# Mathematics 2018 | Study Mode

Question 11
A
$$2 (1 + 3m)$$
B
$$2 (1 + 3m^2)$$
C
$$2(1 - 3m)$$
D
$$2(1 - 3m^2)$$
##### Explanation

$$\frac{2 - 18m^2}{1 + 3m}$$ = $$\frac{2(1 - 9)m^2}{1 + 3m}$$

= $$\frac{2(1 + 3m)(1 - 3m)}{1 + 3m}$$

= $$2(1 - 3m)$$

Question 12
A

y = $$x^2 - 5x - 6$$

B

y = $$x^2 + 5x - 6$$

C

y = $$x^2 + x - 6$$

D

y = $$x^2 - x - 6$$

##### Explanation

Since the curve cuts the x-axis at x = -2 and x = 3,

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

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

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

Hence, the equation of the curve is

y = $$x^2 - x - 6$$

Question 13
A
14m
B
10m
C
7m
D
5m
##### Explanation

Volume of a cylinder = $$\pi r^2$$h

385 = $$\frac{22}{7}$$ x $$r^2$$ x 10

385 x 7 = 22 x $$r^2$$ x 10

$$r^2$$ = $$\frac{385 \times 7}{22 \times 10}$$

= 12.25

r = $$\sqrt{12.25}$$

= 3.5m

Hence, diameter of tank = 2r

= 2 x 3.5 = 7m

Question 14
A
113$$cm^3$$
B
131$$cm^3$$
C
311$$cm^3$$
D
414$$cm^3$$
##### Explanation

Surface area of a sphere = $$4 \pi r^2$$

$$4 \pi r^2$$ = $$\frac{792}{7}cm^2$$

4 x $$\frac{22}{7}$$ x $$r^2$$ = $$\frac{792}{7}$$

$$r^2$$ = $$\frac{792}{7}$$ x $$\frac{7}{4 \times 22}$$

= 9

r = $$\sqrt{9}$$

= 3cm

Hence, volume of sphere

= $$\frac{4}{3} \pi r^3$$

= $$\frac{4}{3} \times \frac{22}{7} \times 3 \times 3 \times 3$$

= $$\frac{4 \times 22 \times 9}{7}$$

$$\approx$$ = 113.143

= 113$$cm^3$$ (to the nearest whole number)

Question 15
A
$$45^o$$
B
$$84^o$$
C
$$85^o$$
D
$$95^o$$
##### Explanation

x + 2x + 2x + (x + $$30^o$$) + (x + $$20^o$$) + (x - $$10^o$$) = (2n - 4) x $$90^o$$

8x + 50 $$^o$$ - 10$$^o$$ = (2 x 6 -4) x 90$$^o$$

8x + 40$$^o$$ = 8 x 90$$^o$$ = 720$$^o$$

8x = 720$$^o$$ - 40$$^o$$ = 680$$^o$$

x = $$\frac{680^o}{8}$$

= 85$$^o$$

Question 16
A
8 units
B
11 units
C
15 units
D
17 units
##### Explanation

|MN| = $$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$

= $$\sqrt{(-3 -5)^2 + (8 - 7)^2}$$

= $$\sqrt{(-8)^2 + (8 + 7)^2}$$

= $$\sqrt{64 + (15)^2}$$

= $$\sqrt{64 + 225}$$

= $$\sqrt{289}$$

= 17 units

Question 17
A
1
B
2
C
3
D
9
##### Explanation

Using the two - point from

$$\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}$$

$$\frac{y - 2}{-2 - 2} = \frac{x - 4}{-8 - 4}$$

$$\frac{y - 2}{-4} = \frac{x - 4}{-12}$$

$$\frac{-12(y -2)}{-4}$$ = x - 4

3(y -2) = x -4

3y - 6 = x - 4

3y = x - 4 + 6

3y = x + 2...

By comparing the equations;

3y = px + , p = 1

Question 18
A
2
B
4
C
6
D
8
##### Explanation

Mean = $$\frac{\sum x}{n}$$

4 = $$\frac{1 + 3 + 5 + 7 + x}{5}$$

4 x 5 = 16 + x

20 - 16 = x

4 = x

x = 4

Question 19
A
$$\frac{9}{25}$$
B
$$\frac{1}{5}$$
C
$$\frac{6}{25}$$
D
$$\frac{2}{5}$$
##### Explanation

Prob. (team scored 4 goals) = Prob. (team scored 7 goals) = $$\frac{3}{25}$$

Hence, probability that a team selected at random scored either 4 or 7 goals;

= $$\frac{6}{25} + \frac{3}{25}$$

= $$\frac{9}{25}$$

Question 20
A
$$\frac{3}{25}$$
B
$$\frac{1}{5}$$
C
$$\frac{6}{25}$$
D
$$\frac{2}{5}$$
##### Explanation

No. of teams that scored at most 3 goals = 3 + 1 + 6 = 10

Hence, probability that a team selected at random scored at most 3 goals

= $$\frac{10}{25}$$ = $$\frac{2}{5}$$

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