2003 - WAEC Mathematics Past Questions and Answers - page 5
41
In the diagram /PS/ = 9 cm, /OR/ = 5cm, \(P\hat{S}R = 63^o\) and \(S\hat{P}Q = P\hat{Q}R = 90^o\). Find, correct to the nearest whole number, the area of the trapezium,
A
55cm2
B
25cm2
C
22cm2
D
13cm2
correct option: a
Considering the triangle in the diagram
\(tan\theta = \frac{opp}{hyp}\
Tan 63^{\circ} = \frac{h}{4}\
h = 4 tan 63^{\circ}\
Area of trapezium = \frac{1}{2}h(a+b)\
\left(\frac{1}{2} \times 4 tan 63^{\circ}[5+9]\right)\
=28\times 1.963 = 54.96 = 55cm^2\)
Users' Answers & Comments\(tan\theta = \frac{opp}{hyp}\
Tan 63^{\circ} = \frac{h}{4}\
h = 4 tan 63^{\circ}\
Area of trapezium = \frac{1}{2}h(a+b)\
\left(\frac{1}{2} \times 4 tan 63^{\circ}[5+9]\right)\
=28\times 1.963 = 54.96 = 55cm^2\)
42
A right circular cone is such that its radius r is twice its height h. Find its volume in terms of h
A
\(\frac{2}{3}\pi h^2\)
B
\(\frac{1}{12}\pi h^3\)
C
\(\frac{4}{3}\pi h^2\)
D
\(\frac{4}{3}\pi h^3\)
correct option: d
Volume of a cone = \(\frac{\pi r^2 h}{3}\)
r = 2h.
V = \(\frac{\pi \times (2h)^2 \times h}{3}\)
= \(\frac{4}{3} \pi h^3\)
43
A man made a loss of 15% by selling an article for N595. Find the cost price of the article
A
N600.00
B
N684.25
C
N700.00
D
N892.50
correct option: c
15% loss = N595
\(\implies\) (100 - 15)% of CP = N595
85% of CP = N595
CP = \(\frac{595 \times 100}{85}\)
= N700.00
44
The bearing of P from Q is x, where 270o < x < 360o. Find the bearing of Q from P
A
(x - 90)o
B
(x-270)o
C
(x - 135)o
D
(x - 180)o
correct option: d
Bearing of Q and P
\(180^{\circ} – (360^{\circ}-x)\
180^{\circ}-360^{\circ}+x\
-180^{\circ}+x\
x-180^{\circ}\)
Users' Answers & Comments\(180^{\circ} – (360^{\circ}-x)\
180^{\circ}-360^{\circ}+x\
-180^{\circ}+x\
x-180^{\circ}\)
45
Which of the following is not a measure of dispersion?
A
Range
B
Mean deviation
C
Mean
D
Standard deviation
correct option: c
Users' Answers & Comments