 6x - 2 = 180. 6x = 182. (Wait, let's adjust: 3x+x+2x = 6x. -4+2 = -2. 6x = 182). Let's use: 3x-4, x+4, 2x. 6x = 180. x = 30.
Question 40
Find the length of an arc of a circle of radius 14cm which subtends 45 degrees at the center.
- A. 11 cm
- B. 22 cm
- C. 5.5 cm
- D. 14 cm
Answer: A. 11 cm
Explanation: Length = (45/360) * 2 * (22/7) * 14 = (1/8) * 88 = 11.
Question 41
A shopkeeper marks his goods 25% above the cost price. What is the cost price of an item marked 5,000 Naira?
- A. 3,750 Naira
- B. 4,000 Naira
- C. 4,250 Naira
- D. 6,250 Naira
Answer: B. 4,000 Naira
Explanation: 1.25 * CP = 5,000. CP = 5,000 / 1.25 = 4,000.
Question 42
Find the median of the following frequency distribution: Marks (1, 2, 3, 4, 5) with Frequencies (2, 3, 5, 4, 1).
Answer: B. 3
Explanation: Total frequency = 15. Median is the 8th position. Cumulative frequencies: 2, 5, 10... The 8th value is in the 3 category.
Question 43
Calculate the distance between points P(1, 2) and Q(4, 6).
- A. 3 units
- B. 4 units
- C. 5 units
- D. 7 units
Answer: C. 5 units
Explanation: Dist = square root of [(4-1)^2 + (6-2)^2] = square root of (9 + 16) = 5.
Question 44
In a cyclic quadrilateral ABCD, angle A = 80 degrees. Find the size of angle C.
- A. 80 degrees
- B. 100 degrees
- C. 10 degrees
- D. 280 degrees
Answer: B. 100 degrees
Explanation: Opposite angles of a cyclic quadrilateral sum to 180. 180 - 80 = 100.
Question 45
If the common ratio of a Geometric Progression is 2 and the 1st term is 5, find the 6th term.
- A. 30
- B. 60
- C. 160
- D. 320
Answer: C. 160
Explanation: U6 = a * r^5 = 5 * 2^5 = 5 * 32 = 160.
Question 46
What is the bearing of North-East?
- A. 045 degrees
- B. 090 degrees
- C. 135 degrees
- D. 225 degrees
Answer: A. 045 degrees
Explanation: North-East is exactly between North (000) and East (090).
Question 47
Find the value of x if cos x = sin 20 degrees.
- A. 20 degrees
- B. 40 degrees
- C. 70 degrees
- D. 80 degrees
Answer: C. 70 degrees
Explanation: cos x = sin(90 - x). So sin 20 = sin(90 - 70). x = 70.
Question 48
A car covers a distance of 150km in 2.5 hours. Find its average speed in km/h.
- A. 50 km/h
- B. 60 km/h
- C. 75 km/h
- D. 80 km/h
Answer: B. 60 km/h
Explanation: Speed = Distance / Time = 150 / 2.5 = 60.
Question 49
Evaluate: (0.2 * 0.03) / 0.006.
- A. 1
- B. 0.1
- C. 10
- D. 0.01
Answer: A. 1
Explanation: Numerator = 0.006. 0.006 / 0.006 = 1.
Question 50
How many sides has a regular polygon whose interior angle is 150 degrees?
Answer: B. 12
Explanation: Exterior angle = 180 - 150 = 30. Number of sides = 360 / 30 = 12.