# 2013 - WAEC Mathematics Past Questions and Answers - page 2

11
If x = 64 and y = 27, evaluate: $$\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}$$
A
2$$\frac{1}{5}$$
B
1
C
$$\frac{5}{11}$$
D
$$\frac{11}{43}$$
correct option: c
$$\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}$$

substitute x = 64 and y = 27

$$\frac{64^{\frac{1}{2}} - 27^{\frac{1}{3}}}{27 - 64^{\frac{2}{3}}} = \frac{\sqrt{64} - 3\sqrt{27}}{27 - (3\sqrt{64})^2}$$

= $$\frac{8 - 3}{27 - 16}$$

= $$\frac{5}{11}$$
12
If $$\frac{1}{2}$$x + 2y = 3 and $$\frac{3}{2}$$x and $$\frac{3}{2}$$x - 2y = 1, find (x + y)
A
3
B
2
C
1
D
5
correct option: a
$$\frac{1}{2}$$x + 2y = 3......(i)(multiply by 2)

$$\frac{3}{2}$$x - 2y = 1......(ii)(multiply by 2)

x + 4y = 6......(iii)

3x - 4y = 2.....(iv) add (iii) and (iv)

4x = 8, x = $$\frac{8}{4}$$ = 2

substitute x = 2 into equation (iii)

x + 4y = 6

2 + 4y = 6

4y = 6 - 2

4y = 4

y = $$\frac{4}{4}$$

= 1(x + y)

2 + 1 = 3
13
Given that p$$\frac{1}{3}$$ = $$\frac{3\sqrt{q}}{r}$$, make q the subject of the equation
A
q = p$$\sqrt{r}$$
B
q = p3r
C
q = pr3
D
q = pr$$\frac{1}{3}$$
correct option: d
p$$\frac{1}{3}$$ = $$\frac{3\sqrt{q}}{r}$$(cross multiply)

3$$\sqrt{q}$$ = r x 3$$\frac{\sqrt{q}}{r}$$(cross multiply)

3$$\sqrt{q}$$ = r x 3$$\sqrt{p}$$ cube root both side

q = 3$$\sqrt{r}$$ x p

q = r$$\frac{1}{3}$$p = pr$$\frac{1}{3}$$
14
A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord
A
2$$\sqrt{21}$$cm
B
$$\sqrt{42}$$cm
C
2$$\sqrt{19}$$cm
D
$$\sqrt{21}$$cm
correct option: a
From $$\bigtriangleup$$ OMQ find /MQ/ by Pythagoras OQ2 = OM2 + MQ2

52 = 22 + MQ2

25 = 4 + MQ2

25 - 4 = MQ2

21 - MQ2

MQ2 = 21

MQ2 = $$\sqrt{21}$$

Length of chord = 2 x $$\sqrt{21}$$ = 2$$\sqrt{21}$$cm
15
A cube and cuboid have the same base area. The volume of the cube is 64cm3 while that of the cuboid is 80cm3. Find the height of the cuboid
A
1cm
B
3cm
C
5cm
D
6cm
correct option: a
16
If sin x = $$\frac{5}{13}$$ and 0o $$\leq$$ x $$\leq$$ 90o, find the value of (cos x - tan x)
A
$$\frac{7}{13}$$
B
$$\frac{12}{13}$$
C
$$\frac{79}{156}$$
D
$$\frac{209}{156}$$
correct option: c
Sin x = $$\frac{5}{13}$$

0o $$\leq$$ x $$\leq$$ 90o, (cos x - tan x)

AC2 = AB2 + BC2

132 = 52 + BC2

169 - 25 + BC2

169 - 25 = BC2

144 = BC2

Cos x = $$\frac{Adj}{Hyp}$$ = $$\frac{12}{13}$$

BC = $$\sqrt{144}$$

BC = 12

tan x = $$\frac{opp}{adj} = \frac{5}{12}$$

BC = 12

cos x - tan x = $$\frac{12}{13} - \frac{5}{12}$$

$$\frac{144 - 65}{156} = \frac{79}{156}$$
17
An object is 6m away from the base of a mast. The angle of depression of the object from the top pf the mast is 50o, Find, correct to 2 decimal places, the height of the mast
A
8.60m
B
7.51m
C
7.15m
D
1.19m
correct option: c
Tan 50o = $$\frac{h}{6}$$

h = 6 tan 50

= 6 x 1.1917

= 7.1505

= 7.15
18
The bearing of Y from X is 060o and the bearing of Z from Y = 060o. Find the bearing of X from Z
A
300o
B
240o
C
180o
D
120o
correct option: b
19
Which of the following is not a probability of Mary scoring 85% in a mathematics test?
A
0.15
B
0.57
C
0.94
D
1.01
correct option: d
The probability not scoring 85% is = 1 - pro(scoring 85%)

= 1 - $$\frac{85}{100}$$ = 1 - 0.85

= 0.15

not scoring would be less than 1
20
If 2 log x (3$$\frac{3}{8}$$) = 6, find the value of x
A
$$\frac{3}{2}$$
B
$$\frac{4}{3}$$
C
$$\frac{2}{3}$$
D
$$\frac{1}{2}$$
correct option: a
2 log x (3$$\frac{3}{8}$$) = 6(divide both sides by 2)

$$\frac{2 log_x(3 \frac{3}{8})}{2} = \frac{6}{2}$$

$$\log_x \frac{27}{8} = 3$$

$$\frac{27}{8} = x^3$$

$$x^3 = \frac{27}{8}$$

x = $$\sqrt{\frac{27}{8}}$$

= ($$\frac{27}{8}$$)$$\frac{1}{3}$$

= $$\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}$$

= $$\frac{3}{2}$$