Mathematics 2009 | Study Mode

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Question 81
A
4
B
3
C
2
D
1
Explanation
x(4 - x)

4x - x2

\(\frac{dy}{dx}\) = 4 - 2x

\(\frac{dy}{dx}\) = 0

2x = 4

x = \(\frac{4}{2}\)

= 2

Correct option: C
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Question 82
A
2.3 cm
B
4.0cm
C
5.2
D
g
Explanation
S = (t3 - t2 - t + 5)cm

\(\frac{ds}{dt}\) = 3t2 - 2t - 1

= (3t + 1)(t - 1)

t = -\(\frac{1}{3}\) or t = 1

Substitute value of t

s = (13 - 12 - 1 + 5)cm

= 4.0 cm

Correct option: B
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Question 83
A
sec\(\theta\) tan\(\theta\) + k
B
tan\(\theta\) + k
C
2 sec\(\theta\) + k
D
sec\(\theta\) + k
Explanation
\(\int\) sec2\(\theta\) d \(\theta\) = tan\(\theta\) + k

Correct option: B
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Question 84
A
180
B
120
C
110
D
40
Explanation

3x + 170 = 260

3x = 260 - 170

3x = 90 \(\to\) x = 30

for days \(\leq\) 4, we have

therefore, 40 + 30 + 50 =120

= 180


Correct option: B
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Question 85
A
4
B
3
C
2
D
1
Explanation
\(\begin{array}{c|c} x & f & fx\\ \hline 5 & 3 & 15\\ 8 & 2 & 16 \\ 6 & 4 & 24\\ k & 1 & k\\ & \sum f & \sum fx = 55 + k\end{array}\)

mean \(\bar{x}\) = \(\frac{55 + k}{10}\)

= 5.7

k = 2

Correct option: C
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Question 86
A
0.5
B
1
C
1.5
D
2
Explanation
deviation x - \(\bar{x}\)

x - 2 + 2x - 2 + (x + 1) - 2 + 3x - 2 = 0

x - 2 + 2x - 2 -2x - 2 + 3x - 2 = 0

= 4x - 8

4x = 8

x = \(\frac{8}{4}\)

= 2

Correct option: D
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Question 87
A
720
B
504
C
336
D
210
Explanation
\(\frac{n!}{n - r!}\) = \(\frac{9!}{9 - 3!}\)

= \(\frac{9!}{6!}\)

= 9 x 8 x 7

= 502

Correct option: B
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Question 88
A
15
B
28
C
30
D
45
Explanation
\(\frac{\begin{pmatrix} 8 \\ 3 \end{pmatrix}}{\begin{pmatrix} 4 \\ 1 \end{pmatrix}\begin{pmatrix} 4\\ 1\end{pmatrix}}\)(Two boys and a girl) OR \(\frac{\begin{pmatrix} 8 \\ 3 \end{pmatrix}}{\begin{pmatrix} 4 \\ 1 \end{pmatrix}\begin{pmatrix} 4\\ 1\end{pmatrix}}\)(Two girls and a boy in the committee)

\(\frac{336}{24}\) or \(\frac{336}{24}\)

14 + 14

= 28

Correct option: B
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Question 89
A
\(\frac{2}{3}\)
B
\(\frac{4}{9}\)
C
\(\frac{8}{27}\)
D
\(\frac{1}{27}\)
Explanation
p(pass) = \(\frac{2}{3}\)

p(fail) = \(\frac{1}{3}\)

p(pass at 5 marks) = \(\frac{1}{3}\) x \(\frac{1}{3}\) x \(\frac{1}{3}\)

= \(\frac{1}{27}\)

Correct option: D
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Question 90
A
\(\frac{3}{5}\)
B
\(\frac{2}{5}\)
C
\(\frac{7}{20}\)
D
\(\frac{1}{5}\)
Explanation
p (pass at 5mark) = \(\frac{12}{20}\)

= \(\frac{3}{5}\)

Correct option: A

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