WAEC Past Questions and Answers - Page 4243

21,212.

In the diagram above, PR is perpendicular from P to QS, PQ = 2cm, QR = 1cm and PR = RS. what is the size of the angle QPS?

A.

135o

B.

105o

C.

90o

D.

75o

E.

60o

Correct answer is D

\(\Delta RPS\) = Isosceles triangle

\(\therefore < RPS = \​​​​​​​frac{180° - 90°}{2}\)

= 45°

In \(\Delta QPR\),\(\sin < QPR = \frac{1}{2}\)

= 30°

\(\therefore < QPS = 30° + 45° = 75°\)

21,213.

A rope of length 18m is used to form a sector of a circle of radius 3.5m on a school playing field. What is the size of the angle of the sector, correct to the nearest degree?

A.

33o

B.

40o

C.

90o

D.

180o

E.

270o

Correct answer is D

Circumference = 2πr
2 x 22/7 x 3.5 ≅ 22m
22m = 360o
11m = 360/22 x 11  = 180o

21,214.

In the diagram above, O is the centre of the circle through points L, M and N, if ∠MLN = 74o and ∠MNL = 39o, calculate ∠LON.

A.

67o

B.

100o

C.

113o

D.

126o

E.

134o

Correct answer is E

From the diagram, < LMN = 180° - (74° + 39°) (sum of angle in a triangle)

= 67°

< LON = 2 x 67° (angle subtended at the centre is twice the angle at the circumference)

= 134°

21,215.

A cone is made from a sector of circle of radius 14cm and angle of 90o. What is the area of the curved surface of the cone? (Take x = 22/7)

A.

22cm2

B.

38.5cm2

C.

77cm2

D.

154cm2

E.

308cm2

Correct answer is D

Length of arc =
θ/360
* 2πr


=> r =
90/360
*
14/4
= 3.5

slant height t = 14cm
curved surface area of cone = πrl
=> 3.142 x 3.5 x 14 = 153.95