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Find the diagram Sin 70^\circ x = 10 Sin 70^\circ = 9.3969 Hence, length of chord MN = 2x = 2 \times 9.3969 = 18.79 = 19cm (nearest cm)

\(x^{2} + 2xy + y^{2} + 3x + 3y - 18\) \(x^{2} + 2xy + 3x + y^{2} + 3y -18\) \(x^{2} + 2xy - 3x + 6x + y^{2} -3y + 6y -18\) \(x^{2} + 2xy -3x + y^{2} -3y + 6x + 6y -18\) \(x^{2} + xy -3x + xy + y^{2} - 3y + 6x + 6y -18\) x(x + y - 3) + y(x + y - 3) + 6(x + y - 3) = (x + y - 3)(x + y + 6) = (x + y + 6)(x + y -3)

p = s + \(\frac{sm^2}{nr}\) p = s + ( 1 + \(\frac{m^2}{nr}\)) p = s (1 + \(\frac{nr + m^2}{nr}\)) nr \times p = s (nr + m2) s = \(\frac{nrp}{nr + m^2}\)

x * y is an operation on 3x + 2y − 1 Find 3A − 1 x = 3, y = −1 3 * − 1 on 3x + 2y − 1 3(3) + 2(−1) −1 = 9 − 2 − 1 = 6

Gradient of line joining points (3, 2), (1, 4) Gradient = \(\frac{\text{Change in Y}}{\text{Change in X}}\) = \(\frac{y_2 - Y_1}{x_2 - x_1}\)\) (X1, Y1) = (3, 2) (X2, Y2) = (1, 4) Gradient = \(\frac{4 − 2}{1 + 3}\) = \(\frac{2}{-2}\) = −1

(\(\sqrt[3]{64a^3})^{-1}\) \(\frac{1}{(\sqrt[3]{64a^3})}\) = \(\frac{1}{4a}\)

\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\)= m + n√6 \(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\) x \(\frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}}\) \(\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}\) \(\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2}\) = \(\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8}\) = \(\frac{0 - 4 \sqrt{6} - 6}{5}\) = \(\frac{10 - 5 \sqrt{6}}{5}\) = − 2 + √6 ∴ m + n\(\sqrt{6}\) = − 2 + √6 m = − 2, n = 1

1/\alpha + 1/\beta = \beta+\alpha/\alpha\beta 3x2 + 5x - 2 = 0 x2 + 5x/3 - 2/3 = 0 \alpha\beta = -2/3 \beta+\alpha = -5/3 Thus; \beta+\alpha/\alpha\beta = -2/3 -2/3 = -5/2

0.4, −0.4, 0.3, 0.47, −0.53, 0.2, −0.2 Range is the difference between the highest and lowest value i.e Highest − Lowest − 0.53, −0.4, −0.2, 0.2, 0.3, 0.4, 0.47 0.47 is the highest − 0.53 is the lowest ∴ = 0.47 − (− 0.53) ∴0.47 + 0.53 = 1.0

1 − (\(\frac{1}{5}\) x 1\(\frac{2}{3}\)) + (5 + 1\(\frac{2}{3}\)) 1 − (\(\frac{1}{5}\) x \(\frac{5}{3}\)) + (5 + \(\frac{5}{3}\)) 1 − \(\frac{1}{3}\) + \(\frac{20}{3}\) = \(\frac{22}{3}\)

(2x2 - x + 1) × (3 - 2x); 3(2x2 - x + 1) - 2x (2x2 - x + 1) 6x2 - 3x + 3 - 4x3 + 2x2 - 2x -4x3 + 8x2 -5x + 3

0.0000407 to 2 s.f 0.000041 (2 s.f)

\(x \propto \frac{1}{y}\), y \(\propto\) z x = \(\frac{k}{y}\) y = mz Since y = mz, x = \(\frac{k}{mz}\), where k and m are constants. Hence, x \(\propto\) \(\frac{1}{z}\)

\(\frac{3\frac{1}{4} \times 1\frac{3}{5}}{11\frac{1}{3} - 5 \frac{1}{3}}\) = \(\frac{\frac{26}{5}}{\frac{18}{3}}\) = \(\frac{26}{5} \div \frac{18}{3}\) = \(\frac{26}{5} \times \frac{3}{18}\) = \(\frac{13}{15}\)

Tunde: Ola \(\to\) 1 : 2 ; Ola; Musa \(\to\) 4 : 5 \(\frac{1}{2}\) x \(\frac{4}{5}\) = \(\frac{2}{5}\)