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 variance of 2, 4, 7, 8 and 9 

A.

7.2

B.

6.8

C.

3.5

D.

2.6

Correct answer is B

x

2

4

7

8

9

(\(\bar{x} - \bar{x}\))

-4

-2

1

2

4

 

(\(\bar{x} - \bar{x})^2\)

16

4

1

4

9

_________

\(\sum (x - x)^2\) = 34

 

\(\bar{x} = \frac{2 + 4 + 7 + 8 + 9}{5} = 6

variance = \(\frac{34}{5}\)

= 6.8

192.

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\(^o\) 

193.

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\(^o\) 

194.

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