# Mathematics 2018 | Study Mode

Question 21
A
5.0 cm
B
7.0 cm
C
8.5 cm
D
12.0 cm
##### Explanation

Total surface area of hemisphere is

3$$\pi r^2$$ = 75$$\pi cm^2$$

$$r^2$$ = $$\frac{75 \pi}{3 \pi}$$

$$r^2$$ = 25

r = $$\sqrt{25}$$

r = 5cm

Question 22
A
0 or 5
B
-5 or 5
C
-11 or 5
D
0 or 1
##### Explanation

The expression $$\frac{x - 5}{x(x - 1)}$$ is defined whten

x(x - 5) = 0.38

either x = 0 or x - 5 = 0

Hence, x = 0 or x = 5

Question 23
A
x = $$\frac{-3}{2}$$ or 2
B
x = -2 or $$\frac{3}{2}$$
C
x = -3 or 2
D
x = 3 or -2
##### Explanation

$$2x^2 - x - 6$$ = 0

$$2x^2 - 4x + 3x - 6$$ = 0

2x(x - 2) + 3(x - 2) = 0

(2x + 3) (x - 2) = 0

Either; 2x + 3 = 0 or x - 2 = 0

x = $$\frac{-3}{2}$$ or x = 2

Question 24
A
(3x + 2)(1 - x)
B
(3x + 2)(2x + 1)
C
3$$(x + 2)^2$$
D
3(x + 1)(1 - x)
##### Explanation

$$(x + 2)^2$$ - $$(2x + 1)^2$$

= $$(x^2 + 4x + 4) - (4x^2 + 4x + 1)$$

= $$x^2$$ + 4x + 4 - 4 $$x^2$$ - 4x - 1

= -3 $$x^2$$ + 3

= 3 - 3 $$x^2$$

= 3(1 - $$x^2$$)

= 3(1 + x)(1 - x)

Question 25
A
2$$^n$$ x 3(n + 1)
B
2$$^n$$ x 3n
C
2$$^n$$ x 3$$^n$$
D
2$$^n$$ x 3$$^n - 1$$
##### Explanation

2 x 3, 4 x 6, 8 x 9, 16 x 12,...

2$$^1$$ x 3 x 1, 2$$^2$$ x 3 x 2, 2$$^3$$ x 3 x 3, 2$$^4$$ x 3 x 4,.... 2$$^n$$ x 3n

Question 26
A
1
B
2
C
3
D
4
##### Explanation

3x $$\equiv$$ 4(mod 5)

In modulo 5, multiples of 5 that give solution to the given equation are 5, 20, 35, 50,... but 5 will yield the leaast value of x.

Thus; 3x = 4 + 5 = 9

x = $$\frac{9}{3}$$

x = 3

Question 27
A
6
B
7
C
8
D
9
##### Explanation

$$Q_1 = \frac{1}{4}$$Nth

$$\frac{1}{4} \times 11^{th}$$ no.

= 2$$\frac{3}{4}th$$ ($$\cong$$ 4)

$$Q_3 = \frac{3}{4}$$ Nth

= $$\frac{3}{4}$$ x 11th no.

= 8$$\frac{1}{4}$$ no. ($$\cong$$ 11) ($$\cong$$ 11)

Hence, interquartile range

= $$Q_3 = Q_1$$

= 11 - 4

= 7

Question 28
A
2:3
B
3:4
C
3:8
D
1:2
##### Explanation

$$\frac{x}{y}$$ = $$\frac{1}{4} \div \frac{3}{8}$$ = $$\frac{1}{4} \times \frac{8}{3}$$ = $$\frac{2}{3}$$

$$\frac{y}{z}$$ = $$\frac{1}{3} \div \frac{4}{9}$$ = $$\frac{1}{3} \times \frac{9}{4}$$ = $$\frac{3}{4}$$

But,

x = $$\frac{2}{5}T_1$$, y = $$\frac{3}{5}T_1$$

y = $$\frac{3}{7}T_2$$, z = $$\frac{4}{7}T_2$$

Using y = y

$$\frac{3}{5}T_1$$ = x = $$\frac{3}{7}T_2$$

$$\frac{T_1}{T_2}$$ = $$\frac{3}{7}$$ x $$\frac{5}{3}$$ = $$\frac{15}{21}$$

$$T_1 = 15$$ and $$T_2 = 21$$

Thus , x = $$\frac{2}{5}$$ x 15 = 6

y = $$\frac{3}{5}$$ x 15 = 9

y = $$\frac{3}{7}$$ x 21 = 9

z = $$\frac{4}{7}$$ x 21 = 12

Hence; x : z = 6 : 12

= 1 : 2

Question 29
A
$$\frac{153}{250}$$
B
$$\frac{68}{111}$$
C
$$\frac{61}{100}$$
D
$$\frac{21}{33}$$
##### Explanation

0.612 = $$\frac{0.612}{1}$$ x $$\frac{1000}{1000}$$

= $$\frac{612}{1000}$$

= $$\frac{153}{250}$$

Question 30
A
27m
B
13.5 $$\sqrt{3m}$$
C
13.5 $$\sqrt{2m}$$
D
9$$\sqrt{3m}$$
##### Explanation

From the diagram,

tan 30$$^o$$ = $$\frac{h}{27}$$

h = 27 tan 30$$^o$$

= 27 x $$\frac{1}{\sqrt{3}}$$

= $$\frac{27}{\sqrt{3}}$$ x $$\frac{\sqrt{3}}{\sqrt{3}}$$

= $$\frac{27 \sqrt{3}}{3}$$

= 9$$\sqrt{3m}$$

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