Printable · GCSE Higher · ages 14-16

Ratio, proportion and rates of change worksheet — GCSE Higher

Fifteen questions across the ratio, proportion and rates of change statements at Higher 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 Higher

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

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1.A map has a scale of 1:25000. A road on the map is 6 cm long. Work out the real-life length of the road, giving your answer in kilometres.
(a)1500 km
(b)1.5 km
(c)15 km
(d)0.15 km
2.A cyclist travels d kilometres in t hours. Write down an expression, in terms of d and t, for the cyclist's average speed in km/h.
(a)d + t
(b)d × t
(c)t ÷ d
(d)d ÷ t
3.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.
(a)0.84
(b)1.4
(c)1.2
(d)7.2
4.A post 2 metres tall casts a shadow 3 metres long. At the same time a nearby tree casts a shadow 12 metres long. Work out the height of the tree.
(a)24 m
(b)4 m
(c)8 m
(d)18 m
5.A baker uses 450 g of flour and 300 g of butter in a batch of pastry. Write the mass of butter as a fraction of the total mass of flour and butter, in its simplest form.
(a)3/2
(b)2/5
(c)2/3
(d)3/5
6.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
7.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.
(a)£7.80
(b)£438.75
(c)£51.00
(d)£0.13
8.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
9.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.
(a)£2620.00
(b)£2740.00
(c)£2743.60
(d)£4243.60
10.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
11.A shop's profit, P pounds, is in direct proportion to the number of items sold, n. When 15 items are sold, the profit is £45. Write down the ratio n : P in its simplest form for this shop.
(a)1 : 45
(b)3 : 1
(c)1 : 3
(d)15 : 3
12.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
(a)−1/3
(b)−3
(c)−12
(d)3
13.A box holds 60 crayons. 25 of the crayons are broken and the rest are unbroken. Write the number of unbroken crayons as a fraction of the number of broken crayons. Give your answer in its simplest form.
(a)5/7
(b)2/5
(c)7/12
(d)7/5
14.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
15.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.
(a)4
(b)0.8
(c)16
(d)3

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