2002 NECO Mathematics Past Questions

Questions

1. 1.

   Evaluate 1.25 × 10$^2$ × 0.125 × 10$^3$ × 12.5 × 10$^{-4}$ leaving your answer in standard form

   1. A.1.995 × 103
   2. B.1.95 × 102
   3. C.1.95 × 101
   4. D.1.95 × 10-2
   5. E.1.95 × 10-3

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   Answer: C. 1.95 × 101

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2. 2.

   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.$\sqrt{3}$

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   Answer: C. $\frac{1}{2}$

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3. 3.

   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.$\frac{81}{125}$

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   Answer: E. $\frac{81}{125}$

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4. 4.

   Simplify 2a2 -4ab - 6a2 - 10ab + 5ab - 5a2

   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)

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   Answer: C. -9a (a + b)

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5. 5.

   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.$\frac{34}{25}$

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   Answer: E. $\frac{34}{25}$

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6. 6.

   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

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   Answer: C. 22cm

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7. 7.

   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$^3$

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   Answer: C. 125.0cm$^3$

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8. 8.

   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

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   Answer: C. 0.5

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9. 9.

   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 × 10-1m3
   2. B.3.9 × 10-2m3
   3. C.3.9 × 10-3m3
   4. D.3.9 × 10-4m3
   5. E.3.9 × 10-5m3

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   Answer: D. 3.9 × 10-4m3

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10. 10.

    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

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    Answer: C. N40.00

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11. 11.

    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

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    Answer: B. x ≥ 3

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12. 12.

    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

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    Answer: D. 12cm

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13. 13.

    A quadratic equation with roots -1$\frac{1}{2}$ and $\frac{1}{4}$ is

    1. A.x2 + 3x + 4 = 0
    2. B.8x2 + 10x + 3 = 0
    3. C.8x2 +12x – 3 = 0
    4. D.8x2 + 10x-3.= 0
    5. E.8x2 + 12x + 3 = 0

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    Answer: D. 8x2 + 10x-3.= 0

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14. 14.

    What must be added to 3x2 - 5x 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.-$\frac{6}{5}$

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    Answer: B. $\frac{25}{36}$

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15. 15.

    If , sT = $\sqrt{\frac{[(a + T)T]}{a}}$ what does T equal?

    1. A.T = (a2s2 – 1)
    2. B.T = (a2s2– 1) ÷ a
    3. C.T = a ÷ (a2 - s2)
    4. D.T = a ÷ (a2s2 – 1)
    5. E.T = (as – 1)2

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    Answer: D. T = a ÷ (a2s2 – 1)

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16. 16.

    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

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    Answer: B. 1$\frac{2}{3}$ years

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17. 17.

    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)

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

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18. 18.

    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

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    Answer: E. 3.0cm

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19. 19.

    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

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    Answer: E. 62.76m

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20. 20.

    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 ms2
    2. B.11.31 ms2
    3. C.32.00 ms2
    4. D.56.57 ms2
    5. E.160.00 ms2

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    Answer: C. 32.00 ms2

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21. 21.

    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

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    Answer: E. 36.61km

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22. 22.

    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$^2$

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    Answer: D. 44cm$^2$

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23. 23.

    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

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    Answer: C. 1.54

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24. 24.

    Simplify [1 ÷ (x + 1)] - [2 ÷ (x - 1)] + [3 ÷ (x2 - 1)]

    1. A.- 3x ÷ (x2 - 1)
    2. B.- x ÷ (x2 -1)
    3. C.x ÷ (x2 - 1)
    4. D.(x + 1) ÷ (x2 - 1)
    5. E.(x + 4) ÷ (x2 - 1)

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    Answer: B. - x ÷ (x2 -1)

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25. 25.

    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

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    Answer: C. 80$\sqrt{3}$m

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26. 26.

    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

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    Answer: E. 3 : 2 : 8

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27. 27.

    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

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    Answer: A. 1.11

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28. 28.

    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}

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

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29. 29.

    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$^2$

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    Answer: A. 312cm$^2$

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30. 30.

    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

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    Answer: C. N1800.00

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31. 31.

    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.$\frac{9}{13}$

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    Answer: E. $\frac{9}{13}$

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32. 32.

    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.$\frac{1}{24}$

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    Answer: D. $\frac{1}{4}$

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