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Mathematics past questions: WAEC SSCE 2025

48 objective questions, with answers. Free to read and practise.

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48 questions, one at a time, marked as you go or at the end. No account needed.

  1. 1.
    A 120º sector of a circle of radius 21 cm is bent to form a cone. What is the base radius of the cone?
    1. A.3 \(\frac{1}{2}\) cm
    2. B.10 \(\frac{1}{2}\) cm
    3. C.14 cm
    4. D.7 cm
    Show answer

    Answer: D 7 cm

  2. 2.
    A cylindrical container, closed at both ends, has a radius of 7 cm and a height of 5 cm. Use this information to answer the questions below. Find the total surface area of the container.
    Diagram for this question
    1. A.35 cm \(^2\)
    2. B.528 cm \(^2\)
    3. C.154 cm \(^2\)
    4. D.220 cm \(^2\)
    Show answer

    Answer: B 528 cm \(^2\)

  3. 3.
    A cylindrical container, closed at both ends, has a radius of 7 cm and a height of 5 cm. Use this information to answer the questions below. What is the volume of the container?
    Diagram for this question
    1. A.770 cm \(^3\)
    2. B.35 cm \(^3\)
    3. C.220 cm \(^3\)
    4. D.154 cm \(^3\)
    Show answer

    Answer: A 770 cm \(^3\)

  4. 4.
    A hollow sphere has a volume of k cm \(^3\) and a surface area of k cm \(^2\) . Calculate the diameter of the sphere.
    1. A.3 cm
    2. B.9 cm
    3. C.More information needed
    4. D.6 cm
    Show answer

    Answer: A 3 cm

  5. 5.
    A water tank of height \(\frac{1}{2}\) m has a square base of side 1 \(\frac{1}{2}\) m. If it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? [1000 litres = 1 m \(^3\) ]
    1. A.375 litres
    2. B.3750 litres
    3. C.37.5 litres
    4. D.37500 litres
    Show answer

    Answer: A 375 litres

  6. 6.
    By selling some crates of soft drinks for ₦600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?
    1. A.₦400.00
    2. B.₦1200.00
    3. C.₦900.00
    4. D.₦450.00
    Show answer

    Answer: A ₦400.00

  7. 7.
    Express 0.000834 in standard form.
    1. A.8.34 x 10 \(^{-4}\)
    2. B.8.34 x 10 \(^{-3}\)
    3. C.8.34 x 10 \(^4\)
    4. D.8.34 x 10 \(^3\)
    Show answer

    Answer: A 8.34 x 10 \(^{-4}\)

  8. 8.
    Factorize the expression x(a - c) + y(c - a)
    1. A.(a - c)(y - x)
    2. B.(a + c)(x + y)
    3. C.(a + c)(x - y)
    4. D.(a - c)(x - y)
    Show answer

    Answer: D (a - c)(x - y)

  9. 9.
    Find (101 \(_2\) ) \(^2\) , expressing the answer in base 2.
    1. A.11101
    2. B.10101
    3. C.10010
    4. D.11001
    Show answer

    Answer: D 11001

  10. 10.
    Find the median of the following numbers: 2.64, 2.50, 2.72, 2.91, and 2.35
    1. A.2.50
    2. B.2.64
    3. C.2.91
    4. D.2.72
    Show answer

    Answer: B 2.64

  11. 11.
    Find the nth term U \(_n\) of the A.P. 11, 4, -3, …
    1. A.U \(_n\) = 19 - 7n
    2. B.U \(_n\) = 19 + 7n
    3. C.U \(_n\) = 18 - 7n
    4. D.U \(_n\) = 18 + 7n
    Show answer

    Answer: C U \(_n\) = 18 - 7n

  12. 12.
    Find the roots of the equation y = 3x \(^2\) + x - 7.
    Diagram for this question
    1. A.1.4 and -1.7
    2. B.2.0 and -1.9
    3. C.1.0 and -1.2
    4. D.1.1 and -1.3
    Show answer

    Answer: A 1.4 and -1.7

  13. 13.
    Find the total surface area of a solid circular cone with base radius 3 cm and slant height 4 cm. [Take π = \(\frac{22}{7}\) ]
    1. A.66 cm \(^2\)
    2. B.37 \(\frac{5}{7}\) cm \(^2\)
    3. C.75 \(\frac{3}{7}\) cm \(^2\)
    4. D.78 \(\frac{6}{7}\) cm \(^2\)
    Show answer

    Answer: A 66 cm \(^2\)

  14. 14.
    Find the values of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\)
    1. A.+5 or -1
    2. B.-5 or +1
    3. C.-5 or -1
    4. D.+4 or +1
    Show answer

    Answer: B -5 or +1

  15. 15.
    From a box containing 2 red, 6 white, and 5 black balls, a ball is randomly selected. What is the probability that the selected ball is black?
    1. A.\(\frac{5}{13}\)
    2. B.\(\frac{5}{11}\)
    3. C.\(\frac{2}{13}\)
    4. D.\(\frac{5}{6}\)
    Show answer

    Answer: A \(\frac{5}{13}\)

  16. 16.
    Given that log \(_2a\) = log \(_84\) , find a.
    1. A.2 \(^{\frac{1}{2}}\)
    2. B.2 \(^{\frac{2}{3}}\)
    3. C.4 \(^{\frac{2}{3}}\)
    4. D.4 \(^{\frac{1}{2}}\)
    Show answer

    Answer: B 2 \(^{\frac{2}{3}}\)

  17. 17.
    If \(\frac{16}{9}\) , x, 1, y are in geometric progression (G.P.). Find the product of x and y.
    1. A.\(\frac{16}{9}\)
    2. B.\(\frac{3}{4}\)
    3. C.1
    4. D.\(\frac{4}{3}\)
    Show answer

    Answer: C 1

  18. 18.
    If log \(_{10}\) x = 2.3675 and log \(_{10}\) y = 2.9738, what is the value of x + y, correct to three significant figures
    1. A.0.118
    2. B.0.903
    3. C.0.117
    4. D.0.944
    Show answer

    Answer: A 0.118

  19. 19.
    If R = {2, 4, 6, 7} and S = {1, 2, 4, 8} then R ∪ S equals
    1. A.{1, 2, 4, 6, 7, 8}
    2. B.{1, 2, 4, 7, 8}
    3. C.{1, 4, 7, 8}
    4. D.{2, 6, 7}
    Show answer

    Answer: A {1, 2, 4, 6, 7, 8}

  20. 20.
    If three children share ₦10.50 among themselves in the ratio 6:7:8, how much is the largest share?
    1. A.₦3.50
    2. B.₦4.00
    3. C.₦4.50
    4. D.₦3.00
    Show answer

    Answer: B ₦4.00

  21. 21.
    If y ∝ \(\frac{1}{x^2}\) and x = 3, when y = 4, find y when x = 2
    1. A.3
    2. B.9
    3. C.1
    4. D.18
    Show answer

    Answer: B 9

  22. 22.
    In the diagram above, < PRQ = 90º, < QPR = 30º and |PQ| = 10 cm. Find y
    Diagram for this question
    1. A.6cm
    2. B.4cm
    3. C.5cm
    4. D.3cm
    Show answer

    Answer: C 5cm

  23. 23.
    In the diagram above, AB||CD. What is the size of the angle marked x?
    Diagram for this question
    1. A.93°
    2. B.77°
    3. C.103°
    4. D.62°
    Show answer

    Answer: A 93°

  24. 24.
    In the diagram above, AO is perpendicular to OB. Find x.
    Diagram for this question
    1. A.15°
    2. B.22.5°
    3. C.7.5°
    4. D.30°
    Show answer

    Answer: D 30°

  25. 25.
    In the diagram above, PQ is parallel to TU, < PQR = 50º, < QRS = 86º, and < STU = 64º. Calculate the value of x
    Diagram for this question
    1. A.100°
    2. B.108°
    3. C.120°
    4. D.136°
    Show answer

    Answer: A 100°

  26. 26.
    In the diagram above, the shaded portion is
    Diagram for this question
    1. A.(P ∪ Q) \(^1\) ∩ R
    2. B.P \(^1\) ∩ Q ∩ R
    3. C.P \(^1\) ∩ R
    4. D.Q \(^1\) ∩ R
    Show answer

    Answer: C P \(^1\) ∩ R

  27. 27.
    In the diagram above, the value of angles b + c is
    Diagram for this question
    1. A.a°
    2. B.90°
    3. C.180°
    4. D.d°
    Show answer

    Answer: C 180°

  28. 28.
    In the diagram above. O is the centre of the circle and |BD| = |DC|. If < DCB = 35º, find < BAO
    Diagram for this question
    1. A.25°
    2. B.30°
    3. C.20°
    4. D.35°
    Show answer

    Answer: C 20°

  29. 29.
    In the diagram below, AB||DC, the bisectors of < BAC and < ACD meet at E. Find the value of < AEC
    Diagram for this question
    1. A.45°
    2. B.60°
    3. C.30°
    4. D.90°
    Show answer

    Answer: D 90°

  30. 30.
    In the diagram,|AB| = 12cm, |AE| = 8cm, |DC| = 9cm and BD||DC. Find the length of EC.
    Diagram for this question
    1. A.6cm
    2. B.5cm
    3. C.8cm
    4. D.9cm
    Show answer

    Answer: A 6cm

  31. 31.
    Simplify 0.027 \(^{-\frac{1}{3}}\)
    1. A.\(\frac{3}{10}\)
    2. B.3 \(\frac{1}{3}\)
    3. C.\(\frac{1}{3}\)
    4. D.3
    Show answer

    Answer: B 3 \(\frac{1}{3}\)

  32. 32.
    Solve the equation (x + 2)(x - 7) = 0
    1. A.-1 or 8
    2. B.-4 or 5
    3. C.-3 or 6
    4. D.-2 or 7
    Show answer

    Answer: D -2 or 7

  33. 33.
    Solve the equation 3x \(^2\) + 25x - 18 = 0
    1. A.-3, 2
    2. B.-9, \(\frac{2}{3}\)
    3. C.-2, 9
    4. D.-2, 3
    Show answer

    Answer: B -9, \(\frac{2}{3}\)

  34. 34.
    Solve the following simultaneous equations: x + y = \(\frac{3}{2}\) , x - y = \(\frac{5}{2}\) . And use your result to find the value of 2y + x.
    1. A.-2
    2. B.\(\frac{1}{2}\)
    3. C.1
    4. D.-1
    Show answer

    Answer: C 1

  35. 35.
    Solve the inequality \(\frac{1}{3}\) (2x - 1) < 5
    1. A.x < -5
    2. B.x < 8
    3. C.x < -6
    4. D.x < 7
    Show answer

    Answer: B x < 8

  36. 36.
    The angle of a sector of a circle is 108 °. If the radius of the circle is 3 \(\frac{1}{2}\) cm, find the perimeter of the sector.
    1. A.6 \(\frac{3}{5}\) cm
    2. B.7 \(\frac{2}{10}\) cm
    3. C.6 \(\frac{4}{5}\) cm
    4. D.13 \(\frac{3}{5}\) cm
    Show answer

    Answer: D 13 \(\frac{3}{5}\) cm

  37. 37.
    The bearing of two points Q and R from a point P are 030º and 120º, respectively. If |PQ| = 12 m and |PR| = 5 m, find the distance QR.
    1. A.11 m
    2. B.13 m
    3. C.9 m
    4. D.7 m
    Show answer

    Answer: B 13 m

  38. 38.
    The diagonals AC and BD of a rhombus ABCD are 16 cm and 12 cm long, respectively. Calculate the area of the rhombus.
    1. A.96 cm \(^2\)
    2. B.36 cm \(^2\)
    3. C.48 cm \(^2\)
    4. D.24 cm \(^2\)
    Show answer

    Answer: A 96 cm \(^2\)

  39. 39.
    The diagram above shows a cone with the dimensions of its frustum indicated. Calculate the height of the cone.
    Diagram for this question
    1. A.24 cm
    2. B.15 cm
    3. C.8 cm
    4. D.12 cm
    Show answer

    Answer: A 24 cm

  40. 40.
    The locus of a point which is equidistant from two given fixed points is the
    1. A.Angle bisector of the straight lines joining them.
    2. B.Parallel line to the straight line joining them.
    3. C.Perpendicular to the straight line joining them.
    4. D.Perpendicular bisector of the straight line joining them.
    Show answer

    Answer: D Perpendicular bisector of the straight line joining them.

  41. 41.
    The mean of 20 observations in an experiment is 4. If the observed largest value is 23, find the mean of the remaining observations.
    1. A.4
    2. B.2.60
    3. C.2.85
    4. D.3
    Show answer

    Answer: D 3

  42. 42.
    The positions of two countries, P and Q, are (15ºN, 12ºE) and (65ºN, 12ºE) respectively. What is the difference in latitude?
    1. A.50°
    2. B.104°
    3. C.80°
    4. D.100°
    Show answer

    Answer: A 50°

  43. 43.
    What is the minimum value of y?
    Diagram for this question
    1. A.-7
    2. B.-10
    3. C.-4
    4. D.-1
    Show answer

    Answer: A -7

  44. 44.
    What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, 8, 10, 9, 8, and 14?
    1. A.8
    2. B.9
    3. C.10
    4. D.11
    Show answer

    Answer: A 8

  45. 45.
    What is the smaller value of x for which x \(^2\) - 3x + 2 = 0 ?
    1. A.4
    2. B.2
    3. C.3
    4. D.1
    Show answer

    Answer: D 1

  46. 46.
    Which of the following angles is an exterior angle of a regular polygon?
    1. A.95°
    2. B.78°
    3. C.72°
    4. D.85°
    Show answer

    Answer: C 72°

  47. 47.
    Which of the following could be the inequality illustrated in the sketch graph above?
    Diagram for this question
    1. A.y ≤ -3x + 3
    2. B.y ≤ 3x + 2
    3. C.y ≥ -2x + 3
    4. D.y ≤ x + 3
    Show answer

    Answer: A y ≤ -3x + 3

  48. 48.
    Without using tables, find the value of: \(\frac{sin 20°}{cos 70°} + \frac{cos 25°}{sin 65°}\)
    1. A.2
    2. B.0
    3. C.1
    4. D.-1
    Show answer

    Answer: A 2

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