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 · 15 questions

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1.Write the ratio 5 : 8 in the form 1 : n.
(a)1:0.6
(b)1:1.6
(c)1:1.5
(d)0.6:1
2.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.
(a)8000
(b)40
(c)20
(d)400
3.A mortar mix is made from sand and cement in the ratio 5 : 3. Write the ratio of sand to the total mix in its simplest form.
(a)8:5
(b)5:8
(c)3:8
(d)5:3
4.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
5.The number of euros, e, received is directly proportional to the number of pounds, p, exchanged. Exchanging £40 gives 46 euros. Work out how many euros are received for £65, giving your answer to the nearest euro.
(a)57
(b)75
(c)74
(d)71
6.A curve has equation y = 2x² + 5. Work out an estimate for the gradient of the curve at x = 3, using a chord between the points where x = 2 and x = 4.
y = 2x² + 5
(a)25
(b)24
(c)0.08
(d)12
7.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.
(a)100 cm²
(b)10000 cm²
(c)1000000 cm²
(d)200 cm²
8.Work out the value of x when 4/x = 2/5.
(a)10
(b)2.5
(c)20
(d)8
9.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
10.A force of 250 N acts on an area of 0.5 m². Using pressure = force ÷ area, work out the pressure, in pascals.
(a)50
(b)125
(c)500
(d)249.5
11.The height of water in a tank, h metres, t minutes after a tap is opened is modelled by h = 0.02t² + 0.5. Estimate the instantaneous rate of change of the height at t = 10, using the gradient of the chord joining t = 9 and t = 11.
(a)0.22 m/min
(b)2.50 m/min
(c)0.80 m/min
(d)0.40 m/min
12.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.
(a)y = 3x + 4
(b)y = 3/(4x)
(c)y = 4x/3
(d)y = 3x/4
13.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.
(a)£598
(b)£494
(c)£478.40
(d)£416
14.300 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%
15.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.
(a)4:3:1
(b)4:3:2
(c)2:150:50
(d)3:4:1

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