(a) Using a ruler and a pair of compasses only, (i) construct \(\Delta\) XYZ such that |XY| = 8 cm and < YXZ = < ZYX = 45°. (ii) locate a point P inside the triangle equidistant from XY and XZ and also equidistance from YX and YZ. (iii) construct a circle touching the three sides of the triangle (iv) measure the radius of the circle.

(b) The length of the sides of a hexagon are x - 5, 2x, 2x, 2x + 7, 2x and 2x - 1. If the perimeter is 144 cm, find the value of x.

The following table shows the distribution of test scores in a class.

(a) If the mean score of the class is 6, find the : (i) value of k (ii) median score.

(b) Draw a bar chart for the distribution.

(c) If a pupil is picked at random, what is the probability that he/ she will score less than 6?

(a) 

The diagram shows a pyramid standing on a cuboid. The dimensions of the cuboid are 4m by 3m by 2m and the slant edge of the pyramid is 5m. Calculet the volume of the shape.

(b) The 2nd, 3rd and 4th terms of an A.P are x - 2, 5 and x + 2 respectively. Calculate the value of x.

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

Using a scale of 2 cm to 30° on the x- axis and 2 cm to 0.5 unit on the y- axis, draw the graph of \(y = 2\sin x - \cos 2x\), for \(0° \leq x \leq 180°\).

(b) Using the same axes, draw the graph of \(y = 1.25\).

(c) Use your graphs to find the : (i) values of x for which \(2\sin x - \cos 2x = 0\) ; (ii) the roots of the equation \(2\sin x - \cos 2x = 1.25\).

(a) Two lines AB and CD intersect at x such that \(\stackrel\frown{CAX}\) is equal to \(\stackrel\frown{BDX}\). If |AX| = 6 cm, |XB| = 4 cm and |CX| = 3 cm, find |XD|.

(b) 

The diagram shows the positions of three points X, Y and Z on a horizontal plane. The bearing of Y from X is 312° and that of Y from Z is 022°. If |XY| = 32 km and |ZY| = 50 km, calculate, correct to one decimal place : (i) |XZ| ; (ii) the bearing of Z from X.