Mathematics 2012 | Study Mode

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Question 11
A
-871
B
-781
C
-187
D
-178
Explanation
Hence f(x) = 2x3 - 11x2 + 8x - 1

f(-3) = 2(-3)3 - 11(-3)2 + 8(-3) - 1

= 2(-27) - 11(9) + 8(-3) - 1

= -54 - 99 - 24 - 1

= -178

Correct option: D
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Question 12
A
x = 0, y = -2
B
x = 0, y = 2
C
x = 2, y = 0
D
x = -2, y = 0
Explanation
x2 - y2 = 4 .... (1)
x + y = 2 .... (2)

Simplify eqn (1)

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

From eqn (2)
x + y = 2 so substitute it into simplified eqn (1), we have

2 (x - y) = 4

therefore,
x - y = 2 ... (1)
x + y = 2
---------
2x = 4
---------

x = 2, when y = 0

Correct option: C
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Question 13
A
\(\sqrt{17}\)
B
\(\frac{4}{3}\)
C
\(\frac{8}{3}\)
D
\(\frac{2}{3}\)
Explanation
y \(\alpha \sqrt{n}\)

y = k\(\sqrt{n}\)

when y = 4, n = 4
4 = k\(\sqrt{4}\)

4 = 2k

k = 2

Therefore,

y = 2\(\sqrt{n}\)

y = 2\(\sqrt{\frac{16}{9}}\)

y = 2\((\frac{4}{3})\)

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

Correct option: C
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Question 14
A
24
B
27
C
32
D
36
Explanation
U \(\alpha \frac{1}{V^3}\)

U = \(\frac{k}{V^3}\)

k = UV3

k = 81 x 23 = 81 x 8

When V = 3,

U = \(\frac{k}{V^3}\)

U = \(\frac{81 \times 8}{3^3}\)

U = \(\frac{81 \times 8}{27}\) = 24

Correct option: A
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Question 15
A
\(y > \frac{2}{3}\)
B
\(y < \frac{2}{3}\)
C
\(y > -\frac{2}{3}\)
D
\(y < -\frac{2}{3}\)
Explanation
\(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\)

Collect like terms

\(\frac{y}{5} - \frac{y}{2} < \frac{2}{5} - \frac{1}{5}\)

\(\frac{2y - 5y}{10} < \frac{2 - 1}{5}\)

\(\frac{-3y}{10} < \frac{1}{5}\)

\(y > \frac{-2}{3}\)

Correct option: C
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Question 16
A
2 < m < 5
B
-3 < m < 4
C
3 < m < 4
D
-4 < m < 3
Explanation
(m - 3)(m - 4) < 0

(m - 3) < 0 ; (m - 4) < 0

m < 3 ; m < 4

3 < m < 4

Correct option: C
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Question 17
A
24
B
23
C
-24
D
-25
Explanation
n2 - 6n - 4

For the 3rd term,
32 - 6(3) - 4

9 - 18 -4 = -13

For the 4th term,
42 - 6(4) - 4

16 - 24 - 4 = -12

Sum of both terms

-13 - 12 = -25

Correct option: D
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Question 18
A
\(-\frac{1}{5}\)
B
\(-\frac{1}{4}\)
C
\(-\frac{1}{3}\)
D
\(-\frac{1}{2}\)
Explanation
Sr = \(\frac{a}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8} \times \frac{1}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8(1 - r)}\)

\(-\frac{1}{10}\) = \(\frac{1}{8 - 8r}\)

cross multiply...

-1(8 - 8r) = -10

-8 + 8r = -10

8r = -2

r = -1/4

Correct option: B
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Question 19
A
11
B
13
C
15
D
22
Explanation
p * q = pq + p - q

First execute for 3 * 4

==> 3(4) + 3 - 4 = 12 + 3 - 4 = 11

Now we execute for 2 * 11

==> 2(11) + 2 - 11 = 22 + 2 - 11 = 13

Correct option: B
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Question 20
A
\(-\frac{4}{5}\)
B
\(-\frac{2}{5}\)
C
4
D
5
Explanation
m \(\propto\) n = \(\frac{mn}{2} - a\)

Identify = e = 2

a \(\propto\) a-1 = e

a \(\propto\) a-1 = 2

-5 \(\propto\) a-1 = 2

\(\frac{-5 \times a^{-1}}{2} = 2\)

\(a^{-1} = \frac{2 \times 2}{-5}\)

\(a^{-1} = -\frac{4}{5}\)

Correct option: A

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