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Mathematics past questions: NECO SSCE 2002

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

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

  1. 1.
    A boy leaves station X on a bearing of 035° to station y which is 21km away. He then travels to another station Z on a bearing of 125°. If Z is directly East of X, what is the distance from X to his present position?
    1. A.3.0km
    2. B.12.04km
    3. C.17.2km
    4. D.34.18km
    5. E.36.61km
    Show answer

    Answer: E 36.61km

  2. 2.
    A cone was developed from a sector of a circle with radius10cm and an angle at the centre of 108°. What is the radius of the cone?
    1. A.9.0cm
    2. B.8.5cm
    3. C.7.2cm
    4. D.4.3cm
    5. E.3.0cm
    Show answer

    Answer: E 3.0cm

  3. 3.
    A girl on top of a storey building 36m high dropped a N10.00 note on the ground below. If the angle of depression of the N10.00 note is 35°, how far is the money from the girl?
    1. A.20.64m
    2. B.29.48m
    3. C.44.49m
    4. D.49.55m
    5. E.62.76m
    Show answer

    Answer: E 62.76m

  4. 4.
    A petrol attendant recorded the number of vehicles that bought petrol from him for -3 hours and recorded 12 cars and 27 buses. What is the probability that the next vehicle will be a bus?
    1. A.\(\frac{4}{39}\)
    2. B.\(\frac{4}{13}\)
    3. C.\(\frac{5}{13}\)
    4. D.\(\frac{6}{13}\)
    5. E.\(\frac{9}{13}\)
    Show answer

    Answer: E \(\frac{9}{13}\)

  5. 5.
    A quadratic equation with roots -1 \(\frac{1}{2}\) and \(\frac{1}{4}\) is
    1. A.\(x ^{2} + 3\)x + 4 = 0
    2. B.\(8x ^{2} + 10\)x + 3 = 0
    3. C.\(8x ^{2} +12\)x – 3 = 0
    4. D.\(8x ^{2} + 10\)x-3.= 0
    5. E.\(8x ^{2} + 12\)x + 3 = 0
    Show answer

    Answer: D \(8x ^{2} + 10\)x-3.= 0

  6. 6.
    A wire was shaped to form a square of area 81cm \(^2\) . An equilateral triangle was formed by the same wire,What is the length of a side of the triangle formed?
    1. A.3cm
    2. B.6cm
    3. C.9cm
    4. D.12cm
    5. E.27cm
    Show answer

    Answer: D 12cm

  7. 7.
    After what length of time will N2400.00 yield an interest of N60.00 at 1 \(\frac{1}{2}\) % per annum?
    1. A.2 \(\frac{4}{5}\) years
    2. B.1 \(\frac{2}{3}\) years
    3. C.1 \(\frac{1}{2}\) years
    4. D.1 years
    5. E.\(\frac{3}{5}\) year
    Show answer

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

  8. 8.
    An amount of money is shared among P,Q and R such that for every 3P gets, Q gets 2 and for every 1Q gets, R gets 4. Find P: Q : R
    1. A.3 : 1 : 4
    2. B.3 : 2 : 1
    3. C.3 : 2 : 4
    4. D.3 : 3 : 4
    5. E.3 : 2 : 8
    Show answer

    Answer: E 3 : 2 : 8

  9. 9.
    Evaluate 1.25 × 10 \(^2\) × 0.125 × 10 \(^3\) × 12.5 × 10 \(^{-4}\) leaving your answer in standard form
    1. A.\(1.995 × 10 ^{3}\)
    2. B.\(1.95 × 10 ^{2}\)
    3. C.\(1.95 × 10 ^{1}\)
    4. D.\(1.95 × 10 ^{-2}\)
    5. E.\(1.95 × 10 ^{-3}\)
    Show answer

    Answer: C \(1.95 × 10 ^{1}\)

  10. 10.
    Given that the universal set U={14,15,16,17,18,19,20}, J ={16,19,20} and K= {14,15,18}, find (J' ∩ K')1.
    1. A.{17}
    2. B.{16, 17, 19, 20}
    3. C.{1, 4, 15, 17, 18}
    4. D.{14, 15, 16, 18, 19, 20}
    5. E.{14, 15, 16, 17, 18, 19, 20}
    Show answer

    Answer: D {14, 15, 16, 18, 19, 20}

  11. 11.
    If , sT = \(\sqrt{\frac{[(a + T)T]}{a}}\) what does T equal?
    1. A.\(T = (a ^{2} s ^{2} – 1)\)
    2. B.\(T = (a ^{2} s ^{2} – 1) ÷ a\)
    3. C.\(T = a ÷ (a ^{2} - s ^{2} )\)
    4. D.\(T = a ÷ (a ^{2} s ^{2} – 1)\)
    5. E.T = (as \(– 1) ^{2}\)
    Show answer

    Answer: D \(T = a ÷ (a ^{2} s ^{2} – 1)\)

  12. 12.
    If \(\frac{t}{L}\) = \(\sqrt{(\frac{4\pi^2}{g}})\) , what is the value of g when L = 4.5; t = 5 secs
    1. A.3.20 m\(s ^{2}\)
    2. B.11.31 m\(s ^{2}\)
    3. C.32.00 m\(s ^{2}\)
    4. D.56.57 m\(s ^{2}\)
    5. E.160.00 m\(s ^{2}\)
    Show answer

    Answer: C 32.00 m\(s ^{2}\)

  13. 13.
    If sin 30° = 0.5, what is the cosine of its complement?
    1. A.-0.866
    2. B.-0.5
    3. C.0.5
    4. D.0.866
    5. E.1
    Show answer

    Answer: C 0.5

  14. 14.
    If sin θ = \(\frac{\sqrt{3}}{2}\) and 0 < θ < 180°, what is cos θ ?
    1. A.\(\frac{1}{\sqrt{3}}\)
    2. B.\(\frac{2}{\sqrt{3}}\)
    3. C.\(\frac{1}{2}\)
    4. D.\(\frac{\sqrt{3}}{2}\)
    5. E.\(\sqrt{3}\)
    Show answer

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

  15. 15.
    One bag contains 4 white balls and 2 black balls. Another bag contains 3 white balls and 5 black balls, if one ball is drawn from each bag, what is the probability that both are white?
    1. A.\(\frac{2}{3}\)
    2. B.\(\frac{3}{8}\)
    3. C.\(\frac{7}{24}\)
    4. D.\(\frac{1}{4}\)
    5. E.\(\frac{1}{24}\)
    Show answer

    Answer: D \(\frac{1}{4}\)

  16. 16.
    Simplify \([1 ÷ (x + 1)] - [2 ÷ (x - 1)] + [3 ÷ (x^{2} - 1)]\)
    1. A.- 3x \(÷ (x ^{2} - 1)\)
    2. B.\(- x ÷ (x ^{2} -1)\)
    3. C.\(x ÷ (x ^{2} - 1)\)
    4. D.\((x + 1) ÷ (x ^{2} - 1)\)
    5. E.\((x + 4) ÷ (x ^{2} - 1)\)
    Show answer

    Answer: B \(- x ÷ (x ^{2} -1)\)

  17. 17.
    Simplify \(2a^{2} -4\)ab \(- 6a^{2} - 10\)ab + 5ab \(- 5a^{2}\)
    1. A.-9(a + b)
    2. B.9(a + b)
    3. C.-9a (a + b)
    4. D.9a(a - b)
    5. E.9b(a + b)
    Show answer

    Answer: C -9a (a + b)

  18. 18.
    Solve the equation: \(\frac{1}{3}x\) + \(\frac{2}{5}\) = \(\frac{3}{4}x\) - \(\frac{1}{6}\)
    1. A.\(\frac{17}{30}\)
    2. B.\(\frac{65}{102}\)
    3. C.\(\frac{25}{34}\)
    4. D.\(\frac{102}{75}\)
    5. E.\(\frac{34}{25}\)
    Show answer

    Answer: E \(\frac{34}{25}\)

  19. 19.
    The angle of elevation of the top (T) of a palm tree from a point (R) on the ground is 30°. The distance from R to the base (B) of the palm tree is 120m. What is the distance between T and R?
    1. A.60m
    2. B.60 \(\sqrt{3}\) m
    3. C.80 \(\sqrt{3}\) m
    4. D.120 \(\sqrt{3}\) m
    5. E.240m
    Show answer

    Answer: C 80 \(\sqrt{3}\) m

  20. 20.
    The length, breadth and height of a cuboid are 8cm, 7 \(\frac{1}{2}\) cm and 6 \(\frac{1}{2}\) cm respectively. What Is its volume in m3 (leave your answer in standard form)?
    1. A.\(3.9 × 10 ^{-1} m ^{3}\)
    2. B.\(3.9 × 10 ^{-2} m ^{3}\)
    3. C.\(3.9 × 10 ^{-3} m ^{3}\)
    4. D.\(3.9 × 10 ^{-4} m ^{3}\)
    5. E.\(3.9 × 10 ^{-5} m ^{3}\)
    Show answer

    Answer: D \(3.9 × 10 ^{-4} m ^{3}\)

  21. 21.
    The mean and the range of the set of numbers: 1.20, 1.00, 0.90, 1.40, 0.80, 0.80, 1.20 and 1.10 are p and q respectively. What is the value of p ÷ q?
    1. A.1.11
    2. B.65
    3. C.1.85
    4. D.2.45
    5. E.3.85
    Show answer

    Answer: C 1.85

  22. 22.
    The mean heights of 3 groups of students consisting of 20, 16 and 14 students are 1.67m, 1.50m and 1.40m Respectively. What is the mean height of all the students?
    1. A.1.52m
    2. B.1.53m
    3. C.1.54
    4. D.1.55m
    5. E.1.56m
    Show answer

    Answer: C 1.54

  23. 23.
    The probability that a student will pass a mathematics test is ⅗. If 3 students are chosen at random, what is the probability that at least 2 of them will pass the test?
    1. A.\(\frac{27}{125}\)
    2. B.\(\frac{9}{25}\)
    3. C.\(\frac{72}{125}\)
    4. D.\(\frac{76}{125}\)
    5. E.\(\frac{81}{125}\)
    Show answer

    Answer: E \(\frac{81}{125}\)

  24. 24.
    Three sets of rice x, y and z are sold for N15.00, N35.00 and N60.00 respectively per kg. It they are mixed in the ratio of 1: 3 : 2, what is the cast per kg of the mixture?
    1. A.N45.00
    2. B.N42.50
    3. C.N40.00
    4. D.N35.50
    5. E.N25.80
    Show answer

    Answer: C N40.00

  25. 25.
    Twice a number, x, is added to 5, the result is at least 11. What is the range of values of x?
    1. A.x > 3
    2. B.x ≥ 3
    3. C.x ≤ 3
    4. D.x < 3
    5. E.x ≤ -3
    Show answer

    Answer: B x ≥ 3

  26. 26.
    Two parallel chords of a circle are respectively 46cm and 40cm long. If the radius of the circle is 25cm and the centre of the circle lies between the two chords, what is the distance between the chords?
    1. A.7cm
    2. B.15cm
    3. C.22cm
    4. D.26cm
    5. E.30cm
    Show answer

    Answer: D 26cm

  27. 27.
    What are the factors of 2x \(^2\) - xy - 3y \(^2\) ?
    1. A.(2x + 3y\()(x + y) ^{2}\)
    2. B.(2x + 3y)(x + y)
    3. C.(2x + 3y)(x - y)
    4. D.(2x - 3y)(x + y)
    5. E.(2x - 3y)(x - y)
    Show answer

    Answer: D (2x - 3y)(x + y)

  28. 28.
    What is the total surface area of a cuboid whose dimensions are 12cm × 8cm × 3cm?
    1. A.312cm \(^2\)
    2. B.96cm \(^2\)
    3. C.36cm \(^2\)
    4. D.24cm \(^2\)
    5. E.12cm \(^2\)
    Show answer

    Answer: A 312cm \(^2\)

  29. 29.
    What is the total surface area of a cylinder with radius 2cm and height 1.5cm, correct to 2 significant figures?
    1. A.440cm \(^2\)
    2. B.220cm \(^2\)
    3. C.88cm \(^2\)
    4. D.44cm \(^2\)
    5. E.22cm \(^2\)
    Show answer

    Answer: D 44cm \(^2\)

  30. 30.
    What is the volume of a cube if the diagonal of one of the sides is \(\sqrt{50}\) cm?
    1. A.7.07cm \(^3\)
    2. B.50.0cm \(^3\)
    3. C.125.0cm \(^3\)
    4. D.353.4cm \(^3\)
    5. E.625.0cm \(^3\)
    Show answer

    Answer: C 125.0cm \(^3\)

  31. 31.
    What must be added to \(3x^{2} - 5\)x to make it a perfect square?
    1. A.\(\frac{36}{25}\)
    2. B.\(\frac{25}{36}\)
    3. C.- \(\frac{25}{36}\)
    4. D.- \(\frac{5}{6}\)
    5. E.- \(\frac{6}{5}\)
    Show answer

    Answer: B \(\frac{25}{36}\)

  32. 32.
    When a shirt is sold for N12000.00, a loss of 20% is recorded. How much should it be sold for to gain 20%?
    1. A.N4800.00
    2. B.N400
    3. C.N1800.00
    4. D.N1500.00
    5. E.N960.00
    Show answer

    Answer: C N1800.00

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