WAEC Mathematics Past Questions & Answers - Page 81

401.

In the diagram, O is the centre, \(\bar{RT}\) is a diameter, < PQT = 33\(^o\) and <TOS = 76\(^o\). Using the diagram, calculate the value of angle PTR.

A.

73o

B.

67o

C.

57o

D.

37o

Correct answer is C

In the diagram given, < PRT = 3\(^o\) (Change in same segment)

< TPR = 90\(^o\) (angle in a semicircle)

Hence, < PTR = 180\(^o\) - (90 + 33)\(^o\)

= 180\(^o\) - 123\(^o\)

= 57\(^o\)

402.

In the diagram, PQ//RT, QR//Su,

A.

134o

B.

132o

C.

96o

D.

48o

Correct answer is B

In the diagram; a = b = 48o (alternate < S)

x = 180o - b (angles on a str. line)

x = 180o - 48o

= 132o

403.

In the diagram, PTR is a tangent to the centre O. If angles TON = 108°, Calculate the size of angle PTN

A.

132o

B.

126o

C.

108o

D.

102o

Correct answer is B

In the diagram; 108° + x + x = 180° (sum of angle in a triangle)

108° + 2x = 180°

x = 180° - 108°

= 72°

x = \(\frac{72^o}{2}\)

= 36°

(Angle between tangent and a chord through the point of contact)

Hence, angle PTN = 90 + 36

= 126°

404.

In the diagram, O is the centre. If PQ//RS and ∠ONS = 140°, find the size of ∠POM.

A.

40o

B.

50o

C.

60o

D.

80o

Correct answer is A

In the diagram above,

∠MNO = 140° and angles on a straight line is 180°

: ∠NMO = (180 - 140)° = 40°

Hence; ∠POM = 40° ( alternate angle ∠S)

405.

The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take \(\pi = \frac{22}{7}\)]

A.

14cm

B.

7m

C.

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

D.

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

Correct answer is C

Volume of rectangular tank = L x B x H

= 2 x 7 x 11

= 154cm3

volume of cylindrical tank = \(\pi r^2h\)

154 = \(\frac{22}{7} \times r^2 \times 4\)

r2 = \(\frac{154 \times 7}{22 \times 4}\)

= \(\frac{49}{4}\)

r = \(\sqrt{\frac{49}{4}} = \frac{7}{2}\)

= 3\(\frac{1}{2}\)m