Mathematics 2012 | Study Mode

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Question 1
A
2211 
B
2121 
C
1212 
D
1122 
Explanation.
Share Answer First, convert to base 10

726 = (7 x 61) + (2 x 60)

= 42 + 2

= 4410

\(\begin{array}{c|c} 3 & 44 \\ \hline 3 & 14 & r 2 \\ \hline 3 & 4 & r 2 \\ \hline 3 & 1 & r 1 \\ \hline 3 & 0 & r 1 \end{array}\)

Ans = 1122 = D

Correct Option:
D
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Question 2
A
\(1\frac{1}{4}\) 
B
\(1\frac{1}{6}\) 
C
\(\frac{5}{6}\) 
D
\(\frac{4}{5}\) 
Explanation.
Share Answer \(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)

\(\frac{8}{3} \times \frac{3}{2} \div \frac{24}{5}\)

\(\frac{8}{3} \times \frac{3}{2} \times \frac{5}{24}\)

\(\frac{5}{6}\)

Correct Option:
C
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Question 4
A
N525 
B
N1,025 
C
N1,950 
D
N2,975 
Explanation.
Share Answer Amount spent on children = \(\frac{15}{100} \times 3500 = N525\)

Amount spent = Amount on children + Additional amount on food

Amount Spent = N525 + N1950 = N2475

Therefore amount left = N3,500 - N2,475 = N1,025

Correct Option:
B
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Question 6
A
\(\frac{1}{3}\) 
B
\(\frac{1}{9}\) 
C
\(\frac{1}{27}\) 
D
\(\frac{1}{81}\) 
Explanation.
Share Answer log3x2 = -8

x2 = 3-8

x = \(3^{-8 \times \frac{1}{2}}\)

x = 3-4

x = \(\frac{1}{3^4}\)

x = \(\frac{1}{81}\)

Correct Option:
D
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Question 7
A
\(2\sqrt{6}\) 
B
\(4\sqrt{6}\) 
C
\(8\sqrt{6}\) 
D
\(16\sqrt{6}\) 
Explanation.
Share Answer \((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)

= \([(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]\)

= \((\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]\)

= \((2\sqrt{6})(4)\)

= \(8\sqrt{6}\)

Correct Option:
C
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Question 9
A
B
C
D
Explanation.
Share Answer n(f \(\cap\) v) + n(f) + n(v) + n(f \(\cap\) v) = 46

3 + 19 + 23 + x = 46

22 + 23 + x = 46

45 + x = 46

x = 46 - 45

x = 1

Correct Option:
A
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Question 10
A
\(\frac{1}{c}(\frac{w - 2v}{v + w})\) 
B
\(\frac{1}{c}(\frac{w - 2v}{v - w})\) 
C
\(\frac{1}{c}(\frac{w + 2v}{v - w})\) 
D
\(\frac{1}{c}(\frac{w + 2v}{v + w})\) 
Explanation.
Share Answer w = \(\frac{v(2 + cn)}{1 - cn}\)

2v + cnv = w(1 - cn)

2v + cnv = w - cnw

2v - w = -cnv - cnw

Multiply through by negative sign

-2v + w = cnv + cnw

-2v + w = n(cv + cw)

n = \(\frac{-2v + w}{cv + cw}\)

n = \(\frac{1}{c}\frac{-2v + w}{v + w}\)

Re-arrange...

n = \(\frac{1}{c}\frac{w - 2v}{v + w}\)

Correct Option:
A
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