Ratio, proportion and rates of change worksheet — GCSE Foundation

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

2.A smoothie recipe combines 350 cm³ of mango juice with 650 cm³ of orange juice. Work out the total volume of the smoothie in litres.

3.Square P has sides of length 3 cm. Square Q has sides of length 12 cm. Write the ratio of the area of square P to the area of square Q in its simplest form.

4.A statue exerts a downward force of 68.4 N on its base, which has an area of 2.85 m². Work out the pressure that the statue exerts on its base, in N/m².

5.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.

6.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.

7.Two investors put money into a business in the ratio 3:5. The first investor puts in £1,200. Work out the total amount invested by both investors.

8.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.

9.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?

10.A map has a scale of 1 : 20 000. A different map of the same area has a scale of 1 : 80 000. A lake's shoreline is drawn 5 cm long on the first map. Work out the length of the same shoreline on the second map, in centimetres.

11.Two scale plans of the same football pitch are drawn: Plan A has a scale of 1 : 1000 and Plan B has a scale of 1 : 200. A pitch length is 8 cm on Plan A. Work out the length of the same pitch on Plan B, in centimetres.

12.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.

13.The amount of fuel left in a car's tank, F litres, is plotted against the distance travelled, d miles, and the points lie on a straight line. The line passes through (0, 45) and (150, 15). Work out the gradient of the line and say what it tells you.

14.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.

15.The mass of a length of copper pipe is proportional to its length. A pipe of length 4.5 m has a mass of 12.6 kg. Work out the mass of a pipe of the same type of length 9.5 m.