2017 Mathematics NECO Objective Past Questions

1. Question

Simplify \( \scriptsize 1 \normalsize \frac{1}{2} \scriptsize + \scriptsize 2 \normalsize \frac{1}{3} \scriptsize \; \times \; \normalsize \frac{3}{4} \scriptsize \; – \; \normalsize \frac{1}{2} \)

\(\scriptsize 3 \frac{3}{4}\)
\( \scriptsize 3\frac{1}{4}\)
\( \scriptsize 2\frac{3}{4}\)
\(\scriptsize 1\frac{3}{4}\)
\(\scriptsize 1\frac{1}{4}\)

2. Question

Evaluate \(\frac{16.54}{0.0536} \scriptsize\times 18.25\)

Leave your answer to three significant figures.

16.697
16.820
16.900
16.909
16.910

3. Question

Simplify \(\normalsize \frac {8^2\; \times \; 4^0\; \times\; 8 ^{-3}}{7^3 \; \div\; 7^6}\)

\(\frac {343}{8} \)
\(\frac {343}{7} \)
\(\frac {343}{5} \)
\(\frac{243}{8} \)
\(\frac{243}{5} \)

4. Question

Simplify \( \scriptsize\frac{1}{3} log_2 \scriptsize64 \)

2
3
4
6
12

5. Question

\(\scriptsize If \; log_{10} 2 = 0.3010\; and\; log_{10}3 = 0.4771 \\ \scriptsize Find\; log_{10} 54.\)

Correct to the nearest whole number.

6
5
3
2
1

6. Question

Evaluate 0.6721 x 0.0261 and express your answer in standard form

1754 x 10⁴
1754 x 10³
1.754 x 10^-3
1.754 x 10^-2
1.754 x 10^-1

7. Question

The first term of a geometric progression is 6 if its common ratio is\( \scriptsize \frac {2}{3}\), find the 5^th

\( \frac{128}{243} \)
\( \frac{61}{81} \)
\(\frac {8}{3} \)
\(\frac {16}{9} \)
\(\frac {32}{27} \)

8. Question

The first and last terms of an Arithmetic progression are 6 and 153 respectively. If there are 50 terms in the sequence, find its common difference.

9
7
6
4
3

9. Question

Given that 244x = 10224. What is the positive value of x?

3
4
5
6
7

10. Question

If 30145 = 21125 + y5, find the value of y.

10131
5131
5126
902
402

11. Question

Simplify \(\frac{2 \; \sqrt{5}}{2\sqrt{5 \; – \; 1}}\)

\(\frac{1}{19}\scriptsize\left (10 \: + \; 5\sqrt{5}\right)\)
\(\frac{1}{19}\scriptsize\left (12\; – \; 4\sqrt{5} \right)\)
\(\frac{1}{19}\scriptsize\left (12\; + \; 4\sqrt{5} \right)\)
\(\frac{1}{19}\scriptsize\left (12\; – \; 5\sqrt{5} \right)\)
\(\frac{1}{19}\scriptsize\left (12\; + \; 5\sqrt{5} \right)\)

12. Question

A shareholder bought shares worth N100, 000.00 on ordinary share at N00 each. If a dividend of 15 kobo per share is declared, how much dividend was received?

N13,333.33
N12,000.00
N10,000.00
N9,500.00
N7,500.00

13. Question

Find the future value of an ordinary annuity of N500.00 paid yearly for 4 years at 10% per annum.

N700.00
N732.05
N923.50
N1,232.05
N2320.50

14. Question

Find the determinant of the matrix

\( K = \begin{pmatrix} 3 \; 0 \; -1 \\ 1 \; 2 \; -3 \\ -2 \; -1 \; 1 \end{pmatrix}\)

-6
-3
0
3
6

15. Question

Find the sum of the first 40 even positive integers.

1,600
1640
1680
3200
3280

16. Question

The first term of an Arithmetic progression is -3, if the sixth term is 22. Find the mean of the common difference and the first term.

1
4
5
7
8

17. Question

Find the perimeter of a sector of a circle with radius 7cm which subtends an angle of 180⁰ at the centre of the circle.

36cm
44cm
58cm
74cm
108cm

18. Question

Victoria went for a doctor’s appointment on Monday. If her next appointment is 45 days after, which day of the week will it be?

Friday
Monday
Saturday
Thursday
Wednesday

19. Question

Solve the inequality 3x – 5 ≥ 20 – 2x

x > 4
x ≥ 4
x ≥ 5
x < 5
x ≤ 5

20. Question

\(\scriptsize (2a\; + \; b)^2 \; -\;(b\;-\;2a)^2 \)

-8ab
4ab
8ab
-4ab
16ab

21. Question

If \(\scriptsize 4x^2\; – \;12x \) as a perfect square by using method of completing the square

36
9
\(\frac{9}{4} \)
\(\frac{-9}{4} \)
-9

22. Question

If (a – 3) is one of the factors of a² + 14a – 51, find the other factor.

(a – 11)
(a + 17)
(a – 17)
(a + 48)
(a – 48)

23. Question

Find the gradient of a straight line joining the points (-3, 0) and (0, 5).

20
10
\(\scriptsize 1 \frac{2}{3}\)
\(\frac{-3}{2} \)
\(\frac {-5}{3} \)

24. Question

A quadratic equation whose roots are \( \scriptsize \frac{-5}{4} \; and \; \scriptsize \frac{3}{4} \; is \)

\(\scriptsize 16x^2\; + \; 2x \; – \; 15 = 0 \)
\(\scriptsize 16x^2\; – \; 2x \; + \; 15 = 0 \)
\(\scriptsize 16x^2\; – \; 4x \; – \; 15 = 0 \)
\(\scriptsize 16x^2\; – \; 8x \; + \; 15 = 0 \)
\(\scriptsize 16x^2\; + \; 8x \; – \; 15 = 0 \)

25. Question

If P varies directly as \(\scriptsize \sqrt{Q}\) and P = 6 when Q = 81, find the value of P When Q = \(\scriptsize \frac{1}{4}\)

3
\(\normalsize \frac {1}{2} \)
\(\normalsize \frac {1}{3} \)
– \(\normalsize \frac {1}{2} \)
-3

26. Question

What is the maximum value of y?

6.05
4.05
-4.05
-5.05
-10.05

27. Question

What is the value of y when x = 0?

9
6
5
-9
-15

28. Question

Let P: I study hard

q: I pass physics

r: I am happy.

Translate P ⇒ (q v r) into statement

I am happy but I pass physics
I pass physics and I am happy
If I do not study hard, then I pass physics and I am happy
If I study hard, then I pass physics and I am happy
If I study hard, then I pass physics or I am happy

29. Question

Let P: I like bread with egg

q: I like ginger in tea

Translate “I like ginger in tea but not bread with egg” into symbol

q ∨ p
q ∧ p
q ∨ ≈ p
q ∧ ≈ p
≈ q ∧ p

30. Question

Given that (2x -1) (x + 5) = 2×2 – mx – 5. Find the value of m.

11
5
-5
-9
-10

31. Question

Find the midpoint of a line joining the points M (4, 0), N(3, P).

\(\left (\frac {p}{2}, \frac {7}{2} \right ) \)
\(\left (\frac {7}{2}, \frac {p}{2} \right ) \)
\(\left (\frac {1}{2}, \frac {p}{2} \right ) \)
\(\left (\frac {p}{2}, \frac {1}{2} \right ) \)
\( \left ( \scriptsize 0, \normalsize \frac {7}{2} \right ) \)

32. Question

Find the equation of a line with gradient 3, passing through (1, 4).

3x – y = 1
3x – y = -2
y – 3x = 1
y – 3x = -4
y – 3x = 3

33. Question

solve the simultaneous equations

\(\scriptsize y = \normalsize \frac{1}{3} \scriptsize x -1, 3x – 2y = 4 \)

\(\frac {12}{7}, \frac{5}{7} \)
\(\frac {7}{6}, \frac{-5}{7} \)
\(\frac {6}{7}, \frac{-5}{7} \)
\(\frac {-5}{7}, \frac{6}{7} \)
\(\frac {3}{5}, \frac{2}{7} \)

34. Question

Given that Sin \(\scriptsize \theta = \normalsize \frac{7}{9} , \) find the value of \( \scriptsize 9cos \theta \)

\(\frac {7}{81} \)
\(\frac {4\sqrt{2}}{9} \)
\(\scriptsize 4\sqrt{2} \)
\(\scriptsize 9 \sqrt{2} \)
\(\scriptsize 36 \sqrt{2} \)

35. Question

Find the value of x in the figure below.

\(\scriptsize 2\sqrt{2cm} \)
\(\scriptsize 3 \sqrt{2cm} \)
\(\scriptsize 3\sqrt{3cm} \)
\(\scriptsize \sqrt{3cm} \)
\(\frac{\sqrt{3}}{2} \scriptsize cm\)

36. Question

In the figure below, ABC is isosceles. Calculate <BED

\(\scriptsize 105^{\circ}\)
\(\scriptsize 100^{\circ}\)
\(\scriptsize 95^{\circ}\)
\(\scriptsize 85^{\circ}\)
\(\scriptsize 75^{\circ}\)

37. Question

In the figure above, if the area of the square is 162cm², calculate the radius of the circle.

12cm
10cm
9cm
8cm
7cm

38. Question

Calculate the area of the shaded region in the figure below.

\(\scriptsize 16.73cm^2 \)
\(\scriptsize 27.75cm^2 \)
\(\scriptsize 48.05cm^2 \)
\(\scriptsize 93.20cm^2 \)
\(\scriptsize 110.00cm^2 \)

39. Question

In the diagram above, AOB is a diameter. Find the angle marked x.

\(\scriptsize 60^{\circ} \)
\(\scriptsize 55^{\circ} \)
\(\scriptsize 50^{\circ} \)
\(\scriptsize 45^{\circ} \)
\(\scriptsize 30^{\circ} \)

40. Question

In the figure above, AD is a chord of a circle centre at O. find <ACD

\(\scriptsize 90^{\circ} \)
\(\scriptsize 80^{\circ} \)
\(\scriptsize 70^{\circ} \)
\(\scriptsize 50^{\circ} \)
\(\scriptsize 40^{\circ} \)

41. Question

In the figure above, ABCD is a cyclic quadrilateral and O is the centre of the circle. find <ACB

\(\scriptsize 20^{\circ} \)
\(\scriptsize 40^{\circ} \)
\(\scriptsize 60^{\circ} \)
\(\scriptsize 80^{\circ} \)
\(\scriptsize 100^{\circ} \)

42. Question

Calculate, correct to the nearest degree, the parallel of latitude in the southern hemisphere along which a journey of 320km makes a change of 210 in longitude.

\((\scriptsize Take\; \Lambda \normalsize \frac {22}{7} \; \scriptsize and \; \scriptsize R = 6400km) \)

80
160
660
820
920

43. Question

The positions of two cities M and N are (140N, 300E) and (720N, 300E) respectively. How far is city N from M?

\(\scriptsize Take \; \lambda = \normalsize \frac {22}{71}, \scriptsize R = 6400km \)

9610.16km
8610.16km
6481.27km
6400.27km
5364.18km

44. Question

Calculate the volume of a sphere with radius 6cm \(\scriptsize (Take \; \Lambda \; = \; 3.14)\)

\( \scriptsize 2716.96cm^3 \)
\( \scriptsize 904.32cm^3 \)
\( \scriptsize 902.88cm^3 \)
\( \scriptsize 452.16cm^3 \)
\( \scriptsize 216.00cm^3 \)

45. Question

What is the value of x if the gradient of the line joining (-2, x) and (x, 3) is \(\normalsize \frac {1}{2} \)

-3
-2
1
2
3

46. Question

An arc of a circle of radius 6cm subtends and angle of 450 at the centre of the circle. Find the length of the arc in terms of \(\scriptsize \Lambda .\)

\(\scriptsize 7\Lambda cm \)
\(\scriptsize 2\Lambda cm \)
\(\normalsize \frac {3}{2} \scriptsize \Lambda cm \)
\(\normalsize \frac { \Lambda}{2} \scriptsize cm \)
\(\normalsize \frac { \Lambda}{6} \scriptsize cm \)

47. Question

Find the distance between the points C (3, 3) and D(-1, 5).

\(\scriptsize 4\sqrt{17} \)
\(\scriptsize 3\sqrt{17} \)
\(\scriptsize 4\sqrt{5} \)
\(\scriptsize 2\sqrt{5} \)
\(\scriptsize \sqrt{3} \)

48. Question

The bearing of a town Q from a town P is 0450. Find the bearing of P from Q.

0450
0900
1350
1800
2250

49. Question

Find the mean of \(\scriptsize 4\normalsize \frac{1}{2}, \scriptsize 7, 6, 5, 8, \scriptsize 5 \normalsize \frac{1}{2}, \scriptsize 3.25 , \scriptsize 5 \normalsize \frac{1}{2}, \scriptsize 1 \normalsize \frac{1}{4} \; \scriptsize and \; \scriptsize 3 \normalsize \frac{1}{2} \)

\(\scriptsize 1 \normalsize \frac{1}{4} \)
\(\scriptsize 3 \normalsize \frac{1}{2} \)
5
\(\scriptsize 5 \normalsize \frac{1}{2} \)
\(\scriptsize 3 \normalsize \frac{1}{2} \)

50. Question

Find the mode of the date below;

6.7
6.3
5.8
5.2
5.2
4.4

NECO: MATHEMATICS

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