(a) Copy and complete the table of values for the equation \(y = 2x^{2} - 7x - 9\) for \(-3 \leq x \leq 6\).

(b) Using scales of 2cm to 1 unit on the x- axis and 2cm to 4 units on the y- axis, draw the graphs of \(y = 2x^{2} - 7x - 9\) for \(-3 \leq x \leq 6\).

(c) Use the graph to estimate the :

(i) roots of the equation \(2x^{2} - 7x = 26\);

(ii) coordinates of the minimum point of y;

(iii) range of values for which \(2x^{2} - 7x < 9\).

The table shows the distribution of marks scored by some students in a test.

(a) If the mean mark is \(3\frac{6}{23}\), find the value of m.

(b) Find the : (i) interquartile range

(ii) probability of selecting a student who scored at least 4 marks in the test.

(a) PQ is a tangent to a circle RST at the point S. PRT is a straight line, < TPS = 34° and < TSQ = 65°.

(i) Illustrate the information in a diagram;  (ii)  find the value of : (a) < RTS ; (b) < SRP.

(b) 

In the diagram, /VZ/ = /YZ/, < YXZ = 20° and < ZVY = 52°. Calculate the size of < WYZ.

(a) Given that \(\sin x = \frac{5}{13}, 0° < x < 90°\), find \(\frac{\cos x - 2\sin x}{2\tan x}\).

(b) A ladder, LA, leans against a vertical pole at a point L which is 9.6metres above the groung. Another ladder, LB, 12 metres long, leans on the opposite side of the pole and at the same point L. If A and B are 10 metres apart and on the same straight line as the foot of the pole, calculate, correct to 2 significant figures, the :

(i) length of ladder LA  (ii) angle which LA makes with the ground.

(a) It takes 8 students two- thirds of an hour to fill 12 tanks with water. How many tanks of water will 4 students fill in one- third of an hour at the same rate?

(b) A chord, 20 cm long, is 12 cm from the centre of the circle. Calculate, correct to one decimal place, the :

(i) angle subtended by the chord at the centre of the circle;

(ii) perimeter of the minor segment cut off by the chord.  [Take \(\pi = 3.142\)].