# 2006 - WAEC Mathematics Past Questions & Answers - page 1

1
Evaluate (0.13)$$^3$$correct to three significant figures
A
0.00219
B
0.00220
C
0.00300
D
0.00390
CORRECT OPTION: b
(0.13)$$^3$$ = 0.13 x 0.13 x 0.13 = 0.002197

= 0.00220 (3 s.f)
2

Simplify: 11011$$_2$$ - 1101$$_2$$

A
101000$$_2$$
B
1100$$_2$$
C
1110$$_2$$
D
1011$$_2$$
CORRECT OPTION: c

11011$$_2$$ - 1101$$_2$$ = 1110$$_2$$

3
Simplify $$\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}$$
A
25
B
$$\frac{1}{5}$$
C
1
D
$$\frac{1}{25}$$
CORRECT OPTION: c
$$\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}$$ = $$\frac{25^{4 - \frac{1}{6}}}{(\frac{1}{5})^{-7 + \frac{1}{6}}}$$

= $$\frac{25^{\frac{1}{2}}}{(\frac{1}{5})^{-1}}$$

= $$\frac{(5^2)^{\frac{1}{2}}}{(5^{-1})^{-1}}$$

= $$\frac{5}{5}$$

= 1
4
Simplify $$\frac{x - 4}{4} - \frac{x - 3}{6}$$
A
$$\frac{x - 18}{12}$$
B
$$\frac{x - 6}{12}$$
C
$$\frac{x - 18}{24}$$
D
$$\frac{x - 6}{24}$$
CORRECT OPTION: b
$$\frac{x - 4}{4} - \frac{x - 3}{6}$$ = $$\frac{3(x - 4) - 2(x - 3)}{12}$$

= $$\frac{3x -12 - 2x + 6}{12}$$

= $$\frac{3x - 2x - 12 + 6}{12}$$

= $$\frac{x - 6}{12}$$
5
Given that y = 1 - $$\frac{2x}{4x - 3}$$, find the value of x for which y is undefined
A
3
B
$$\frac{3}{4}$$
C
$$\frac{-3}{4}$$
D
-3
CORRECT OPTION: b
for undefined expression, the denomination is zero 4x - 3 = 0

4x = 3; x = $$\frac{3}{4}$$
6
P is a point on the same plane with a fixed point A. If P moves such that it is always equidistant from A, the locus of P is
A
a straight line joining A and P
B
the perpendicular bisector of AP
C
a circle with centre A
D
the triangle with centre P
CORRECT OPTION: c
7
A fair coin is tossed three times. Find the probability of getting two heads and one tail.
A
$$\frac{1}{2}$$
B
$$\frac{3}{8}$$
C
$$\frac{1}{4}$$
D
$$\frac{1}{8}$$
CORRECT OPTION: b
Pr(head) = $$\frac{1}{2}$$, Pr(tail) = $$\frac{1}{2}$$:Pr(2 heads)

= $$\frac{1}{2}$$ x $$\frac{1}{2}$$ = $$\frac{1}{4}$$

Pr(2 heads and tail) 3 times

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

= $$\frac{3}{8}$$
8
If 30% of y is equal to x, what in terms of x, is 30% of 3y?
A
$$\frac{x}{9}$$
B
$$\frac{x}{3}$$
C
x
D
3x
CORRECT OPTION: d
If 30% of y = x, then 30% of 3y = 3x
9
A baker used 40% of a 50kg bag of flour. If $$\frac{1}{8}$$ of the amount used was for the cake, how many kilogram of flour was used for the cake?
A
2$$\frac{1}{2}$$
B
6$$\frac{1}{2}$$
C
15$$\frac{3}{8}$$
D
17$$\frac{1}{2}$$
CORRECT OPTION: a
$$\frac{40}{100} \times 50$$kg = 20kg

$$\frac{1}{8}$$ of 20kg for cake; $$\frac{1}{8}$$ x $$\frac{20}{1}$$

= 2$$\frac{1}{2}$$kg
10
If tan y = 0.404, where y is acute, find cos 2y
A
0.035
B
0.719
C
0.808
D
0.927
CORRECT OPTION: b
tan y = 0.404; y = tan-1 0.0404(tables);y = 22o

cos 2y = cos 2(22o); cos 44o

= 0.719
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