Ratio, proportion and rates of change worksheet — GCSE Foundation

1.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.

2.A cartographer is choosing a scale for a map to show a small park in as much detail as possible. Which of these scales would show the MOST detail — 1 : 500, 1 : 5000, or 1 : 50 000? Give the correct scale and reason.

3.Three numbers are in the ratio 1:2:3. The three numbers add up to 72. Work out the largest of the three numbers.

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

5.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.

6.At a youth club the ratio of juniors to seniors is 3:5. There are 40 members altogether. Work out how many seniors there are.

7.A candle burns down at a constant rate. Its height, h cm, is plotted against time, t minutes, on a straight-line graph. The gradient of the line is −0.3. Which statement correctly describes what the gradient means?

8.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.

9.Two mathematically similar flags are made in different sizes. The length scale factor from the smaller flag to the larger flag is 5. Work out the area scale factor from the smaller flag to the larger flag.

10.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.

11.A map has a scale of 1 : 25 000. A footpath measures 6 cm on the map. Work out the real length of the footpath, in kilometres.

12.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

13.A scale drawing states '1 cm represents 25 m'. Which of these is the correct way to write this scale in the form 1 : n?

14.Two quantities, P and Q, are in inverse proportion. A graph is drawn with P on the vertical axis and Q on the horizontal axis. Write down which description fits the shape of this graph.

15.A material has a density of 2 g/cm³. Work out the mass of 5 cm³ of this material.