(a) Using mathematical tables, find ; (i) \(2 \sin 63.35°\) ; (ii) \(\log \cos 44.74°\);

(b) Find the value of K given that \(\log K - \log (K - 2) = \log 5\);

(c) Use logarithm tables to evaluate \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)

(a) Given that \(p = x + ym^{3}\), find m in terms of p, x and y.

(b) Using the method of completing the square, find the roots of the equation \(x^{2} - 6x + 7 = 0\), correct to 1 decimal place.

(c) The product of two consecutive positive odd numbers is 195. By constructing a quadratic equation and solving it, find the two numbers.

(a) Copy and complete the table for the relation \(y = 2 \cos 2x - 1\).

(b) Using a scale of 2cm = 30° on the x- axis and 2cm = 1 unit on the y- axis, draw the graph of \(y = 2 \cos 2x - 1\) for \(0° \leq x \leq 180°\).

(c) On the same axis, draw the graph of \(y = \frac{1}{180} (x - 360)\)

(d) Use your graphs to find the : (i) values of x for which \(2 \cos 2x + \frac{1}{2} = 0\); (ii) roots of the equation \(2 \cos 2x - \frac{x}{180} + 1 = 0\).

(a) Using a ruler and a pair of compasses only, construct triangle ABC with /AB/ = 7.5cm, /BC/ = 8.1cm and < ABC = 105°.

(b) Locate a point D on BC such that /BD/ : /DC/ is 3 : 2.

(c) Through D, construct a line I perpendicular to BC.

(d) If the line I meets AC at P, measure /BP/.

(a) A man travels from a village X on a bearing of 060° to a village Y which is 20km away. From Y, he travels to a village Z, on a bearing of 195°. If Z is directly east of X, calculate, correct to three significant figures, the distance of :

(i) Y from Z ; (ii) Z from X .

(b) An aircraft flies due South from an airfield on latitude 36°N, longitude 138°E to an airfield on latitude 36°S, longitude 138°E. 

(i) Calculate the distance travelled, correct to three significant figures ; (ii) if the speed of the aircraft is 800km per hour, calculate the time taken, correct to the nearest hour.

[Take \(\pi = \frac{22}{7}\), R = 6400km].