Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Write 3 hours 45 minutes as a decimal number of hours.

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

3.A printer's ink cartridge level, I millilitres, is plotted against the number of pages printed, p, and the points lie on a straight line. The line passes through (0, 24) and (300, 9). The printer has now printed 300 pages. Work out how many more pages it can print before the cartridge is empty.

4.A laptop is bought for £600. Its value decreases by 20% after 1 year. Work out the value of the laptop after 1 year.

5.Ffion is paid £11.20 per hour. She works 6 hours on Monday and 4.5 hours on Tuesday. Work out her total pay for the two days.

6.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.

7.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.

8.A water butt is being filled from a hosepipe at a constant rate while a small leak drains water out at a constant rate, giving a constant net rate of change. The volume of water in the butt, V litres, is shown on a straight-line graph against time, t minutes. The line passes through the points (5, 20) and (15, 60). The butt is empty at t = 0. Work out how many minutes it takes to reach a volume of 100 litres.

9.Two mathematically similar cylinders have volumes 64 cm³ and 216 cm³. Work out the ratio of the height of the smaller cylinder to the height of the larger cylinder, in simplest form.

10.A shop sells identical pens. The total cost, C pence, of n pens is given by C = 12n. Write the ratio n : C in its simplest form.

11.Given that 1 mile ≈ 1.6 km, work out a speed of 55 mph in km/h.

12.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.

13.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.

14.A straight-line graph shows the distance travelled, d kilometres, against the time taken, t hours, for a cyclist. The line passes through the origin and has a gradient of 18. Write down what the gradient of this line represents.

15.A statue exerts a downward force of 68.4 N on its base, which has an area of 2.85 m². Work out the pressure that the statue exerts on its base, in N/m².