# Mathematics 2008 | Study Mode

Question 51
A
42%
B
41%
C
40%
D
25%
##### Explanation

Question 52
A
$$\frac{3}{8}$$
B
$$\frac{2}{3}$$
C
$$\frac{3}{4}$$
D
$$\frac{3}{2}$$
##### Explanation
Simplify 16$$\frac{1}{2}$$ x 4$$\frac{1}{2}$$ x 27$$\frac{1}{3}$$

= 16$$\frac{1}{2}$$ x 4$$\frac{1}{2}$$ x 27$$\frac{1}{3}$$

= $$\frac{1}{\sqrt{16}^1} \times \frac{1}{\sqrt{4}^1}$$ x (3$$\sqrt{27}$$)1

= $$\frac{1}{4}$$ x $$\frac{1}{2}$$ x $$\frac{3}{1}$$

= $$\frac{3}{8}$$

Question 53
A
4
B
16
C
32
D
64
##### Explanation
$$logX^{\frac{1}{2}}$$ 64 = 3, find the value of X

recall that X = 10p

log10X = P

64 = $$X^{\frac{1}{2}}$$

43 = $$X^{\frac{1}{2}}$$

$$4^{3 \times \frac{1}{2}}$$ = $$X^{\frac{1}{2} \times \frac{1}{3}}$$

4 = $$X^{\frac{1}{2}}$$

(4)2 = $$X^{\frac{1}{2} \times 2}$$

x = 16

Question 54
A
(-3, -2)
B
(-2, 3)
C
(3, 2)
D
(2, -3)
##### Explanation
$$\frac{1 + \sqrt{2}}{1 - \sqrt{2}}$$ x $$\frac{1 + \sqrt{2}}{1 + \sqrt{2}}$$

= $$\frac{(1 + \sqrt{2}) (1 + \sqrt{2})}{(1 - \sqrt{2})(1 + \sqrt{2})}$$

= $$\frac{1 + \sqrt{2} + \sqrt{2} + (\sqrt{2})^2}{1 + \sqrt{2} - \sqrt{2} - (\sqrt{2})^2}$$

= $$\frac{1 + 2\sqrt{2} + \sqrt{2}}{1^2 - 2}$$

= $$\frac{3 + 2\sqrt{2}}{-1}$$

-3 - 2$$\sqrt{2}$$ = x + y$$\sqrt{2}$$

x = -3, y = -2

= (-3, -2)

Question 55
A
{1, 3}
B
{5,10}
C
$$\Phi$$
D
(4, 6)
##### Explanation
X = {n2 + 1 : n = 0, 2, 3}

y = {n + 1 : n = 2, 3, 4, 5}

find x y

x = (n2 + 1)(22 + 1)(32 + 1)

y = (2 + 1) (3 + 1)(5 + 1)

x = {1, 5, 10}

y = {3, 4, 6}

x y = $$\Phi$$

Question 56
A
$$\frac{9L^2}{16m^2P}$$
B
$$\frac{3L}{4m \sqrt{P}}$$
C
$$\frac {\sqrt{3L}}{4mP}$$
D
$$\frac{3L^2}{16m^2P}$$
##### Explanation
L = $$\frac {4}{3}$$ m $$\sqrt{PQ}$$

make Q the subject

$$\frac {L}{1}$$ = $$\frac {4}{3}$$ m $$\sqrt{PQ}$$

3L = 4m $$\sqrt{PQ}$$

Taking the square of both sides

(3L)2 = (4m $$\sqrt{PQ}$$)

$$\frac {9L^2}{16m^2P}$$ = $$\frac {16m^2PQ}{16m^2P}$$

Q = $$\frac {9L^2}{16m^2P}$$

Question 57
A
4
B
5
C
6
D
7

Question 58
A
(x + 5y)(7x + y)
B
(x + 5y)(7x - y)
C
(x - 5y)(7x + y)
D
(x - 5y)(7x -y)
##### Explanation
(4x + 3y)2 - (3x - 2y)2

= 16x2 + 24xy + 9y - (9x2 - 12xy + 4y2)

= 7x2 + 36xy + 5y

= 7x2 + xy + 35xy + 5y2

= (7x2 + xy) + (35xy + 5y2)

= x(7x + y) + 5y(7x + y)

= (7x + y)(x + 5y)

Question 59
A
30
B
21
C
16
D
12
##### Explanation
x - 3 x y2

x - 3 = ky2

when x = 5, y = 2

5 - 3 = k(2)2

2 = 4k

k = $$\frac{2}{4}$$

k = $$\frac{1}{2}$$

Find x when y = 6

from x - 3 = ky2

x - 3 = $$\frac{1}{2}$$ky2

x - 3 = $$\frac{1}{2}$$ x 36

x - 3 = 18

x = 18 + 3

x = 21

Question 60
A
$$\pm$$16
B
$$\pm$$8
C
$$\pm$$4
D
$$\pm$$2
##### Explanation
P $$\alpha$$ $$\frac{1}{q^2}$$

p = $$\frac{k}{q^2}$$

k = pq2

k = 8 x 42

k = 8 x 16 = 128

find k = pq2

q2 = $$\frac{k}{p}$$

q = $$\frac{k}{p}$$

q = $$\frac{128}{32}$$

q = 4

q = $$\pm$$2

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