WAEC Further Mathematics Past Questions & Answers

496.

A circular ink blot on a piece of paper increases its area at the rate $4mm^{2}/s$ . Find the rate of the radius of the blot when the radius is 8mm. $[\pi = \frac{22}{7}]$

0.20 mm/s

0.08 mm/s

0.25 mm/s

0.05 mm/s

View answer & explanation

Correct answer is B

Given: $\frac{\mathrm d A}{\mathrm d t} = 4 mm^{2}/s$

$\frac{\mathrm d A}{\mathrm d t} = (\frac{\mathrm d A}{\mathrm d r})(\frac{\mathrm d r}{\mathrm d t})$

$A = \pi r^{2} \implies \frac{\mathrm d A}{\mathrm d r} = 2\pi r$

$\implies 4 = 2\pi r \times \frac{\mathrm d r}{\mathrm d t}$

$\frac{\mathrm d r}{\mathrm d t} = \frac{4}{2\pi r} = \frac{4 \times 7}{2 \times 22 \times 8}$

= $0.07954 mm/s \approxeq 0.08 mm/s$

497.

The sales of five salesgirls on a certain day are as follows; GH¢ 26.00, GH¢ 39.00, GH¢ 33.00, GH¢ 25.00 and GH¢ 37.00. Calculate the standard deviation if the mean sale is GH¢ 32.00.

GH¢ 5.65

GH¢ 5.66

GH¢ 6.5

GH¢ 6.56

View answer & explanation

Correct answer is B

$x$	$x - \bar{x}$	$(x - \bar{x})^{2}$
26.00	-6	36
39.00	7	49
33.00	1	1
25.00	-7	49
37.00	5	25
		$\sum (x - \bar{x})^{2}$ =160

$S.D = \sqrt{\frac{(x - \bar{x})^{2}}{n}}$

$S.D = \sqrt{\frac{160}{5}} = \sqrt{32}$

= $GH¢ 5.656 \approxeq GH¢ 5.66$

498.

Forces 50N and 80N act on a body as shown in the diagram. Find, correct to the nearest whole number, the horizontal component of the resultant force.

13N

43N

57N

95N

View answer & explanation

Correct answer is A

Given a force F, the horizontal component = $F\cos \theta$

R = $-50\cos 30 + 80\cos 45$

= $-50(\frac{\sqrt{3}}{2}) + 80(\frac{\sqrt{2}}{2})$

= $-25\sqrt{3} + 40\sqrt{2} = -43.30 + 56.67$

= $13.37N \approxeq 13N$

499.

A committee consists of 5 boys namely: Kofi, John, Ojo, Ozo and James and 3 girls namely: Rose, Ugo and Ama. In how many ways can a sub-committee consisting of 3 boys and 2 girls be chosen, if Ozo must be on the sub-committee?

View answer & explanation

Correct answer is C

Since Ozo is a boy and must be in the sub-committee, we have 2 spaces for the boys and 2 for the girls.

= $^{4}C_{2} \times ^{3}C_{2}$

= $\frac{4!}{(4 - 2)! 2!} \times \frac{3!}{(3 - 2)! 2!} = 6 \times 3 = 18$

500.

The function $f : F \to R$

= $f(x) = \begin{cases} 3x + 2 : x > 4 \\ 3x - 2 : x = 4 \\ 5x - 3 : x < 4 \end{cases}$ . Find f(4) - f(-3).

-26

-28

View answer & explanation

Correct answer is A

$f(4) = 3(4) - 2 = 12 - 2 = 10$

$f(-3) = 5(-3) - 3 = -15 - 3 = -18$

$f(4) - f(-3) = 10 - (-18) = 28$

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