2005 - WAEC Mathematics Past Questions and Answers - page 4
31
A train moving at a uniform speed covers 36km in 21 minutes. How long does it take to cover 60km?
A
35 mins
B
40 mins
C
45 mins
D
90 mins
correct option: a
Since 36km in 21 minutes
1km in \(\frac{21}{36}\)minutes
60km in \(\left(\frac{21}{36}\times 60\right)\)minutes = \(\frac{70}{2}\)min
= 35 mins
Users' Answers & Comments1km in \(\frac{21}{36}\)minutes
60km in \(\left(\frac{21}{36}\times 60\right)\)minutes = \(\frac{70}{2}\)min
= 35 mins
32
The salary of a man was increased in the ratio 40:47. calculate the percentage increase in the salary
A
85.1%
B
58.5%
C
17.5%
D
14.9%
correct option: c
\(\%Increase = \frac{Actual \hspace{1mm}increase}{initial \hspace{1mm}ratio}\times 100\%\)
Actual increase = 7; Initial ratio = 40
\(=\left(\frac{7}{40} \times 100\%\right)=\frac{35}{2}=17.5\%\)
Users' Answers & CommentsActual increase = 7; Initial ratio = 40
\(=\left(\frac{7}{40} \times 100\%\right)=\frac{35}{2}=17.5\%\)
33
A regular polygon has 9 sides. What is the size of one of its exterior angles?
A
20o
B
40o
C
90o
D
140o
correct option: b
Exterior angle \(=\frac{360}{n}\) where n = no of sides
\(=\frac{360}{9}=40^{\circ}\)
Users' Answers & Comments\(=\frac{360}{9}=40^{\circ}\)
34
Simplify: \(\frac{2}{3xy} - \frac{3}{yz}\)
A
\(\frac{2-x}{12xyz}\)
B
\(\frac{2z-3x}{12xyz}\)
C
\(\frac{4z-3x}{12xyz}\)
D
\(\frac{8z-9x}{12xyz}\)
correct option: d
\(\frac{2}{3xy} - \frac{3}{yz} = \frac{2(4)-3(3x)}{12xyz} = \frac{8z-9x}{12xyz}\)
Users' Answers & Comments35
The total surface area of the walls of a room 7m long, 5m wide and xm high is 96m2. Find the value of x
A
\(\frac{2}{3}\)
B
2
C
4
D
8
correct option: b
T.S.A of the wall \(=7\time 5 + 7 \times x + 5 \times x +7 \times 5 = 96\
70 + 7x + 5x = 96 \Rightarrow 12x = 96-70=26\
x = \frac{26}{12}=2\)
Users' Answers & Comments70 + 7x + 5x = 96 \Rightarrow 12x = 96-70=26\
x = \frac{26}{12}=2\)
36
For what values of y is the expression \(\frac{6y-1}{y^2 - y-6}\)
A
\(\frac{1}{6}, \frac{1}{4}\)
B
3, -2
C
-3, 2
D
0,1
correct option: b
The expression is not defines when y2 - y - 6 = 0
=> y2 - 3y + 2y - 6 = 0 => (y-3)(y+2) = 0 => y
-3 = 0 or y + 2 = 0 => y = 3 or -2
Users' Answers & Comments=> y2 - 3y + 2y - 6 = 0 => (y-3)(y+2) = 0 => y
-3 = 0 or y + 2 = 0 => y = 3 or -2
37
What are the roots of the equation?
A
-1 and 1
B
4 and 1
C
1 and 4
D
4 and 4
correct option: c
The two points of contact of the curve with the x-axis are x = 1 and x = 4. The roots of the equation are x = 1 and x = 4
Users' Answers & Comments38
What is the equation of the curve?
A
\(y=x^2+6x+4\)
B
\(y=x^2-5x-4\)
C
\(y=x^2-5x+4\)
D
\(y=x^2+5x-4\)
correct option: c
The factor for the curve are (x-1)(x-4). The product off the curves gives \(=x^2-5x+4=y\)
Users' Answers & Comments39
In the diagram PQRS is a circle, |PT| = |QT| and ∠QPT = 70o what is the size of ∠PRS?
A
40o
B
70o
C
80o
D
140o
correct option: b
∠QPT = ∠QTP = 70o. Since ∠QTR = 140o
∠PRS = TSR = 1/2(180-40) = 70o
Users' Answers & Comments∠PRS = TSR = 1/2(180-40) = 70o
40
The angle of elevation of the top of a cliff 15 meters high from a landmark is 60o. How far is the landmark from the foot of the cliff? Leave your answer in surd form
A
\(15\sqrt{3}m\)
B
\(15\sqrt{2}m\)
C
\(10\sqrt{3}m\)
D
\(5\sqrt{3}m\)
correct option: d
\(tan 60^{\circ} = \frac{15}{x} \Rightarrow x = \frac{15}{tan60^{\circ}\
x = \left(\frac{15}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\right)m \Rightarrow 5\sqrt{3}m\)
Users' Answers & Commentsx = \left(\frac{15}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\right)m \Rightarrow 5\sqrt{3}m\)