1991 - WAEC Mathematics Past Questions and Answers - page 1

4.62 x 10^-2

5846 \(\approxeq\) 5850 (to 3 s.f.)

log 6 + log 2 - log 12

= \(\log (\frac{6 \times 2}{12})\)

= \(\log 1\)

= 0

For the log to be 2.6025, there must be three digits before the decimal point.

\((\frac{1}{4})^{-1\frac{1}{2}}\)

= \((\frac{1}{4})^{-\frac{3}{2}}\)

= \((\sqrt{\frac{1}{4}})^{-3}\)

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

= \(2^3\)

= 8

\(\frac{y + 2}{y^2 - 3y - 10}\) 

\(y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0\)

\(y(y - 5) + 2(y - 5) = 0\)

\((y - 5)(y + 2) = 0\)

\(\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}\)

\(\therefore\) At y = 5, the expression \(\frac{y + 2}{y^2 - 3y - 10}\) is undefined.

3a\(^2\) - 11a + 6

3a\(^2\) - 9a - 2a + 6

3a(a - 3) - 2(a - 3) 

= (3a - 2)(a - 3)

3a + 10 = a\(^2\)

a\(^2\) - 3a - 10 = 0

a\(^2\) - 5a + 2a - 10 = 0

a(a - 5) + 2(a - 5) = 0

(a - 5)(a + 2) = 0

a = 5 or a = -2.

\((\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}\)

= \((\frac{6y - 15x}{2xy}) \div \frac{6}{xy}\)

= \(\frac{6y - 15x}{2xy} \times \frac{xy}{6}\)

= \(\frac{3(2y - 5x)}{2xy} \times \frac{xy}{6}\)

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

¹/₄(2ⁿ - 2ⁿ⁺²) = 2^-2(2ⁿ - 2ⁿ x 2²) = 2ⁿ x ^-2(1 - 2²)= 2^2n-2
(2⁰ - 2²) = 2^2n-2 - 2ⁿ