# Mathematics 2018 | Study Mode

Question 31
A
$$\frac{|PN|}{|PR|}$$
B
$$\frac{|PM|}{|PQ|}$$
C
$$\frac{|PM|}{|PR|}$$
D
$$\frac{|PR|}{|PQ|}$$
##### Explanation

$$\frac{|PN|}{|PQ|}$$ = $$\frac{|PM|}{|PR|}$$

Question 32
A
If p is true and q is true
B
If p is true and q is false
C
If p is false and q is false
D
If p is false and q is true
##### Explanation

From the truth table above, p $$\to$$ q would be false if p is true and q is false

Question 33
A
0.0
B
0.5
C
1.0
D
1.5
##### Explanation

First arrange the numbers in ascending order of magnitude; 0, 0, 1, 1, 1, 1, 2, 2, 3, 4

Counting from the right, the fifth number is 1

Counting from the left, the fifth number is 1

Hence, median = $$frac{1 + 1}{2}$$

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

= 1

Question 34
A
8
B
9
C
10
D
12
##### Explanation

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

= $$\frac{350}{10}$$

= 35

= $$\frac{\sum f |d|}{\sum f}$$

= $$\frac{90}{10}$$

= 9

Question 35
A

63$$^o$$

B

117$$^o$$

C

126$$^o$$

D

234$$^o$$

##### Explanation

In the diagram,

$$\alpha$$ = 180$$^o$$ - 177$$^o$$ (angles on a straight line)

$$\alpha$$ = 63$$^o$$

t = 2 x 63$$^o$$ (angle at centre = 2 x angle at circum)

= 126$$^o$$

Question 36
A

40$$^o$$

B

65$$^o$$

C

85$$^o$$

D

95$$^o$$

##### Explanation

In the diagram,

a = 50$$^o$$ (alternate angles)

b$$_1$$ + a 35$$^o$$ = 180$$^o$$ (sum of angles on a straight line)

i.e; b$$_1$$ + 50$$^o$$ + 35$$^o$$

= 180v

b$$_1$$ + 180$$^o$$ - 85$$^o$$ = 90$$^o$$

But b$$_2$$ = $$b_1$$ = 95$$^o$$ (angles in alternate segement)

Question 37
A

Trapezium

B

Prism

C

Rectangle

D

Rhombus

##### Explanation

Question 38
A

110$$^o$$

B

135$$^o$$

C

165$$^o$$

D

225$$^o$$

##### Explanation

In the diagram,

Thus, m = 2 x 55$$^o$$ (is a bisector of obtuse

m = 110$$^o$$

n = $$\frac{1}{2}$$ x 110$$^o$$ (angle at centre = 2 x angle at circum)

n = 55$$^o$$

= 165$$^o$$

Question 39
A

25cm$$^2$$

B

24cm$$^2$$

C

16cm$$^2$$

D

12cm$$^2$$

##### Explanation

Area of shaded part = 2 x area of $$\bigtriangleup$$SPQ

= 2 x $$\frac{1}{2}$$ 8 x 3 =24cm

Hence, area of the unshaded part of the rectangle = area of rectangle - area of shaded part

= 8 x 6 - 24

= 48 - 24

= 24 cm$$^2$$

Question 40
A

i

B

ii

C

iii

D

iv

##### Explanation

x + 2 $$\geq$$ 2x + 1

x - 2x $$\geq$$ 1 - 2

-x $$\geq$$ -1

$$\frac{-x}{-1}$$ $$\geq$$ $$\frac{-1}{-1}$$

x $$\leq$$ 1

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