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Further Mathematics Questions and Answers

Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.

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446.

The distance s in metres covered by a particle in t seconds is $s = \frac{3}{2}t^{2} - 3t$ . Find its acceleration.

$1 ms^{-2}$

$2 ms^{-2}$

$3 ms^{-2}$

$4 ms^{-2}$

View answer & explanation

Correct answer is C

The two time differentiation of distance with respect to time will give the acceleration.

$s = \frac{3}{2}t^{2} - 3t$

$\frac{\mathrm d s}{\mathrm d t} = v = 3t - 3$

$\frac{\mathrm d v}{\mathrm d t} = a = 3$

447.

A box contains 4 red and 3 blue identical balls. If two are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.

$\frac{4}{7}$

$\frac{2}{7}$

$\frac{1}{7}$

$\frac{1}{12}$

View answer & explanation

Correct answer is A

P(one blue, other red) = P(1st red then blue) or P(1st blue then red)

= $(\frac{4}{7} \times \frac{3}{6}) + (\frac{3}{7} \times \frac{4}{6})$

= $\frac{2}{7} + \frac{2}{7} = \frac{4}{7}$

448.

Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.

40°

44°

45°

54°

View answer & explanation

Correct answer is C

$2x + y = 4 \equiv y = 4 - 2x \implies m_{1} = -2$

$-3x + y + 7 = 0 \equiv y = -7 + 3x \implies m_{2} = 3$

$\tan \theta = \frac{m_{1} - m_{2}}{1 - m_{1}m_{2}} = \frac{-2 - 3}{1 - (-2)(3)} = \frac{-5}{-5} = 1$

$\tan \theta = 1 \implies \theta = 45°$

449.

Find the number of different arrangements of the word IKOTITINA.

30240

60840

120960

362880

View answer & explanation

Correct answer is A

IKOTITINA has 9 letters with 2Ts and 3Is. Therefore, the number of different arrangements

= $\frac{9!}{2!3!} = \frac{9.8.7.6.5.4}{2} = 30240$

450.

A straight line makes intercepts of -3 and 2 on the x- and y- axes respectively. Find the equation of the line.

2x + 3y + 6 = 0

3x - 2y - 6 = 0

-3x + 2y - 6 = 0

-2x + 3y - 6 =0

View answer & explanation

Correct answer is D

Equation of a straight line : y = mx + b

where m = the slope of the line

b = y- intercept

Given the two points (-3, 0) and (0, 2).

$m = \frac{2 - 0}{0 - (-3)} = \frac{2}{3}$

$y = \frac{2}{3}x + 2 \implies 3y = 2x + 6$

$-2x + 3y - 6 = 0$

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