1993 - WAEC Mathematics Past Questions and Answers - page 1

\(\frac{\log \sqrt{27}}{\log 81}\)

= \(\frac{\log \sqrt{3^3}}{\log 3^4}\)

= \(\frac{\log 3^{\frac{3}{2}}}{\log 3^4}\)

= \(\frac{\frac{3}{2} \log 3}{4 \log 3}\)

= \(\frac{\frac{3}{2}}{4}\)

= \(\frac{3}{8}\)

2s\(^2\) - 3st - 2t\(^2\)

= 2s\(^2\) - 4st + st - 2t\(^2\)

= 2s(s - 2t) + t(s - 2t)

= (2s + t)(s - 2t)

x\(^2\) - 2x - 3 = 0

x\(^2\) - 3x + x - 3 = 0

x(x - 3) + 1(x - 3) = 0

(x + 1)(x - 3) = 0

x = (-1, 3)

S = {1, 2, 3, 4, 5, 6};  T = {2, 4, 5, 7}; R = {1, 4, 5}

(S∩T) ∪ R = {2, 4, 5}  ∪ {1, 4, 5}

= {1, 2, 4, 5}

\(\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})\)

\(\frac{3}{4} \div \frac{5}{4} \times (\frac{9 - 4}{6})\)

= \(\frac{3}{4} \times \frac{4}{5} \times \frac{5}{6}\)

= \(\frac{1}{2}\)

3m + 3 > 9

3m > 9 - 3

3m > 6

m > 2

\(89_{10}\)

\(89_{10} = 1011001_{2}\)

when n = 2

(-1)\(^{n-2}\) 2\(^{n+1}\) = 2

When n = 3

(-1)\(^{n-2}\) 2\(^{n+1}\) = -4

Sum = 2 - 4 = -2

\(\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}\)

= \(\frac{16^{\frac{3}{4}}}{4^{\frac{1}{2}} \times 4^{\frac{1}{2}}}\)

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

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

= 2