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Mathematics past questions: NECO SSCE 2005

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

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

  1. 1.
    3 - 7, 8 - 12, 13 - 17, 18 - 22. Which of the following is/are true? I. The class Interval is 4 II. The class boundaries are 2.5, 7.5, 12.5, 18.5, 22.5 III. The mid-marks are 5, 10, 15, and 20
    1. A.I only
    2. B.II only
    3. C.III only
    4. D.I and II only
    5. E.I and III only
    Show answer

    Answer: E I and III only

  2. 2.
    A bag contains 4 blue and 8 red identical balls. If two balls are picked at random with replacement, what is the probability of picking two balls of different colours?
    1. A.1
    2. B.\(\frac{13}{26}\)
    3. C.\(\frac{5}{18}\)
    4. D.\(\frac{4}{9}\)
    5. E.\(\frac{2}{9}\)
    Show answer

    Answer: D \(\frac{4}{9}\)

  3. 3.
    A car dealer sells a car and makes a profit of 15%. If the car costs N320,000.00, how much did he sell the car?
    1. A.N272,000.00
    2. B.N296,000.00
    3. C.N300,000.00
    4. D.N368,000.00
    5. E.N400,000.00
    Show answer

    Answer: D N368,000.00

  4. 4.
    A chord 20cm long subtends an angle of 60° at the circumference of a circle, what is the diameter of the circle the nearest cm?
    1. A.12cm
    2. B.20cm
    3. C.23cm
    4. D.60cm
    5. E.80cm
    Show answer

    Answer: C 23cm

  5. 5.
    A flagpole is placed at the top of a tower. The angles of elevation of the bottom and top of the flagpole from a point on the ground 10m away are 40° and 50° respectively. Find the length of the flagpole.
    1. A.1.8m
    2. B.3.5m
    3. C.8.4m
    4. D.11.9m
    5. E.17.3m
    Show answer

    Answer: B 3.5m

  6. 6.
    A is at 50°N and B is at 10°N, If A and B are on the same longitude, find the distance AS. Correct your answer to Four significant figures. (Earth radius = 6400km)
    1. A.6468km
    2. B.5469km
    3. C.4470km
    4. D.3470km
    5. E.2488km
    Show answer

    Answer: C 4470km

  7. 7.
    A ship sails 6km from a port on a bearing 070° and then 8km on a bearing of 040°. Find the distance from the port.
    1. A.7.21km
    2. B.13.53km
    3. C.16.86km
    4. D.44.57km
    5. E.67.17km
    Show answer

    Answer: B 13.53km

  8. 8.
    A surveyor measured the length of a obtained 42.55 metres. If his measurement was more than the actual length and the percentage error of his measurement was 8%, calculate the actual length of the land
    1. A.39.40 metres
    2. B.46.20 metres
    3. C.46.25 metres
    4. D.46.50 metres
    5. E.48.25 metres
    Show answer

    Answer: A 39.40 metres

  9. 9.
    Calculate without using tables Tan 45° + Cos 60°
    1. A.\(\sqrt{\frac{3}{2}}\) - 1
    2. B.\(\frac{1}{2}\)
    3. C.1 \(\frac{1}{2}\)
    4. D.\(\sqrt{\frac{3}{2}}\) + 1
    5. E.2
    Show answer

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

  10. 10.
    Evaluate 0.0025 × 2.5 × 10 \(^2\) to 2 significant figures.
    1. A.\(0.625 × 10 ^{-3}\)
    2. B.\(0.63 × 10 ^{-2}\)
    3. C.\(6.25 × 10 ^{-3}\)
    4. D.\(6.3 × 10 ^{-2}\)
    5. E.\(6.3 × 10 ^{-1}\)
    Show answer

    Answer: E \(6.3 × 10 ^{-1}\)

  11. 11.
    Evaluate log 18 + log6 - log16 \(^{\frac{1}{2}}\)
    1. A.log 3
    2. B.log 9
    3. C.log 20
    4. D.3 log 2
    5. E.3 log 3
    Show answer

    Answer: E 3 log 3

  12. 12.
    Find the absolute mean deviation of the sample 10, 12, 14, 11, 13.
    1. A.14.6
    2. B.14
    3. C.12
    4. D.6.2
    5. E.1.2
    Show answer

    Answer: E 1.2

  13. 13.
    Find the Iength of a diagonal of a square whose area is 288c\(m^{2}\).
    1. A.24cm
    2. B.48cm
    3. C.95cm
    4. D.100cm
    5. E.124cm
    Show answer

    Answer: A 24cm

  14. 14.
    Find the standard deviation of the numbers 6, 9, 10, 8 and 7
    1. A.1.4
    2. B.2
    3. C.2.4
    4. D.5
    5. E.8
    Show answer

    Answer: A 1.4

  15. 15.
    Find the value of 2a - b if a + b = 8 and 4a - b = 22
    1. A.2
    2. B.4
    3. C.6
    4. D.8
    5. E.10
    Show answer

    Answer: E 10

  16. 16.
    For what value(s) of x is the expression \((x^{2} + 15\)x + 50) ÷ (x - 5) not defined
    1. A.-5, -10
    2. B.-10
    3. C.-5
    4. D.5
    5. E.10, 5
    Show answer

    Answer: D 5

  17. 17.
    If (x - a) is a factor of bx - ax \(+ x^{2} -\) ab, what is the other factor?
    1. A.(x + b)
    2. B.(b - a)
    3. C.(x - a)
    4. D.(a + b)
    5. E.(a - b)
    Show answer

    Answer: A (x + b)

  18. 18.
    If \(25a^{2} = 5^{-1} × 125\). Find the value of a?
    1. A.a = -1
    2. B.a = 1
    3. C.a = ±1
    4. D.a = ±5
    5. E.a = 25
    Show answer

    Answer: C a = ±1

  19. 19.
    If 2x : ( x + 1) = 3 : 2, what is the value of x?
    1. A.\(\frac{1}{2}\)
    2. B.1
    3. C.1 \(\frac{1}{2}\)
    4. D.3
    5. E.3 \(\frac{1}{2}\)
    Show answer

    Answer: D 3

  20. 20.
    If 7 is subtracted from twice a certain number x, the result is at most 5. What is the range of the number?
    1. A.x < 2
    2. B.x < 3
    3. C.x < 4
    4. D.x < 5
    5. E.x < 6
    Show answer

    Answer: E x < 6

  21. 21.
    If a = {x : 1 < x < 9} ; b = {x : 0 < x < 9} ; C = {x : 2 x < 9} and a, b, c U, what are the elements in U?
    1. A.U = {-1 < x < 9}
    2. B.U = {0 < x < 9}
    3. C.U = {1 < x < 9}
    4. D.U = {1 < x < 10}
    5. E.{2 < x < 10}
    Show answer

    Answer: B U = {0 < x < 9}

  22. 22.
    If A(I,2,3,...,10) ; B = (-5,-4,.....,-1) ; C = (-1, 0, 1, 2,....5) List all the elements in (B ∪ C) ∩ A
    1. A.(-1,2,...5)
    2. B.(-1,1,....5)
    3. C.(1,2,..5)
    4. D.(2,3,...10)
    5. E.(1,2,...10)
    Show answer

    Answer: C (1,2,..5)

  23. 23.
    If log 3 = 0.4771 and log 2 = 0.3010, what is the value of log 12?
    1. A.0.0432
    2. B.0.4322
    3. C.1.0791
    4. D.1.2552
    5. E.1.5225
    Show answer

    Answer: C 1.0791

  24. 24.
    If x + \(\frac{1}{x}\) = 8, find x \(^2\) + \(\frac{1}{x^2}\)
    1. A.64
    2. B.62
    3. C.32
    4. D.16
    5. E.4
    Show answer

    Answer: B 62

  25. 25.
    If y \(^2\) + 14y + k is a perfect square, then k =
    1. A.4
    2. B.7
    3. C.28
    4. D.49
    5. E.196
    Show answer

    Answer: D 49

  26. 26.
    In Δ ABC, A = 60°, C = 90° and AC = 12m. Find the Length of the hypotenuse.
    1. A.24m
    2. B.14m
    3. C.12m
    4. D.7m
    5. E.6m
    Show answer

    Answer: A 24m

  27. 27.
    Mohammed is 8 years older than Joy now. In five years' time he will be twice as old as Joy. How old is Joy now?
    1. A.1 \(\frac{1}{2}\) years
    2. B.3years
    3. C.4 \(\frac{1}{2}\) years
    4. D.6 years
    5. E.8 years
    Show answer

    Answer: B 3years

  28. 28.
    Simplify (6 - x - x2) ÷ (x2 - 4)
    1. A.(3 + x) ÷ (x + 2)
    2. B.(x - 3) ÷ (x - 2)
    3. C.(x - 3) ÷ (x + 3)
    4. D.(3 - x) ÷ (x + 2)
    5. E.(3 - x) ÷ (x - 2)
    Show answer

    Answer: A (3 + x) ÷ (x + 2)

  29. 29.
    Simplify \(P^{-6} × P^{3} × P^{2} ÷ P^{4} × P^{0}\)
    1. A.\(p ^{5}\)
    2. B.\(p ^{4}\)
    3. C.\(p ^{3}\)
    4. D.\(p ^{-3}\)
    5. E.\(p ^{-5}\)
    Show answer

    Answer: E \(p ^{-5}\)

  30. 30.
    Solve for x in the quadratic equation\(. 2x^{2} + 12\)x + 10 = 0
    1. A.x = -5, -1
    2. B.x = -5,1
    3. C.x = -3, -2
    4. D.x = 3, 2
    5. E.x = 6, 5
    Show answer

    Answer: A x = -5, -1

  31. 31.
    T varies directly as D and inversely as A. Given that T = 6, D = 3, and A = 2, find A when T = 3 and D = 6.
    1. A.4
    2. B.6
    3. C.8
    4. D.12
    5. E.24
    Show answer

    Answer: C 8

  32. 32.
    The diagonals of a rhombus are 6cm and 8cm. Find the area of the rhombus.
    1. A.96c\(m ^{2}\)
    2. B.48c\(m ^{2}\)
    3. C.24c\(m ^{2}\)
    4. D.0.14c\(m ^{2}\)
    5. E.12cm2
    Show answer

    Answer: C 24c\(m ^{2}\)

  33. 33.
    The parallel sides of a trapezium are 13cm and 7cm. If the area of the trapezium is 50cm2, find the perpendicular distance between the parallel sides.
    1. A.5cm
    2. B.6cm
    3. C.7cm
    4. D.10cm
    5. E.12cm
    Show answer

    Answer: A 5cm

  34. 34.
    Two fair dice are tossed together once. What is the probability of getting a total of at least 9 from the outcome?
    1. A.\(\frac{1}{9}\)
    2. B.\(\frac{1}{6}\)
    3. C.\(\frac{5}{18}\)
    4. D.\(\frac{1}{3}\)
    5. E.\(\frac{13}{18}\)
    Show answer

    Answer: C \(\frac{5}{18}\)

  35. 35.
    What is the positive difference between the squares of 2.5 and 2.1 to 1 significant figures?
    1. A.– 2.0
    2. B.– 184
    3. C.-1.84
    4. D.2
    5. E.18.4
    Show answer

    Answer: D 2

  36. 36.
    What is the Value of 11101 \(_{two}\) + 10011 \(_{two}\) - 10001 \(_{two}\) ?
    1. A.10001 \(_{two}\)
    2. B.10011 \(_{two}\)
    3. C.10111 \(_{two}\)
    4. D.11111 \(_{two}\)
    5. E.111111 \(_{two}\)
    Show answer

    Answer: D 11111 \(_{two}\)

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