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.A coach journey of 240 km takes 3 hours. For this fixed distance the average speed needed is inversely proportional to the time taken. Work out the average speed needed to complete the same journey in 2 hours.
(a)160 km/h
(b)480 km/h
(c)120 km/h
(d)80 km/h
2.A rope of length A is 1.5 times as long as a rope of length B. Write the ratio A : B in its simplest form.
(a)2 : 3
(b)3 : 5
(c)3 : 2
(d)1.5 : 1
3.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.
(a)£600.00
(b)£408.00
(c)£624.32
(d)£5624.32
4.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.
(a)9 : 16
(b)27 : 4
(c)27 : 64
(d)3 : 4
5.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.
(a)3.2 km
(b)20 km
(c)40 km
(d)5 km
6.A curve has equation y = x² + 2x. Work out the average rate of change of y with respect to x over the interval from x = 1 to x = 4.
y = x² + 2x
(a)7
(b)3
(c)21
(d)−7
7.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.
(a)3000
(b)1500
(c)750
(d)2000
8.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.
(a)£8748
(b)£9180
(c)£7800
(d)£8262
9.In a fruit drink, 3/8 of the total volume is orange juice and the rest is apple juice. Write down the ratio of orange juice to apple juice, in its simplest form.
(a)8 : 5
(b)5 : 3
(c)3 : 5
(d)3 : 8
10.A taxi journey of m miles costs C pounds, where C = 2.5m + 3. A driver says the ratio C : m is the same for every journey. Is the driver correct? Give a reason for your answer.
(a)The driver is correct — the ratio C : m is the same for every journey.
(b)The ratio C : m is not constant because the formula includes a fixed charge of £3 as well as the charge per mile.
(c)The ratio C : m is not constant because the charge per mile, £2.50, is not a whole number.
(d)The ratio C : m is not constant because C increases as m increases.
11.A post 2 metres tall casts a shadow 3 metres long. At the same time a nearby tree casts a shadow 12 metres long. Work out the height of the tree.
(a)24 m
(b)4 m
(c)8 m
(d)18 m
12.A fruit squash is made by mixing squash and water. In a jug, 2/9 of the total volume is squash. A caterer makes up 4.5 litres of the squash mixture. Work out how many litres of squash are in the mixture.
(a)2.25 litres
(b)3.50 litres
(c)0.50 litres
(d)1.00 litres
13.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.
(a)£99
(b)£56.50
(c)£30
(d)£82.50
14.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.
(a)4
(b)0.8
(c)16
(d)3
15.A car travels at a constant speed. It travels 150 miles in 3 hours. At the same speed, work out how far it travels in 5 hours.
(a)90 miles
(b)200 miles
(c)250 miles
(d)300 miles

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