2001 NECO Mathematics Past Questions

Questions

1. 1.

   If the mean of 3, 5, 8, k, 14 and 17 is 11, what is the value of k

   1. A.58
   2. B.38
   3. C.19
   4. D.11
   5. E.967

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   Answer: C. 19

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2. 2.

   If sin θ = $\frac{4}{5}$ where 0° ∠ θ ∠ 90º, what is the value of cos θ + tan θ?

   1. A.$\frac{14}{15}$
   2. B.$\frac{29}{15}$
   3. C.$\frac{13}{8}$
   4. D.$\frac{144}{15}$
   5. E.$\frac{24}{5}$

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   Answer: B. $\frac{29}{15}$

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3. 3.

   If the volume of a cube is (8 x $10^3$)cm$^3$, what is the surface area of the cube?

   1. A.2,400 cm$^2$
   2. B.1,600 cm$^2$
   3. C.120 cm$^2$
   4. D.24 cm$^2$
   5. E.16 cm$^2$

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   Answer: A. 2,400 cm$^2$

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4. 4.

   Find the 19th term of the A.P. $\frac{5}{6}$, $\frac{8}{6}$, $\frac{11}{6}$.................

   1. A.7$\frac{1}{2}$
   2. B.9
   3. C.9$\frac{1}{2}$
   4. D.9$\frac{5}{6}$
   5. E.10

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   Answer: D. 9$\frac{5}{6}$

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5. 5.

   A chord is drawn 12cm away from the centre of a circle of radius 13cm. What is the length of the chord?

   1. A.169.00 cm
   2. B.144.00 cm
   3. C.25.00 cm
   4. D.17.69 cm
   5. E.10.00 cm

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   Answer: E. 10.00 cm

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6. 6.

   If n{A} = 6, n{B} = 5 and n{A ∩ B} = 2, find n{A ∪ B}

   1. A.7
   2. B.8
   3. C.9
   4. D.13
   5. E.15

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   Answer: C. 9

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7. 7.

   An arc of a circle subtends an angle of 75° at the centre of the circle. If the diameter of the circle is 7cm, what Is the length of the arc? (take π = 3.142)

   1. A.4.58 cm
   2. B.8.02 cm
   3. C.16.04 cm
   4. D.32.08 cm
   5. E.34 cm

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   Answer: A. 4.58 cm

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8. 8.

   If t varies inversely as the cube of s, and t = 24, when s = 3, find t when s = 2

   1. A.8
   2. B.24
   3. C.27
   4. D.81
   5. E.648

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   Answer: D. 81

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9. 9.

   Mr Aborowa bought a car for N200,000.00 and later sold it for N170,000.00. What is the percentage loss?

   1. A.11.60%
   2. B.7.60%
   3. C.15%
   4. D.17.65%

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   Answer: C. 15%

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10. 10.

    Given that (3 - y) ÷ 2x = (6y + 7) ÷ (4x - 5), find the value of x when y = 2

    1. A.$\frac{64}{5}$
    2. B.6
    3. C.$\frac{5}{34}$
    4. D.$\frac{-5}{34}$
    5. E.$\frac{-64}{5}$

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    Answer: D. $\frac{-5}{34}$

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11. 11.

    51 women wore coloured shoes to a party, out of which 21 wore purple and 9 wore white. if a woman is selected at Random. What is the probability that she is wearing neither a purple shoe nor a white shoe?

    1. A.$\frac{10}{17}$
    2. B.$\frac{7}{17}$
    3. C.$\frac{20}{51}$
    4. D.$\frac{3}{17}$
    5. E.$\frac{1}{51}$

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    Answer: B. $\frac{7}{17}$

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12. 12.

    The lengths of the sides of a triangle are 15m, 21m, and 28cm. What is the size of the angle facing the side 21m (correct to one decimal place)?

    1. A.85.7°
    2. B.47.5°
    3. C.41.5°
    4. D.41.4°
    5. E.38.2°

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    Answer: B. 47.5°

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13. 13.

    The bearing of a point Y from point x is 150°. What is the bearing of X from Y?

    1. A.330°
    2. B.240°
    3. C.150°
    4. D.120°
    5. E.30°

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    Answer: A. 330°

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14. 14.

    Two fair coins are tossed at the same time. what is the probability of getting a head?

    1. A.1
    2. B.$\frac{3}{4}$
    3. C.$\frac{1}{2}$
    4. D.$\frac{1}{3}$
    5. E.$\frac{1}{4}$

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

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15. 15.

    In an acute angle-triangle XYZ, XZ = 9cm, YZ = 11cm and ∠XZY = 35° Calculate ∠YXZ, correct to the nearest degree.

    1. A.57°
    2. B.45°
    3. C.33°
    4. D.16°
    5. E.89°

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    Answer: E. 89°

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16. 16.

    Convert ($101.011)_2$ to base 10

    1. A.63
    2. B.43
    3. C.10
    4. D.$\frac{77}{8}$
    5. E.$\frac{43}{8}$

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    Answer: E. $\frac{43}{8}$

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17. 17.

    From the top of a storey-buliding, the angle of depression of a mango on a tree 20m away from the base of the storey building is 68°. if the mango is 4.5 m above the ground, what is the height of the storey building to the nearest metre?

    1. A.55m
    2. B.54m
    3. C.50m
    4. D.49m
    5. E.45m

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    Answer: B. 54m

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18. 18.

    Evaluate ($\frac{1}{343}$)$^{\frac{1}{3}}$ + (64)$^{-\frac{1}{3}}$ - $\frac{4}{9}$$^{-\frac{1}{2}}$

    1. A.-$\frac{17}{36}$
    2. B.-$\frac{3}{28}$
    3. C.-$\frac{31}{28}$
    4. D.$\frac{17}{36}$
    5. E.$\frac{1}{4}$

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    Answer: C. -$\frac{31}{28}$

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19. 19.

    Express 0.03785 in standard form correct to 3 significant figures.

    1. A.3 × 10$^{-2}$
    2. B.3.78 × 10$^{-2}$
    3. C.3.79 × 10$^{-2}$
    4. D.3.79 × 10$^{-1}$
    5. E.3.78 × 10$^{-2}$

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    Answer: C. 3.79 × 10$^{-2}$

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20. 20.

    Two beads are drawn at random, one after the other, with replacement, from a box containing 5 red and 7 white identical beads. What is the probability that the beads are the same colour

    1. A.$\frac{119}{144}$
    2. B.$\frac{95}{144}$
    3. C.$\frac{37}{72}$
    4. D.$\frac{49}{144}$
    5. E.$\frac{1}{6}$

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    Answer: C. $\frac{37}{72}$

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21. 21.

    Simplify $\sqrt{6a^{-2}} \times \sqrt{24a^6}$

    1. A.± 16a$^2$
    2. B.± 16a
    3. C.± 14a$^2$
    4. D.± 12a$^2$
    5. E.± 12a

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    Answer: D. ± 12a$^2$

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22. 22.

    Find the value of x in the equation: 9$^x$ = 729

    1. A.81
    2. B.27
    3. C.18
    4. D.9
    5. E.3

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    Answer: E. 3

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23. 23.

    Find the value of k such that $t^2$ + kt + $\frac{25}{4}$ is a perfect square

    1. A.5
    2. B.3
    3. C.$\frac{5}{2}$
    4. D.$\frac{5}{4}$
    5. E.$\frac{1}{5}$

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    Answer: A. 5

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24. 24.

    If 3 boys shared x oranges among themselves in the ratio 3:5:8, and smallest share was 45 oranges, find the value of x

    1. A.75
    2. B.120
    3. C.165
    4. D.195
    5. E.240

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    Answer: E. 240

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25. 25.

    If s = $\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}$what does y equal?

    1. A.$\sqrt{\frac{(b^2 - a^2)}{(s^2 - x^2)}}$
    2. B.$\sqrt{\frac{(b^2 - a^2)}{(s^2 \times 2)}}$
    3. C.$\sqrt{\frac{x^2 - a^2 - b^2}{s}}$
    4. D.$\frac{x^2 - a^2 - b^2}{s}$
    5. E.$\sqrt{\frac{(b^2 x^2)}{(a^2 - s^2 x^2)}}$

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    Answer: E. $\sqrt{\frac{(b^2 x^2)}{(a^2 - s^2 x^2)}}$

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26. 26.

    The surface area of a sphere is 616m2. what is the volume of-the sphere (correct to two significant figures)? (take π = 3.142)

    1. A.14 cm$^3$
    2. B.210 cm$^3$
    3. C.1,400 cm$^3$
    4. D.2,100 cm$^3$
    5. E.4,300 cm$^3$

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    Answer: C. 1,400 cm$^3$

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27. 27.

    Solve the equation x$^2$ - 3x - 10 = 0

    1. A.-2 or -5
    2. B.-3 or -10
    3. C.5 or -2
    4. D.2 or 5
    5. E.3 or 10

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    Answer: C. 5 or -2

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28. 28.

    The first term of a G.P is 7. Find its 4th term, if its common ratio is 3.

    1. A.567
    2. B.280
    3. C.189
    4. D.63
    5. E.21

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    Answer: C. 189

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29. 29.

    The angle of elevation of the top T of a pole from a point X on the horizontal ground is 32°, if X is 68 m away from the foot F of the pole, calculate the height FT of the pole, correct to one decimal place.

    1. A.128.3m
    2. B.108.8m
    3. C.80.2m
    4. D.57.7m
    5. E.42.5m

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    Answer: E. 42.5m

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30. 30.

    A trader sold an article for N4,600.00 thereby making a profit of 15%. Calculate the cost price of the article

    1. A.N3450.00
    2. B.N3910.00
    3. C.N4000.00
    4. D.N5290.00
    5. E.N6900.00

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    Answer: C. N4000.00

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31. 31.

    The radius of a sphere is 21cm. If s and v represent the curved surface area and volume respectively, what is s : v? (take π = 3.142)

    1. A.1:03
    2. B.1:07
    3. C.3:01
    4. D.3:07
    5. E.7:01

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    Answer: B. 1:07

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32. 32.

    If cos x = - $\frac{5}{13}$ where 180° < X < 270°, what is the value of tan x -sin x ?

    1. A.$\frac{111}{13}$
    2. B.$\frac{321}{65}$
    3. C.$\frac{216}{65}$
    4. D.$\frac{112}{13}$
    5. E.$\frac{131}{65}$

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    Answer: C. $\frac{216}{65}$

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33. 33.

    A bottle of malt costs three times as much as a bottle of Mirinda. If 5 bottles of malt and 4 bottles of Mirinda cost N380.00 altogether, how much does a bottle of malt cost?

    1. A.N90.00
    2. B.N80.000
    3. C.N60.000
    4. D.N40.000
    5. E.N20.000

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    Answer: C. N60.000

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34. 34.

    The mean age of 12 boys involved survey is 19 years, 3 months. lf the-age of one of the boys is 22 years, what is the mean age of the other-boys?

    1. A.10.5 years
    2. B.19.0 years
    3. C.35.4 years
    4. D.264.0 years
    5. E.423.5 years

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    Answer: B. 19.0 years

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35. 35.

    Simplify 27$^{-\frac{1}{3}}$ $\times$ 64$^{-\frac{1}{3}}$ $\times$ 4$^{\frac{1}{3}}$

    1. A.48
    2. B.12
    3. C.$\frac{4}{3}$
    4. D.$\frac{1}{12}$
    5. E.$\frac{1}{48}$

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    Answer: D. $\frac{1}{12}$

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