Printable · GCSE Higher · ages 14-16

Ratio, proportion and rates of change worksheet — GCSE Higher

Fifteen questions across the ratio, proportion and rates of change statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Ratio, proportion and rates of change worksheet — GCSE Higher

Maths · GCSE Higher · Ratio, proportion and rates of change · 15 questions

MathsUKwww.geekhero.co.uk

1.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.
(a)40 km/h
(b)24 km/h
(c)13.5 km/h
(d)0.4 km/h
2.A cleaning solution is made by mixing disinfectant and water in the ratio 1 : 9. Priti wants to make 6 litres of the solution in total. Work out how much disinfectant she needs.
(a)0.6 litres
(b)5.4 litres
(c)0.667 litres
(d)6 litres
3.A force of 250 N acts on an area of 0.5 m². Using pressure = force ÷ area, work out the pressure, in pascals.
(a)50
(b)125
(c)500
(d)249.5
4.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.
(a)8000
(b)40
(c)20
(d)400
5.A jug holds 3 litres of a drink that is 60% fruit juice. 1 litre of water is added to the jug. Work out the percentage of the new mixture that is fruit juice.
(a)60%
(b)75%
(c)45%
(d)15%
6.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.
(a)4/5
(b)5/6
(c)5/9
(d)5/4
7.The volume of water in a paddling pool, in litres, is plotted against the time since the tap was turned on, in minutes. What are the units of the gradient of a tangent to this graph?
(a)minutes
(b)litres per minute
(c)litres
(d)minutes for each litre
8.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.
(a)20%
(b)120%
(c)17%
(d)14%
9.A map has a scale of 1 : 25 000. A footpath measures 6 cm on the map. Work out the real length of the footpath, in kilometres.
(a)1.5 km
(b)0.15 km
(c)150 km
(d)150000 km
10.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.
(a)4 hours
(b)2 hours 40 minutes
(c)3 hours
(d)5 hours 20 minutes
11.A car uses fuel at a constant rate. It uses 24 litres of fuel to travel 300 km. Assuming the same rate, work out how many litres of fuel are needed for a journey of 175 km.
(a)21 litres
(b)1.4 litres
(c)14 litres
(d)24 litres
12.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.
(a)28.8 km/h
(b)2.88 km/h
(c)28800 km/h
(d)2.22 km/h
13.A lorry is carrying a load of mass m tonnes. Given that 1 tonne = 1000 kg, write down an expression for the mass of the load in kilograms.
(a)1000m
(b)m − 1000
(c)m/1000
(d)1000 + m
14.A company's turnover was £128 000 in 2023 and £176 000 in 2024. Work out the multiplier that changes the 2023 turnover into the 2024 turnover.
(a)1.375
(b)0.375
(c)0.727
(d)137.5
15.A curve has equation y = 2x² + 5. Work out an estimate for the gradient of the curve at x = 3, using a chord between the points where x = 2 and x = 4.
y = 2x² + 5
(a)25
(b)24
(c)0.08
(d)12

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