2012 - JAMB Mathematics Past Questions and Answers - page 1

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

\(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)

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

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

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

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

log₃x² = -8

x² = 3^-8

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

\((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)

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

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

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

= \(8\sqrt{6}\)

P = {2,3,5}

Q = {2,3}

P \(\cap\) Q = {2,3}

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

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