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0 \(\geq\) x \(\geq\) 2 \(\to\) 0, 1, 2 If x = 0, \(\frac{9}{1 + 2x^2}\) \(\frac{9}{1 + 2(0)^2}\) = \(\frac{9}{1}\) = 3 If x = 2, \(\frac{9}{1 + 2(1)^2}\) = \(\frac{9}{3}\) = 3 If x = 2, \(\frac{9}{1 + 2(2)^2}\) = \(\frac{9}{9}\) = 1 The least value of \(\frac{9}{1 + 2x^2}\) is 1 when x = 2

f(x - 2) = 3\(x^2\) + 4x + 1 x - 2 = 1 then x = 3 When x = 3, f(1) = 3(3)2 + 4 x 3 = 1 27 + 12 +1 = 40

\(p : q = \frac{1}{3} : \frac{1}{2}\) \(\frac{p}{q} = \frac{2}{3}\) \(2q = 3p ... (1)\) \(q : r = \frac{2}{5} : \frac{4}{7}\) \(\frac{q}{r} = \frac{2}{5} \times \frac{7}{4} = \frac{7}{10}\) \(10q = 7r ... (2)\) Eliminating q, we have (1) : \(2q = 3p \) \(10q = 15p\) \(\implies 15p = 7r\) \(\therefore \frac{p}{r} = \frac{7}{15}\) \(p : r = 7 : 15\)

4 bags of rice - M 56 each 3 tins of milk - M 4 each \(M 56 \times 4 = M 323\) \(M 4 \times 3 = M 15\) \(M (323 + 15) = M 341\)

\(\frac{1}{p^2}\) + \(\frac{1}{q^2}\) = \(\frac{q^2 + p^2}{p^2 + q^2}\) \(\frac{\frac{2}{x}}{\frac{p^2 + q^2}{p^2 q^2}}\) m = \(\frac{2p^2q^2}{x(p^2 + q^2)}\) = 2p2q2 = mx(p2 + q2) x = \(\frac{2p^2q^2}{m(q^2 + p^2)}\)

to find the values of x for which the expression is undefined, let x\(^2\) + x - 2 = 0 By factorizing, we have (x + 2)(x - 1) = 0 when x + 2 = 0, when x - 1 = 0, x = -2 or x = 1 The two values are -2 and 1

1km = 1000m 60sec. = 1 mins 60 mins. = 1 hr 130000m per sec = 130000 x 3600 = 468000000m/hr = 468 x 108 m/hr

\(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\) = 3e + f = 2 x 1 \(\frac{-e + 3f}{3e - f}\) = \(\frac{5 \times 3}{2}\) = \(\frac{3e + 9f = 15}{10f = 17}\) f = \(\frac{17}{10}\) Sub. for equ. (1) 3e + \(\frac{17}{10}\) = 2 3e = 2 - \(\frac{17}{10}\) \(\frac{3}{10}\) e = \(\frac{3}{10}\) x \(\frac{1}{3}\) = \(\frac{1}{10}\) = e + 3f = \(\frac{1}{10}\) + \(\frac{3 \times}{10}\) = \(\frac{52}{10}\) f - 3e = \(\frac{17}{10}\) - 3 x \(\frac{1}{10}\) = \(\frac{14}{10}\) = \(\frac{52}{10}\) x \(\frac{10}{14}\) = \(\frac{26}{7}\)

Maximum error in measurement to 2 decimal places Maximum error = \(\frac{1}{2}\) x 0.001 = 0.005

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

3 kg of garri at N13.00 per kg = N39.00 half a cow = N160.00 24 oranges at 10k each = N2.40 balance = N20.60 Adding all together = N222.00

Vol. of the 1st section is side x height vol. = 3 x 8 = 24cm3 vol. of the second section is 3 x 1 = 3 = 24cm3, 3cm3

f\(^{\frac{1}{2}}\)g\(^2\)h\(^{\frac{1}{3}}\) \(\div\) f\(^{\frac{5}{2}}\)g\(^o\)h\(^{\frac{7}{3}}\) = f\(^{\frac{1}{2} - \frac{5}{2}}\) g\(^{2 - 0}\) h\(^{\frac{1}{3} - \frac{7}{3}}\) = f\(^{-2}\) g\(^2\) h\(^{-2}\) = \(\frac{g^2}{f^2h^2}\) = (\(\frac{g}{fh}\))\(^2\)

y = 5x, when x = 0 y = 0, when x = 1 y = 5 intercept on y axis is 0

y \(\alpha\) \(\frac{1}{x^2}\) y = \(\frac{k}{x^2}\) k = x\(^2\)y = (2)\(^2\) x 10 = 40 y = \(\frac{40}{x^2}\) = \(\frac{40}{(10)^2}\) = \(\frac{40}{100}\) = 0.4