# Mathematics 2009 | Study Mode

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

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

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

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

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

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

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

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

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 $$\frac{1}{3}$$

= $$\frac{1}{27}$$

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

= $$\frac{3}{5}$$

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