Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.

2.8 identical pens cost £6.40 in total. Work out the cost of 5 of the same pens.

3.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.

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

5.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.

6.A blue ribbon is 45 cm long. A red ribbon is 30 cm long. Write the length of the blue ribbon as a fraction of the length of the red ribbon. Give your answer in its simplest form.

7.On a straight-line graph the volume of water, V litres, in a tank is plotted on the vertical axis and the time, t minutes, on the horizontal axis. The line passes through (2, 50) and (6, 130). Work out the gradient of the line and give its units.

8.Work out the difference between 45% of 70 and 35% of 80.

9.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.

10.Last week Priya worked 5 shifts of 7 hours. This week she worked 4 shifts of 8 hours. Write the number of hours she worked last week as a fraction of the number of hours she worked this week.

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.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.

13.A plan is drawn to a scale of 1 : 25. A real fence is 10 m long. Work out the length of the fence on the plan, in centimetres.

14.A concrete block exerts a force of 45 N on the ground through a base with an area of 0.05 m². Work out the pressure on the ground, in N/m².

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