Ratio, proportion and rates of change worksheet — GCSE Higher

1.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.

2.A process is modelled by the recurrence P_{n+1} = 0.6P_n + 40. As n increases, P_n approaches a long-run value L, which satisfies L = 0.6L + 40. Solve this equation to find L.

3.A map has a scale of 1 : 25 000. Two towns are 5 km apart in real life. Work out the distance between the towns on the map, in centimetres.

4.A savings account pays 3.5% compound interest each year. Bilal invests £1200. Work out how much interest, in total, he earns after 2 years, to the nearest penny.

5.Two broadband providers show their monthly cost on straight-line graphs, with the cost in pounds on the vertical axis and the data used in gigabytes on the horizontal axis. Provider X's line passes through (0, 15) and (100, 35). Provider Y's line passes through (0, 5) and (100, 45). Work out which provider is cheaper for a customer who uses 40 gigabytes in a month.

6.6 identical printers can print a batch of exam papers in 40 minutes, all working at the same rate. Working at the same rate, work out how many minutes 4 of these printers would take to print the same batch.

7.The exchange rate is £1 = €1.15. Convert £200 to euros.

8.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.

9.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.

10.A savings account starts with £500. Each year, 4% interest is added, and then £30 is withdrawn from the account. Which recurrence correctly models the balance, £S_n, after n years, with S_0 = 500?

11.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.

12.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.

13.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.

14.The total cost, in pounds, of manufacturing a batch of components is plotted against the number of components produced. A tangent to this graph at a particular point has gradient 3.60. What does the value 3.60 represent?

15.The depth of water in a tank, in cm, is recorded every 10 seconds: at t = 10, depth = 32; at t = 20, depth = 45; at t = 30, depth = 56. Use the most appropriate chord from these readings to estimate the instantaneous rate of change of depth at t = 20.