Ratio, proportion and rates of change worksheet — GCSE Higher

1.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.

2.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.

3.An oven is preheating. Its temperature, T °C, is plotted against time, t minutes, on a straight-line graph. The line passes through the points (2, 60) and (6, 140). Work out the gradient of the line.

4.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.

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.Write 75p : £1.50 as a ratio of whole numbers in its simplest form.

7.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.

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 cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.

10.y is directly proportional to x. When x = 8, y = 20. Work out the value of y when x = 12.

11.A printer prints pages at a constant rate. It prints 45 pages in 6 minutes. Work out how many pages it prints in 10 minutes.

12.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.

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

14.The price of a games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.

15.A recipe for pastry uses flour and butter in the ratio 3:2. A baker has 180 g of butter and wants to make pastry using all of it. Work out the total mass of pastry the baker can make.