Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A toy manufacturer makes a model aircraft that is mathematically similar to the real aircraft, at a scale of 1 : 48. The wingspan of the model is 15 cm. Work out the wingspan of the real aircraft, giving your answer in metres.

2.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.

3.A force of 250 N acts on an area of 0.5 m². Using pressure = force ÷ area, work out the pressure, in pascals.

4.A scale drawing of a park has a scale of 1 : 2500. On the drawing, the distance between the entrance and the lake is 4.4 cm. A jogger runs from the entrance to the lake and then back to the entrance. Work out the total distance the jogger runs, in kilometres.

5.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.

6.A garden centre sells two mathematically similar sacks of grass seed. The amount of lawn a sack can treat is proportional to the volume of seed inside it. The smaller sack is 20 cm tall and treats a lawn of area 30 m². The larger sack is 40 cm tall. A gardener needs to treat a lawn with an area of 500 m² using only the larger sacks. Work out the minimum number of larger sacks needed.

7.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?

8.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.

9.Last week Priya worked 5 shifts of 7 hours. This week she worked 4 shifts of 8 hours. Write the number of hours she worked last week as a fraction of the number of hours she worked this week.

10.Two mathematically similar water bottles have a volume scale factor of 8 from the smaller bottle to the larger bottle. Work out the surface area scale factor from the smaller bottle to the larger bottle.

11.A film runs for 2.25 hours. Work out the length of the film in minutes.

12.A metal block has a mass of 270 g and a volume of 30 cm³. Work out the density of the block, in g/cm³.

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

14.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².

15.Two mathematically similar garden ponds have surface areas of 12 m² and 27 m². The fencing needed to go around the smaller pond costs £96. Assuming the cost of fencing is proportional to the perimeter of the pond, work out the cost of fencing the larger pond.