2007 - JAMB Mathematics Past Questions and Answers - page 3

d = \(\sqrt{\frac{42W}{5L}}\), square both sides

= d² = \(\frac{42W}{5L}\)

cross multiply: 5d²L = 42W

divide both sides by 5d²

L = \(\frac{42W}{5d^2}\)

T₁ = \(\frac{3}{2}\) = \(\frac{5}{2}\) - 1

T₂ = 3 = 5 - 3

T₃ = 7 = 10 - 3 = 5.2 - 3

T₄ = 16 = 20 - 4 = 5.2² - 4

T₅ = 35 = 40 - 5 = 5.2³ - 5

T₆ = 74 = 80 - 6 = 5.2⁴ - 6

Tn = 5.2^{n - 2} - n

\(\begin{pmatrix} 3 & -2 \ -7 & 5\end{pmatrix}\) + 2\(\begin{pmatrix} -2 & 4 \ 3 & -1\end{pmatrix}\) = \(\begin{pmatrix} 3 & -2 \ -7 & 5\end{pmatrix}\) + \(\begin{pmatrix} -4 & 8 \ 6 & -2\end{pmatrix}\)

= \(\begin{pmatrix} 3 & -4 \ -7 & 6\end{pmatrix}\) + 2\(\begin{pmatrix} -2 & 8 \ 5 & -2\end{pmatrix}\)

= \(\begin{pmatrix}-1 & 6 \ -1 & 3\end{pmatrix}\)

p = {1, 3, 5, 7, 9, 11}, Q = {2, 4, 6, 8, 10, 12}

p ∩ Q = \(\phi\)

\(\frac{3}{5}\) \(\div\) (\(\frac{2}{7}\) x \(\frac{4}{3}\) \(\div\) \(\frac{4}{9}\)) = \(\frac{2}{3}\) \(\div\) (\(\frac{2}{7}\) x \(\frac{4}{3}\) x \(\frac{9}{4}\))

= \(\frac{3}{5}\) \(\div\) \(\frac{6}{7}\)

= \(\frac{3}{5}\) x \(\frac{7}{6}\)

= \(\frac{7}{10}\)

Let the cost price be C. For the profit of 5%, selling price = 105% C = N60,000

therefore C = \(\frac{100}{105}\) x N60,000

For a profit of 26%, the selling price = 126%C

= \(\frac{126}{100}\)C x \(\frac{100}{105}\) x N60,000

= N72,000

2(3^{2x - 1}) = 162, 3^{2x - 1} = 81

= 3⁴

2x - 1 = 4 , 2x = 5

x = \(\frac{5}{2}\)

1011²₂ - 101²₂ = (1011 - 101)₂ (1011 + 101)₄

= 110₂ x 10000₂

= 1100000₂

\(\sqrt{12} - \sqrt{147}\) + y\(\sqrt{3}\) = 0

\(\sqrt{4 \times 3 } - \sqrt{49 \times 3}\) + y\(\sqrt{3}\) = 0

y - 5 = 0

y = 5

\(\frac{(0.5625)^2 - (0.4375)^2}{0.04}\) = \(\frac{(0.5625 - 0.4375)(0.5625 - 0.4375)}{0.04}\)

= \(\frac{0.1250 \times 1}{0.04}\)

= \(\frac{12.50}{0.04}\)