# Mathematics (2015) | Study Mode

Question 51
A

$$10 \sqrt{3}$$

B

$$5 \sqrt{3}$$

C

$$20 \sqrt{3}$$

D

$$15 \sqrt{3}$$

##### Explanation

$$\sqrt{30} \times\sqrt{40}$$

$$\sqrt{30} \times \sqrt{40}$$

$$\sqrt{3 \times 10 \times 4 \times 10}$$

$$\sqrt{400 \times 3}$$

$$\sqrt{400 \times 3}$$

$$20 \times \sqrt{3}$$

$$20 \sqrt{3}$$

Question 52
A
x = 5 or 1
B
x = 7 or 1
C
x = 7 or 0
D
x = 7 or ? 2
##### Explanation
Let x represent the first number;

Then, the other is (5 ? x) , since their sum is 5 and their product is 14

x(5 ? x) = 14

5x ? x2 = 14

x2 ? 5x ? 14 = 0

(x2 ? 7x) + (2x ? 14) = 0

x(x ? 7) + 2(x ? 7) = 0

(x ? 7)(x + 2) = 0

Either (x ? 7) = 0 or (x + 2) = 0

x = 7 or x = ? 2

The two numbers are 7 and ? 2

Question 53
A

3/-2

B

-7/4

C

4/6

D

7/4

##### Explanation

$$5^{(x - 2)} = (125^{-1} )^{(x + 3)}\\ 5^{(x - 2)} = (5- 3)^{x + 3}\\ 5^{(x - 2)} = 5^{- 3x - 9}\\ x + 3x = - 9 + 2\\ 4x = - 7\\ x = \frac{-7}{4}$$

Question 54
A

11112

B

110112

C

101112

D

110012

##### Explanation

Convert the binary to base 10 and they convert back to base two

100112 + xxxxx2 + 111002 + 1012 = 10011112

(1 $$\times$$ 24 + 0 $$\times$$ 23 + 1 $$\times$$ 22 + 1 $$\times$$ 21 + 1 $$\times$$ 20) + xxxxx2 +(1 $$\times$$ 24 + 1 $$\times$$ 23 + 1 $$\times$$ 22 + 0 $$\times$$ 21 + 0 $$\times$$ 20) + (1 $$\times$$ 22 + 0 $$\times$$ 21 + 1 $$\times$$ 20)

= (16 + 0 + 0 + 2 + 1) + xxxxx2 + (16 + 8 + 4 + 0 + 0 ) + (4 + 0 + 1)

=(64 + 0 + 0 + 8 + 4 + 2 + 1)

19 + xxxxx2 + 33 = 79

xxxxx2 + 52 = 79

xxxxx2 = 79 - 52

xxxxx2 = 2710

$$\begin{array}{c|c} 2 & 27 \\ \hline 2 & 13 \text{ rem 1}\\ 2 & 6 \text{ rem 1}\\ 2 & 3 \text{ rem 0}\\ 2 & 1 \text{ rem 1}\\ & 0 \text{ rem 1}\\ \end{array}\uparrow$$

2710 = 110112

Therefore xxxxx2 = 2710 = 110112

Question 55
A

17.1cm2

B

27.2cm2

C

47.1cm2

D

37.3cm2

##### Explanation

Find the slant height

$$l^2 = h^2 + r^2(h = 4cm,r = 3cm)$$

$$l^2 = 4^2 + 3^2 = 16 + 9 = 25$$

$$l^2 = 25$$

Squaring both sides

l = 5cm

The area of curved surface (s) =(3)(5)

15= 15 $$\times$$ 3.14

= 47.1cm2

Question 56
A

4

B

5

C

6

D

3

##### Explanation

Each exterior angle = 180 -120=60

Exterior angle =360/n

60 = 360/n

n =360/6

= 6

Question 57
A
N100
B
N20
C
N80
D
N150
##### Explanation
25% of N80 = 25/100 $$\times$$ 80

= N20.00

Question 58
A
7.51
B
7.71
C
5.5
D
7.55
2.04 x 3.7
=
204
x 37
-----
7548 = 7.548

= 7.55(2dp)

Question 59
A

3%

B

2%

C

4%

D

1%

##### Explanation

Let assume the cost price is 100%

Marked up price + cost price = 20 + 100 = 120%

Discount at 20% = 20/100 $$\times$$ 120 % of cost price

Selling price = cost price - gain

= (120 - 24)% of cost price

= 96% of cost price

Loss = (100- 96)% of cost price

= 4% of cost price

- He will wake 4% loss

Question 60
A

10.3cm2

B

15.7cm2

C

50.3cm2

D

17.4cm2

##### Explanation

Area of a circle (A) = r2

= 3.142

A = 3.142 $$\times$$ (4)2

= 3.142 $$\times$$ 16

= 50.272

A = 50.3cm2 (1dp)

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