2013 - WAEC Mathematics Past Questions and Answers - page 4
31
The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. ( Take \(\pi = \frac{22}{7}\))
A
48cm3
B
47cm3
C
38cm3
D
12cm3
correct option: c
Volume of a cone = \(\frac{1}{3} \pi r^2h\)
h2 = 52 = 32
= 25 - 9 = 16
h = \(\sqrt{16}\)
h = 4cm
v = \(\frac{1}{3} \times \frac{22}{7} \times 3^2 \times 4\)
\(\frac{1}{3} \times \frac{22}{7} \times 9 \times 4\)
= \(\frac{22 \times 3 \times 4}{7}\)
= 37.7cm3
= 38cm3
Users' Answers & Commentsh2 = 52 = 32
= 25 - 9 = 16
h = \(\sqrt{16}\)
h = 4cm
v = \(\frac{1}{3} \times \frac{22}{7} \times 3^2 \times 4\)
\(\frac{1}{3} \times \frac{22}{7} \times 9 \times 4\)
= \(\frac{22 \times 3 \times 4}{7}\)
= 37.7cm3
= 38cm3
32
The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used
A
1: 1,000,000
B
1: 500,000
C
1: 100,000
D
1: 10,000
correct option: a
1km = 100,000cm
on the map 1 cm represent every 10 km which is equal to (10 x 100,000cm)
= 1,000,000cm
the scale is 1:1,000,000
Users' Answers & Commentson the map 1 cm represent every 10 km which is equal to (10 x 100,000cm)
= 1,000,000cm
the scale is 1:1,000,000
33
Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M
A
(x + 2)2
B
x(x + 2)
C
xv + 2
D
x2 - x
correct option: d
(x = 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2)m
(m + 2)[(x2 - 3x + 2) + 2(x - 1)] = (x + 2)M
divide both side by (x + 2)
(x2 - 3x + 2) + 2(x - 1) = M
x2 - 3x + 2 + 2x - 2 = M
x2 - 3x + 2 + 2x - 2 = M
x2 - 3x + 2x = M
x2 - x = M
M = x2 - x
Users' Answers & Comments(m + 2)[(x2 - 3x + 2) + 2(x - 1)] = (x + 2)M
divide both side by (x + 2)
(x2 - 3x + 2) + 2(x - 1) = M
x2 - 3x + 2 + 2x - 2 = M
x2 - 3x + 2 + 2x - 2 = M
x2 - 3x + 2x = M
x2 - x = M
M = x2 - x
34
An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. calculate the arc of the sector (Take \(\pi = \frac{22}{7}\))
A
8800cm2
B
8448cm2
C
4400cm2
D
4224cm2
correct option: a
L2 = 962 + 282
= 9216 + 784
= 10000
L = \(\sqrt{10000}\)
= 100cm
curved surface area = \(\pi r l\)
= \(\frac{22}{7} \times 28 \times 100\)
= 8800cm2
area of cone = area of sector
area of sector = 8800cm2
Users' Answers & Comments= 9216 + 784
= 10000
L = \(\sqrt{10000}\)
= 100cm
curved surface area = \(\pi r l\)
= \(\frac{22}{7} \times 28 \times 100\)
= 8800cm2
area of cone = area of sector
area of sector = 8800cm2
35
In the diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and < PQR = 90o, find the perimeter of the polygon PQRST.
A
112cm
B
98cm
C
86cm
D
84cm
correct option: a
Users' Answers & Comments36
in the diagram, the height of a flagpole |TF| and the length of its shadow |FL| re in the ratio 6:8. Using k as a constant of proportionality, find the shortest distance between T and L
A
7K units
B
10K units
C
12K units
D
14k units
correct option: b
by Pythagoras x2 = 62 + 82
36 + 64 = 100
x = \(\sqrt{100}\)
x = 10
Users' Answers & Comments36 + 64 = 100
x = \(\sqrt{100}\)
x = 10
37
In the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?
A
\(\bigtriangleup\) ZYX = \(\bigtriangleup\) OMN
B
\(\bigtriangleup\) YZX = \(\bigtriangleup\) NOM
C
\(\bigtriangleup\) ZXY= \(\bigtriangleup\) MON
D
\(\bigtriangleup\) XYZ= \(\bigtriangleup\) NOM
correct option: d
Users' Answers & Comments38
In the diagram, PQRS is a rhombus and < PSQ = 35o. Calculate the size of < PRO
A
65o
B
55o
C
45o
D
35o
39
Find the value of m in the diagram
A
34o
B
27o
C
23o
D
17o
correct option: d
\(\bigtriangleup\) ABC, A + 153 = 180 (angles on straight line)
< A = 180 - 153 = 27
< B = 2m(vertically opposite angles)
< C = 7m (corresponding ngles)
< A + < B + < C = 180 (sum of int. angles of \(\bigtriangleup\))
i.e. 27 + 2m + 7m = 180o
9m = 180 - 27
9m = 153
m = \(\frac{153}{9}\)
= 17
Users' Answers & Comments< A = 180 - 153 = 27
< B = 2m(vertically opposite angles)
< C = 7m (corresponding ngles)
< A + < B + < C = 180 (sum of int. angles of \(\bigtriangleup\))
i.e. 27 + 2m + 7m = 180o
9m = 180 - 27
9m = 153
m = \(\frac{153}{9}\)
= 17
40
In the diagram, O is the centre of the circle. OM||XZ and < ZOM = 25o
A
50o
B
55o
C
60o
D
65o
correct option: c
Users' Answers & Comments