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 · Non-calculator · 15 questions

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1.A plan is drawn to a scale of 1 : 500. Work out how many metres are represented by 1 cm on the plan.
(a)500 m
(b)5 m
(c)50 m
(d)0.5 m
2.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?
(a)They are not in inverse proportion, because y ÷ x is different for each pair (3.75 and 1.67).
(b)They are in inverse proportion, because x × y = 60 for both pairs.
(c)They are in inverse proportion, because x × y = 40 for both pairs.
(d)They are not in inverse proportion, because x + y is different for each pair (19 and 16).
3.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.
(a)15 litres
(b)5 litres
(c)3 litres
(d)2 litres
4.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
5.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.
(a)12
(b)10
(c)18.75
(d)20
6.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.
(a)80 km/h
(b)75 km/h
(c)82.5 km/h
(d)60 km/h
7.A recipe for 8 muffins needs 200 g of sugar. Sam wants to make 20 muffins for a bake sale, and he already has 350 g of sugar. Work out how many more grams of sugar he needs to buy.
(a)150 g
(b)850 g
(c)0 g
(d)500 g
8.A sunflower is 140 cm tall. A tomato plant is 80 cm tall. Write the height of the tomato plant as a fraction of the height of the sunflower, giving your answer in its simplest form.
(a)7/4
(b)3/7
(c)4/11
(d)4/7
9.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.
(a)25 : 1
(b)1 : 5
(c)1 : 25
(d)1 : 10
10.Write 3 hours 45 minutes as a decimal number of hours.
(a)3.67
(b)4.15
(c)3.45
(d)3.75
11.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
(a)45%
(b)145%
(c)36%
(d)31%
12.A car uses 6 litres of petrol to travel 90 km. Write the ratio of the distance travelled in km to the amount of petrol used in litres, in its simplest form.
(a)15:1
(b)5:2
(c)14:1
(d)1:15
13.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.
(a)1:2
(b)1:200000
(c)1:2000
(d)1:20000
14.In a recipe the mass of chocolate to the mass of milk is in the ratio 1:4. Amelia uses 200 g of milk. Work out the mass of chocolate she needs.
(a)800 g
(b)250 g
(c)40 g
(d)50 g
15.A material has a density of 2 g/cm³. Work out the mass of 5 cm³ of this material.
(a)7 g
(b)2.5 g
(c)10 g
(d)0.4 g

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