Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Two mathematically similar water bottles have a volume scale factor of 8 from the smaller bottle to the larger bottle. Work out the surface area scale factor from the smaller bottle to the larger bottle.

2.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.

3.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.

4.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.

5.A map has a scale of 1 : 50 000. Two villages are 4 cm apart on the map. Work out the real distance between the villages, in kilometres.

6.In a car park there are 35 cars and 15 vans. Write the ratio of the number of vans to the number of cars in its simplest form.

7.The ratio of the number of pages Mia has read to the number of pages Leo has read is 7 : 4. Mia has read 84 pages. Work out how many pages they have read altogether.

8.Write the ratio 4 : 9 in the form 1 : n.

9.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.

10.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.

11.A material has a density of 2 g/cm³. Work out the mass of 5 cm³ of this material.

12.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.

13.A straight-line graph shows the cost, C pounds, of hiring a bike for h hours. The line passes through the points (1, 12) and (4, 27). Which of these statements about the line is true?

14.Two numbers are in the ratio 2 : 3. The smaller number is 8. Work out the larger number.

15.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.