# Mathematics (2015) | Study Mode

Question 51
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)

Question 52
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

Question 53
A

157cm3

B

155cm3

C

175cm3

D

145cm3

##### Explanation

V = 1/3r2 h

Volume of a cone (Vc) = 1/3 $$\times$$ 3.14 $$\times$$ (5)2 $$\times$$ 6

= 156.9cm3

157cm3

Question 54
A

1/2

B

1/3

C

2/5

D

3/4

##### Explanation

Prob.(A outcome) = $$\frac{1}{6}$$, Prob.(B outcome) =

P(A B) = 1/12, Prob.(A $$\cup$$ B)

Prob.(A $$\cup$$ B) = Prob.(A) + Prob.(B) $$\cup$$ Prob.(A B)

1/6 + 1/4 + 1/12

= (2 + 3 ? 1) 12

= 4/12

= 1/3

Prob.(A $$\cup$$ B) = 1/3

Question 55
A
16
B
8
C
10
D
12
##### Explanation
Z has 4 elements, power = number of subset = 2p

Z = 2n = 24

= 16

Question 56
A

x = 1, y = 1/2

B

x = 2, y = 1/2

C

x =0, y = 1

D

x = 2, y = 1

##### Explanation

$$27^x 81^{(x + 2y)} = 9$$

$$27^x = 9 \times 81^{(x+2y)}$$

$${(3^{3} )}^x =32 \times 3^{4(x + 2y)}$$

$$=3^{(2 + 4x + 8y)}$$

$$3^{3x} = 3^{ (2 + 4x + 8y)}$$

3x = 2 + 4x + 8y

3x - 4x - 8y = 2 ----- (1)

x + 4y = 0 ------- (2)

- 4y = 2

y = (- 2) 4 = -

y = -

Substitute the value of y into equation (2)

i.e x + 4y = 0

x + 4( - 1/2) = 0

x - 2 = 0

x = 2

- x = 2,y = -

Method II

$$27^x 31^{(x + 2y) }= 9$$

3^{3x} $$\times$$ $$3^{( - 4x - 8y)} = 32$$

$$3^{(3x - 8y)} = 32$$

- x - 8y=2 ---- (1)

x + 4y = 0 ----- (2)

- 4 = 2

y= 2/4 =

y =

Substitute the value of y into equation 2

x + 4y=0

x + 4 (- 1) 2) = 0

x - 2 = 0

x = 2

x = 2, y =

Question 57
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 58
A

x = 1 twice

B

x = 0 or 1

C

x = 3 or 1

D

x = 2 twice

##### Explanation

-(2x + 2 ) - -x = 1

-(2x + 2) = 1 + -x

Square both sides

-(2x + 2)2 = (1 + -x)2

((2x + 2)2) = 1 + -x + -x+ x

2x + 2 = 1 + 2-x +x

Collect the like term together

2x - x + 2 - 1 = 2 -x
x + 1 = 2-x

Square both sides

(x + 1)2 = (2-x)2

x2 + 2x + 1 = 4x

x2 + 2x - 4x + 1 = 0

(x2- x)(x + 1)= 0

x(x - 1) -1(x - 1)

(x - 1)(x -1)

Either (x - 1) = 0 or (x - 1) = 0

x = 1 or 1

x = 1 twice

Question 59
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 60
A

3/-2

B

-7/4

C

4/6

D

7/4

##### Explanation

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

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