Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A 5 kg bag of potatoes costs £4.50. Work out the cost per kilogram.

2.A force of 20 N acts on an area of 4 m². Using pressure = force ÷ area, work out the pressure, in pascals.

3.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.

4.Write the ratio 4 : 9 in the form 1 : n.

5.A sunflower is 140 cm tall. A tomato plant is 80 cm tall. Write the height of the tomato plant as a fraction of the height of the sunflower, giving your answer in its simplest form.

6.The number of euros, e, received is directly proportional to the number of pounds, p, exchanged. Exchanging £40 gives 46 euros. Work out how many euros are received for £65, giving your answer to the nearest euro.

7.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.

8.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.

9.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.

10.A spring's extension is directly proportional to the force applied to it. A force of 5 N produces an extension of 12 mm. Work out the extension produced by a force of 20 N.

11.Maya is paid £105.30 for working 9 hours. Work out her rate of pay, in £ per hour.

12.A fruit bowl contains 9 apples and 21 oranges. Write down the ratio of apples to oranges in its simplest form.

13.A coach journey of 240 km takes 3 hours. For this fixed distance the average speed needed is inversely proportional to the time taken. Work out the average speed needed to complete the same journey in 2 hours.

14.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

15.A plumber charges a call-out fee plus an hourly rate. The total charge, C pounds, for a job lasting h hours is shown on a straight-line graph. The line passes through the points (2, 70) and (5, 130). Work out the call-out fee, in pounds.