Ratio, proportion and rates of change worksheet — GCSE Higher

1.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.

2.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.

3.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.

4.The ratio of the number of pages Mia has read to the number of pages Leo has read is 7 : 4. Mia has read 84 pages. Work out how many pages they have read altogether.

5.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.

6.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.

7.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?

8.A water tank has a capacity of 500 litres. It currently holds 350 litres of water. Write the amount of empty space in the tank as a fraction of the tank's capacity. Give your answer in its simplest form.

9.A tangent to a curve at the point where x = 3 passes through the points (1, 4) and (5, 20). Work out the gradient of the tangent at x = 3, and hence the instantaneous rate of change of y with respect to x at that point.

10.A taxi journey of m miles costs C pounds, where C = 2.5m + 3. A driver says the ratio C : m is the same for every journey. Is the driver correct? Give a reason for your answer.

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.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.

13.A salt solution has a concentration of 10%. The solution contains 50 g of salt. Work out the total mass of the solution.

14.The price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.

15.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.