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.

Non-calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Ratio, proportion and rates of change worksheet — GCSE Foundation

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

MathsUKwww.geekhero.co.uk

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.To make orange paint, red and yellow paint are mixed in the ratio 6:15. Write the amount of red paint as a fraction of the amount of yellow paint, in its simplest form.
(a)5/7
(b)2/5
(c)2/7
(d)5/2
3.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.
(a)9.2 kg/m³
(b)92 kg/m³
(c)920 kg/m³
(d)0.00092 kg/m³
4.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.
(a)5:3
(b)2:5
(c)2:3
(d)3:2
5.A cartographer is choosing a scale for a map to show a small park in as much detail as possible. Which of these scales would show the MOST detail — 1 : 500, 1 : 5000, or 1 : 50 000? Give the correct scale and reason.
(a)1 : 50 000 — covers the largest real area, most detail
(b)1 : 500 — smallest real distance per cm (5 m), most detail
(c)1 : 5000 — the middle value, most balanced
(d)1 : 500 — smallest ratio, covers largest real distance
6.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.
(a)£11.00
(b)£66.60
(c)£1.60
(d)£5.40
7.Write 400 g : 1.5 kg as a ratio in its simplest form.
(a)4 : 15
(b)40 : 150
(c)4 : 1.5
(d)15 : 4
8.Write 3/4 as a percentage.
(a)133%
(b)34%
(c)0.75%
(d)75%
9.A hosepipe fills a paddling pool at a constant rate. The volume of water in the pool increases by 15 litres every 3 minutes. Write down the gradient of the graph of volume against time.
(a)45
(b)18
(c)0.2
(d)5
10.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.
(a)1 : 2 000 000
(b)1 : 200 000
(c)1 : 12 000 000
(d)1 : 20 000
11.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
12.To make a shade of green paint, the amount of yellow paint used is always 0.75 times the amount of blue paint used. Write the amount of blue paint as a fraction of the amount of yellow paint, in its simplest form.
(a)40/3
(b)1/4
(c)3/4
(d)4/3
13.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.
(a)121%
(b)11%
(c)21%
(d)20%
14.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.
15.Simplify the ratio 45 : 30 : 75 to its simplest form.
(a)2 : 3 : 5
(b)15 : 10 : 25
(c)9 : 6 : 15
(d)3 : 2 : 5

Build your own mix at the worksheet builder.