# Mathematics 2009 | Study Mode

Question 1
A
11219
B
21129
C
21139
D
22119

Question 2
A
5
B
6
C
7
D
10
##### Explanation
5*X1 + 5*Xo + 5*X1 + 2*Xo = 77 (change to base 10)
5*X + 5*1 + 5*X + 2*1 = 77
5X + 5 + 5X + 2 = 77
10X + 7 = 77
10X = 77-7
10X = 70
X = 70/10
X = 7

Question 3
A
4
B
41/6
C
45/6
D
51/6
##### Explanation
$$7\frac{1}{12}-4\frac{3}{4}+2\frac{1}{2}=5\left(\frac{1-9+6}{12}\right)\\ 5\left(\frac{-2}{12}\right)\\ =4\left(\frac{12-2}{12}\right)$$
(carry one from 5 and call it 12)
$$4\frac{10}{12}\\ =4\frac{5}{6}$$

Question 4
A
6.24
B
3.22
C
2.78
D
2.13
##### Explanation
$$\frac{81.81 + 99.44}{20.09 + 36.16}\\ =\frac{181.25}{56.25}\\ =\frac{18125}{5625}\\ \frac{29}{9}\\ =3\frac{2}{9}\\ 3.22$$

Question 5
A
N37,550
B
N40,400
C
N41,400
D
N42,400
##### Explanation
C.P = N34000 + N2000 = N36000
Gain = 100 + 15 = 115%
S.P = $$\frac{115}{100}\times \frac{N3600}{1}$$
= N41400

Question 6
A
7/15
B
8/15
C
2/5
D
4/5

Question 7
A
1/3
B
1/6
C
-1/5
D
-1/3
##### Explanation

52(x-1) x 5(x-1) = 0.04
52x-2 x 5x-1 = 4/100
52x-2 + x-1 = 1/25
53x-3 = 1/52
53x-3 = 5-2 (Equating the indices)
3x-3 = -2
3x = -2+3
3x = 1
X = 1/3

Question 8
A
3.4471
B
2.4471
C
1.4471
D
1.4071
##### Explanation
Log 2 = 0.3010, Log 7 = 0.8451
Log 280 = Log 28 x 10
= Log 7x4x10
=Log7 + Log4 + Log10
= Log7 + Log22 + Log10
= Log7 + 2Log2 + Log10
= 0.8451 + 2(0.3010) + 1
= 0.8451 + 0.6020 + 1
= 2.4471

Question 9
A
17-7
B
4-7
C
15+7
D
7-7
##### Explanation
$$\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\\ =\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\\ =\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\\ =\frac{8-2\sqrt{7}}{2}$$
Factorize then divide by 2
$$=\frac{2(4-\sqrt{7}}{2}\\ =4-\sqrt{7}$$

Question 10
A
{5,10}
B
{5, 10, 15}
C
{2, 5, 10}
D
{5, 10, 15, 20}
##### Explanation
X = {n2+1:n is a positive integer and 1 $$\leq$$ n $$\leq$$ 5}
Implies X = {2, 5, 10, 17, 26} i.e. put n= 1, 2, 3, 4 and 5
Y = {5n:n is a positive integer and 1 $$\leq$$ n $$\leq$$ 5}
Put X = 1, 2, 3, 4, and 5
Y = {5, 10, 15, 20, 25}
X $$\cap$$ Y = {2, 5, 10, 17, 26} $$\cap$$ {5, 10, 15, 20, 25}
= {5, 10}

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