Using ruler and a pair of compasses only, 

(a) construct : 

(i) \(\Delta\)XYZ such that |XY| = 10cm, < XYZ = 30° and < YXZ = 45°.

(ii) locus, \(l_{1}\), of points equidistant from Y and Z.

(iii) locus, \(l_{2}\), of points parallel to XY through Z.

(b) Locate M, the point of intersection of \(l_{1}\) and \(l_{2}\).

(c) Measure < ZMY.

(a) If \(\frac{3p + 4q}{3p - 4q} = 2\), find \(p : q\).

(b)  

The diagram shows the cross section of a bridge with a semi-circular hollow in the middle. If the perimeter of the cross section is 34 cm, calculate the :

(i) length PQ; (ii) area of the cross section. 

[Take \(\pi = \frac{22}{7}\)].

(a) Copy and complete the table of values, correct to one decimal place, for the relation \(y = 3\sin x + 2\cos x\) for \(0° \leq x \leq 360°\).

(b) Using scales of 2cm to 30°mon the x- axis and 2cm to 1 unit on the y- axis, draw the graph of the relation \(y = 3\sin x + 2\cos x\) for \(0°\leq x \leq 360°\).

(c) Use the graph to solve :

(i) \(3\sin x + 2\cos x = 0\)

(ii) \(2 + 2\cos x + 3\sin x = 0\).

(a) Find the equation of a straight line which passes through the point (2, -3) and is parallel to the line \(2x + y = 6\).

(b) The operation \(\Delta\) is defined on the set T = {2, 3, 5, 7} by \(x \Delta y = (x + y + xy) mod 8\).

(i) Construct modulo 8 table for the operation \(\Delta\) on the set T.

(ii) Use the the table to find: (a) \(2 \Delta (5 \Delta 7)\) ; (b) \(2 \Delta n = 5 \Delta 7\).

(a)  Without using Mathematical tables or calculators, simplify:

\(3\frac{4}{9} \div (5\frac{1}{3} - 2\frac{3}{4}) + 5\frac{9}{10}\)

(b) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. Find the probability that the sum of the two numbers is greater than 3 and less than 7.