Ratio, proportion and rates of change worksheet — GCSE Higher

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

2.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.

3.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.

4.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.

5.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.

6.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.

7.Simplify the ratio 12 : 18 : 30 to its simplest form.

8.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.

9.A candidate wants to estimate the instantaneous rate of change of a reservoir's water level, in metres, at t = 5 days after heavy rain began. The reservoir's water level is plotted against time, in days, since the rain began. The candidate uses the chord joining the points at t = 0 days and t = 20 days to estimate the rate of change at t = 5 days. Give a reason why this is likely to be a poor estimate.

10.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.

11.A map has a scale of 1:25000. A road on the map is 6 cm long. Work out the real-life length of the road, giving your answer in kilometres.

12.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.

13.Write 45 minutes : 2 hours as a ratio in its simplest form.

14.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.

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