WAEC Mathematics Past Questions & Answers - Page 39

191.

In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Calculate the value of x.

A.

70\(^o\)

B.

58\(^o\)

C.

55\(^o\)

D.

48\(^o\)

Correct answer is B

x = 180\(^o\) - (52\(^o\) + 70\(^o\))

= 180\(o\) - 122\(^o\)

= 58\(^o\) 

192.

In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Find the value of y. 

A.

70\(^o\)

B.

60\(^o\)

C.

52\(^o\)

D.

18\(^o\)

Correct answer is C

∠QRT = ∠SRT = 52 (opposite angles)

∠SRT = y = 52 (alternate angles)

y = 52\(^o\) 

193.

In the diagram, O is the centre of the circle of radius 18cm. If < zxy = 70\(^o\), calculate the length of arc ZY. [Take \(\pi = \frac{22}{7}\)]
 

A.

11cm

B.

22 cm

C.

44 cm

D.

80 cm

Correct answer is C

Z\({O}\)T = 2 x 70\(^o\) 140\(^o\)

Length = \(\frac{\theta}{360}\) x 2\(\pi\)r

\(\frac{140^o}{360} \times 2 \times \frac{22}{7}\) x 18

= 44cm

195.

If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\) 

A.

\(\frac{8}{3}\)

B.

\(\frac{3}{2}\)

C.

\(\frac{4}{3}\)

D.

\(\frac{2}{3}\)

Correct answer is D

y\(^2\) = 3\(^2\) + 4\(^2\)

y\(^2\) = 9 + 16 

y = \(\sqrt{25}\) 

= 5

\(\frac{\cos x}{2 \sin x} = \frac{4}{5} + 2 \times \frac{3}{5}\)

= \(\frac{4}{5} \times \frac{5}{6}\)

= \(\frac{2}{3}\)