Ratio, proportion and rates of change worksheet — GCSE Higher

1.Two hikers' journeys are shown on separate distance-time graphs. Hiker A's graph has gradient 4.5 km/h. Hiker B's graph has gradient 3.2 km/h. Work out how much faster Hiker A walks than Hiker B, in km/h.

2.Cheng is paid an hourly rate that is proportional to the number of hours she works. She earns £52.50 for 7 hours. Work out how much she earns for 11 hours, assuming the same rate.

3.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.

4.A fruit punch is made from orange juice, pineapple juice and lemonade in the ratio 5:3:2. A jug holds 3.5 litres of punch in total. Work out the volume of pineapple juice needed.

5.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.

6.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.

7.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.

8.A textbook is reduced from £60 to £45. Work out the percentage reduction.

9.In one batch of shortbread, a bakery uses 240 g of butter and 160 g of sugar. Another batch, made in the same ratio, uses 90 g of sugar. Work out how much butter is needed for the second batch.

10.Order these three values from smallest to largest: 3/8, 0.43, 41%.

11.Two mathematically similar triangular flags have areas in the ratio 4 : 25. The height of the smaller flag is 6 cm. Work out the height of the larger flag.

12.Write the ratio 8 : 15 in the form 1 : n.

13.The price of a games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.

14.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.

15.An online shop's total number of orders received is recorded at the end of each day for five consecutive days: Day 1, 1,284 orders; Day 2, 1,509 orders; Day 3, 1,830 orders; Day 4, 2,296 orders; Day 5, 2,510 orders. Work out between which two consecutive days the average rate of increase in orders was greatest.