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Mathematics past questions: NECO SSCE 2004

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

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

  1. 1.
    A bag Contains 2 red, 3 blue and 4 green identical balls. If two balls are picked at random one after the other without replacement, what is the probability that both are green?
    1. A.\(\frac{1}{6}\)
    2. B.\(\frac{1}{3}\)
    3. C.\(\frac{16}{18}\)
    4. D.\(\frac{3}{8}\)
    5. E.\(\frac{4}{9}\)
    Show answer

    Answer: A \(\frac{1}{6}\)

  2. 2.
    A bag contains p dozens of bananas and 3q of these proved to be bad. If I buy one third of the goods ones, how many do I get?
    1. A.P -3q
    2. B.\(\frac{1}{3}\) (p - 3q)
    3. C.3q
    4. D.4p - q
    5. E.12p - 3q
    Show answer

    Answer: D 4p - q

  3. 3.
    A car travels at an average speed of 75km/h. Find its speed in metres per second.
    1. A.270m/s
    2. B.208m/s
    3. C.27.0m/s
    4. D.20.8m/s
    5. E.2.08m/s
    Show answer

    Answer: D 20.8m/s

  4. 4.
    A man is 40m from the foot of a cliff of height 23m. Calculate the angle of elevation of the top of the cliff from the man
    1. A.50° 54'
    2. B.35° 06'
    3. C.30° 00'
    4. D.290 90'
    5. E.29° 54'
    Show answer

    Answer: E 29° 54'

  5. 5.
    A sales boy gave a change of N75.00 to a buyer instead of N80.00, calculate his percentage error, correct to one decimal place?
    1. A.6.00%
    2. B.6.20%
    3. C.6.30%
    4. D.6.60%
    5. E.6.70%
    Show answer

    Answer: C 6.30%

  6. 6.
    Calculate (0.05 × 0.025) ÷ (4.25 × 3.35) and express your answer in standard form
    1. A.\(8.7796 × 10 ^{5}\)
    2. B.\(8.7796 × 10 ^{4}\)
    3. C.\(8.7796 × 10 ^{3}\)
    4. D.\(8.7796 × 10 ^{-3}\)
    5. E.\(8.7796 × 10 ^{-5}\)
    Show answer

    Answer: E \(8.7796 × 10 ^{-5}\)

  7. 7.
    Divide the LCM of 15abc and 20a \(^2\) bc by their HCF
    1. A.10a
    2. B.12a
    3. C.5abc
    4. D.\(12a ^{2}\) bc
    5. E.\(60a ^{2}\) bc
    Show answer

    Answer: B 12a

  8. 8.
    Evaluate (Lo\(g_{13} -\) lo\(g_{5}) ÷ X(\)lo\(g_{5}-\)lo\(g_{13})\) without using tables
    1. A.X
    2. B.–x
    3. C.X-1
    4. D.\(–X ^{-1}\)
    5. E.-1
    Show answer

    Answer: D \(–X ^{-1}\)

  9. 9.
    Evaluate \(1011_{two}\) + \(1101_{two}\) + \(1001_{two}\) - \(111_{two}\)
    1. A.10001 \(_{two}\)
    2. B.11001 \(_{two}\)
    3. C.110001 \(_{two}\)
    4. D.11010 \(_{two}\)
    5. E.10001 \(_{two}\)
    Show answer

    Answer: D 11010 \(_{two}\)

  10. 10.
    Evaluate ut - \(\frac{1}{2}\) ft^{2} when t = 5, u = -20 and f = 10
    1. A.225
    2. B.72
    3. C.-75
    4. D.-125
    5. E.-225
    Show answer

    Answer: E -225

  11. 11.
    Express the product of 0.007 and 0.057 to two significant figures
    1. A.0.0004
    2. B.0.00039
    3. C.0.004
    4. D.0.0039
    5. E.0.04
    Show answer

    Answer: A 0.0004

  12. 12.
    Express the quotient of 0.422 and 0.004 in standard form
    1. A.\(1.055 × 10 ^{2}\)
    2. B.\(10.55 × 10 ^{1}\)
    3. C.\(105 × 10 ^{0}\)
    4. D.\(10.55 × 10 ^{-1}\)
    5. E.\(1.055 × 10 ^{-2}\)
    Show answer

    Answer: A \(1.055 × 10 ^{2}\)

  13. 13.
    Find the area of a triangle ABC such that a = 16cm, b = 14cm, c = 12cm, leave your answer in surd form
    1. A.5 \(\sqrt{15}\) cm ^{2}
    2. B.7 \(\sqrt{15}\) cm ^{2}
    3. C.21 \(\sqrt{3}\) cm ^{2}
    4. D.21 \(\sqrt{5}\) cm ^{2}
    5. E.21 \(\sqrt{15}\) cm ^{2}
    Show answer

    Answer: E 21 \(\sqrt{15}\) cm ^{2}

  14. 14.
    Find the surface area of a sphere whose radius is 3.5cm, correct your answer to one decimal place (π = \(\frac{22}{5}\) )
    1. A.12.8c\(m ^{2}\)
    2. B.25.7c\(m ^{2}\)
    3. C.77.0c\(m ^{2}\)
    4. D.154.0c\(m ^{2}\)
    5. E.179.7c\(m ^{2}\)
    Show answer

    Answer: D 154.0c\(m ^{2}\)

  15. 15.
    Find the value of t such that the expression \(\frac{1}{t}\) + \(\frac{4}{3}\) - \(\frac{5}{6t}\) + 1 is equal to zero
    1. A.\(\frac{1}{6}\)
    2. B.\(\frac{1}{-14}\)
    3. C.- \(\frac{3}{2}\)
    4. D.\(\frac{7}{6}\)
    5. E.\(\frac{2}{5}\)
    Show answer

    Answer: B \(\frac{1}{-14}\)

  16. 16.
    Find x if (x - 2)^{2} = 1 \(\frac{7}{9}\)
    1. A.\(\frac{2}{3}\) or \(\frac{2}{7}\)
    2. B.3 \(\frac{1}{3}\) or \(\frac{2}{3}\)
    3. C.3 \(\frac{7}{9}\) or \(\frac{2}{7}\)
    4. D.3 \(\frac{1}{3}\) or \(\frac{7}{9}\)
    5. E.\(\frac{3}{7}\) or \(\frac{2}{9}\)
    Show answer

    Answer: B 3 \(\frac{1}{3}\) or \(\frac{2}{3}\)

  17. 17.
    Four pupils have an average age of 12years and two other pupils of average age of 10.5years are added. What is the average age of the six pupils?
    1. A.10.5yrs.
    2. B.11yrs.
    3. C.11.5 yrs.
    4. D.12yrs.
    5. E.12.5yrs.
    Show answer

    Answer: C 11.5 yrs.

  18. 18.
    If cos x = 4/5, 0° \(\leq\) x \(\leq\) 90°, find the value of (1 + tan x)/(1 - tan x)
    1. A.9
    2. B.7
    3. C.4
    4. D.\(\frac{7}{16}\)
    5. E.\(\frac{9}{25}\)
    Show answer

    Answer: B 7

  19. 19.
    If log \(_{10}\) 2 = 0.3010 and log \(_{10}\) 3 = 0.4771, simplify: (Log \(_{10}\) 8-log \(_{10}\) 2) ÷ (Log \(_{10}\) 9 - log \(_{10}\) 2)
    1. A.4
    2. B.3
    3. C.-0.92
    4. D.-4
    5. E.0.92
    Show answer

    Answer: E 0.92

  20. 20.
    If the first term of an AP is 1.2 and the common difference is also 2, what is the mean of the first five terms?
    1. A.2
    2. B.4
    3. C.5
    4. D.8
    5. E.10
    Show answer

    Answer: C 5

  21. 21.
    If the mean of the following set of data, 2, 3,3,3, 2,4, 4, and 3 is divided by its mode, the result is:
    1. A.1
    2. B.2
    3. C.3
    4. D.5
    5. E.8
    Show answer

    Answer: A 1

  22. 22.
    If y varies inversely as \(x^{2}\), how does x vary with y?
    1. A.x varies inversely as \(y ^{2}\)
    2. B.x varies inversely as \(\sqrt{y}\)
    3. C.x varies directly as \(y ^{2}\)
    4. D.x varies directly as \(\sqrt{y}\)
    5. E.x varies directly as y
    Show answer

    Answer: B x varies inversely as \(\sqrt{y}\)

  23. 23.
    One of the interior angles of a regular polygon is 120°. Find the number of sides of the polygon
    1. A.3
    2. B.4
    3. C.6
    4. D.9
    5. E.12
    Show answer

    Answer: C 6

  24. 24.
    Simplify \((216^{{\frac{1}{3}}})^{-2}\)
    1. A.\(\frac{1}{36}\)
    2. B.\(\frac{1}{18}\)
    3. C.\(\frac{1}{13}\)
    4. D.\(\frac{1}{6}\)
    5. E.\(\frac{1}{3}\)
    Show answer

    Answer: A \(\frac{1}{36}\)

  25. 25.
    Solve the equation: \(\frac{3}{[2(x - 2)]} - \frac{2}{[3(2 - x)]} = 0\)
    1. A.3
    2. B.2
    3. C.\(\frac{3}{2}\)
    4. D.\(\frac{2}{3}\)
    5. E.-3
    Show answer

    Answer: B 2

  26. 26.
    The 4th term of a G.P is 3 and its first term is 81. What is its common ratio?
    1. A.3
    2. B.\(\frac{2}{3}\)
    3. C.\(\frac{1}{3}\)
    4. D.- \(\frac{1}{3}\)
    5. E.-3
    Show answer

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

  27. 27.
    The angle subtended by a diameter of a circle at the circumference is a/an
    1. A.acute angle
    2. B.obtuse angle
    3. C.reflex angle
    4. D.right angle
    5. E.supplementary angle
    Show answer

    Answer: D right angle

  28. 28.
    The bearing of Y from X is 085º. What is the bearing of X from Y?
    1. A.005°
    2. B.095°
    3. C.185°
    4. D.265°
    5. E.275°
    Show answer

    Answer: D 265°

  29. 29.
    The diagonals of a rhombus are 16cm and 30cm long. What is the perimeter of the rhombus
    1. A.68cm
    2. B.72cm
    3. C.80cm
    4. D.88cm
    5. E.92cm
    Show answer

    Answer: A 68cm

  30. 30.
    The expression \(4x^{2} - 4\) has the following as its factors EXCEPT
    1. A.x - 1
    2. B.x + 1
    3. C.\(x ^{2} -1\)
    4. D.4x + 1
    5. E.4x - 4
    Show answer

    Answer: D 4x + 1

  31. 31.
    The first term of an A.P is equal to thrice the common difference, what is the sixth term of the A.P, if the common difference is 8?
    1. A.64
    2. B.48
    3. C.43
    4. D.24
    5. E.11
    Show answer

    Answer: A 64

  32. 32.
    The nth term of a sequence is given as \(4 \times 3^{(3 - n)}\) . Calculate the third term.
    1. A.12
    2. B.32
    3. C.4
    4. D.3
    5. E.1
    Show answer

    Answer: C 4

  33. 33.
    The roots of a quadratic equation in x, are -m and 2n. Fine equation.
    1. A.\(x ^{2} - x(2\)n-m) – 2mn = 0
    2. B.\(x ^{2} + x(2\)n - m) - 2mn = 0
    3. C.\(x ^{2} + x(m - 2\)n) + 2mn = 0
    4. D.\(X ^{2} + x (m + 2\)n ) + 2mn = 0
    5. E.\(x ^{2} - x (m - 2\)n) - 2mn = 0
    Show answer

    Answer: A \(x ^{2} - x(2\)n-m) – 2mn = 0

  34. 34.
    Two angles of a triangle are 45º each and its longest side is 12cm. Find the length of one of the other sides
    1. A.12cm
    2. B.9 \(\sqrt{2}\) cm
    3. C.6 \(\sqrt{2}\) cm
    4. D.6cm
    5. E.3 \(\sqrt{2}\) cm
    Show answer

    Answer: C 6 \(\sqrt{2}\) cm

  35. 35.
    What must be added to \(b^{2}-3\)ab to make it a perfect square?
    1. A.-3a
    2. B.- \(\frac{3}{2}\)
    3. C.\(\frac{9}{4}\)
    4. D.\(\frac{9a}{4}\)
    5. E.\(\frac{9^2}{4}\)
    Show answer

    Answer: E \(\frac{9^2}{4}\)

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