## Mathematics | Study Mode

Question 31 Mathematics
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 32 Mathematics
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 Mathematics
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 Mathematics
A
B
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 Mathematics
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 Mathematics
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)

<QST = b$$_2$$ = 95$$^o$$

Question 37 Mathematics
A
Trapezium
B
Prism
C
Rectangle
D
Rhombus
Explanation.

No official Explanation yet!

Question 38 Mathematics
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 Mathematics
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 Mathematics
A
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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