Correct Answer: C. 100011

Correct Answer: B. 4m

Explanation

\(v(t) = (3t^{2} - 2t) ms^{-1}\)

\(s(t) = \int v(t) \mathrm {d} t\)

= \(\int (3t^{2} - 2t) \mathrm {d} t = t^{3} - t^{2}\)

\(s(2) = 2^{3} - 2^{2} = 8 - 4 = 4m\)

Correct Answer: d) N5.25K

Correct Answer: D. 110°

Explanation

Vertically opp angles are equal ∠CDE = 70°

Sum of interior angles in a quadilateral = 360°

(90 + 90 + 70 + t)° = 360°

t° = 360° - 250°

t° = 110°

Correct Answer: (c) 21/22; 16/20; 7/11

Explanation

(a) majority of the candidates multiplied through by the L.C.M which is 14 to arrive at 7(1+4x) - 2(5+2x) < 14(x - 2) and when simplified yielded 10x < -25 x -2\(\frac{1}{2}\)

(b) it was expected that they express x = \(\frac{3y}{5}\) or y = \(\frac{5x}{3}\) and thereafter, substitute into the given expression to have \(\frac{2x^2 - y^2}{y^2 - x^2} = \frac{2x^2 - (\frac{5x}{3})^2}{(\frac{5x}{3})^2 - x^2} = \frac{x^(2 - \frac{25}{9})}{x^2(\frac{25}{9} - 1)} = \frac{-7}{16}\)

Explanation

(a) \(\sin 105° = \sin(60 + 45)\)

= \(\sin 60° \cos 45° + \cos 60° \sin 45°\)

= \(\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2} + \frac{1}{2} \times \frac{\sqrt{2}}{2}\)

= \(\frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}\)

(b) a = 11, d = 2.

\(S_{n} = \frac{n}{2} (2a + (n - 1) d\)

\(551 = \frac{n}{2} (2(11) + (n - 1) 2\)

\(551 = \frac{n}{2} (22 + 2n - 2)\)

\(551 = \frac{n}{2} (2n + 20)\)

\(1102 = 2n^{2} + 20n \implies 2n^{2} + 20n - 1102 = 0\)

Divide through by 2.

\(n^{2} + 10n - 551 = 0\)

\(n^{2} - 19n + 29n - 551 = 0\)

\(n(n - 19) + 29(n - 19) = 0\)

\(\text{n = 19 or -29}\)

Since n cannot be negative, n = 19 houses.

(c)(i) \(T_{n} = ar^{n - 1}\) (terms of a G.P)

\(a = 2\)

\(T_{3} = 2 \times r^{3 - 1} = \frac{2}{9}\)

\(r^{2} = \frac{1}{9} \implies r = \frac{1}{3}\)

(ii) \(T_{5} = ar^{5 - 1}\)

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

= \(2 \times \frac{1}{81}\)

= \(\frac{2}{81}\)

Correct Answer: D. 13/25

Correct Answer: B. 125

Explanation

(a) Total no of cards = 52; No of fives = 4; No of red nines = 2.

Prob(of 5) = \(\frac{4}{52} = \frac{1}{13}\)

Prob(red nine) = \(\frac{2}{52} = \frac{1}{26}\)

\(\therefore\) Prob (of 5 or red nine) = \(\frac{1}{13} + \frac{1}{26} = \frac{3}{26}\)

(b) \(\tan < RPQ = \frac{3}{5} = 0.6\)

\(< RPQ = 30.96°\)

\(\therefore\) Bearing of R from P = 150° - 30.96° = 119.04°

\(\approxeq\) 119° (to the nearest degree).