WAEC Further Mathematics Past Questions & Answers - Page 68

336.

Three men, P, Q and R aim at a target, the probabilities that P, Q and R hit the target are \(\frac{1}{2}\), \(\frac{1}{3}\) and \(\frac{3}{4}\) respectively. Find the probability that exactly 2 of them hit the target.

A.

\(1\)

B.

\(\frac{1}{2}\)

C.

\(\frac{5}{12}\)

D.

\(\frac{1}{12}\)

Correct answer is C

\(p(P) = \frac{1}{2}, p(P') = \frac{1}{2}\)

\(p(Q) = \frac{1}{3}, p(Q') = \frac{2}{3}\)

\(p(R) = \frac{3}{4}, p(R') = \frac{1}{4}\)

p(exactly two hit the target) = p(P and Q and R') + p(P and R and Q') + p(Q and R and P')

= \((\frac{1}{2} \times \frac{1}{3} \times \frac{1}{4}) + (\frac{1}{2} \times \frac{3}{4} \times \frac{2}{3}) + (\frac{1}{3} \times \frac{3}{4} \times \frac{1}{2})\)

= \(\frac{1}{24} + \frac{6}{24} + \frac{3}{24}\)

= \(\frac{5}{12}\)

337.

The velocity \(v ms^{-1}\) of a particle moving in a straight line is given by \(v = 3t^{2} - 2t + 1\) at time t secs. Find the acceleration of the particle after 3 seconds.

A.

\(26 ms^{-2}\)

B.

\(18 ms^{-2}\)

C.

\(17 ms^{-2}\)

D.

\(16 ms^{-2}\)

Correct answer is D

\(v(t) = 3t^{2} - 2t + 1\)

\(\frac{\mathrm d v}{\mathrm d t} = a(t) = 6t - 2\)

\(a(3) = 6(3) - 2 = 18 - 2 = 16 ms^{-2}\)

338.

A stone is projected vertically with a speed of 10 m/s from a point 8 metres above the ground. Find the maximum height reached. \([g = 10 ms^{-2}]\).

A.

13 metres

B.

15 metres

C.

18 metres

D.

23 metres

Correct answer is A

\(v^{2} = u^{2} + 2as\)

\(v^{2} = u^{2} - 2gs\)

\(0 = 10^{2} - 2(10)s \implies -100 = -20s\)

\(s = 5 m + 8 m = 13m\) (8m is the height from where it was thrown)

339.

Which of the following is the semi- interquartile range of a distribution?

A.

\(Mode - Median\)

B.

\(\text{Highest score - Lowest score}\)

C.

\(\frac{1}{2}(\text{Upper quartile - Median})\)

D.

\(\frac{1}{2}(\text{Upper quartile - Lower quartile})\)

Correct answer is D

No explanation has been provided for this answer.

340.

If \(P = \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix}\), find \((P^{2} + P)\).

A.

\(\begin{vmatrix} 4 & 3 \\ 6 & 1 \end{vmatrix}\)

B.

\(\begin{vmatrix} 4 & 3 \\ 6 & 4 \end{vmatrix}\)

C.

\(\begin{vmatrix} 2 & 2 \\ 6 & 2 \end{vmatrix}\)

D.

\(\begin{vmatrix} 3 & 2 \\ 6 & 4 \end{vmatrix}\)

Correct answer is B

\( P^{2} = \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix} \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix}\)

\(\begin{vmatrix} 1 \times 1 + 1 \times 2 & 1 \times 1 + 1 \times 1 \\ 2 \times 1 + 1 \times 2 & 2 \times 1 + 1 \times 1 \end{vmatrix}\)

= \(\begin{vmatrix} 3 & 2 \\ 4 & 3 \end{vmatrix} + \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix}\)

= \(\begin{vmatrix} 4 & 3 \\ 6 & 4 \end{vmatrix}\)