(a) Copy and complete the table of values for the relation \(y = 5 - 7x - 6x^{2}\) for \(-3 \leq x \leq 2\).

(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 5 units on the y- axis, draw the :

(i) graph of \(y = 5 - 7x - 6x^{2}\) ; (ii) line \(y = 3\) on the same axis.

(c) Use your graph to find the : (i) roots of the equation \(2 - 7x - 6x^{2} = 0\) ; (ii) maximum value of \(y = 5 - 7x - 6x^{2}\).

Using a ruler and a pair of compasses only, construct (a) triangle QRT with |QR| = 8cm, |RT| = 6cm and |QT| = 4.5cm.

(b) a quadrilateral QRSP which has a common base QR with \(\Delta\)QRT such that QTP is a straight line, PQ || SR, |QP| = 9cm and |RS| = 4.5cm.

(i) Measure |PS| ; (ii) Find the perpendicular distance between RS and PQ ; (iii) What is QRSP?

A surveyor standing at a point X sights a pole Y due east of him and a tower Z of a building on a bearing of 046°. After walking to a point W, a distance of 180m in the South- East direction, he observes the bearing of Z and Y to be 337° and 050° respectively.

(a) Calculate, correct to the nearest metre : (i) |XY| ; (ii) |ZW| 

(b) If N is on XY such that XZ = ZN, find the bearing of Z from N.

In the diagram, ASRTB represents a piece of string passing over a pulley of radius 10cm in a vertical plane. O is the centre of the pulley and AMB is a horizontal straight line touching the pulley at M. Angle SAB = 90° and angle TBA = 60°. 

(a) Calculate (i) the obtuse angle SOT ; (ii) arc SRT ; (iii) |BT| 

(b) Find, correct to the nearest cm, the length of the string. (Take \(\pi = \frac{22}{7}\)).

The table below shows the number of eggs laid by the chickens in a man's farm in a year.

(a) Draw a cumulative frequency curve for the distribution.

(b) Use your graph to find the interquartile range.

(c) If a woman buys a chicken from the farm, what is the probability that the chicken lays at least 60 eggs in a year?