# Mathematics 2009 | Study Mode

Question 41
A
2/3
B
4/9
C
8/27
D
1/27
##### Explanation
P(pass) = 2/3
P(not pass) = 1 - 2/3 = 1/3
P(not passing any of the 3 Exams) = 1/3 x 1/3 x 1/3
= 1/27

Question 42
A
100m
B
753 m
C
1003m
D
2003m
##### Explanation
 Tan 60 = 300 x

 x = 300 Tan 60

 x = 300 3

x = (300/3) x (3/3)
 x = 3003 .....3

x = 1003

Question 43
A
15
B
28
C
30
D
45

Question 44
A
720
B
504
C
336
D
210
##### Explanation
 9P3 = _9! ways (9-3)!

 = 9! 6!

 = 9x8x7x6! ___6!

= 504 ways

Question 45
A
11219
B
21129
C
21139
D
22119
##### Explanation
You borrow 1 which transforms to 9, because of it's base

1863099
-164189
________
22119
________

Question 46
A
5
B
6
C
7
D
10
##### Explanation
5 x X1 + 5 x XO + 5 x X1 + 2 x XO = 77

5X + 5 + 5X + 2 = 77

10X + 7 = 77

10X = 77 - 7

10X = 70

X = $$\frac{70}{10}$$

= 7

Question 47
A
4
B
4$$\frac{1}{6}$$
C
4$$\frac{5}{6}$$
D
5$$\frac{1}{6}$$
##### Explanation
7$$\frac{1}{12}$$ - 4$$\frac{3}{2}$$ + 2$$\frac{1}{2}$$

Take care of the whole numbers

7 - 4 + 2 = 5

therefore, 5$$\frac{1}{12}$$ - $$\frac{3}{4}$$ + $$\frac{1}{2}$$

LCM = 12

5$$\frac{1 - 9 + 6}{12}$$

4$$\frac{13 - 9 + 6}{12}$$

= 4$$\frac{10}{12}$$

or = 4$$\frac{5}{6}$$

Question 48
A
6.21
B
3.22
C
2.78
D
2.13
##### Explanation
$$\frac{81.81 + 99.44}{20.09 + 36.16}$$

= $$\frac{181.25}{56.25}$$

= 3.22

Question 49
A
$$\frac{7}{16}$$
B
$$\frac{8}{15}$$
C
$$\frac{2}{3}$$
D
$$\frac{4}{5}$$
##### Explanation
Spent $$\frac{1}{5}$$ on books remaining $$\frac{4}{5}$$

spent $$\frac{1}{3}$$ of $$\frac{4}{5}$$ on food

$$\frac{4}{5}$$ x $$\frac{1}{3}$$ = $$\frac{4}{15}$$

therefore, $$\frac{4}{5}$$ - $$\frac{4}{15}$$

= $$\frac{12 - 4}{15}$$

= $$\frac{8}{15}$$

Question 50
A
2.3 cm
B
4.0 cm
C
5.2 cm
D
6.0 cm
##### Explanation
S = t3 - t2 - t + 5
ds/dt = 3t2 - 2t - 1
As ds = 0
3t2 - 2t - 1 = 0
(3t+1)(t-1) = 0
t = 1 or -1/3
At min pt t = -1/3
S = t3 - t2 - t + 5 put t = -1/3
= (-1/3)3 - (-1/3)2 - (-1/3) + 5
= -1/27 - 1/9 + 1/3 + 5
= 140 / 27
= 5.2

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