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.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.
(a)1 : 2 000 000
(b)1 : 200 000
(c)1 : 12 000 000
(d)1 : 20 000
2.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
3.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.
(a)25:1
(b)1:25
(c)25:8
(d)8:25
4.It takes 2 identical pumps 10 hours to empty a flooded basement. Working at the same rate, work out how many hours 5 of these pumps would take to empty the same basement.
(a)4 hours
(b)7 hours
(c)20 hours
(d)25 hours
5.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.
(a)25 : 1
(b)1 : 5
(c)1 : 25
(d)1 : 10
6.Four graphs are described below. Each shows one quantity plotted against another. Write down the description of the graph that shows two quantities in direct proportion.
(a)A curve that falls steeply and then levels off, never touching either axis
(b)A straight line crossing the vertical axis at 5, rising from left to right
(c)A straight line through the origin, rising from left to right
(d)A horizontal straight line at a height of 3 above the horizontal axis
7.Given that a is 40% of b, write the ratio a : b in its simplest form.
(a)2 : 3
(b)2 : 5
(c)3 : 2
(d)5 : 2
8.3 builders put up a fence in 12 days. All the builders work at the same rate, so the number of days is inversely proportional to the number of builders. Work out how long 9 builders take to put up the same fence.
(a)4 days
(b)9 days
(c)6 days
(d)36 days
9.A glass holds 250 ml of squash. Work out how many of these glasses are needed to fill a 1 litre bottle.
(a)4
(b)1250
(c)40
(d)0.25
10.A bag contains red counters and blue counters in the ratio 5:3. There are 56 counters in the bag altogether. Work out how many counters are blue.
(a)35
(b)7
(c)28
(d)21
11.Sam has £24. Tom has £16. Write the amount of money Sam has as a fraction of the amount of money Tom has, giving your answer in its simplest form.
(a)3/2
(b)2/3
(c)3/5
(d)1/2
12.300 g of a salt solution of concentration 10% is poured into 200 g of a salt solution of concentration 25%. Work out the concentration of salt in the mixture.
(a)17.5%
(b)26.7%
(c)16%
(d)19%
13.A force of 20 N acts on an area of 4 m². Using pressure = force ÷ area, work out the pressure, in pascals.
(a)5
(b)24
(c)80
(d)16
14.A solution is made by dissolving 50 g of sugar in 200 g of water. Work out the concentration of sugar in the solution as a percentage.
(a)20%
(b)25%
(c)80%
(d)0.2%
15.In a mix of mortar the ratio of the mass of sand to the mass of cement is 5 : 2. Write the mass of cement as a fraction of the total mass of the mix.
(a)5/7
(b)2/5
(c)2/7
(d)7/2

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