Ratio, proportion and rates of change worksheet — GCSE Higher

1.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.

2.y is directly proportional to √x. When x = 25, y = 20. Construct the equation connecting x and y, then work out the value of x when y = 32.

3.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

4.A coach travels the 54 miles from London to Brighton in 1 hour 30 minutes. Work out the average speed of the coach, in mph.

5.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.

6.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.

7.A lorry is carrying a load of mass m tonnes. Given that 1 tonne = 1000 kg, write down an expression for the mass of the load in kilograms.

8.A cyclist rides 19.3 km in 47 minutes. Work out her average speed, in km/h, to 1 decimal place.

9.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.

10.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

11.An architect builds a scale model of a staircase before construction. The model is mathematically similar to the real staircase, at a scale of 1 : 10. The model covers a floor area of 0.4 m² on the plan. Work out the floor area the real staircase will cover, giving your answer in m².

12.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.

13.A tangent to a distance–time graph, with distance in kilometres and time in minutes, has gradient 0.78 kilometres per minute at a particular point. Work out the instantaneous rate of change of distance with time, in kilometres per hour.

14.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.

15.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.