Q1. (a) A manufacturer makes three types of paperclips, A, B and C. Each paperclip of type B weighs 20% more than type A and each of type C weighs 0.12 g more than type B.
The total mass of 12000 of type A, 8000 of type B and 5000 of type C is 11.64 kg.
Determine the mass of EACH of the three types of paperclip. (8)
(b) Salesman A is paid a basic salary of £32000. He receives 25% commission on all sales above £50000. Salesman B, in another firm, is paid a basic salary of £35000 with 20% commission on all sales above £40000. In a particular year both make sales of £150000.
Calculate the salaries for both A and B for that year. (8)
Q6. (a) A patrol boat travelled 27 miles from port A on a course 031° and then 18 miles on a course 111°. After a brief stop it returns to port A by the shortest route.
Calculate EACH of the following:
(i) the course that must be set in order to return to port A; (6)
(ii) the return distance to port A. (4)
(b) An alternating voltage, v volts, is given by the formula:
where t is the time in seconds. (t > 0)
Calculate the least value of t when v = 20 volts. (6)
Q9. (a) A piece of lead pipe 350mm long has an internal diameter of 40mm and a wall thickness of 5mm. It is melted down and recast into a solid hemisphere.
The density of the lead is 11340 kg per m3.
Determine EACH of the following:
(i) the diameter of the hemisphere; (5)
(ii) the mass of the hemisphere. (1)
(b) Fig Q 9(b) shows the graphs of the functions
Determine EACH of the following
(i) the co-ordinates of points A and B; (4)
(ii) the area of triangle AOB. (6)
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