Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

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

3.Simplify the ratio 45 : 30 : 75 to its simplest form.

4.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.

5.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.

6.Cheng is paid an hourly rate that is proportional to the number of hours she works. She earns £52.50 for 7 hours. Work out how much she earns for 11 hours, assuming the same rate.

7.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.

8.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.

9.A cleaning solution is made by mixing disinfectant and water in the ratio 1 : 9. Priti wants to make 6 litres of the solution in total. Work out how much disinfectant she needs.

10.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.

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

12.In a mix of mortar the ratio of the mass of sand to the mass of cement is 5 : 2. Write the mass of cement as a fraction of the total mass of the mix.

13.A straight-line graph shows the number of pages printed, p, plotted against the time in minutes, t, since a printer started a print job. The line passes through the points (2, 30) and (5, 90). Work out the gradient of the line.

14.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.

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