## Mathematics 2014 | Study Mode

Question 1
A
11010112
B
10010012
C
10010112
D
10011112
Explanation.

No official Explanation yet!

Question 2
A
N53,000
B
N52,000
C
N51,000
D
N50,000
Explanation.
SP = Nx
CP = N60,000
Percentage loss = 15%
Using percentage loss...

$$\frac{CP - SP}{CP} = \text{100%}$$

$$\text{15%} = \frac{60000 - x}{60000} \times \text{100%}$$

$$\text{15%} \times 60000 = (60000 - x)\text{100%}$$

$$60000 - x = \frac{\text{15%} \times 60000}{\text{100%}}$$

60000 - x = 3 x 3000

60000 -x = 9000

x = 60000 - 9000

x = N51,000

Question 3
A
8.6 x 10-3
B
8.3 x 10-2
C
8.6 x 10-1
D
8.6 x 10
Explanation.
0.00043 x 2000

= 43 x 10-5 x 2 x 103

= 43 x 2 x 10-5+3

= 86 x 10-2

= 8.6 x 101 x 10-2

= 8.6 x 10-1

Question 4
A
N40,500
B
N45,000
C
N52,500
D
N62,000
Explanation.
Let;
M = Man monthly net earnings

Then;

$$\text{N4500} = \frac{\text{10%}}{\text{100%}} \times M$$

$$M = \frac{\text{N4500} \times \text{100%}}{\text{10%}}$$

M = N45,000

Question 5
A
6.6252
B
6.6253
C
66.252
D
66.253
Explanation.
If log 7.5 = 0.8751
Then 2log75 + log750
= 2(1.8751) + 2.8751
= 3.7502 + 2.8751
= 6.6253

Question 6
A
B
C
D
10
Explanation.
8x-2 = 2/25

x-2 = 2/25 x 1/8

x-2 = 2/200

x-2 = 1/100

1/x2 = 1/100

x2 = 100

x = 10

Question 7
A
3$$\sqrt{6} - 7$$
B
3$$\sqrt{6} - 7$$
C
3$$\sqrt{6} - 1$$
D
3$$\sqrt{6} + 1$$
Explanation.
$$= \frac{2\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}}$$

$$= \frac{2\sqrt{2}(\sqrt{2}) + (2\sqrt{2})(-\sqrt{3})-\sqrt{3}(\sqrt{2})-\sqrt{3}(-\sqrt{3})}{(\sqrt{2})^2-(\sqrt{3})^2}$$

$$= \frac{2 \times 2 - 2\sqrt{6} - \sqrt{6} + 3}{2 - 3}$$

$$= \frac{4 - 3\sqrt{6} + 3}{-1}$$

$$= \frac{7 - 3\sqrt{6}}{-1}$$

$$= \frac{7}{-1} - \frac{3\sqrt{6}}{-1}$$

$$= -7 + 3\sqrt{6}$$

$$= 3\sqrt{6}-7$$

Question 8
A
B
C
D
Explanation.
$$= log_2 \frac{8 \times 16}{4}$$

$$= log_2 32$$

$$= log_2 2^5$$

$$= 5log_2 2$$

$$= 5 \times 1$$

$$= 5$$

Question 9
A
{6}
B
{7}
C
{6,7}
D
{5,6}
Explanation.
Q = (P $$\cup$$ Q) - P
{6,7}

Question 10
A
$$\frac{k + w}{t^2}$$
B
$$\frac{k - w}{t^2}$$
C
$$\frac{k + w}{t}$$
D
$$\frac{k - w}{t}$$
Explanation.
gt2 - k - w = 0

gt2 = k + w

$$g = \frac{k + w}{t^2}$$

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