2011 - WAEC Mathematics Past Questions & Answers - page 1

1
If N112.00 exchanges for D14.95, calculate the value of D1.00 in naira
A
0.13
B
7.49
C
8.00
D
13.00
CORRECT OPTION: b
D14.95 = N112.00

D1.00 = \(\frac{N112}{D14.95} \times\) D1.00

= 7.49
2
Solve for x in the equation; \(\frac{3}{5}\)(2x - 1) = \(\frac{1}{4}\)(5x - 3)
A
zero
B
1
C
2
D
3
CORRECT OPTION: d
\(\frac{3}{5}\)(2x - 1) = \(\frac{1}{4}\)(5x - 3)

\(\frac{6x}{5} - \frac{3}{5} = \frac{5x}{4} - \frac{3}{4}\)

\(\frac{6x}{5} - \frac{5x}{4} = \frac{3}{5} - \frac{3}{4}\)

\(\frac{24x - 25x}{20} = \frac{12 - 15}{20}\)

\(\frac{-x}{20} = \frac{-3}{20}\)

-20x = -60

x = \(\frac{-60}{-20}\)

x = 3
3
Given that cos xo = \(\frac{1}{r}\), express tan x in terms of r
A
\(\frac{1}{\sqrt{r}}\)
B
\(\sqrt{r}\)
C
\(\sqrt{r^2 + 1}\)
D
\(\sqrt{r^2 - 1}\)
CORRECT OPTION: d
cos xo = \(\frac{1}{r}\); \(\sqrt{r^2 - 1}\)

By Pythagoras r2 = 12 + x2 - 1

x = \(\sqrt{r^2 - 1}\)

tan xo = \(\sqrt{r^2 - 1}\)

= \(\sqrt{r^2 - 1}\)
4
Solve the equation; 3x - 2y = 7, x + 2y = -3
A
x = 1, y = -2
B
x = 1, y = 3
C
x = -2, y = -1
D
x = 4, y = -3
CORRECT OPTION: a
3x - 2y = 7; Solve by elimination method

x + 2y = -3

3x - 2y = 7.....(i)

-3x + 6y = -9.....(ii)

-8y = 16

y = \(\frac{16}{-8} = -2\)

Put y = -2 into equation (i); 3x - 2y = 7

3x - 2(-2) = 7

3x + 4 = 7

3x = 7 - 4

3x = 3

x = \(\frac{3}{3}\) = 1
5
If a number is chosen at random from the set {x: 4 \(\leq x \leq 45\)}. Find the probability that it is a multiple of 3 or a multiple of 4
A
\(\frac{1}{12}\)
B
\(\frac{5}{12}\)
C
\(\frac{7}{2}\)
D
\(\frac{11}{12}\)
CORRECT OPTION: c
set = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

multiple of 3 = 6, 9, 12, 15

multiple of 4 = 4, 8, 12

Prob(multiple of 3 or 4) = Prob(multiple of 3) + pro(multiple of 4)

= \(\frac{4}{12} + \frac{3}{12} = \frac{7}{2}\)
6
One of the factors of (mn - nq - n2 + mq) is (m - n). The other factor is
A
(n - q)
B
(q - n)
C
(n + q)
D
(q - m)
CORRECT OPTION: a
mn - nq - n2 + mq

mn - n2 - nq + mq

(mn - n) - (nq - mq)

n(m - n) - q(n - m)

= n - q
7
A cylindrical container has a base radius of 14cm and height 18cm. How many litres of liquid can it hold? correct to the nearest litre [Take \(\pi = \frac{22}{7}\)]
A
11
B
14
C
16
D
18
CORRECT OPTION: a
Volume of cylinder = \(\pi r^2 h\)

= \(\frac{22}{7} \times 14^2\) x 14 x 18 = 22 x 28 x 18

= 11088cm3

1000cm3 = \(\frac{1}{1000}\) x 11088cm3

= 11.088

= 11
8
A regular polygon of n sides has each exterior angle to 45o. Find the value of n
A
6
B
8
C
12
D
15
CORRECT OPTION: b
Each interior angle = \(\frac{360^o}{n}\)

45o = \(\frac{360^o}{n}\)

45on = 360o

n = \(\frac{360^o}{45}\)

= 8
9
Esther was facing S 20o W. She turned 90o in the clock wise direction. What direction is she facing?
A
N 70o W
B
S 70o W
C
N 20o W
D
S 20o E
CORRECT OPTION: b
10
The cross section section of a uniform prism is a right-angled triangle with sides 3cm. 4cm and 5cm. If its length is 10cm. Calculate the total surface area
A
142cm2
B
132cm2
C
122cm2
D
112cm2
CORRECT OPTION: b
A prism has 3 rectangular faces and 2 triangular faces and 2 rectangular faces = 10(3 + 4 + 5) = 120

Area of triangular faces = \(\sqrt{s(s - a) (s - b) (s - c)}\)

where s = \(\frac{a + b + c}{2}\)

= \(\frac{3 + 4 + 5}{2}\)

= \(\frac{12}{2}\)

= 6

Area of \(\bigtriangleup\) = \(\sqrt{6(6 - 30(6 - 4)(6 - 5)}\)

= \(\sqrt{6 \times 3 \times 2 \times 1}\) = 6

Area of triangle faces = 2 x 6 = 12cm2

Total surface area = Area of rectangular face + Area of \(\bigtriangleup\) = 120 + 12

= 132cm2
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