Mathematics 2008 | Study Mode

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

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Correct option: A
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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 \(\frac{3}{1}\)

= \(\frac{3}{8}\)

Correct option: A
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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

Correct option: B
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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)

Correct option: A
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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 = \(\Phi\)

Correct option: C
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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 = \(\frac {9L^2}{16m^2P}\)

Correct option: A
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Question 57
A
4
B
5
C
6
D
7
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: B
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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)

Correct option: A
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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

Correct option: B
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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

Correct option: D

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