In the diagram, a ladder TF, 10 metres long is placed against a wall at an angle of 70° to the horizontal.

(a) How high up the wall, correct to the nearest metre, does the ladder reach?

(b) If the foot (F) of the ladder is pulled from the wall to F\(^{1}\) by 1 metre, (i) how far, correct to 2 significant figures, does the top T slide down the wall to T\(^{1}\).

(ii) Calculate, correct to the nearest degree, \(QF^{1}T^{1}\).

The cost of maintaining a school is partly constant and partly varies as the number of pupils. With 50 pupils, the cost is $15,705.00 and with 40 pupils, it is $13,305.00.

(a) Find the cost when there are 44 pupils.

(b) If the fee per pupil is $360.00, what is the least number of pupils for which the school can run without a loss?

On a graph sheet, using a scale of 2cm to 2 units on both axes, 

(a) Draw the straight line joining points P(-5, 3) and Q(2, 3);

(b) construct the locus L of points equidistant from P and Q;

(c) by construction, locate points R and S on L, such that PRQS forms a rhombus of sides 5cm;

(d) find : (i) coordinates of R and S; (ii) area of the rhombus in cm\(^{2}\).

(a) A shop owner marked a shirt at a price to enable him to make a gain of 20%. During a special sales period, the shirt was sold at 10% reduction to a customer at N864.00. What was the original cost to the shop owner?

(b) A rectangular lawn of length (x + 5) metres is (x - 2) metres wide. If the diagonal is (x + 6) metres, find ;

(i) the value of x ; (ii) the area of lawn.

(a) Copy and complete the following table of values for \(y = 9 \cos x + 5 \sin x\) to one decimal place.

(b) Using a scale of 2cm to 30° on the x- axis and 2 cm to 1 unit on the y- axis, draw the graph of \(y = 9 \cos x + 5 \sin x\) for \(0° \leq x \leq 210°\).

(c) Use your graph to solve the equation: (i) \(9\cos x + 5\sin x = 0\); (ii) \(9\cos x+ 5\sin x = 3.5\), correct to the nearest degree.

(d) Find the maximum value of y correct to one decimal place.