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.The ratio of the number of red beads to blue beads in a bracelet is 3 : 7. There are 21 blue beads. Work out the number of red beads.
(a)14
(b)9
(c)49
(d)24
2.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
3.A class has 28 pupils. 16 of the pupils are girls and the rest are boys. Write the ratio of girls to boys in its simplest form.
(a)4:7
(b)3:4
(c)8:6
(d)4:3
4.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.
(a)£8748
(b)£9180
(c)£7800
(d)£8262
5.The table shows values of x and y. x: 3, 5, 8. y: 12, 20, 32. Which statement correctly describes the relationship between x and y?
(a)y is always 4 times x.
(b)y is always double x, plus 6.
(c)y is always x plus 9.
(d)x is always 4 times y.
6.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.
(a)3 cm
(b)300000 cm
(c)0.3 cm
(d)30 cm
7.40% of a number is 12 more than 25% of the same number. Work out the number.
(a)48
(b)80
(c)15
(d)30
8.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.
(a)3000
(b)1500
(c)750
(d)2000
9.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
10.A bag of potatoes has a mass of 3 kg. A bag of carrots has a mass of 5 kg. Write the mass of the potatoes as a fraction of the mass of the carrots.
(a)3/5
(b)5/3
(c)2/5
(d)3/8
11.A spring's extension is directly proportional to the force applied to it. A force of 5 N produces an extension of 12 mm. Work out the extension produced by a force of 20 N.
(a)32 mm
(b)3 mm
(c)48 mm
(d)36 mm
12.Tap A fills a swimming pool in 6 hours. Tap B pours water twice as fast as tap A. The time taken to fill the pool is inversely proportional to the rate of flow. Work out how long tap B takes to fill the pool.
(a)3 hours
(b)12 hours
(c)4 hours
(d)1.5 hours
13.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
14.Isla says that the ratio 4:6 is equivalent to the ratio 6:9. Is she correct? Give a reason for your answer.
(a)Yes, because the number 6 appears in both ratios
(b)No, because 9 − 6 is not equal to 6 − 4
(c)No, because 4 × 6 is not equal to 6 × 9
(d)Yes, because 4 × 9 = 6 × 6
15.Jamal is paid £54 for working 6 hours. Work out his rate of pay, in £ per hour.
(a)£9.00
(b)£324.00
(c)£0.11
(d)£48.00

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