Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Write 250 g : 2 kg as a ratio in its simplest form.

2.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.

3.A shop's takings were £4500 in May. In June the takings fell by £900. Write the June takings as a fraction of the May takings, in its simplest form.

4.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.

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

6.A sunflower is 140 cm tall. A tomato plant is 80 cm tall. Write the height of the tomato plant as a fraction of the height of the sunflower, giving your answer in its simplest form.

7.A recipe for pancakes uses 240 g of flour to make pancakes for 6 people. Work out how many grams of flour are needed to make pancakes for 15 people, using the same recipe.

8.3 builders put up a fence in 12 days. All the builders work at the same rate, so the number of days is inversely proportional to the number of builders. Work out how long 9 builders take to put up the same fence.

9.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.

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

11.y is directly proportional to x, and y = 3x. Work out the value of y when x = 4.

12.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.

13.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.

14.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.

15.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.