Ratio, proportion and rates of change worksheet — GCSE Higher

1.In a fruit squash mix, the ratio of squash to water is 2 : 9. A shop wants to make up the mix using 3.4 litres of squash. Work out how many litres of water are needed.

2.Two quantities x and y are in direct proportion. When x = 8, the value of y is 20. Work out the value of y when x = 14.

3.A machine is bought for £8500. Its value depreciates by 6% each year. Work out the value of the machine after 3 years, to the nearest pound.

4.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.

5.A savings account starts with £500. Each year, 4% interest is added, and then £30 is withdrawn from the account. Which recurrence correctly models the balance, £S_n, after n years, with S_0 = 500?

6.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.

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

8.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.

9.A vehicle is worth £18000. Its value decreases by 15% each year. Using the recurrence V_{n+1} = 0.85V_n, with V_0 = 18000, find the first whole number of years after which the vehicle's value drops below £10000.

10.A furniture maker builds two mathematically similar bookcases. The smaller bookcase is 40 cm tall and uses 2 m² of wood. The larger bookcase is 60 cm tall. Work out the area of wood needed for the larger bookcase, giving your answer in m².

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

12.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?

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 map has a scale of 1 : 40 000. A cycle path measures 7.5 cm on the map. Work out the real length of the cycle path, in kilometres.

15.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.