Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².

2.£96 is shared between Ben, Cara and Dev in the ratio 2:3:7. Work out how much Cara receives.

3.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.

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

5.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.

6.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.

7.A jug holds 2 litres. Given that 1 litre = 1000 cm³, work out the capacity of the jug in cm³.

8.Two mathematically similar oil drums have a length scale factor of 3 from the smaller drum to the larger drum. Work out the volume scale factor from the smaller drum to the larger drum.

9.A shop sells rope by the metre. 3 m costs £7.50 and 5 m costs £11.00. Does this data show that the cost is directly proportional to the length of rope bought? Choose the correct verdict and reason.

10.At a youth club the ratio of juniors to seniors is 3:5. There are 40 members altogether. Work out how many seniors there are.

11.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.

12.A model railway is built at a scale where the ratio of model length to real length is 1 : 76. Given that a real carriage is 20.6 metres long, work out the length of the model carriage in centimetres, to 1 decimal place.

13.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.

14.A scale drawing states '1 cm represents 25 m'. Which of these is the correct way to write this scale in the form 1 : n?

15.x is 2/3 of y. Write the ratio x : y in its simplest form.