2013 - WAEC Mathematics Past Questions and Answers - page 1

2.7 x 10^-4 x 6.3 x 10⁶

= 2.7 x 6.3 x 10^-4 x 10⁶

= 17.01 x 10^{-4 + 6}

= 17.01 x 10²

= 1.701 x 10¹ x 10²

= 1.701 x 10^{1 + 2}

= 1.701 x 10³

9(2 - x) = 3

3^{2(2 - x)} = 3

2(2 - x) = 1

4 - 2x = 1

-2x = 1 - 4

-2x = -3

x = \(\frac{-3}{-2}\)

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

\(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)

from numerator \(1 \frac{7}{8} \times 2 \frac{2}{5}\)

= \(\frac{15}{8} \times \frac{12}{5}\)

= \(\frac{3 \times 3}{2 \times 1} = \frac{9}{2}\)

from denominator \(6\frac{3}{4} \div \frac{3}{4}\)

= \(\frac{27}{4} \div \frac{3}{4}\)

= \(\frac{27}{4} \times \frac{4}{3}\)

= \(\frac{9 \times 1}{1 \times 1} = \frac{9}{1}\)

\(\frac{9}{2} \div \frac{9}{1} = \frac{9}{2} \times \frac{1}{9}\)

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

Un = n(n² + 1)

U⁵ = 5(² + 1)

= 5(25 + 1)

= 5(26) = 130

U⁴ = 4(4² + 1) = 4(16 + 1)

= 4(17) = 68

U5 - U4 = 130 - 68

= 62

\(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\)

\(\sqrt{50} - \frac{2}{\sqrt{2}}\) = K\(\sqrt{8}\)

= \(\sqrt{2} \times 25 - \frac{2}{\sqrt{2}}\)

= K \(\sqrt{4 \times 2}\)

\(\frac{5\sqrt{2}}{1} - \frac{2}{\sqrt{2}}\) = 2K\(\sqrt{2}\)

\(\frac{5\sqrt{4} - 2}{\sqrt{2}} = 2K\sqrt{2}\)

\(\frac{10 - 2}{\sqrt{2}} = 2K \sqrt{2}\)

\(\frac{8}{\sqrt{2}} = \frac{2K\sqrt{2}}{1}\)

= 2k\(\sqrt{2} \times \sqrt{2}\) = 8

2k \(\sqrt{4}\) = 8

2k x 2 = 8

4k = 8

k = \(\frac{8}{4}\)

k = 2

% error = \(\frac{error}{\text{actual value}} \times 100\)

error = N72 - N68 = 4

actual value = N72

%error = \(\frac{4}{72} \times 100\)

= \(\frac{100}{18} = \frac{50}{9}\) = 5\(\frac{5}{9}\)%

4 oranges sell for Nx, 1 orange will sell for \(\frac{Nx}{4}\)

24 oranges will sell for: \(\frac{Nx}{4} \times 24\) = n6x

3 mangoes sell for Ny, 1 mango will sell for \(\frac{Ny}{3}\)

12 mangoes will sell for \(\frac{Ny}{3} \times 12\) = 4Ny

total money pay N6x + N4y = N(6x + 4y)

\(\frac{x^2 - y^2}{(x + y)^2} + \frac{(x - y)^2}{(3x + 3y)}\)

\(\frac{(x + y)(x - y)}{(x + y)(x + y)} + \frac{(x - y)(x - y)}{3(x + y)}\)

= \(\frac{3}{x - y}\)

\(\frac{2x - 5}{2} < \frac{(2 - x)}{1}\)

2x - 5 < 4 - 2x

2x + 2x < 4 + 5

4x < 9

x < \(\frac{9}{4}\)

x < 2\(\frac{1}{4}\)