Mathematics (2015) | Study Mode

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Question 51
A

\(10 \sqrt{3}\)

B

\(5 \sqrt{3}\)

C

\(20 \sqrt{3}\)

D

\(15 \sqrt{3}\)

Explanation

\(\sqrt{30} \times\sqrt{40}\)

\(\sqrt{30} \times \sqrt{40}\)

\(\sqrt{3 \times 10 \times 4 \times 10}\)

\(\sqrt{400 \times 3}\)

\(\sqrt{400 \times 3}\)

\(20 \times \sqrt{3}\)

\(20 \sqrt{3}\)


Correct option: C
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Question 52
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


Correct option: B
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Question 53
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


Correct option: C
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Question 54
A

10.3cm2

B

15.7cm2

C

50.3cm2

D

17.4cm2

Explanation

Area of a circle (A) = r2

Radius = 4cm

= 3.142

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

= 3.142 \(\times\) 16

= 50.272

A = 50.3cm2 (1dp)


Correct option: C
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Question 55
A

10.5cm

B

5cm

C

10cm

D

12cm

Explanation

The area of an ellipse (e) =ab/4

Let a rep. the length of its major axis = 14cm

Let b rep. the length of its minor axis = ?

= 3.142

Area of an ellipse = 132cm2

132 = (14 \(\times\) b) 4

132 = (3.142 \(\times\) 14b) 4

3.142 \(\times\) 14b =132 \(\times\) 4

b = (1324 \(\times\) 4) (3.142 \(\times\) 14)
= 528/43.988

= 12cm

The length of its minor axis (b) = 12cm


Correct option: D
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Question 56
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

Correct option: D
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Question 57
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} \)


Correct option: B
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Question 58
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


Correct option: C
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Question 59
A
N100
B
N20
C
N80
D
N150
Explanation
25% of N80 = 25/100 \(\times\) 80

= N20.00

Correct option: B
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Question 60
A
7.51
B
7.71
C
5.5
D
7.55
Explanation
2.04 x 3.7
=
204
x 37
-----
7548 = 7.548

= 7.55(2dp)

Correct option: D

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