(a) Simplify \(\frac{0.016 \times 0.084}{0.48}\) [Leave your answer in standard form].

(b) Eight wooden poles are to be used for pillars and the lengths of the poles form an Arithmetic Progression (A.P). If the second pole is 2m and the sixth is 5m, give the lengths of the poles, in order.

Show on a graph, the area which gives the solution set of the inequalities: \(y - 2x \leq 4 ; 3y + x \geq 6 ; y \geq 7x - 9\).

(a) Prove that the sum of the angles in a triangle is 2 right angles.

(b) The side AB of a triangle ABC is produced to a point D. The bisector of ACB cuts AB at E. Prove that < CAE + < CBD = 2 < CEB.

A carpenter was told to make a rectangular desk with top of dimension 50cm by 40cm. The carpenter actually made the desk 60cm by 35cm. 

(a) Calculate the percentage error in the (i) length and the breadth ; (ii) area of the table top.

(b) Find the product of the two errors in a(i).

The feet of two vertical poles of height 3m and 7m are in line with a point P on the ground, the smaller pole being between the taller pole and P and at a distance of 20m from P. The angle of elevation of the top (T) of the taller pole from the top (R) of the smaller pole is 30°. Calculate the :

(i) distance RT ; (ii) distance of the foot of the taller pole from P, correct to three significant figures ; (iii) angle of elevation of T from P, correct to one decimal place.