JAMB Mathematics Past Questions & Answers - Page 283

8x^-2 = \(\frac{2}{25}\)

= 200x^-2 = 2

= 100x^-2 = 1

x^-2 = \(\frac{1}{100}\)

x^-2 = 10^-2

x = 10

\(\frac{log_5 0.04}{log_3 18 - log_3 2}\)

= \(\frac{log_5 0.04}{log_3(\frac{18}{2})}\)

= \(\frac{log_5 0.04}{log_3 9}\)

= \(\frac{-2}{2}\)

= -1

Let log₅ 0.04 = x

5x = 0.04

x = \(\frac{4}{100}\) = 5^-2

Let log₃ 9 = z

3² = 3²

z = 3

\(\frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4}\)

= \(\frac{36}{420} \times \frac{54}{90} \times \frac{63}{240}\)

= \(\frac{6}{70} \times \frac{18}{30} \times \frac{21}{80}\)

= \(\frac{27}{2000}\)

= 0.0135

\(\approx\) = 0.014

\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\)

\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} - \frac{10}{10} + \frac{3}{4})]\)

= \(\frac{1}{3} \div [\frac{5}{7}(\frac{-1}{10} + \frac{3}{4})]\)

= \(\frac{1}{3} \div [\frac{5}{7}(\frac{-2 + 15}{20})]\)

= \(\frac{1}{3} \div [\frac{5}{7} \times \frac{13}{20}]\)

\(\frac{1}{3} + [\frac{13}{28}]\) = \(\frac{1}{3} \times \frac{28}{13}\)

= \(\frac{28}{39}\)

Let the sum of the 12 numbers be x and the 13th number be y.

\(\frac{x}{12} = 3 \implies x = 36\)

\(\frac{36 + y}{13} = 5 \implies 36 + y = 65\)

\(y = 65 - 36 = 29\)