2008 - JAMB Mathematics Past Questions and Answers - page 1

1101₂ + 10111₂ + 111₂ = 101011

125_x = 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

\(\frac{\left(\frac{3}{8}\div\frac{1}{2}+\frac{1}{2}\right)}{\left(\frac{1}{8}\times\frac{2}{3}+\frac{1}{3}\right)}\\ =\frac{\left(\frac{3}{8}\times\frac{2}{1}+\frac{1}{2}\right)}{\left(\frac{1}{8}\times\frac{2}{3}+\frac{1}{3}\right)}\\ =\frac{\left(\frac{3}{4}-\frac{1}{3}\right)}{\left(\frac{1}{12}+\frac{1}{3}\right)}\\ =\left(\frac{9-4}{12}\right)\div\left(\frac{1+4}{12}\right)\\ =\left(\frac{5}{12}\right)\div\left(\frac{5}{12}\right)\\ =\frac{5}{12}\times\frac{12}{5}\\ =1\)

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

N85 - N60 = N25 increase
∴percentage increase = \(\frac{25}{60}\times \frac{100}{1}\=\frac{125}{3}\=41.67%\\ =42%\)

\(16^{\frac{-1}{2}}\times 4^{\frac{-1}{2}} \times 27^{\frac{1}{3}}\\ =\frac{1}{16^{\frac{1}{2}}}\times \frac{1}{4^{\frac{1}{2}}}\times 27^{\frac{1}{3}}\\ =\frac{1}{\sqrt{16}} \times \frac{1}{\sqrt{4}} \times sqrt[3]{27}\\ =\frac{1}{4} \times \frac{1}{2} \times \frac{3}{1}\\ = \frac{3}{8}\)

If log_x¹/264 = 3
(X ¹/₂)³ = 64
(X ¹/₂)³ = 4 ³
X ¹/₂ = 4
X = 4²
X = 16

\(\frac{1+\sqrt{2}}{1-\sqrt{2}} \times \frac{1+\sqrt{2}}{1+\sqrt{2}}\\ =\frac{1+(1+\sqrt{2})+\sqrt{2}(1+\sqrt{2})}{1^2 - (\sqrt{2})^2}\\ =\frac{(1+\sqrt{2}+\sqrt{2}+2)}{1-2}\\ =\frac{3+2\sqrt{2}}{-1}\\ =-3-2\sqrt{2}\\ ∴X and Y = -3 and -2\)

X = {1,5,10}
Y = {3,4,6}
X∩Y = ∅