Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Write 45 minutes : 2 hours as a ratio in its simplest form.

2.5 tins of soup cost £8 in total. Work out the multiplier that changes the number of tins into the total cost in pounds.

3.A ratio is 3 : 5. Write the first part of the ratio as a fraction of the whole.

4.Work out the time taken to travel 120 km at an average speed of 60 km/h.

5.A recipe uses flour and sugar in the ratio 4 : 1 by mass. The mass of sugar is s grams and the mass of flour is f grams. Write down a formula for f in terms of s.

6.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.

7.Line P passes through the origin and the point (3, 21). Line Q passes through the origin and the point (5, 45). Both lines represent the distance, in metres, run by an athlete against the time, in seconds. Work out the gradient of the steeper line.

8.In a fruit squash mix, the ratio of squash to water is 2 : 9. A shop wants to make up the mix using 3.4 litres of squash. Work out how many litres of water are needed.

9.Write 350 ml : 1.4 l as a ratio in its simplest form.

10.A room is drawn on a plan with a scale of 1 : 200. On the plan the room has an area of 12 cm². Work out the real area of the room, in square metres.

11.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.

12.A car travels 150 km in 3 hours at a constant speed. Work out the average speed of the car, in km/h.

13.A straight-line graph shows the distance travelled, d kilometres, against the time taken, t hours, for a cyclist. The line passes through the origin and has a gradient of 18. Write down what the gradient of this line represents.

14.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.

15.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.