Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.

2.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.

3.A film runs for 2.25 hours. Work out the length of the film in minutes.

4.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.

5.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

6.Two numbers are in the ratio 5 : 8. The larger number is 40. Work out the smaller number.

7.A statue exerts a downward force of 68.4 N on its base, which has an area of 2.85 m². Work out the pressure that the statue exerts on its base, in N/m².

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

9.Two taxi firms show their charges on straight-line graphs, with the cost in pounds on the vertical axis and the distance in miles on the horizontal axis. Firm A's line passes through (0, 4) and (5, 14). Firm B's line passes through (0, 6) and (5, 21). Work out which firm charges more per mile.

10.A shop sells ribbon by the metre. 2 m costs £3.00, 4 m costs £6.00, and 7 m costs £10.50. Does this data show that the cost is directly proportional to the length of ribbon bought? Choose the correct verdict and reason.

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.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.

13.£3000 is invested in a savings account that pays 4% compound interest each year. Work out the value of the investment after 2 years.

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

15.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².