Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Work out the difference between 45% of 70 and 35% of 80.

2.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.

3.A fruit bowl contains 9 apples and 21 oranges. Write down the ratio of apples to oranges in its simplest form.

4.A hosepipe fills a paddling pool at a constant rate. The volume of water in the pool increases by 15 litres every 3 minutes. Write down the gradient of the graph of volume against time.

5.A recipe uses flour and sugar in the ratio 4 : 1 by mass. The mass of sugar is s grams and the mass of flour is f grams. Write down a formula for f in terms of s.

6.A cyclist rides 19.3 km in 47 minutes. Work out her average speed, in km/h, to 1 decimal place.

7.Ollie says that the ratio 6 : 15 is equivalent to the ratio 2 : 5. Is he correct? Give a reason for your answer.

8.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.

9.A water butt is being filled from a hosepipe at a constant rate while a small leak drains water out at a constant rate, giving a constant net rate of change. The volume of water in the butt, V litres, is shown on a straight-line graph against time, t minutes. The line passes through the points (5, 20) and (15, 60). The butt is empty at t = 0. Work out how many minutes it takes to reach a volume of 100 litres.

10.A straight-line graph shows the cost, C pounds, of hiring a bike for h hours. The line passes through the points (1, 12) and (4, 27). Which of these statements about the line is true?

11.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.

12.A class has 28 pupils. 16 of the pupils are girls and the rest are boys. Write the ratio of girls to boys in its simplest form.

13.A spring's extension is directly proportional to the force applied to it. A force of 5 N produces an extension of 12 mm. Work out the extension produced by a force of 20 N.

14.Divide 84 in the ratio 3:4. Work out the smaller share.

15.A metal sample has a mass of 342.6 g and a volume of 18 cm³. Work out the density of the sample, in g/cm³, to 1 decimal place.