Ratio, proportion and rates of change worksheet — GCSE Higher

1.An ice-cream van's daily takings, in £, are modelled by a curve plotted against the average temperature that day, in °C. At a temperature of 22°C, the gradient of the tangent to this curve is 14. What does this gradient tell you about the takings at 22°C?

2.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.

3.A sculptor makes two mathematically similar statues. The smaller statue is 20 cm tall and 80 ml of varnish covers its surface. The larger statue is 50 cm tall. Work out how much varnish is needed to cover the surface of the larger statue.

4.Amelia uses 2 kg of flour to bake 5 cakes. Using the same recipe, work out how many cakes she can bake with 6 kg of flour.

5.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.

6.In a box of pens, 3/7 of the pens are blue and the rest are black. Write down the ratio of the number of blue pens to the number of black pens, in its simplest form.

7.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.

8.A car travels at a constant speed. It travels 150 miles in 3 hours. At the same speed, work out how far it travels in 5 hours.

9.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

10.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

11.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.

12.A graph shows y plotted against x. The graph is a curve that gets closer to both axes but never touches them, and y decreases as x increases. Write down whether this graph could show direct proportion, inverse proportion, or neither.

13.Two cars travel at constant speeds. Car A travels 150 km in 3 hours. Car B travels 180 km in 4 hours. Which car is faster, and what is its speed?

14.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.

15.Work out the value of x when 4/x = 2/5.