Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.

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

3.A glass holds 250 ml of squash. Work out how many of these glasses are needed to fill a 1 litre bottle.

4.In a fruit drink, cranberry juice and apple juice are mixed in the ratio 3:7. Write the amount of apple juice as a fraction of the amount of cranberry juice, in its simplest form.

5.Isla says that the ratio 4:6 is equivalent to the ratio 6:9. Is she correct? Give a reason for your answer.

6.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.

7.A film lasts 105 minutes. A documentary lasts 45 minutes. Write the length of the film as a fraction of the length of the documentary. Give your answer in its simplest form.

8.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.

9.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

10.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.

11.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.

12.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?

13.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.

14.Two mathematically similar rectangles have lengths in the ratio 3 : 5. The area of the smaller rectangle is 27 cm². Work out the area of the larger rectangle.

15.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.