The diagram shows a wooden structure in the form of a cone, mounted on a hemispherical base. The vertical height of the cone is 24cm and the base height 7cm. Calculate, correct to three significant figures, the surface area of the structure. [Take \(\pi = \frac{22}{7}\)].

Using a ruler and a pair of compasses only, construct a triangle ABC, given that |AB| = 8.4cm, |BC| = 6.5cm and < ABC = 30°. Construct the locus: 

(a) \(l_{1}\) of points equidistant from AB and BC, and within the angle ABC;

(b) \(l_{2}\) of points equidistant from B and C. Locate the point of intersection P of \(l_{1}\) and \(l_{2}\). Measure |AP|. 

(a) If \(\cos \alpha = 0.6717\), use mathematical tables to find (i) \(\alpha\) ; (ii) \(\sin \alpha\)

(b) The angle of depression of a point P on the ground, from the top T of a building is 23.6°. If the distance of P from the foot of the building is 50m, calculate the height of the building, correct to the nearest metre.

(a) 

In the diagram, O is the centre of the circle radius 3.2cm. If < PRQ = 42°, calculate, correct to two decimal places, the area of the:

(i) minor sector POQ ; (ii) shaded part.

(b) If the sector POQ in (a) is used to form the curved surface of a cone with vertex O, calculate the base radius of the cone, correct to one decimal place.

When a stone is thrown vertically upwards, its distance d metres after t seconds is given by the formula \(d = 60t - 10t^{2}\). Draw the graph of \(d = 60t - 10t^{2}\) for values of t from 1 to 5 seconds using 2cm to 1 unit on the t- axis and 2cm to 20 units on the d- axis.

(a) Using your graph, (i) how long does it take to reach a height of 70 metres? (ii) determine the height of the stone after 5 seconds. (iii) after how many seconds does it reach its maximum height.

(b) Determine the slope of the graph when t = 4 seconds.