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.Triangle ABC has a right angle at C. AC = 3 cm and BC = 4 cm. Triangle ABC is mathematically similar to triangle PQR, with angle B corresponding to angle Q. Work out the value of tan(angle Q).
(a)3/4
(b)4/3
(c)3/7
(d)4/7
2.A straight-line graph shows the cost, C pounds, of hiring a small van for m miles driven. The line passes through the origin and the point (25, 20). Work out the gradient of the line.
(a)0.8
(b)20
(c)5
(d)1.25
3.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.
(a)2 : 10
(b)4 : 5
(c)2 : 5
(d)5 : 2
4.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.
(a)3 days
(b)12 days
(c)10 days
(d)48 days
5.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
6.Write the ratio 20 : 30 in its simplest form.
(a)4:6
(b)3:2
(c)2:30
(d)2:3
7.Work out 50% of 60.
(a)6
(b)3000
(c)120
(d)30
8.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
9.A map has a scale of 1 : 25 000. A footpath measures 6 cm on the map. Work out the real length of the footpath, in kilometres.
(a)1.5 km
(b)0.15 km
(c)150 km
(d)150000 km
10.The price of a games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.
(a)21%
(b)81%
(c)20%
(d)19%
11.A map has a scale of 1 : 50 000. Two villages are 4 cm apart on the map. Work out the real distance between the villages, in kilometres.
(a)2 km
(b)20 km
(c)200 km
(d)0.2 km
12.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.
(a)20%
(b)120%
(c)17%
(d)14%
13.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.
(a)£3528
(b)£3392
(c)£136
(d)£128
14.Which of these ratios is equivalent to 2:3?
(a)12:8
(b)8:12
(c)4:5
(d)8:3
15.Which of these ratios is already written in its simplest form?
(a)7:14
(b)4:9
(c)10:15
(d)6:8

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