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 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
2.A bag of potatoes has a mass of 3 kg. A bag of carrots has a mass of 5 kg. Write the mass of the potatoes as a fraction of the mass of the carrots.
(a)3/5
(b)5/3
(c)2/5
(d)3/8
3.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
4.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
5.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.
(a)2400p
(b)2.4p
(c)24p
(d)240p
6.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.
(a)80 km/h
(b)75 km/h
(c)82.5 km/h
(d)60 km/h
7.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.
(a)4 : 1
(b)3 : 12
(c)1 : 4
(d)1 : 1.2
8.A concrete mix is made from gravel and cement in the ratio 5 : 1 by mass. The mass of cement is c kg and the total mass of the mix is m kg. Write down a formula for m in terms of c.
(a)m = c + 5
(b)m = c/6
(c)m = 6c
(d)m = 5c
9.Two quantities are connected by the formula y = 0.8x. Write down the ratio y : x in its simplest form.
y = 0.8x
(a)5 : 4
(b)8 : 1
(c)4 : 5
(d)8 : 10
10.Write 400 g : 1.5 kg as a ratio in its simplest form.
(a)4 : 15
(b)40 : 150
(c)4 : 1.5
(d)15 : 4
11.Two mathematically similar rectangles have widths 5 cm and 10 cm. The perimeter of the smaller rectangle is 18 cm. Work out the perimeter of the larger rectangle.
(a)72 cm
(b)9 cm
(c)36 cm
(d)23 cm
12.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
13.Ollie says that the ratio 6 : 15 is equivalent to the ratio 2 : 5. Is he correct? Give a reason for your answer.
(a)Yes — dividing both parts of 6 : 15 by 3 gives 2 : 5
(b)No — ratios must start with an even number to simplify
(c)No — 15 ÷ 6 isn't whole, so it can't simplify
(d)No — 6 : 15 simplifies to 3 : 5, not 2 : 5
14.Write the ratio 27 : 45 in its simplest form.
(a)27 : 45
(b)3 : 5
(c)5 : 3
(d)9 : 15
15.A rectangle has its height and its width in the ratio 3:2. The height of the rectangle is 18 cm. Work out the width of the rectangle.
(a)17 cm
(b)12 cm
(c)27 cm
(d)6 cm

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