2011 - WAEC Mathematics Past Questions and Answers - page 4
31
John pours 96 litres of red oil into a rectangular container with length 220cm and breadth 40cm. Calculate, correct to the nearest cm, the height of the oil in the container
A
11cm
B
18cm
C
21cm
D
34cm
correct option: a
volume of rectangular container = L x B x H
1 litre = 1000cm3
96 litres = \(\frac{1000cm^3}{1 litres}\) x 96 litres
volume = 96000cm3
96000 = 220 x 40 x 11
96--- = 8800H
H = \(\frac{96000}{8800}\)
= 10.97cm
= 11cm
Users' Answers & Comments1 litre = 1000cm3
96 litres = \(\frac{1000cm^3}{1 litres}\) x 96 litres
volume = 96000cm3
96000 = 220 x 40 x 11
96--- = 8800H
H = \(\frac{96000}{8800}\)
= 10.97cm
= 11cm
32
John pours 96 litres of red oil into a rectangular container with length 220cm and breadth 40cm. Calculate, correct to the nearest cm, the height of the oil in the container
A
11cm
B
18cm
C
21cm
D
34cm
correct option: a
volume of rectangular container = L x B x H
1 litre = 1000cm3
96 litres = \(\frac{1000cm^3}{1 litres}\) x 96 litres
volume = 96000cm3
96000 = 220 x 40 x 11
96--- = 8800H
H = \(\frac{96000}{8800}\)
= 10.97cm
= 11cm
Users' Answers & Comments1 litre = 1000cm3
96 litres = \(\frac{1000cm^3}{1 litres}\) x 96 litres
volume = 96000cm3
96000 = 220 x 40 x 11
96--- = 8800H
H = \(\frac{96000}{8800}\)
= 10.97cm
= 11cm
33
in a quiz competition, a student answers n questions correctly and was given D(n + 50) for each question correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?
A
18
B
15
C
12
D
10
correct option: d
let the number of question = n
n(n + 50) = 600
n2 + 50n - 600 - 0 by quadratic formular
x = \(\frac{b \pm \sqrt{b^2 - 4ac}}{2}\)
n = \(\frac{-50 \pm \sqrt{50^2 - 4(1) (-600)}}{2(1)}\)
= \(\frac{-50 \pm \sqrt{4900}}{2}\)
= \(\frac{-50 + 70}{2}\)
= \(\frac{20}{2}\)
= 10
Users' Answers & Commentsn(n + 50) = 600
n2 + 50n - 600 - 0 by quadratic formular
x = \(\frac{b \pm \sqrt{b^2 - 4ac}}{2}\)
n = \(\frac{-50 \pm \sqrt{50^2 - 4(1) (-600)}}{2(1)}\)
= \(\frac{-50 \pm \sqrt{4900}}{2}\)
= \(\frac{-50 + 70}{2}\)
= \(\frac{20}{2}\)
= 10
34
If 27x = 9y. Find the value of \(\frac{x}{y}\)
A
\(\frac{1}{3}\)
B
\(\frac{2}{3}\)
C
1\(\frac{1}{2}\)
D
3
35
a boy looks through a window of a building and sees a mango fruit on the ground 50m away from the foot of the building. If the window is 9m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window
A
9o
B
10o
C
11o
D
12o
correct option: b
tan \(\theta\) = \(\frac{9}{50}\) = 0.18
\(\theta = tan^{-1} 0.18\)
\(\theta\) = 10.20
Users' Answers & Comments\(\theta = tan^{-1} 0.18\)
\(\theta\) = 10.20
36
The diagram shows a cyclic quadrilateral PQRS with its diagonals intersecting at K. Which of the following triangles is similar to triangle QKR?
A
\(\bigtriangleup\) PQK
B
\(\bigtriangleup\) PKS
C
\(\bigtriangleup\) SKR
D
\(\bigtriangleup\) PSR
correct option: c
Users' Answers & Comments37
In the diagram, PO and OR are radii, |PQ| = |QR| and reflex < PQR is 240o. Calculate the value x
A
60o
B
55o
C
50o
D
45o
correct option: a
< Q = \(\frac{240}{2}\) (angle at centre twice that at the circumference)
< Q = 120o
Also < POR = 360 - 240
= 120o
( < s at centre) since /PQ/ = /QR/, < x = < R
Byt < x + < R + O + Q = 360 (sum of interior < s of quadrilateral)
x + R + 120 = 360o
x + R = 360 - 240 = 120; Since x = R
x + x = 120
2x = 120
Since x = R
x + x = 120
2x = 120
x = \(\frac{120}{2}\)
= 60o
Users' Answers & Comments< Q = 120o
Also < POR = 360 - 240
= 120o
( < s at centre) since /PQ/ = /QR/, < x = < R
Byt < x + < R + O + Q = 360 (sum of interior < s of quadrilateral)
x + R + 120 = 360o
x + R = 360 - 240 = 120; Since x = R
x + x = 120
2x = 120
Since x = R
x + x = 120
2x = 120
x = \(\frac{120}{2}\)
= 60o
38
Find the size of the angle marked x in the diagram.
A
108o
B
112o
C
128o
D
142o
correct option: c
x + 52o = 90
x = 90 - 52
x = 38o
k = opposite angle Z
k = 38o
y + k = 90o
y + 38o = 90o
y = 90o - 38o
y = 52o
y = x = 180o(sum of angles on straight line)
52 + x = 180o
x = 180 - 52
x = 128
Users' Answers & Commentsx = 90 - 52
x = 38o
k = opposite angle Z
k = 38o
y + k = 90o
y + 38o = 90o
y = 90o - 38o
y = 52o
y = x = 180o(sum of angles on straight line)
52 + x = 180o
x = 180 - 52
x = 128
39
The histogram shows the age distribution of members of a club. How many members are in the club?
A
52
B
50
C
48
D
40
40
The histogram shows the age distribution of members of a club. What is their modal age?
A
44.5
B
42.5
C
41.5
D
40.5
correct option: a
Users' Answers & Comments