WAEC Mathematics Past Questions & Answers - Page 179

891.

From a point R, 300m north of P, man walks eastward to a place Q which is 600m from P. Find the bearing of P from Q, correct to the nearest degree

026^o

045^o

210^o

240^o

View answer & explanation

Correct answer is D

\(cos\theta = \frac{adj}{hyp}=\frac{300}{600}=\frac{1}{2}\\
\theta = cos^{-1}(0.5000)=60^{\circ}\)
The bearing of P from \(Q = \theta + 180 = 60 + 180 = 240^{\circ}\)

892.

In the diagram, PQRS is a parallelogram and ∠QRT = 30^o. Find x

95^o

100^o

120^o

150^o

View answer & explanation

Correct answer is D

Since ∠QRS = 180^o - 30^o = 150^o and ∠SPQ = ∠QRS (theorem opp. angles in a parallelogram are equal) ∴ x = 150^o

893.

In the diagram PQ and MN are straight lines. Find the value of x

13^o

17^o

28^o

30^o

View answer & explanation

Correct answer is B

The straight line MN = 180 = 2(x+30^o) + 86^o =>
180 = 2x + 60^o + 86^o => 180^o = 2x + 146^o => 2x = 180 - 46 = 34^o => x = 34/2 = 17^o

894.

The probability that John and James pass an examination are 3/4 and 3/5 respectively, find the probability of both boys failing the examination.

\(\frac{1}{10}\)

\(\frac{3}{10}\)

\(\frac{9}{20}\)

\(\frac{11}{20}\)

View answer & explanation

Correct answer is A

Prob.(John pass)\(\frac{3}{4}\) prob.(John fail) \(=1-\frac{3}{4}=\frac{1}{4}\)
Prob.(James pass) \(\frac{3}{5}\) Prob.(James fail) \(=1-\frac{3}{5}=\frac{2}{5}\)
Prob(both boys fail)\(\frac{1}{4}\times \frac{2}{5}=\frac{1}{10}\)

895.

The lengths of the adjacent sides of a right - angled triangle are xcm, (x-1)cm. If the length of the hypotenuse is \(\sqrt{13}cm\), find the value of x

View answer & explanation

Correct answer is B

\(x^2+(x-1)^2 = (\sqrt{13})^2 \Rightarrow x^2 + x^2 - 2x + 1 = 13\\
2x^2 - 2x - 12 = 0\) dividing through by 2
\(x^2 - x- 6 = 0; (x-3)(x-2) = 0 \Rightarrow x = 3 or -2 \)