2002 - WAEC Mathematics Past Questions and Answers - page 4
The angle of depression of a point Q from a vertical tower PR, 30m high, is 40°. If the foot P of the tower is on the same horizontal level as Q, find, correct to 2 decimal places, |PQ|.
\(\tan 40° = \frac{30}{|PQ|}\)
\(|PQ| = \frac{30}{\tan 40°} = \frac{30}{0.839}\)
= 35.75m
210 = \frac{22}{7} \times 14^2 \times h \
h = \frac{210}{22 \times 28}\)
Curved surface area \(= 2r\pi h\
= 2 \times \frac{22}{7} \times 14 \times \frac{210}{22 \times 26} = 30cm^2\)
Simplify \(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
\(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
= \(3(\sqrt{4 \times 3}) + 10\sqrt{3} - (\frac{6}{\sqrt{3}})(\frac{\sqrt{3}}{\sqrt{3}})\)
= \(6\sqrt{3} + 10\sqrt{3} - 2\sqrt{3}\)
= \(14\sqrt{3}\)
Factorize m(2a-b)-2n(b-2a)
m(2a - b) - 2n(b - 2a)
= m(2a - b) - (-2n)(2a - b)
= m(2a - b) + 2n(2a - b)
= (m + 2n)(2a - b)
If q oranges are sold for t Naira, how many oranges can be bought for p naira?
q oranges = t naira
1 naira = \(\frac{q}{t}\)
p naira = \(p(\frac{q}{t})\)
= \(\frac{pq}{t}\) oranges
In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT = 60°, angle PQR = 30° and |PQ| = \(6\sqrt{3}cm\), calculate |RT|
In \(\Delta\) QPT,
\(\frac{PT}{6\sqrt{3}} = \sin 30°\)
PT = \(6\sqrt{3} \times \frac{1}{2} = 3\sqrt{3} cm\)
In \(\Delta\) RPT,
\(\frac{PT}{RT} = \tan 60°\)
\(\frac{3\sqrt{3}}{RT} = \tan 60°\)
\(RT = \frac{3\sqrt{3}}{\sqrt{3}} = 3 cm\)
In the diagram, calculate the value of x
x - 35° = 65° (corresponding angles)
x = 65° + 35° = 100°
In the diagram, \(\bar{PS}\hspace{1mm} and \hspace{1mm}\bar{QT}\) are two altitudes of ∆PQR. Which of the following is equal to ∠RQT?