Q1. (a) In a four cylinder engine the power developed in the No.1 cylinder is 15% more than in the No.3 cylinder. The No.2 cylinder develops 5% less power than in the No.3 cylinder. The No.3 and No.4 cylinders develop the same power.
Express the power of EACH cylinder as a percentage of the total power of the engine. (8)
(b) Solve for b in EACH of the following equations:
(i) (4)
(ii) (4)
Q2. (a) A sheet of metal is to be cut in the shape of a rectangle with a semi-circle at one end as shown in Fig Q2(a).
It has to have an area of 30 cm2 and an overall length of 10 cm.
Calculate the radius of the semi-circle. (8)
(b) The angle, θ radians, that a rotating shaft turns through after t seconds is given by:
where ω and are constants.
When t = 1.2 then = 4.032 and when t = 2.5 then = 9.375
Determine the values of and α. (8)
Q6. (a) A ship on a bearing 197° from a lighthouse measures the angle of elevation of the top of the lighthouse as 13°. After sailing 144 metres the ship is on a bearing 178° from the lighthouse and the angle of elevation to the top of the lighthouse is then 9°.
Calculate the height of the lighthouse. (10)
(b) Fig Q6(b) shows the major segment of a circle of radius 75 mm.
Chord AB is 120 mm.
Determine the perimeter of the segment. (6)
Q7. (a) Fig Q7(a) shows a rectangular sheet of metal with four identical holes drilled in it.
The length of the rectangle is 400 mm and its width is 30x mm.
Each hole has a diameter of 20x mm.
(i) Show that the remaining area, A, is given by . (3)
(ii) Calculate the value of x such that the remaining area, A, is a maximum. (7)
(b) Given : Determine the value of (6)
Q9. (a) A solid conic frustum is placed within a hollow open-topped cylinder as illustrated in Fig Q9(a). The frustum and the cylinder have the same axis of symmetry and the same height (30cm). The end diameters of the frustum are 10 cm and 15 cm. The diameter of the cylinder is 20 cm.
Calculate the volume of the space within the cylinder. (12)
(b) Determine the mass of 400 steel ball bearings of diameter 10 mm. (4)
Note: The density of the steel is 7900 kg/m3.
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