Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Which of these ratios is already written in its simplest form?

2.A metal block has a mass of 270 g and a volume of 30 cm³. Work out the density of the block, in g/cm³.

3.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.

4.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.

5.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.

6.Two cars travel at constant speeds. Car A travels 150 km in 3 hours. Car B travels 180 km in 4 hours. Which car is faster, and what is its speed?

7.3 builders put up a fence in 12 days. All the builders work at the same rate, so the number of days is inversely proportional to the number of builders. Work out how long 9 builders take to put up the same fence.

8.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.

9.A car travels 150 km in 3 hours at a constant speed. Work out the average speed of the car, in km/h.

10.The ratio of two lengths is 0.6 : 1.5. Write this ratio in its simplest whole-number form.

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.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.

13.3 pencils cost £1.20. Work out the cost of 7 pencils.

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

15.A baker uses 450 g of flour and 300 g of butter in a batch of pastry. Write the mass of butter as a fraction of the total mass of flour and butter, in its simplest form.