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.Two mathematically similar containers have a volume scale factor of 64 (the larger container's volume is 64 times the smaller container's volume). Work out the length scale factor between the two containers.
(a)4
(b)8
(c)64
(d)32
2.Write the ratio 6a : 9a in its simplest form, where a is a positive number.
(a)6:9
(b)2a:3a
(c)2:3
(d)3:2
3.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.
(a)15000 m
(b)1500 m
(c)50000 m
(d)150 m
4.y is directly proportional to x. If the value of x is trebled (multiplied by 3), what happens to the value of y?
(a)y stays the same
(b)y is divided by 3
(c)y is trebled
(d)y increases by 3
5.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.
(a)15 km/h
(b)30 km/h
(c)45 km/h
(d)20 km/h
6.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.
(a)10
(b)15
(c)60
(d)12
7.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.
(a)3
(b)1.6
(c)13
(d)40
8.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
9.The amount of fuel left in a car's tank, F litres, is plotted against the distance travelled, d miles, and the points lie on a straight line. The line passes through (0, 45) and (150, 15). Work out the gradient of the line and say what it tells you.
(a)−5, the car uses 5 litres of fuel for each mile
(b)−30, the car uses 30 litres of fuel for each mile
(c)−0.2, the car uses 0.2 litres of fuel for each mile
(d)0.2, the car gains 0.2 litres of fuel for each mile
10.Two mathematically similar water bottles have a volume scale factor of 8 from the smaller bottle to the larger bottle. Work out the surface area scale factor from the smaller bottle to the larger bottle.
(a)8
(b)4
(c)2
(d)64
11.A block of wood has a mass of 60 g and a volume of 100 cm³. Work out the density of the block, in g/cm³.
(a)6000 g/cm³
(b)1.67 g/cm³
(c)40 g/cm³
(d)0.6 g/cm³
12.Write 250 g : 2 kg as a ratio in its simplest form.
(a)1:8
(b)5:40
(c)125:1
(d)8:1
13.Last week Priya worked 5 shifts of 7 hours. This week she worked 4 shifts of 8 hours. Write the number of hours she worked last week as a fraction of the number of hours she worked this week.
(a)35/32
(b)35/67
(c)32/35
(d)3/32
14.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.
(a)£15
(b)£57.60
(c)£22.50
(d)£54
15.In a class, 50% of the students study French, 30% study Spanish and the rest study German. Write down the ratio of French : Spanish : German students, in its simplest form.
(a)5:3:1
(b)3:5:2
(c)50:30:20
(d)5:3:2

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