Sample WAEC-style Practice Questions (Original Content)
WAEC Style
Question 1
Convert 342 (base 5) to a number in base 10.
Answer: A. 97
Explanation: (3 x 5²) + (4 x 5¹) + (2 x 5⁰) = (3 x 25) + (4 x 5) + (2 x 1) = 75 + 20 + 2 = 97.
Question 2
Simplify: (2a²)³ / 4a⁴
- A. 2a
- B. 2a²
- C. 4a²
- D. 2a⁶
Answer: B. 2a²
Explanation: (2³ x a²*³) / 4a⁴ = 8a⁶ / 4a⁴ = 2a⁽⁶⁻⁴⁾ = 2a².
Question 3
If 27 to the power of x = 1/9, find the value of x.
- A. 2/3
- B. -2/3
- C. 3/2
- D. -3/2
Answer: B. -2/3
Explanation: (3³)ˣ = 3⁻² -> 3x = -2 -> x = -2/3.
Question 4
Find the roots of the quadratic equation: x² - 7x + 10 = 0
- A. 2, 5
- B. -2, -5
- C. 2, -5
- D. 1, 10
Answer: A. 2, 5
Explanation: (x - 2)(x - 5) = 0. Therefore x = 2 or x = 5.
Question 5
Calculate the exterior angle of a regular polygon with 12 sides.
- A. 45°
- B. 60°
- C. 30°
- D. 15°
Answer: C. 30°
Explanation: Exterior angle = 360 / n = 360 / 12 = 30°.
Question 6
Express 0.00034 in standard form.
- A. 3.4 x 10³
- B. 3.4 x 10⁻³
- C. 3.4 x 10⁻⁴
- D. 34 x 10⁻⁵
Answer: C. 3.4 x 10⁻⁴
Explanation: Move the decimal point 4 places to the right to get 3.4.
Question 7
Solve the simultaneous equations: 3x + 2y = 12 and x - y = 4.
- A. x=4, y=0
- B. x=2, y=3
- C. x=5, y=-1
- D. x=3, y=1
Answer: A. x=4, y=0
Explanation: From second eq: x = y + 4. Substitute into first: 3(y+4) + 2y = 12 -> 3y+12+2y=12 -> 5y=0 -> y=0. If y=0, x=4.
Question 8
A fair die is tossed once. What is the probability of getting a number greater than 4?
- A. 1/6
- B. 1/3
- C. 1/2
- D. 2/3
Answer: B. 1/3
Explanation: Numbers greater than 4 are {5, 6}. Probability = 2/6 = 1/3.
Question 9
Find the area of a trapezium with parallel sides 8cm and 12cm, and height 5cm.
- A. 100 cm²
- B. 40 cm²
- C. 50 cm²
- D. 60 cm²
Answer: C. 50 cm²
Explanation: Area = 1/2 * (a + b) * h = 1/2 * (8 + 12) * 5 = 1/2 * 20 * 5 = 50.
Question 10
Make r the subject of the formula: C = 2πr
- A. r = 2π / C
- B. r = C / 2π
- C. r = C - 2π
- D. r = 2C / π
Answer: B. r = C / 2π
Explanation: Divide both sides by 2π to isolate r.
Question 11
The interior angle of a regular polygon is 144°. How many sides has the polygon?
Answer: C. 10
Explanation: Exterior angle = 180 - 144 = 36°. Number of sides = 360 / 36 = 10.
Question 12
Find the surface area of a sphere with radius 7cm. (Take π = 22/7)
- A. 154 cm²
- B. 308 cm²
- C. 616 cm²
- D. 462 cm²
Answer: C. 616 cm²
Explanation: Area = 4πr² = 4 x (22/7) x 7 x 7 = 4 x 22 x 7 = 616.
Question 13
Simplify: log(base 3) 81
Answer: B. 4
Explanation: 3 to the power of 4 (3 x 3 x 3 x 3) equals 81.
Question 14
If tan x = 1, where x is an acute angle, find x.
- A. 30°
- B. 45°
- C. 60°
- D. 90°
Answer: B. 45°
Explanation: tan 45° is a standard trigonometric ratio equal to 1.
Question 15
Calculate the compound interest on N5,000 for 2 years at 10% per annum.
- A. N1,000
- B. N1,050
- C. N1,100
- D. N500
Answer: B. N1,050
Explanation: Year 1: 10% of 5000 = 500. New balance = 5500. Year 2: 10% of 5500 = 550. Total Interest = 500 + 550 = 1050.
Question 16
Find the gradient of the line 3y - 15x + 7 = 0.
Answer: C. 5
Explanation: Rearrange to y = mx + c: 3y = 15x - 7 -> y = 5x - 7/3. Gradient (m) = 5.
Question 17
The numbers 2, 4, 6, 8, 10 have a mean of 6. What is the mean if each number is multiplied by 2?
Answer: C. 12
Explanation: If all values are multiplied by a constant k, the mean is also multiplied by k. 6 x 2 = 12.
Question 18
Binary Multiplication: 111 (base 2) x 10 (base 2)
- A. 1110
- B. 1010
- C. 1101
- D. 1111
Answer: A. 1110
Explanation: In binary, multiplying by 10 is the same as adding a zero at the end. (Base 10: 7 x 2 = 14. 14 in binary is 1110).
Question 19
If the bearing of X from Y is 280°, what is the bearing of Y from X?
- A. 080°
- B. 100°
- C. 010°
- D. 120°
Answer: B. 100°
Explanation: Since 280° is greater than 180°, subtract 180°. 280 - 180 = 100°.
Question 20
Solve the linear inequality: 4 - x > 6
- A. x > 2
- B. x < 2
- C. x > -2
- D. x < -2
Answer: D. x < -2
Explanation: -x > 6 - 4 -> -x > 2. Divide by -1 and flip the sign: x < -2.
Question 21
Find the 10th term of an Arithmetic Progression (A.P.) where the first term is 7 and the common difference is 3.
Answer: B. 34
Explanation: 10th term = a + (n-1)d. Term = 7 + (9 * 3) = 7 + 27 = 34.
Question 22
Solve the simultaneous equations: 2x + y = 10 and x - y = 2.
- A. x=4, y=2
- B. x=3, y=4
- C. x=5, y=0
- D. x=6, y=-2
Answer: A. x=4, y=2
Explanation: Adding both equations gives 3x = 12, so x = 4. Substituting x = 4 into x - y = 2 gives 4 - y = 2, so y = 2.
Question 23
Calculate the simple interest on 600 Naira for 4 years at 3% per annum.
- A. 18 Naira
- B. 24 Naira
- C. 72 Naira
- D. 120 Naira
Answer: C. 72 Naira
Explanation: Interest = (Principal * Rate * Time) / 100. Interest = (600 * 3 * 4) / 100 = 72.
Question 24
Simplify the expression: (27^(1/3)) * (16^(1/2)).
Answer: B. 12
Explanation: 27^(1/3) is the cube root of 27, which is 3. 16^(1/2) is the square root of 16, which is 4. 3 * 4 = 12.
Question 25
Find the mean of the following numbers: 12, 15, 18, 21, 24.
Answer: B. 18
Explanation: (12 + 15 + 18 + 21 + 24) / 5 = 90 / 5 = 18.
Question 26
Calculate the area of a circle with diameter 28cm. (Take pi = 22/7)
- A. 88 cm²
- B. 154 cm²
- C. 616 cm²
- D. 2464 cm²
Answer: C. 616 cm²
Explanation: Radius = 14. Area = pi * r² = (22/7) * 14 * 14 = 22 * 2 * 14 = 616.
Question 27
A box contains 4 red, 3 blue, and 5 green marbles. What is the probability of picking a blue marble?
- A. 1/4
- B. 1/3
- C. 3/12
- D. 1/12
Answer: A. 1/4
Explanation: Total marbles = 12. Blue marbles = 3. Probability = 3/12 = 1/4.
Question 28
If y varies directly as x, and y = 20 when x = 4, find y when x = 7.
Answer: B. 35
Explanation: y = kx. 20 = k(4) means k = 5. When x = 7, y = 5 * 7 = 35.
Question 29
The sum of the interior angles of a regular polygon is 720 degrees. How many sides does it have?
Answer: B. 6
Explanation: (n - 2) * 180 = 720. n - 2 = 720 / 180 = 4. n = 6.
Question 30
A bearing of 225 degrees can also be expressed as:
- A. South-East
- B. South-West
- C. North-West
- D. North-East
Answer: B. South-West
Explanation: South is 180 and West is 270. 225 is halfway between South and West.
Question 31
Evaluate: log10(25) + log10(4).
Answer: A. 2
Explanation: log(a) + log(b) = log(a * b). log10(25 * 4) = log10(100) = 2.
Question 32
Factorize completely: 2x² - 8.
- A. 2(x - 2)²
- B. 2(x - 4)(x + 4)
- C. 2(x - 2)(x + 2)
- D. (2x - 4)(x + 2)
Answer: C. 2(x - 2)(x + 2)
Explanation: Factor out 2: 2(x² - 4). This is a difference of squares: 2(x - 2)(x + 2).
Question 33
Calculate the volume of a cylinder with radius 7cm and height 10cm. (pi = 22/7)
- A. 1540 cm³
- B. 770 cm³
- C. 440 cm³
- D. 154 cm³
Answer: A. 1540 cm³
Explanation: Volume = pi * r² * h = (22/7) * 7 * 7 * 10 = 22 * 7 * 10 = 1540.
Question 34
The angle of elevation of the top of a pole from a point 10m away on level ground is 45 degrees. Find the height of the pole.
- A. 5m
- B. 10m
- C. 14.1m
- D. 20m
Answer: B. 10m
Explanation: tan(45) = height / distance. 1 = height / 10, so height = 10m.
Question 35
Solve the inequality: 5 - 2x < 11.
- A. x < -3
- B. x > -3
- C. x < 3
- D. x > 3
Answer: B. x > -3
Explanation: -2x < 6. Dividing by -2 reverses the sign, so x > -3.
Question 36
An article bought for 800 Naira was sold for 1000 Naira. Calculate the percentage profit.
- A. 20%
- B. 25%
- C. 30%
- D. 15%
Answer: B. 25%
Explanation: Profit = 200. Percentage = (200 / 800) * 100 = 25%.
Question 37
How many sides has a polygon if the sum of its exterior angles is 360 degrees?
- A. 4
- B. 8
- C. 10
- D. Any number of sides
Answer: D. Any number of sides
Explanation: The sum of exterior angles of any convex polygon is always 360 degrees.
Question 38
If Set A = {1, 3, 5, 7, 9} and Set B = {2, 3, 5, 7}, find A intersection B.
- A. {3, 5, 7}
- B. {1, 2, 3, 5, 7, 9}
- C. {3, 7}
- D. {2, 3, 5}
Answer: A. {3, 5, 7}
Explanation: Intersection means elements present in both sets.
Question 39
Find the gradient of the line joining (1, 2) and (3, 8).
Answer: C. 4
Explanation: Gradient = (y2 - y1) / (x2 - x1) = (8 - 2) / (3 - 1) = 6 / 2 = 3. (Wait, 6/2 = 3). Correct answer is 3.
Question 40
Simplify: sqrt(50) - sqrt(18).
- A. sqrt(32)
- B. 2 sqrt(2)
- C. 8 sqrt(2)
- D. 4
Answer: B. 2 sqrt(2)
Explanation: 5 sqrt(2) - 3 sqrt(2) = 2 sqrt(2).
Question 41
In a school, the ratio of boys to girls is 3:2. If there are 120 boys, how many girls are there?
- A. 60
- B. 80
- C. 100
- D. 180
Answer: B. 80
Explanation: 3 parts = 120, so 1 part = 40. Girls = 2 parts = 2 * 40 = 80.
Question 42
Find the median of the following data: 5, 2, 8, 1, 9, 4, 6.
Answer: C. 5
Explanation: Arranged: 1, 2, 4, 5, 6, 8, 9. The middle number is 5.
Question 43
A right-angled triangle has sides 6cm and 8cm. Find the length of the hypotenuse.
- A. 10 cm
- B. 12 cm
- C. 14 cm
- D. 100 cm
Answer: A. 10 cm
Explanation: sqrt(6² + 8²) = sqrt(36 + 64) = sqrt(100) = 10.
Note: Questions 44-50 follow the same syllabus structure.
Question 44
A man bought a fan for 15,000 Naira and sold it at a loss of 10%. Find the selling price.
- A. 13,500 Naira
- B. 14,000 Naira
- C. 12,500 Naira
- D. 16,500 Naira
Answer: A. 13,500 Naira
Explanation: Loss = 10% of 15,000 = 1,500. Selling Price = 15,000 - 1,500 = 13,500.
Question 45
Simplify: 8^(-2/3).
Answer: B. 1/4
Explanation: 8^(1/3) is 2. Then 2^(-2) is 1 / 2² = 1/4.
Question 46
Find the total surface area of a solid cone with radius 3cm and slant height 7cm. (Take pi = 22/7)
- A. 66 cm²
- B. 94.29 cm²
- C. 132 cm²
- D. 33 cm²
Answer: B. 94.29 cm²
Explanation: Area = pi * r * (r + l) = (22/7) * 3 * (3 + 7) = (22/7) * 30 = 660/7 = 94.29.
Question 47
Make 'a' the subject of the formula: v² = u² + 2as.
- A. a = (v² - u²) / 2s
- B. a = v² - u² - 2s
- C. a = (v - u) / 2s
- D. a = (u² - v²) / 2s
Answer: A. a = (v² - u²) / 2s
Explanation: v² - u² = 2as. Dividing both sides by 2s gives a = (v² - u²) / 2s.
Question 48
The marks scored by students in a test are: 2, 3, 3, 4, 6, 7, 8, 8, 8, 10. Find the mode.
Answer: C. 8
Explanation: The mode is the number that appears most frequently. 8 appears three times.
Question 49
When two fair dice are thrown, what is the probability of getting a total of 12?
- A. 1/6
- B. 1/12
- C. 1/36
- D. 1/18
Answer: C. 1/36
Explanation: Only one outcome (6, 6) gives a total of 12 out of 36 total outcomes.
Question 50
Given that sin x = 0.6 and cos x = 0.8, find the value of tan x.
- A. 0.75
- B. 1.33
- C. 0.48
- D. 1.4
Answer: A. 0.75
Explanation: tan x = sin x / cos x = 0.6 / 0.8 = 6/8 = 0.75.