Ratio, proportion and rates of change worksheet — GCSE Higher

1.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.

2.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.

3.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.

4.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.

5.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.

6.The length of ribbon A is 5/12 of the length of ribbon B. Write the length of ribbon B as a fraction of the length of ribbon A.

7.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.

8.A toy manufacturer makes a model aircraft that is mathematically similar to the real aircraft, at a scale of 1 : 48. The wingspan of the model is 15 cm. Work out the wingspan of the real aircraft, giving your answer in metres.

9.A tangent to the graph of population against time at the point where t = 4 passes through (2, 180) and (6, 260). Work out the instantaneous rate of change of the population at t = 4, in people per year.

10.Two straight-line graphs represent y = 2x and y = 5x. For the same value of x, where x ≠ 0, write down the ratio of the y-value on the first graph to the y-value on the second graph, in its simplest form.

11.A spring's extension is directly proportional to the force applied to it. A force of 5 N produces an extension of 12 mm. Work out the extension produced by a force of 20 N.

12.A salt solution has a concentration of 10%. The solution contains 50 g of salt. Work out the total mass of the solution.

13.A map has a scale of 1 : 100 000. Two railway stations are 8 km apart in real life. Work out the distance between the stations on the map, in centimetres.

14.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.

15.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?