# Mathematics 2008 | Study Mode

Question 81
A
2t
B
2t - 1
C
$$\frac{2}{3}$$t + 1
D
2t - $$\frac{1}{3}$$
##### Explanation
$$\frac{t + 2t - 1 + t - 2 + 2t - 1 + 4t + 2t + 2}{6}$$

= $$\frac{12t - 2}{6}$$

= $$\frac {12t}{6}$$ - $$\frac{2}{6}$$

= 2t - $$\frac{1}{3}$$

Question 82
A
o
B
1
C
2
D
4
##### Explanation
0, 0, 1, 1, 2, 4, 4, 4, 4

median = 2

Question 83
A
3x + 3
B
3x + 1
C
2x + 5
D
2x + 1
Range = H - L

= 4x - (x - 1)

= 4x - x + 1

= 3x + 1

Question 84
A
1
B
2
C
5
D
7
##### Explanation
$$\begin{array}{c|c} x & f & fx & x - \bar{x} & f(x - \bar{x}) \\ \hline 2 & 1 & 2 & -3 & -3 & 3\\ 4 & 1 & 4 & -1 & 1 & 1\\ 5 & 1 & 5 & 0 & 0 & 0 \\9 & 1 & 9 & 4 & 4 & 4 \\ \hline & 4 & 20 & & & 8 \end{array}$$

x = $$\frac{\sum fx}{\sum fx}$$

= $$\frac{20}{4}$$

= 5

MD = $$\frac{\sum f(x - \bar{x})}{\sum f}$$

= $$\frac{8}{4}$$

= 2

Question 85
A
$$\frac{10!}{2!2!3!}$$
B
$$\frac{10!}{2!3!}$$
C
$$\frac{10!}{2!2!}$$
D
$$\frac{10!}{3!2!2!}$$
##### Explanation
Acceptance

$$\frac{10!}{3!2!2!}$$

Question 86
A
218
B
216
C
215
D
210
##### Explanation
$$^{10}C_{6}$$

$$\frac{10!}{(n - r)!r!}$$

n = 10, r = 6

= $$\frac{10!}{(10 - 6)!6!}$$

= $$\frac{10!}{4!6!}$$

= $$\frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1}$$

= 5 x 3 x 2 x 7

= 210

Question 87
A
$$\frac{1}{11}$$
B
$$\frac{2}{11}$$
C
$$\frac{3}{11}$$
D
$$\frac{4}{11}$$
##### Explanation
Obstruction

if a T is picked

p = $$\frac{2}{11}$$

Question 88
A
$$\frac{3}{10}$$
B
$$\frac{1}{5}$$
C
$$\frac{1}{6}$$
D
$$\frac{1}{10}$$
##### Explanation
$$\begin{array}{c|c}Number & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Frequency & 12 & 18 & x & 30 & 2x & 45\end{array}$$

12 + 18 + x + 30 + 2x + 45 = 150

3x + 105 = 150

3x = 150 - 105

3x = 45

x = $$\frac{45}{3}$$

x = 15

probability of 5 = $$\frac{30}{150}$$

= $$\frac{1}{5}$$

Question 89
A
100o
B
80o
C
50o
D
30o
##### Explanation
50 + 30 + y = 180

80 + y = 180

y = 100

180 + x = 180o

x = 180o - 100o

x = 80o

Question 90
A
90o
B
53o
C
36o
D
26o
##### Explanation
74 + x + x = 180

2x = 180 - 74

2x = 103

x = 53

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