Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A post 2 metres tall casts a shadow 3 metres long. At the same time a nearby tree casts a shadow 12 metres long. Work out the height of the tree.

2.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.

3.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.

4.Triangle ABC has a right angle at C. AC = 3 cm and BC = 4 cm. Triangle ABC is mathematically similar to triangle PQR, with angle B corresponding to angle Q. Work out the value of tan(angle Q).

5.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.

6.Isla says that the ratio 4:6 is equivalent to the ratio 6:9. Is she correct? Give a reason for your answer.

7.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.

8.y is directly proportional to x, and y = 3x. Work out the value of y when x = 4.

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

10.The number of calories burned, E, by a runner is plotted against the time, m minutes, on a straight-line graph. The line passes through the origin and the point (10, 80). Work out the gradient of the line.

11.Freya buys three items whose prices are in the ratio 2:3:5. Altogether she pays £400. Work out the price of the most expensive item.

12.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.

13.A section of a kitchen wall has an area of 45,000 cm². Work out the area of this section in m².

14.A necklace uses 22 blue beads and 8 red beads. Write the number of blue beads as a fraction of the number of red beads. Give your answer as a mixed number in its simplest form.

15.A tap fills a tank at a rate of 15 litres per minute. Given that 1 litre = 1000 cm³, work out the rate at which the tank fills in cm³ per second.