2014 - WAEC Mathematics Past Questions & Answers - page 1

1
Simplify 10\(\frac{2}{5} - 6 \frac{2}{3} + 3\)
A
6\(\frac{4}{15}\)
B
6\(\frac{11}{15}\)
C
7\(\frac{4}{15}\)
D
7\(\frac{11}{15}\)
CORRECT OPTION: b
10\(\frac{2}{5} - 6 \frac{2}{3} + 3\)

\(\frac{52}{5} - \frac{20}{3} + \frac{3}{1}\)

= \(\frac{156 - 100 + 45}{15}\)

\(\frac{156 + 45 - 100}{15}\)

= \(\frac{201 - 100}{15}\)

= \(\frac{101}{15}\)

= 6\(\frac{11}{15}\)
2
If 23x = 325, find the value of x
A
7
B
6
C
5
D
4
CORRECT OPTION: a
23x = 325

2 \(\times x^1 + 3 \times x^0 = 3 \times 5^1 + 2 \times 5^0\)

= 2x + 3 = 15 + 2

2x + 3 = 17

2x = 17 - 3

2x = 14

x = \(\frac{14}{2}\)

x = 7
3
The volume of a cube is 512cm3. Find the length of its side
A
6cm
B
7cm
C
8cm
D
9cm
CORRECT OPTION: c
volume of cube = L x L x L

512cm3 = L3

L3 = 512cm3

L = 3\(\sqrt{512}\)

L (512)\(\frac{1}{3}\)

= (29)\(\frac{1}{3}\)

23 = 8cm
4
If one student is selected at random, find the probability that he/she scored at most 2 marks
A
\(\frac{11}{18}\)
B
\(\frac{11}{20}\)
C
\(\frac{7}{22}\)
D
\(\frac{5}{19}\)
CORRECT OPTION: b
at most 2 marks = 5 + 2 + 4 students = 11 students

probability(at most 2 marks) = \(\frac{11}{20}\)
5
Simplify: \(\sqrt{12} ( \sqrt{48} - \sqrt{3}\))
A
18
B
16
C
14
D
12
CORRECT OPTION: a
\(\sqrt{12} ( \sqrt{48} - \sqrt{3}\))

\(\sqrt{4 \times 3} (6 \times 3 - \sqrt{3}) = 2 \sqrt{3}(4 \sqrt{3} - \sqrt{3})\)

= 2\(\sqrt{3} \times \sqrt{3} (4 - 1) 2\sqrt{9}(3) = 2 \times 3 \times 3 = 18\)
6
Given that x > y and 3 < y, which of the following is/are true? i. y > 3 ii. x < 3 iii. x > y > 3
A
i
B
i and ii
C
i and iii
D
i, ii and iii
CORRECT OPTION: c
x > y and 3 < y; then 3 < y means that y > 3

x > 3 to give the possible

x > y > 3
7
Three quarters of a number added to two and a half of the number gives 13. Find the number
A
4
B
5
C
6
D
7
CORRECT OPTION: a
let the number be x

2\(\frac{1}{2}x + \frac{3}{4}x = 13\)

\(\frac{5}{2}x + \frac{3}{4}x = 13\)

multiply through by 4

4(\(\frac{5}{2}\))x + 4(\(\frac{3}{4}\))x = 13 x 4

2(5x) + 3x = 52

10x + 3x = 52

13x = 52

x = \(\frac{52}{13}\)

x = 4
8
If x = {0, 2, 4, 6}, y = {1, 2, 3, 4} and z = {1, 3} are subsets of u = {x:0 \(\geq\) x \(\geq\) 6}, find x \(\cap\) (Y' \(\cup\) Z)
A
{0, 2, 6}
B
{1, 3}
C
{0, 6)
D
{9}
CORRECT OPTION: c
x = {0, 2, 4, 6}; y = {1, 2, 3, 4}; z = {1, 3}

u = {0, 1, 2, 3, 4, 5, 6}

y' = {0, 5, 6}

to find x \(\cap\) (Y' \(\cup\) Z)

first find y' \(\cup\) z = {0, 1, 3, 5, 6}

then x \(\cap\) (Y' \(\cup\) Z) = {0, 6}
9
Find the truth set of the equation x2 = 3(2x + 9)
A
{x : x = 3, x = 9}
B
{x : x = -3, x = -9}
C
{x : x = 3, x = -9}
D
{x : x = -3, x = 9}
CORRECT OPTION: d
x2 = 3(2x + 9)

x2 = 6x + 27

x2 - 6x - 27 = 0

x2 - 9x + 3x - 27 = 0

x(x - 9) + 3(x - 9) = (x + 3)(x - 9) = 0

x + 3 = 0 or x - 9 = 0

x = -3 or x = 9

x = -3, x = 9
10
The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q.
A
10\(sqrt{2}\)
B
4\(sqrt{5}\)
C
5\(sqrt{2}\)
D
2\(sqrt{5}\)
CORRECT OPTION: d
p(4, 3) Q(2 - 1)

distance = \(\sqrt{(x_2 - x_1)^2 + (Y_2 - y_1)^2}\)

= \(\sqrt{(2 - 4)^2 + (-1 - 3)^2}\)

= \(\sqrt{(-2)^2 = (-4)^2}\)

= \(\sqrt{4 + 16}\)

= \(\sqrt{20}\)

= \(\sqrt{4 \times 5}\)

= 2\(\sqrt{5}\)
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