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.A shop's takings were £4500 in May. In June the takings fell by £900. Write the June takings as a fraction of the May takings, in its simplest form.
(a)4/5
(b)1/5
(c)5/4
(d)4/9
2.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
3.A fixed job of fitting a solar array is shared between installers, and the time taken is inversely proportional to the number of installers working on it at once. With 4 installers the job takes 18 hours. Construct the equation connecting time T and number of installers n, then work out how long it would take with 6 installers.
(a)27 hours
(b)72 hours
(c)18 hours
(d)12 hours
4.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
5.A 750 g box of cereal costs £2.70. A 500 g box of the same cereal costs £1.95. Work out which box is better value, and its cost per 100 g.
(a)The 750 g box, at 54p per 100 g
(b)The 500 g box, because £1.95 is the lower total price
(c)The 500 g box, at 39p per 100 g
(d)The 750 g box, at 36p per 100 g
6.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
7.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.
(a)15 litres
(b)5 litres
(c)3 litres
(d)2 litres
8.A shop's daily profit, in pounds, is plotted against the price charged for an item, in pounds. A tangent to the profit graph at a price of £15 passes through the points (12, 540) and (18, 480). Work out the instantaneous rate of change of profit with respect to price at £15, and state whether profit is increasing or decreasing there.
(a)Profit is increasing by £6 per £1 rise in price.
(b)Profit is increasing by £10 per £1 rise in price.
(c)Profit is decreasing by £60 per £1 rise in price.
(d)Profit is decreasing by £10 per £1 rise in price.
9.1 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
10.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
(a)9%
(b)120%
(c)20%
(d)16.7%
11.A recipe for 6 muffins needs 150 g of flour. Aisha wants to make 15 muffins using the same recipe. Work out how much flour she needs.
(a)375 g
(b)60 g
(c)150 g
(d)300 g
12.Write 350 ml : 1.4 l as a ratio in its simplest form.
(a)2:8
(b)25:1
(c)4:1
(d)1:4
13.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.
(a)£29.69
(b)£76.00
(c)£57.00
(d)£123.50
14.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.
(a)510 cm
(b)720 cm
(c)11.25 cm
(d)90 cm
15.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
(a)−1/3
(b)−3
(c)−12
(d)3

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