Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A 1.5 kg bag of pasta costs £2.85 and a 2.4 kg bag of the same pasta costs £4.32. Work out which bag gives better value for money.

2.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.

3.£3000 is invested in a savings account that pays 4% compound interest each year. Work out the value of the investment after 2 years.

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

5.A charity collects donations from adults and children in the ratio 5:2. Altogether, £238 is collected. Work out how much more the adults donate than the children.

6.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.

7.A graph shows two quantities, x and y, in direct proportion. Write down which statement about the graph must be true.

8.A scale drawing of a garden uses a scale of 1 : 20. Write down a formula for the real length, L metres, in terms of the length on the drawing, d centimetres, given that 1 metre = 100 centimetres.

9.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

10.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.

11.Before a charity campaign, donations were £6400 per month. Donations grew by 8% in the first year after the campaign, and then fell by 3% in the second year as interest faded. Work out the amount donated per month at the end of the second year, to the nearest pound.

12.The value of a rare coin increases by 12% each year. The coin is currently worth £270. Work out the value of the coin after 2 years, giving your answer to the nearest penny.

13.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.

14.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.

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