Ratio, proportion and rates of change worksheet — GCSE Higher

1.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.

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

3.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.

4.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.

5.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.

6.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?

7.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.

8.The number of subscribers to a streaming app, in thousands, is plotted against time, in months since launch. A tangent to the graph at t = 6 months has gradient 4.8. A tangent at t = 18 months has gradient 1.1. A manager claims the app is growing faster at 18 months than it was at 6 months. Work out how the growth rate has changed, and decide whether the manager is correct.

9.Two quantities x and y are in the ratio x : y = 2 : 5, and y = kx for a constant k. Work out the value of k.

10.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.

11.An Ordnance Survey map has a scale of 1 : 50 000. A cycle route measures 9.4 cm on the map. Work out the real length of the route, in kilometres.

12.A patient is given a dose of 200 mg of a drug. Each hour, 30% of the drug remaining in the bloodstream is eliminated, and then a further dose of 50 mg is given. Using the recurrence D_{n+1} = 0.7D_n + 50, with D_0 = 200, work out the amount of drug in the bloodstream after 2 hours.

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

14.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.

15.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.