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 cordial drink is made by mixing cordial concentrate and water in the ratio 1 : 6. Freya says that a 700 ml jug of this drink contains 100 ml of concentrate. Is she correct? Give a reason for your answer.
(a)No — half of 700 ml (350 ml) should be concentrate
(b)No — 600 ml is concentrate, 100 ml is water
(c)Yes — 700 ÷ 7 = 100 ml for the 1 part of concentrate
(d)No — divide 700 by 6, not 7: about 117 ml
2.A plan is drawn to a scale of 1 : 25. A real fence is 10 m long. Work out the length of the fence on the plan, in centimetres.
(a)0.4 cm
(b)4 cm
(c)25000 cm
(d)40 cm
3.Triangle ABC is mathematically similar to triangle PQR, with AB corresponding to PQ and BC corresponding to QR. AB = 6 cm, BC = 8 cm and PQ = 12 cm. Work out the length of QR.
(a)32 cm
(b)24 cm
(c)16 cm
(d)14 cm
4.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
5.Two mathematically similar logos are printed on a poster. They have areas 20 cm² and 45 cm². Nadia says that the length scale factor from the smaller logo to the larger logo is 45 ÷ 20 = 2.25. Give a reason why Nadia is incorrect, and work out the correct length scale factor.
(a)2.25
(b)0.67
(c)4.5
(d)1.5
6.Two numbers are in the ratio 2 : 3. The smaller number is 8. Work out the larger number.
(a)24
(b)12
(c)16
(d)9
7.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
(a)60
(b)16
(c)11.25
(d)20
8.x is 2/3 of y. Write the ratio x : y in its simplest form.
(a)3 : 2
(b)3 : 5
(c)2 : 5
(d)2 : 3
9.A metal block has a mass of 270 g and a volume of 30 cm³. Work out the density of the block, in g/cm³.
(a)8100 g/cm³
(b)240 g/cm³
(c)9 g/cm³
(d)270 g/cm³
10.A watering can holds 4500 cm³ of water. Given that 1 litre = 1000 cm³, work out the capacity of the watering can in litres.
(a)45 litres
(b)0.45 litres
(c)4.5 litres
(d)450 litres
11.A kettle uses 2.1 kWh of energy. A toaster uses 0.9 kWh of energy. Write the energy used by the kettle as a fraction of the energy used by the toaster, giving your answer in its simplest form.
(a)7/10
(b)4/3
(c)3/7
(d)7/3
12.Work out 25% of 200.
(a)50
(b)100
(c)25
(d)800
13.Ffion is paid £11.20 per hour. She works 6 hours on Monday and 4.5 hours on Tuesday. Work out her total pay for the two days.
(a)£67.20
(b)£50.40
(c)£106.40
(d)£117.60
14.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.
(a)3200p
(b)32p
(c)3.2p
(d)0.32p
15.Write 45 minutes : 2 hours as a ratio in its simplest form.
(a)9:24
(b)8:3
(c)45:2
(d)3:8

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