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 shop's takings were £4500 in May. In June the takings fell by £900. Write the June takings as a fraction of the May takings, in its simplest form.
(a)4/5
(b)1/5
(c)5/4
(d)4/9
2.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
3.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
(a)8:1
(b)8:4
(c)1:8
(d)2:4
4.A tangent to a curve at the point where x = 3 passes through the points (1, 2) and (5, 14). A candidate says: "The gradient of the tangent at x = 3 is 3, because 14 − 2 = 12 and 12 ÷ 4 = 3." Which statement is correct?
(a)The gradient is 3; the candidate's method is right.
(b)The gradient is −3; the subtraction was done the wrong way round.
(c)The gradient is 16; the two changes were added instead of divided.
(d)The gradient is 1/3; the division was done the wrong way round.
5.Order these three values from smallest to largest: 3/8, 0.43, 41%.
(a)3/8, 41%, 0.43
(b)0.43, 41%, 3/8
(c)3/8, 0.43, 41%
(d)41%, 0.43, 3/8
6.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.
(a)3:1
(b)3:2
(c)2:3
(d)2:1
7.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.
(a)600 litres
(b)6 litres
(c)0.6 litres
(d)60 litres
8.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.
(a)£600.00
(b)£408.00
(c)£624.32
(d)£5624.32
9.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
10.The height of a ball, in metres, above the ground is plotted against time, in seconds, after it is thrown. The tangent to the graph at t = 1.5 seconds has gradient 2. Which of these four statements about the ball at t = 1.5 seconds is correct?
(a)Height is 2 m at t = 1.5 s
(b)Speed is 2 m/s² at t = 1.5 s
(c)Height rising at 2 m/s at t = 1.5 s
(d)Ball travelled 2 m from t = 1 to t = 2 s
11.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
12.A necklace is made using gold beads and silver beads in the ratio 7:3. There are 40 more gold beads than silver beads. Work out the total number of beads in the necklace.
(a)100
(b)40
(c)70
(d)30
13.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.
(a)8000
(b)40
(c)20
(d)400
14.In a fruit bowl, the number of bananas is 3/4 of the number of apples. There are 16 apples in the bowl. Write the number of apples as a fraction of the number of bananas. Give your answer in its simplest form.
(a)3/4
(b)4/3
(c)4/7
(d)4/1
15.A recipe for 8 muffins needs 200 g of sugar. Sam wants to make 20 muffins for a bake sale, and he already has 350 g of sugar. Work out how many more grams of sugar he needs to buy.
(a)150 g
(b)850 g
(c)0 g
(d)500 g

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