Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.

2.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?

3.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.

4.A runner's speed is 8 m/s. Given that there are 3600 seconds in an hour and 1000 metres in a kilometre, work out the runner's speed in km/h.

5.A film runs for 2.25 hours. Work out the length of the film in minutes.

6.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.

7.A coach travels the 54 miles from London to Brighton in 1 hour 30 minutes. Work out the average speed of the coach, in mph.

8.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?

9.A force of 20 N acts on an area of 4 m². Using pressure = force ÷ area, work out the pressure, in pascals.

10.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.

11.A rectangular room is drawn on a plan with a scale of 1 : 50. On the plan, the room measures 8 cm by 6 cm. Work out the real area of the room, in square metres.

12.A garden centre sells two mathematically similar sacks of grass seed. The amount of lawn a sack can treat is proportional to the volume of seed inside it. The smaller sack is 20 cm tall and treats a lawn of area 30 m². The larger sack is 40 cm tall. A gardener needs to treat a lawn with an area of 500 m² using only the larger sacks. Work out the minimum number of larger sacks needed.

13.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.

14.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

15.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.