Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A candle burns down at a constant rate. Its height, h cm, is plotted against time, t minutes, on a straight-line graph. The gradient of the line is −0.3. Which statement correctly describes what the gradient means?

2.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.

3.A glass holds 250 ml of squash. Work out how many of these glasses are needed to fill a 1 litre bottle.

4.Which of these ratios is equivalent to 2:3?

5.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.

6.A plan is drawn to a scale of 1 : 500. Work out how many metres are represented by 1 cm on the plan.

7.A scale model of a bus is built so that 5 cm on the model represents 60 cm on the real bus. Write the ratio of the length of the model to the length of the real bus, in its simplest form.

8.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.

9.Write the ratio 5 : 8 in the form 1 : n.

10.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.

11.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.

12.Triangle A and triangle B are mathematically similar. A side of triangle A is 4 cm long and the corresponding side of triangle B is 10 cm long. Write the ratio of the length in triangle A to the length in triangle B in its simplest form.

13.5 tins of soup cost £8 in total. Work out the multiplier that changes the number of tins into the total cost in pounds.

14.A post 2 metres tall casts a shadow 3 metres long. At the same time a nearby tree casts a shadow 12 metres long. Work out the height of the tree.

15.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.