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.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?
(a)They are not in direct proportion, because y − x is different for each pair (9 and 15).
(b)They are not in direct proportion, because x + y is different for each pair (21 and 35).
(c)They are in direct proportion, because y ÷ x = 2.5 for both pairs.
(d)They are in direct proportion, because x × y = 90 and 250.
2.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
3.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
4.Write £3.60 : £2.40 as a ratio in its simplest form.
(a)360 : 240
(b)36 : 24
(c)2 : 3
(d)3 : 2
5.An ice-cream van's daily takings, in £, are modelled by a curve plotted against the average temperature that day, in °C. At a temperature of 22°C, the gradient of the tangent to this curve is 14. What does this gradient tell you about the takings at 22°C?
(a)Takings rise about £14 per 1°C fall
(b)Takings rise about £14 per 1°C rise
(c)Takings rose £14 in total, 0°C to 22°C
(d)Takings are £14 at 22°C
6.A recipe needs 1.2 kg of flour. Dan has 750 g of flour in his cupboard. Write the mass of flour the recipe needs as a fraction of the mass of flour Dan has. Give your answer in its simplest form.
(a)4/25
(b)8/13
(c)5/8
(d)8/5
7.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
8.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.
y = 3x
(a)40
(b)16
(c)28
(d)4
9.A sprinter's distance from the start line, in metres, is plotted against time, in seconds. A tangent to the graph at t = 2 seconds has gradient 6. A tangent at t = 8 seconds has gradient 9.5. Which statement correctly compares the sprinter's speed at these two times?
(a)Slower at t = 8s — decelerating
(b)Average speed for race is 9.5 m/s
(c)3.5 m further covered by t = 8s
(d)Faster at t = 8s — still accelerating
10.A textbook is reduced from £60 to £45. Work out the percentage reduction.
(a)33%
(b)15%
(c)75%
(d)25%
11.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.
(a)9 : 25
(b)5 : 3
(c)18 : 50
(d)3 : 5
12.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.
(a)£39
(b)£52
(c)£91
(d)£13
13.Simplify the ratio 45 : 30 : 75 to its simplest form.
(a)2 : 3 : 5
(b)15 : 10 : 25
(c)9 : 6 : 15
(d)3 : 2 : 5
14.A shop's number of online orders is proportional to its number of in-store orders. Last month there were 45 in-store orders and 180 online orders. Write the ratio of online orders to in-store orders, in its simplest form.
(a)3:1
(b)1:4
(c)4:5
(d)4:1
15.Write 250 g : 2 kg as a ratio in its simplest form.
(a)1:8
(b)5:40
(c)125:1
(d)8:1

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