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.The population of a town, P thousand, is plotted against time, t years, since 2020. A tangent to the graph at t = 6 has gradient 2.5. What does this gradient represent?
(a)The population is growing at 2.5 people per year.
(b)The total growth in population by t = 6 is 2.5 thousand.
(c)The average population since t = 0 is 2.5 thousand.
(d)The population is growing at 2500 people per year.
2.Two mathematically similar polygons have perimeters in the ratio 2 : 5. Write the ratio of their areas in its simplest form.
(a)8 : 125
(b)4 : 25
(c)4 : 5
(d)2 : 5
3.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
4.Write 45 minutes : 2 hours as a ratio in its simplest form.
(a)9:24
(b)8:3
(c)45:2
(d)3:8
5.The ratio of the amount Noah has saved to the amount Grace has saved is 4:5. Noah has saved £200. Work out how much they have saved altogether.
(a)£250
(b)£400
(c)£450
(d)£360
6.y is directly proportional to x². When x = 3, y = 45. Construct the equation connecting x and y, then work out the value of y when x = 5.
(a)50
(b)25
(c)75
(d)125
7.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
8.A car travels for 3 hours at an average speed of 80 km/h and then for 1 hour at an average speed of 40 km/h. Work out the average speed for the whole journey.
(a)70 km/h
(b)80 km/h
(c)60 km/h
(d)280 km/h
9.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.
10.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.
(a)7.8 kg/m³
(b)78000 kg/m³
(c)7800 kg/m³
(d)780 kg/m³
11.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.
(a)3.2 km
(b)20 km
(c)40 km
(d)5 km
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.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.
(a)C = n + 1
(b)C = n/1.5
(c)C = 1.5n
(d)C = 3n
14.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
15.Two numbers A and B are in the ratio 3:5. When 6 is added to B, the ratio of A to the new value of B is 1:2. Work out the value of A.
(a)18
(b)30
(c)9
(d)6

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