# Mathematics 2018 | Study Mode

Question 11
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 12
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 13
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 14
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 15
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 16
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 17
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 18
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

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

Question 19
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 20
A
1$$\frac{1}{2}$$
B
2
C
2$$\frac{1}{2}$$
D
3
##### Explanation

If x : y : z = 3 : 3 : 4, evaluate $$\frac{9x + 3y}{6x - 2y}$$

$$\frac{x}{y}$$ = $$\frac{2}{3}$$ and $$\frac{y}{z}$$ = $$\frac{3}{4}$$

Thus; x = $$\frac{2}{3}T_1$$ and z = $$\frac{3}{5}T_1$$

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

Using y = y

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

$$\frac{T_1}{T_2}$$ =$$\frac{15}{21}$$

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

Therefore;

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

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

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

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

Hence;

$$\frac{9x + 3y}{6z - 2y}$$ = $$\frac{9(6) + 3(9)}{6(12) - 2(9)}$$

$$\frac{54 + 27}{72 - 18}$$ = $$\frac{81}{54}$$ = $$\frac{3}{2}$$

= 1$$\frac{1}{2}$$

Try this quiz in in E-test/CBT Mode
switch to

Question Map