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.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
2.Which of these ratios is equivalent to 2:3?
(a)12:8
(b)8:12
(c)4:5
(d)8:3
3.A straight-line graph shows the cost, C pounds, of hiring a bike for h hours. The line passes through the points (1, 12) and (4, 27). Which of these statements about the line is true?
(a)The hourly rate is £5 and the fixed fee is £7
(b)The hourly rate is £5 and the fixed fee is £12
(c)The hourly rate is £7 and the fixed fee is £5
(d)The hourly rate is £15 and the fixed fee is £7
4.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.
(a)18/25
(b)25/18
(c)3/25
(d)3/5
5.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
6.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.
(a)22p
(b)79200p
(c)2.2p
(d)1320p
7.3 kg of apples cost £6. Work out the cost of 5 kg of the same apples.
(a)£3.60
(b)£10
(c)£11
(d)£30
8.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.
(a)50 minutes
(b)20 minutes
(c)15 minutes
(d)25 minutes
9.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).
10.A film lasts 105 minutes. A documentary lasts 45 minutes. Write the length of the film as a fraction of the length of the documentary. Give your answer in its simplest form.
(a)3/7
(b)4/3
(c)7/10
(d)7/3
11.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
12.Write 250 g : 2 kg as a ratio in its simplest form.
(a)1:8
(b)5:40
(c)125:1
(d)8:1
13.A parcel of flour has a mass of 750 g. A sack of flour has a mass of 4 kg. Write the mass of the parcel as a fraction of the mass of the sack. Give your answer in its simplest form.
(a)15/8
(b)3/20
(c)16/3
(d)3/16
14.A mobile phone tariff is shown on a straight-line graph with the monthly cost, C pounds, on the vertical axis and the amount of data used, g gigabytes, on the horizontal axis. The line passes through (0, 10) and (8, 26). Work out the gradient and say what it represents.
(a)3.25, the cost in pounds of each extra gigabyte
(b)2, the cost in pounds of each extra gigabyte
(c)10, the cost in pounds of each extra gigabyte
(d)2, the fixed monthly charge in pounds
15.Ollie says that the ratio 6 : 15 is equivalent to the ratio 2 : 5. Is he correct? Give a reason for your answer.
(a)Yes — dividing both parts of 6 : 15 by 3 gives 2 : 5
(b)No — ratios must start with an even number to simplify
(c)No — 15 ÷ 6 isn't whole, so it can't simplify
(d)No — 6 : 15 simplifies to 3 : 5, not 2 : 5

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