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Mathematics past questions: WAEC SSCE 2023

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 bag contains 4 white marbles and 3 blue marbles. Another bag contains 5 red and 6 blue marbles. If a marble is picked at random from each bag, find the probability that they are of the same colour.
    1. A.\(\frac{9}{11}\)
    2. B.\(\frac{18}{77}\)
    3. C.\(\frac{1}{2}\)
    4. D.\(\frac{11}{12}\)
    Show answer

    Answer: B \(\frac{18}{77}\)

  2. 2.
    A line L passing through the point (6, -13) is parallel to the line which passes through (7, 4) and (-3, 9). Find the equation of the line L.
    1. A.y = \(\frac{1}{2}x - 10\)
    2. B.y = \(\frac{-1}{2}x + 10\)
    3. C.y = \(\frac{-1}{2}x - 10\)
    4. D.y = \(\frac{1}{2}x +10\)
    Show answer

    Answer: C y = \(\frac{-1}{2}x - 10\)

  3. 3.
    A notebook of length 15 cm was measured to be 16.8 cm, calculate, correct to two d.p, the percentage error in the measurement.
    1. A.12.00%
    2. B.11.71%
    3. C.10.71%
    4. D.11.21%
    Show answer

    Answer: A 12.00%

  4. 4.
    A number is chosen at random from 40 and 50 inclusive. Find the probability that the number is prime.
    1. A.\(\frac{8}{11}\)
    2. B.\(\frac{3}{11}\)
    3. C.\(\frac{4}{11}\)
    4. D.\(\frac{5}{11}\)
    Show answer

    Answer: B \(\frac{3}{11}\)

  5. 5.
    A student measured the height of a pole as 5.98 m which is less than the actual height. If the percentage error is 5%, find correct to two d.p the actual height of the pole.
    1. A.6.29m
    2. B.7.67m
    3. C.7.18m
    4. D.6.65m
    Show answer

    Answer: A 6.29m

  6. 6.
    An empty cylindrical tank is 140 cm in diameter. If 200 litres of water was poured into the tank. Calculate, correct to the nearest centimeter, the height of the water in the tank. ( \(Take \pi = \frac{22}{7})\)
    1. A.91cm
    2. B.7cm
    3. C.13cm
    4. D.57cm
    Show answer

    Answer: C 13cm

  7. 7.
    An equilateral triangle has a side 2 cm. Calculate the height of the triangle.
    Diagram for this question
    1. A.5cm
    2. B.\(\sqrt5\) cm
    3. C.3cm
    4. D.\(\sqrt{ 3}\) cm
    Show answer

    Answer: D \(\sqrt{ 3}\) cm

  8. 8.
    Arrange the following in ascending order of magnitude \(110_{two}, 31_{eight}, 42_{five}\)
    1. A.\(110_{two}, 31_{five}, 42_{eight}\)
    2. B.\(42_{five}, 110_{two}, 31_{eight}\)
    3. C.\(42_{five}, 31_{eight}, 110_{two}\)
    4. D.\(110_{two}, 42_{five}, 31_{eight}\)
    Show answer

    Answer: D \(110_{two}, 42_{five}, 31_{eight}\)

  9. 9.
    Consider the statements: p: Siah is from Foya. q: Foya is in Lofa. Write in symbolic for the statement: "If Siah is from Foya, then Foya is in Lofa"
    1. A.~q ⇔ p
    2. B.q ⇒ p
    3. C.p ⇒ q
    4. D.p ⇔ q
    Show answer

    Answer: C p ⇒ q

  10. 10.
    Evaluate, correct to three decimal place \(\frac{4.314 × 0.000056}{0.0067}\)
    1. A.0.037
    2. B.0.004
    3. C.0.361
    4. D.0.036
    Show answer

    Answer: D 0.036

  11. 11.
    Express \(413_7\) to base 5
    1. A.\(2311_5\)
    2. B.\(1131_5\)
    3. C.\(1311_5\)
    4. D.\(2132_5\)
    Show answer

    Answer: C \(1311_5\)

  12. 12.
    Factorize completely: \(x^2 - (y + z)^2\)
    1. A.(x - y - z)(x - y - z)
    2. B.(x + y + z)(x - y - z)
    3. C.(x + y + z)(x + y - z)
    4. D.(x + y - z)(x - y + z)
    Show answer

    Answer: B (x + y + z)(x - y - z)

  13. 13.
    Find the gradient of the line passing through the points \((\frac{1}{2}, \frac{- 1}{3}) and ( 3 , \frac{2}{3})\)
    1. A.\(\frac{2}{5}\)
    2. B.\(\frac{5}{2}\)
    3. C.\(\frac{2}{7}\)
    4. D.\(\frac{7}{2}\)
    Show answer

    Answer: A \(\frac{2}{5}\)

  14. 14.
    Find the mean deviation of assets of numbers: 14, 15, 16, 17, 18, and 19.
    1. A.2.5
    2. B.1.7
    3. C.1.5
    4. D.3.5
    Show answer

    Answer: C 1.5

  15. 15.
    Find the quadratic equation whose roots are \(\frac{2}{3} and \frac{- 3}{4}\)
    1. A.\(12y^2 - y - 6 = 0\)
    2. B.\(12y^2 - y + 6 = 0\)
    3. C.\(12y^2 + y - 6 = 0\)
    4. D.\(y^2 + y - 6 = 0\)
    Show answer

    Answer: C \(12y^2 + y - 6 = 0\)

  16. 16.
    Find the roots of the equations: 3m \(^2\) - 2m - 65 = 0
    1. A.\(( -5, \frac{-13}{3})\)
    2. B.\(( 5, \frac{-13}{3})\)
    3. C.\(( 5, \frac{13}{3})\)
    4. D.\(( -5, \frac{13}{3})\)
    Show answer

    Answer: B \(( 5, \frac{-13}{3})\)

  17. 17.
    Find the value of a in the equation: cos (a + 14)° = sin (4a + 6)°
    1. A.15
    2. B.17
    3. C.14
    4. D.21
    Show answer

    Answer: C 14

  18. 18.
    Find the value of m in the diagram above.
    Diagram for this question
    1. A.\(40^0\)
    2. B.\(50^0\)
    3. C.\(130^0\)
    4. D.\(140^0\)
    Show answer

    Answer: C \(130^0\)

  19. 19.
    For what value of x is \(\frac{ x^2 + 2 }{ 10x^2 - 13x - 3}\) is undefined?.
    1. A.\(\frac{1}{5}, \frac{3}{2}\)
    2. B.\(\frac{-1}{5}, \frac{3}{2}\)
    3. C.\(\frac{1}{5}, \frac{-3}{2}\)
    4. D.\(\frac{-1}{5}, \frac{-3}{2}\)
    Show answer

    Answer: B \(\frac{-1}{5}, \frac{3}{2}\)

  20. 20.
    How many students scored at least 3 marks?
    Diagram for this question
    1. A.44
    2. B.52
    3. C.38
    4. D.18
    Show answer

    Answer: A 44

  21. 21.
    If 2x - 3y = -11 and 3x + 2y = 3, evaluate \((y - x)^2\)
    1. A.16
    2. B.25
    3. C.9
    4. D.4
    Show answer

    Answer: A 16

  22. 22.
    In the diagram above, M, N, R are points on the circle centre O. ∠ORN = 48° and ∠RNM = 124°. Find ∠OMN.
    Diagram for this question
    1. A.\(58^0\)
    2. B.\(64^0\)
    3. C.\(48^0\)
    4. D.\(76^0\)
    Show answer

    Answer: D \(76^0\)

  23. 23.
    In the diagram above, O is the centre of a circle NST. |NT| = |ST| and ∠NTS = 36°. Find the measure of the angle marked t.
    Diagram for this question
    1. A.\(72^0\)
    2. B.\(54^0\)
    3. C.\(36^0\)
    4. D.\(108^0\)
    Show answer

    Answer: C \(36^0\)

  24. 24.
    In the diagram, NR is a diameter, ∠MNR = x° and, ∠SRN = (5x + 20)°. Find the value of 2x.
    Diagram for this question
    1. A.\(42^0\)
    2. B.\(35^0\)
    3. C.\(20^0\)
    4. D.\(90^0\)
    Show answer

    Answer: B \(35^0\)

  25. 25.
    In the diagram, O is the center of the circle QRS and ∠SQR = 28°. Find ∠ORS.
    Diagram for this question
    1. A.\(56^0\)
    2. B.\(28^0\)
    3. C.\(76^0\)
    4. D.\(62^0\)
    Show answer

    Answer: D \(62^0\)

  26. 26.
    John was facing S35°E. If he turned 90° in the anticlockwise direction, find his new direction.
    1. A.S55°E.
    2. B.S35°W.
    3. C.N55°E.
    4. D.N35°W.
    Show answer

    Answer: C N55°E.

  27. 27.
    M varies jointly as the square of n and square root of q. If M = 24 when n = 2 and q = 4, find M when n = 5, q = 9.
    1. A.288
    2. B.400
    3. C.300
    4. D.225
    Show answer

    Answer: D 225

  28. 28.
    m:n = \(2\frac{1}{3} : 1\frac{1}{5}\) and n : q = \(1\frac{1}{2} : 1\frac{1}{3}\) , find q : m.
    1. A.35 : 18
    2. B.16 : 35
    3. C.18 : 35
    4. D.35 : 16
    Show answer

    Answer: B 16 : 35

  29. 29.
    make x the subject of the relation \(y = \frac{ax^3 - b}{3z}\)
    1. A.x = \(\sqrt[3] \frac{ax^3 - b}{3z}\)
    2. B.x = \(\sqrt[3] \frac{3yz - b}{a}\)
    3. C.x = \(\sqrt[3] \frac{3yz + b}{a}\)
    4. D.x = \(\sqrt[3] \frac{3yzb}{a}\)
    Show answer

    Answer: C x = \(\sqrt[3] \frac{3yz + b}{a}\)

  30. 30.
    Mr Manu is 4 times as old as his son, Adu. 7 years ago the sum of their ages was 76. How old is Adu?
    1. A.22years
    2. B.12years
    3. C.18years
    4. D.15 years
    Show answer

    Answer: C 18years

  31. 31.
    Mrs Kebeh stands at a distance of 110 m away from a building of vertical height 58 m. If Kebeh is 2 m tall, find the angle of elevation of the top of the building from her eye.
    1. A.\(27^0\)
    2. B.\(28^0\)
    3. C.\(20^0\)
    4. D.\(26^0\)
    Show answer

    Answer: A \(27^0\)

  32. 32.
    One-third of the sum of two numbers is 12, twice their difference is 12. Find the numbers.
    1. A.22 and 14
    2. B.20 and 16
    3. C.21 and 15
    4. D.23 and 13
    Show answer

    Answer: C 21 and 15

  33. 33.
    Simplify \(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
    1. A.10 \(\sqrt{3}\)
    2. B.18 \(\sqrt{3}\)
    3. C.14 \(\sqrt{3}\)
    4. D.7 \(\sqrt{3}\)
    Show answer

    Answer: C 14 \(\sqrt{3}\)

  34. 34.
    Solve \(1 + \sqrt[3]{ x - 3} = 4\)
    1. A.30
    2. B.6
    3. C.12
    4. D.66
    Show answer

    Answer: A 30

  35. 35.
    Solve \(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
    1. A.\(\frac{3}{2}\)
    2. B.\(\frac{1}{2}\)
    3. C.\(\frac{1}{3}\)
    4. D.\(\frac{5}{3}\)
    Show answer

    Answer: B \(\frac{1}{2}\)

  36. 36.
    Solve: \(log_3 x + log_3 (x - 8) = 2\)
    1. A.8
    2. B.6
    3. C.9
    4. D.7
    Show answer

    Answer: C 9

  37. 37.
    The angle of a sector of a circle of radius 3.4 cm is 115°. Find the area of the sector. \((Take \pi = \frac{22}{7})\)
    1. A.\(11.6cm^2\)
    2. B.\(12.7cm^2\)
    3. C.\(10.2cm^2\)
    4. D.\(9.4cm^2\)
    Show answer

    Answer: A \(11.6cm^2\)

  38. 38.
    The angle of elevation of the top of a building from a point Z on the ground is 50°. If the height of the building is 124 m, find the distance from Z to the foot of the building.
    1. A.147.78m
    2. B.104.05m
    3. C.161.87m
    4. D.192.91m
    Show answer

    Answer: B 104.05m

  39. 39.
    The bar chart represents the distribution of marks scored by students in an economics examination. Use the bar chart to answer questions 30 to 32 If the failed mark was 4, what is the probability that a student selected at random passed?
    Diagram for this question
    1. A.0.36
    2. B.0.74
    3. C.0.52
    4. D.0.64
    Show answer

    Answer: D 0.64

  40. 40.
    The interior angle of a regular polygon is 6 times its exterior angle find the number of sides of the polygon.
    1. A.12
    2. B.15
    3. C.10
    4. D.14
    Show answer

    Answer: D 14

  41. 41.
    The length of the diagonal of a square is 12 cm. Calculate the area of the square.
    1. A.\(36 cm^2\)
    2. B.\(48 cm^2\)
    3. C.\(72 cm^2\)
    4. D.\(18 cm^2\)
    Show answer

    Answer: C \(72 cm^2\)

  42. 42.
    The price of a shoe was decreased by 22%. If the new price is $27.3. what is the original price.
    1. A.$62.30
    2. B.$42.30
    3. C.$72.00
    4. D.$35.00
    Show answer

    Answer: D $35.00

  43. 43.
    The radius and height of a solid cylinder is 8 cm and 14 cm respectively. Find, correct to two d.p the total surface area. (Take \(\pi = \frac{22}{7})\)
    1. A.\(1,106.29cm^2\)
    2. B.\(1,016.29cm^2\)
    3. C.\(1,106.89cm^2\)
    4. D.\(1,206.27cm^2\)
    Show answer

    Answer: A \(1,106.29cm^2\)

  44. 44.
    The radius of a sphere is 3 cm. Find, in terms of π, its volume.
    1. A.\(30\pi cm^3\)
    2. B.\(108\pi cm^3\)
    3. C.\(27\pi cm^3\)
    4. D.\(36\pi cm^3\)
    Show answer

    Answer: D \(36\pi cm^3\)

  45. 45.
    The truth set of \(8 + 2x - x^2\) = 0 is {p, q}. Evaluate p + q.
    1. A.4
    2. B.2
    3. C.-6
    4. D.-2
    Show answer

    Answer: B 2

  46. 46.
    There are 30 students in a class. 15 study woodwork and 13 study metal work. 6 study neither of the 2 subjects. How many student study woodwork but not metal work?
    1. A.13
    2. B.11
    3. C.5
    4. D.9
    Show answer

    Answer: B 11

  47. 47.
    What percentage of the students scored at most 5 marks?
    Diagram for this question
    1. A.58.5%
    2. B.63.2%
    3. C.38.3%
    4. D.41.5%
    Show answer

    Answer: A 58.5%

  48. 48.
    Write the name of a triangle with the vertices (1, -3), (6, 2) and (0,4)?
    1. A.Scalene triangle
    2. B.Isosceles triangle
    3. C.Right -angle triangle
    4. D.Equilateral triangle
    Show answer

    Answer: B Isosceles triangle

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