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 = ∅