Sample WAEC-style Practice Questions (Original Content)
WAEC Style
Question 1
Simplify: (3/4 - 1/3) ÷ 5/12
Show Answer
Answer: A. 1
Explanation: (3/4 - 1/3) = (9-4)/12 = 5/12. Then, 5/12 ÷ 5/12 = 1.
Question 2
If 3, x, y, 18 are in Arithmetic Progression (A.P), find the values of x and y.
A. 8, 13
B. 7, 11
C. 9, 12
D. 6, 9
Show Answer
Answer: A. 8, 13
Explanation: Common difference d = (18 - 3)/3 = 5. So, x = 3+5=8 and y = 8+5=13.
Question 3
Solve for x: 5^(2x - 1) = 125
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Answer: B. 2
Explanation: 5^(2x - 1) = 5³. Therefore 2x - 1 = 3 -> 2x = 4 -> x = 2.
Question 4
A car depreciates by 10% of its value every year. If it is worth N2,000,000 now, what will be its value in 2 years?
A. N1,600,000
B. N1,800,000
C. N1,620,000
D. N1,750,000
Show Answer
Answer: C. N1,620,000
Explanation: Year 1: 2,000,000 - 200,000 = 1,800,000. Year 2: 1,800,000 - 180,000 = 1,620,000.
Question 5
Find the length of the diagonal of a square whose area is 50 cm².
A. 5 cm
B. 10 cm
C. 15 cm
D. 25 cm
Show Answer
Answer: B. 10 cm
Explanation: Side s² = 50. Diagonal d = √(s² + s²) = √(50 + 50) = √100 = 10.
Question 6
Evaluate (111 base 2)² and leave your answer in base 2.
A. 110001
B. 101010
C. 111111
D. 100011
Show Answer
Answer: A. 110001
Explanation: 111 (base 2) = 7 (base 10). 7² = 49. 49 in base 2 is 110001.
Question 7
If the mean of 2, 4, 8, and q is 6, find the value of q.
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Answer: C. 10
Explanation: (2 + 4 + 8 + q) / 4 = 6 -> 14 + q = 24 -> q = 10.
Question 8
A point P(x, y) is translated 3 units right and 2 units down to P'(5, 1). Find the coordinates of P.
A. (8, 3)
B. (2, -1)
C. (2, 3)
D. (8, -1)
Show Answer
Answer: C. (2, 3)
Explanation: x + 3 = 5 -> x = 2. y - 2 = 1 -> y = 3.
Question 9
The probability of an event happening is 0.35. What is the probability that the event will NOT happen?
A. 0.35
B. 0.55
C. 0.65
D. 0.75
Show Answer
Answer: C. 0.65
Explanation: P(not E) = 1 - P(E) = 1 - 0.35 = 0.65.
Question 10
Simplify: √48 - √27
A. √21
B. 3√3
C. √3
D. 7√3
Show Answer
Answer: C. √3
Explanation: √48 = 4√3. √27 = 3√3. 4√3 - 3√3 = √3.
Question 11
Find the sum of the first 20 terms of the sequence: 5, 5, 5, 5, ...
Show Answer
Answer: C. 100
Explanation: Sum = 5 x 20 = 100.
Question 12
If sin x = 4/5 and x is acute, find the value of tan x.
A. 3/4
B. 4/3
C. 3/5
D. 5/3
Show Answer
Answer: B. 4/3
Explanation: Opp = 4, Hyp = 5. Using Pythagoras, Adj = √(5² - 4²) = 3. Tan x = Opp/Adj = 4/3.
Question 13
In a circle of radius 14cm, calculate the length of an arc that subtends an angle of 90° at the center. (π = 22/7)
A. 11 cm
B. 22 cm
C. 44 cm
D. 88 cm
Show Answer
Answer: B. 22 cm
Explanation: Length = (90/360) x 2 x (22/7) x 14 = 1/4 x 2 x 22 x 2 = 22.
Question 14
Solve for m: 2m/3 - 1/2 = 1/6
Show Answer
Answer: A. 1
Explanation: Multiply by 6: 4m - 3 = 1 -> 4m = 4 -> m = 1.
Question 15
Find the gradient of a line perpendicular to the line y = -2x + 5.
A. -2
B. 2
C. -1/2
D. 1/2
Show Answer
Answer: D. 1/2
Explanation: For perpendicular lines, m1 * m2 = -1. (-2) * m2 = -1 -> m2 = 1/2.
Question 16
Calculate the variance of the numbers: 10, 10, 10, 10, 10.
Show Answer
Answer: D. 0
Explanation: Since all numbers are identical, there is no deviation from the mean, so variance is 0.
Question 17
Rationalize the denominator: 6 / √3
A. 2
B. 2√3
C. 6√3
D. 3√2
Show Answer
Answer: B. 2√3
Explanation: (6 / √3) x (√3 / √3) = 6√3 / 3 = 2√3.
Question 18
The ratio of the areas of two similar triangles is 16:25. What is the ratio of their corresponding sides?
A. 4:5
B. 16:25
C. 256:625
D. 2:3
Show Answer
Answer: A. 4:5
Explanation: Side ratio = Square root of Area ratio = √16 : √25 = 4:5.
Question 19
Find the value of x: log(base x) 64 = 3
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Answer: B. 4
Explanation: x³ = 64. Since 4 x 4 x 4 = 64, x = 4.
Question 20
A boy is x years old. His father is 3 times as old as the boy. In 10 years' time, the sum of their ages will be 60. Find x.
Show Answer
Answer: A. 10
Explanation: (x+10) + (3x+10) = 60 -> 4x + 20 = 60 -> 4x = 40 -> x = 10.
Question 21
Convert 110111 (base 2) to a number in base 10.
Show Answer
Answer: A. 55
Explanation: (1*32) + (1*16) + (0*8) + (1*4) + (1*2) + (1*1) = 32 + 16 + 4 + 2 + 1 = 55.
Question 22
Make h the subject of the formula: V = (1/3) * pi * r² * h.
A. h = V / (3 * pi * r²)
B. h = 3V / (pi * r²)
C. h = sqrt(3V / pi)
D. h = 3V * pi * r²
Show Answer
Answer: B. h = 3V / (pi * r²)
Explanation: Multiply both sides by 3 to get 3V = pi * r² * h. Then divide by (pi * r²) to isolate h.
Question 23
A student measured a line to be 10.5 cm instead of 10.0 cm. Calculate the percentage error.
A. 5%
B. 0.5%
C. 5.5%
D. 10%
Show Answer
Answer: A. 5%
Explanation: Error = 10.5 - 10.0 = 0.5. Percentage error = (0.5 / 10.0) * 100 = 5%.
Question 24
Find the roots of the quadratic equation: x² - 7x + 10 = 0.
A. 2 and 5
B. -2 and -5
C. 1 and 10
D. -1 and -10
Show Answer
Answer: A. 2 and 5
Explanation: (x - 2)(x - 5) = 0. Therefore, x = 2 or x = 5.
Question 25
In a class of 40 students, 25 like Mathematics and 20 like English. If 10 like both, how many students like neither?
Show Answer
Answer: A. 5
Explanation: n(M union E) = n(M) + n(E) - n(M intersect E) = 25 + 20 - 10 = 35. Neither = 40 - 35 = 5.
Question 26
The sum of the interior angles of a regular polygon is 1080 degrees. Find the number of sides.
Show Answer
Answer: B. 8
Explanation: (n - 2) * 180 = 1080. n - 2 = 1080 / 180 = 6. n = 8.
Question 27
Calculate the curved surface area of a cone with radius 7 cm and slant height 10 cm. (pi = 22/7)
A. 154 cm²
B. 220 cm²
C. 440 cm²
D. 70 cm²
Show Answer
Answer: B. 220 cm²
Explanation: Curved Surface Area = pi * r * l = (22/7) * 7 * 10 = 220.
Question 28
If tan theta = 5/12, find the value of sin theta.
A. 5/13
B. 12/13
C. 13/5
D. 13/12
Show Answer
Answer: A. 5/13
Explanation: Opp = 5, Adj = 12. Hyp = sqrt(5² + 12²) = 13. Sin = Opp/Hyp = 5/13.
Question 29
Find the range of the following set of scores: 15, 22, 18, 11, 29, 25, 14.
Show Answer
Answer: B. 18
Explanation: Range = Highest value - Lowest value = 29 - 11 = 18.
Question 30
Simplify: (8^2) * (2^3) / (4^4).
Show Answer
Answer: A. 2
Explanation: (2^6 * 2^3) / 2^8 = 2^9 / 2^8 = 2^1 = 2.
Question 31
Share 120 Naira between Kofi and Ama in the ratio 3:5. How much does Ama get?
A. 45 Naira
B. 75 Naira
C. 60 Naira
D. 80 Naira
Show Answer
Answer: B. 75 Naira
Explanation: Total parts = 8. Ama's share = (5/8) * 120 = 5 * 15 = 75.
Question 32
A fair coin is tossed twice. What is the probability of getting at least one head?
A. 1/4
B. 1/2
C. 3/4
D. 1
Show Answer
Answer: C. 3/4
Explanation: Possible outcomes: HH, HT, TH, TT. Those with at least one head: HH, HT, TH (3 outcomes out of 4).
Question 33
Find the midpoint of the line joining points P(2, 4) and Q(6, 10).
A. (4, 7)
B. (8, 14)
C. (4, 3)
D. (2, 3)
Show Answer
Answer: A. (4, 7)
Explanation: Midpoint = [(2+6)/2, (4+10)/2] = [8/2, 14/2] = (4, 7).
Question 34
Express 0.003597 correct to three significant figures.
A. 0.003
B. 0.0036
C. 0.00360
D. 0.00359
Show Answer
Answer: C. 0.00360
Explanation: The first three significant digits are 3, 5, and 9. Because the next digit is 7, we round 9 up, which makes it 0.00360.
Question 35
Calculate the compound interest on 2000 Naira for 2 years at 10% per annum.
A. 400 Naira
B. 420 Naira
C. 2420 Naira
D. 200 Naira
Show Answer
Answer: B. 420 Naira
Explanation: Amount = 2000 * (1.10)² = 2000 * 1.21 = 2420. Interest = 2420 - 2000 = 420.
Question 36
Rationalize the denominator: 6 / sqrt(3).
A. 2
B. 2 sqrt(3)
C. 6 sqrt(3)
D. 3 sqrt(2)
Show Answer
Answer: B. 2 sqrt(3)
Explanation: (6 * sqrt(3)) / (sqrt(3) * sqrt(3)) = 6 sqrt(3) / 3 = 2 sqrt(3).
Question 37
A square has a perimeter of 40 cm. Find the length of its diagonal.
A. 10 cm
B. 10 sqrt(2) cm
C. 20 cm
D. 5 sqrt(2) cm
Show Answer
Answer: B. 10 sqrt(2) cm
Explanation: Side = 40/4 = 10. Diagonal = sqrt(10² + 10²) = sqrt(200) = 10 sqrt(2).
Question 38
If (x - 2) is a factor of x² + kx - 6, find the value of k.
Show Answer
Answer: A. 1
Explanation: By factor theorem, f(2) = 0. (2)² + k(2) - 6 = 0. 4 + 2k - 6 = 0. 2k = 2. k = 1.
Question 39
A man walks 4 km North and then 3 km East. What is his bearing from his starting point?
A. 037 degrees
B. 053 degrees
C. 090 degrees
D. 045 degrees
Show Answer
Answer: A. 037 degrees
Explanation: tan theta = Opp/Adj = 3/4 = 0.75. Theta = 36.87 degrees (approx 037).
Question 40
Solve: log3(x) = 4.
Show Answer
Answer: C. 81
Explanation: x = 3 to the power of 4 = 3 * 3 * 3 * 3 = 81.
Question 41
If z varies jointly as x and y, and z = 12 when x = 2 and y = 3, find z when x = 5 and y = 4.
Show Answer
Answer: B. 40
Explanation: z = kxy. 12 = k(2)(3) means k = 2. z = 2(5)(4) = 40.
Question 42
In a pie chart, a section represents 20% of the total data. What is the angle of that sector?
A. 20 degrees
B. 36 degrees
C. 72 degrees
D. 120 degrees
Show Answer
Answer: C. 72 degrees
Explanation: Angle = (20 / 100) * 360 = 0.2 * 360 = 72.
Question 43
Convert the base 10 number 27 to a base 5 number.
A. 102
B. 52
C. 122
D. 100
Show Answer
Answer: A. 102
Explanation: 27 / 5 = 5 remainder 2. 5 / 5 = 1 remainder 0. 1 / 5 = 0 remainder 1. Reading remainders upwards: 102.
Question 44
On a map, 1 cm represents 5 km. If two towns are 4.5 cm apart on the map, what is the actual distance?
A. 22.5 km
B. 20.5 km
C. 9 km
D. 45 km
Show Answer
Answer: A. 22.5 km
Explanation: 4.5 * 5 = 22.5.
Question 45
Find the volume of a rectangular pyramid with base area 30 cm² and height 10 cm.
A. 300 cm³
B. 100 cm³
C. 150 cm³
D. 60 cm³
Show Answer
Answer: B. 100 cm³
Explanation: Volume = (1/3) * Base Area * Height = (1/3) * 30 * 10 = 100.
Question 46
A circle has a radius of 10 cm. Find the length of a chord that is 6 cm from the center.
A. 8 cm
B. 16 cm
C. 12 cm
D. 20 cm
Show Answer
Answer: B. 16 cm
Explanation: Using Pythagoras: (Half-chord)² + 6² = 10². Half-chord = sqrt(100 - 36) = 8. Full chord = 16.
Question 47
Expand and simplify: (x + 3)(x - 5).
A. x² - 2x - 15
B. x² + 2x - 15
C. x² - 8x - 15
D. x² + 8x + 15
Show Answer
Answer: A. x² - 2x - 15
Explanation: x(x - 5) + 3(x - 5) = x² - 5x + 3x - 15 = x² - 2x - 15.
Question 48
A shopkeeper allows a 15% discount on a dress marked 4000 Naira. Find the selling price.
A. 3400 Naira
B. 3600 Naira
C. 3850 Naira
D. 4600 Naira
Show Answer
Answer: A. 3400 Naira
Explanation: Discount = 0.15 * 4000 = 600. Selling Price = 4000 - 600 = 3400.
Question 49
Find the 5th term of the Geometric Progression: 2, 6, 18...
A. 54
B. 162
C. 486
D. 1458
Show Answer
Answer: B. 162
Explanation: a = 2, r = 3. 5th term = a * r⁴ = 2 * 3⁴ = 2 * 81 = 162.
Question 50
The sum of the ages of a father and his son is 50. If the father is 30 years older than the son, find the son's age.
Show Answer
Answer: A. 10
Explanation: x + (x + 30) = 50. 2x = 20. x = 10.