Printable · GCSE Foundation · ages 14-16

Ratio, proportion and rates of change worksheet — GCSE Foundation

Fifteen questions across the ratio, proportion and rates of change statements at Foundation 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 Foundation

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

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1.Two quantities are connected by the formula y = 0.8x. Write down the ratio y : x in its simplest form.
y = 0.8x
(a)5 : 4
(b)8 : 1
(c)4 : 5
(d)8 : 10
2.y is directly proportional to x, and y = 3x. Work out the value of y when x = 4.
y = 3x
(a)1
(b)12
(c)7
(d)34
3.Work out how many seconds there are in 3 minutes and 20 seconds.
(a)200 seconds
(b)320 seconds
(c)180 seconds
(d)23 seconds
4.Two investors put money into a business in the ratio 3:5. The first investor puts in £1,200. Work out the total amount invested by both investors.
(a)£2,400
(b)£2,000
(c)£3,200
(d)£6,000
5.A map has a scale of 1 : 100 000. Two railway stations are 8 km apart in real life. Work out the distance between the stations on the map, in centimetres.
(a)8 cm
(b)800000 cm
(c)0.08 cm
(d)80 cm
6.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
7.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.
8.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
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 textbook is reduced from £60 to £45. Work out the percentage reduction.
(a)33%
(b)15%
(c)75%
(d)25%
11.The ratio of cats to dogs in a shelter is 3:4. There are 18 cats. Work out the total number of animals in the shelter.
(a)42
(b)126
(c)25
(d)24
12.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.
(a)25:1
(b)1:25
(c)25:8
(d)8:25
13.The density of a type of wood is 0.8 g/cm³. Work out the mass of a piece of this wood with a volume of 150 cm³.
(a)149.2 g
(b)187.5 g
(c)1200 g
(d)120 g
14.The number of biscuits, b, that each guest at a party receives is inversely proportional to the number of guests, g. Which equation could show this relationship?
(a)b = g ÷ k
(b)b = k + g
(c)b = kg
(d)b = k ÷ g
15.The value of a rare coin increases by 12% each year. The coin is currently worth £270. Work out the value of the coin after 2 years, giving your answer to the nearest penny.
(a)£334.80
(b)£338.68
(c)£338.69
(d)£302.40

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