Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.

2.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

3.A graph shows two quantities, x and y, in direct proportion. Write down which statement about the graph must be true.

4.The density of a type of wood is 0.8 g/cm³. Work out the mass of a piece of this wood with a volume of 150 cm³.

5.Before a charity campaign, donations were £6400 per month. Donations grew by 8% in the first year after the campaign, and then fell by 3% in the second year as interest faded. Work out the amount donated per month at the end of the second year, to the nearest pound.

6.Two mathematically similar tins have heights 8 cm and 12 cm. Jayden says that the volume of the larger tin is 1.5 times the volume of the smaller tin. Give a reason why Jayden is incorrect, and work out the correct volume scale factor.

7.A photo is enlarged so that its new width is 1.4 times its original width. Write the multiplier that would scale the new width back down to the original width, as a fraction in its simplest form.

8.A map has a scale of 1 : 25 000. Two towns are 5 km apart in real life. Work out the distance between the towns on the map, in centimetres.

9.Given that 1 mile ≈ 1.6 km, work out a speed of 55 mph in km/h.

10.The exchange rate is £1 = €1.15. Convert £200 to euros.

11.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.

12.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.

13.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.

14.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?

15.Write the ratio 8 : 15 in the form 1 : n.