# Mathematics | Study Mode

Question 1
A
0
B
4.0E-5
C
4.1E-5
D
4.07E-5
Explanation.

0.0000407 to 2 s.f

0.000041 (2 s.f)

Question 2
A
x $$\alpha$$ z
B
x $$\alpha$$ $$\frac{1}{z}$$
C
a $$\alpha$$ z$$^2$$
D
x $$\alpha$$ $$\frac{1}{z^2}$$
Explanation.

$$x \propto \frac{1}{y}$$, y $$\propto$$ z

x = $$\frac{k}{y}$$

y = mz

Since y = mz,

x = $$\frac{k}{mz}$$, where k and m are constants. Hence,

x $$\propto$$ $$\frac{1}{z}$$

Question 3
A
$$\frac{14}{15}$$
B
$$\frac{13}{15}$$
C
$$\frac{4}{5}$$
D
$$\frac{11}{15}$$
Explanation.

$$\frac{3\frac{1}{4} \times 1\frac{3}{5}}{11\frac{1}{3} - 5 \frac{1}{3}}$$ = $$\frac{\frac{26}{5}}{\frac{18}{3}}$$ = $$\frac{26}{5} \div \frac{18}{3}$$

= $$\frac{13}{15}$$

Question 4
A
1 : 4
B
1 : 5
C
2 : 5
D
5 : 2
Explanation.

Tunde: Ola $$\to$$ 1 : 2 ; Ola; Musa $$\to$$ 4 : 5

$$\frac{1}{2}$$ x $$\frac{4}{5}$$

= $$\frac{2}{5}$$

Question 5
A
iii only
B
i and ii
C
ii and iii only
D
i, ii and iii
Explanation.

M = {3, 4, 5, 6, 7,}, N = {9, 10, 11, 12}

Question 6
A
a + b + 1
B
ab - 1
C
a - b + 1
D
b - a + 1
Explanation.

$$\frac{\log 7 \times \log 10}{\log 2}$$

log 7 x log 10 $$\div$$ log 2

a + 1 - b

a - b + 1

Question 7
A
0
B
5
C
8
D
9
Explanation.

x = $$\frac{2}{3}$$ and y = - 6

xy - $$\frac{y}{x}$$

$$\frac{2}{3} - (6)^2 - (-6) \div \frac{2}{3}$$

= -4 - (6) x $$\frac{3}{2}$$

= -4 - (-6) x $$\frac{3}{2}$$

= -4 - (-9)

= -4 + 9

= 5

Question 8
A
$$\frac{1}{5}$$
B
$$\frac{2}{5}$$
C
$$\frac{3}{5}$$
D
$$\frac{4}{5}$$
Explanation.

$$\frac{1}{5x} + \frac{1}{x}$$= 3

$$\frac{1 + 5}{5x}$$ = 3

6 = 15x

x = $$\frac{6}{15}$$

= $$\frac{2}{5}$$

Question 9
A
N1,820.00
B
2,000.00
C
N2,020.00
D
N2,040.00
Explanation.

Let a girl's share = x + 20

4x + 5(x + 20) = 18,100

4x + 5x + 100 = 18,100

9x + 100 = 18,100

9x = 18,000

x = $$\frac{18,000}{9}$$

x = 2,000

Question 10
A
7x + 5
B
x - 2
C
7x - 2
D
x - 5
Explanation.

$$7x^2 + 33x - 10$$

$$7x^2 + 35x - 2x - 10$$

7x (x + 5) - 2 (x + 5)

(7x - 2) (x + 5)

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