WAEC Further Mathematics Past Questions & Answers

371.

Two forces (2i - 5j)N and (-3i + 4j)N act on a body of mass 5kg. Find in $ms^{-2}$ , the magnitude of the acceleration of the body.

$\frac{\sqrt{2}}{5}$

$5\sqrt{2}$

$2\sqrt{5}$

$\frac{5\sqrt{2}}{2}$

View answer & explanation

Correct answer is A

$F = F_{1} + F_{2}$

$(2i - 5j) + (-3i + 4j) = (-i - j)$

$F = ma \implies (-1, -1) = 5a$

$a = (-\frac{1}{5}, -\frac{1}{5})$

$|a| = \sqrt{(\frac{-1}{5})^2 + (\frac{-1}{5})^2} = \sqrt{2}{25}$

$|a| = \frac{\sqrt{2}}{5} ms^{-2}$

372.

Yomi was asked to label four seats S, R, P, Q. What is the probability he labelled them in alphabetical order?

$\frac{1}{24}$

$\frac{1}{6}$

$\frac{2}{13}$

$\frac{1}{4}$

View answer & explanation

Correct answer is A

The number of arrangements for the 4 letters = $^{4}P_{4} = \frac{4!}{(4 - 4)!}$

$4! = 24$

Alphabetical order is just 1 of the arrangements for the letters

= $\frac{1}{24}$

373.

Find the direction cosines of the vector $4i - 3j$ .

$\frac{9}{10}, \frac{27}{10}$

$\frac{17}{27}, -\frac{17}{27}$

$\frac{4}{5}, -\frac{3}{5}$

$\frac{4}{7}, \frac{-3}{7}$

View answer & explanation

Correct answer is C

Given $V = xi +yj$ , the direction cosines are $\frac{x}{|V|}, \frac{y}{|V|}$ .

$|4i - 3j| = \sqrt{4^{2} + (-3)^{2}} = \sqrt{25} = 5$

Direction cosines = $\frac{4}{5}, \frac{-3}{5}$ .

374.

If $\overrightarrow{OA} = 3i + 4j$ and $\overrightarrow{OB} = 5i - 6j$ where O is the origin and M is the midpoint of AB, find OM

-2i - 10j

-2i + 2j

4i - j

4i + j

View answer & explanation

Correct answer is C

$\overrightarrow{OA} = (3, 4)$

$\overrightarrow{OB} = (5, -6)$

$\overrightarrow{OM} = (\frac{3 + 5}{2}, \frac{4 + (-6)}{2})$

= $(4, -1) = 4i - j$

375.

Find the least value of n for which $^{3n}C_{2} > 0, n \in R$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{2}{3}$

View answer & explanation

Correct answer is C

$^{3n}C_{2} > 0 \implies \frac{3n!}{(3n - 2)! 2!} > 0$

$\frac{3n(3n - 1)(3n - 2)!}{(3n - 2)! 2} > 0$

$\frac{3n(3n - 1)}{2} > 0$

$3n(3n - 1) > 0 \implies n > 0; n > \frac{1}{3}$

The least number in the option that satisfies $n > 0; n > \frac{1}{3} = \frac{2}{3}$

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