# Mathematics 2008 | Study Mode

Question 1
A
1110112
B
1101102
C
1010112
D
1010102
##### Explanation
11012 + 101112 + 1112 = 101011

Question 2
A
2
B
3
C
4
D
5
##### Explanation
125x = 20
1xX2 + 2xX1 + 5xX0 = 20
X2 + 2X + 5 = 20
X2 + 2X - 15 = 0
(X + 5)( X - 3) = 0
X + 5 implies X = -5
X - 3 implies X = 3
But X cannot be negative
X = 3

Question 3
A
1/4
B
1/3
C
1/2
D
1
##### Explanation
$$\frac{\left(\frac{3}{8}\div\frac{1}{2}+\frac{1}{2}\right)}{\left(\frac{1}{8}\times\frac{2}{3}+\frac{1}{3}\right)}\\ =\frac{\left(\frac{3}{8}\times\frac{2}{1}+\frac{1}{2}\right)}{\left(\frac{1}{8}\times\frac{2}{3}+\frac{1}{3}\right)}\\ =\frac{\left(\frac{3}{4}-\frac{1}{3}\right)}{\left(\frac{1}{12}+\frac{1}{3}\right)}\\ =\left(\frac{9-4}{12}\right)\div\left(\frac{1+4}{12}\right)\\ =\left(\frac{5}{12}\right)\div\left(\frac{5}{12}\right)\\ =\frac{5}{12}\times\frac{12}{5}\\ =1$$

Question 4
A
123000
B
124000
C
125000
D
126000

Question 5
A
N3,000
B
N600
C
N300
D
N150
##### Explanation

$$I = \frac{P \times T \times R}{100}\\ =\frac{7500 \times 8 \times 5}{100}\\ =N3000$$

Question 6
A
42%
B
41%
C
40%
D
25%
##### Explanation
N85 - N60 = N25 increase
percentage increase = $$\frac{25}{60}\times \frac{100}{1}\\=\frac{125}{3}\\=41.67%\\ =42%$$

Question 7
A
3/8
B
2/3
C
3/4
D
3/2
##### Explanation
$$16^{\frac{-1}{2}}\times 4^{\frac{-1}{2}} \times 27^{\frac{1}{3}}\\ =\frac{1}{16^{\frac{1}{2}}}\times \frac{1}{4^{\frac{1}{2}}}\times 27^{\frac{1}{3}}\\ =\frac{1}{\sqrt{16}} \times \frac{1}{\sqrt{4}} \times sqrt[3]{27}\\ =\frac{1}{4} \times \frac{1}{2} \times \frac{3}{1}\\ = \frac{3}{8}$$

Question 8
A
4
B
16
C
32
D
64
If logx1/264 = 3
(X 1/2)3 = 64
(X 1/2)3 = 4 3
X 1/2 = 4
X = 42
X = 16

Question 9
A
(-3, -2)
B
(-2, 3)
C
(3,2)
D
(2,-3)
##### Explanation
$$\frac{1+\sqrt{2}}{1-\sqrt{2}} \times \frac{1+\sqrt{2}}{1+\sqrt{2}}\\ =\frac{1+(1+\sqrt{2})+\sqrt{2}(1+\sqrt{2})}{1^2 - (\sqrt{2})^2}\\ =\frac{(1+\sqrt{2}+\sqrt{2}+2)}{1-2}\\ =\frac{3+2\sqrt{2}}{-1}\\ =-3-2\sqrt{2}\\ X and Y = -3 and -2$$

Question 10
A

{1,3}

B

{5,10}

C

{}

D

{4,6}

##### Explanation

X = {1,5,10}
Y = {3,4,6}
XY ={}

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