Ratio, proportion and rates of change worksheet — GCSE Higher

1.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.

2.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.

3.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.

4.A cyclist rides 19.3 km in 47 minutes. Work out her average speed, in km/h, to 1 decimal place.

5.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.

6.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.

7.A map has a scale of 1 : 40 000. A cycle path measures 7.5 cm on the map. Work out the real length of the cycle path, in kilometres.

8.A cyclist travels d kilometres in t hours. Write down an expression, in terms of d and t, for the cyclist's average speed in km/h.

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

10.The total cost, in pounds, of manufacturing a batch of components is plotted against the number of components produced. A tangent to this graph at a particular point has gradient 3.60. What does the value 3.60 represent?

11.The number of members of a running club increases from 45 to 54. Work out the percentage increase.

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.There are 2500 electric cars registered in a town. The number is predicted to increase by 6% each year. Work out the predicted number of electric cars after 3 years, to the nearest whole number.

14.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.

15.To make a shade of green paint, the amount of yellow paint used is always 0.75 times the amount of blue paint used. Write the amount of blue paint as a fraction of the amount of yellow paint, in its simplest form.