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 · Non-calculator · 15 questions

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1.Tap A fills a swimming pool in 6 hours. Tap B pours water twice as fast as tap A. The time taken to fill the pool is inversely proportional to the rate of flow. Work out how long tap B takes to fill the pool.
(a)3 hours
(b)12 hours
(c)4 hours
(d)1.5 hours
2.Work out the value of x when 4/x = 2/5.
(a)10
(b)2.5
(c)20
(d)8
3.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.
(a)2 : 10
(b)4 : 5
(c)2 : 5
(d)5 : 2
4.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
5.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.
(a)4:3:1
(b)4:3:2
(c)2:150:50
(d)3:4:1
6.Write 250 g : 2 kg as a ratio in its simplest form.
(a)1:8
(b)5:40
(c)125:1
(d)8:1
7.A fixed job of fitting a solar array is shared between installers, and the time taken is inversely proportional to the number of installers working on it at once. With 4 installers the job takes 18 hours. Construct the equation connecting time T and number of installers n, then work out how long it would take with 6 installers.
(a)27 hours
(b)72 hours
(c)18 hours
(d)12 hours
8.The number of tickets a group can afford is inversely proportional to the price per ticket. At £4 per ticket, the group can afford 12 tickets. Work out how many tickets the group can afford at £6 per ticket.
(a)6
(b)18
(c)12
(d)8
9.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
10.A baker uses 450 g of flour and 300 g of butter in a batch of pastry. Write the mass of butter as a fraction of the total mass of flour and butter, in its simplest form.
(a)3/2
(b)2/5
(c)2/3
(d)3/5
11.The temperature of a chemical reaction, in °C, is modelled by T = 80 − 6t + 0.5t², where t is the time in minutes after the reaction starts. Which of these four statements about the reaction between t = 2 and t = 6 minutes is correct?
(a)Instant rate at t = 6 is −2°C/min
(b)Instant rate at t = 2 is −2°C/min
(c)Average rate, t = 2 to 6, is −2°C/min
(d)Temperature falls 2°C in total
12.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.
(a)15000 m
(b)1500 m
(c)50000 m
(d)150 m
13.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.
(a)£29.69
(b)£76.00
(c)£57.00
(d)£123.50
14.A tangent to the graph of population against time at the point where t = 4 passes through (2, 180) and (6, 260). Work out the instantaneous rate of change of the population at t = 4, in people per year.
(a)20 people/year
(b)84 people/year
(c)80 people/year
(d)−20 people/year
15.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.
(a)15 km/h
(b)30 km/h
(c)45 km/h
(d)20 km/h

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