Ratio, proportion and rates of change worksheet — GCSE Higher

1.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.

2.A jumper normally costs £45. In a sale it is reduced by 20%. Work out the sale price, then write the sale price as a fraction of the normal price. Give your answer in its simplest form.

3.A shop buys a bike for £150 and sells it, making a profit of £45. Write the selling price as a fraction of the cost price, giving your answer in its simplest form.

4.To make orange paint, red and yellow paint are mixed in the ratio 6:15. Write the amount of red paint as a fraction of the amount of yellow paint, in its simplest form.

5.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.

6.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.

7.A cup of tea is cooling. Its temperature, in °C, is plotted against time, in minutes, since it was poured. At t = 4 minutes, the gradient of the tangent to the graph is −3.2. What does this tell you about the tea at t = 4 minutes?

8.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.

9.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.

10.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.

11.A candidate wants to estimate the instantaneous rate of change of a reservoir's water level, in metres, at t = 5 days after heavy rain began. The reservoir's water level is plotted against time, in days, since the rain began. The candidate uses the chord joining the points at t = 0 days and t = 20 days to estimate the rate of change at t = 5 days. Give a reason why this is likely to be a poor estimate.

12.A recipe for pastry uses flour and butter in the ratio 3:2. A baker has 180 g of butter and wants to make pastry using all of it. Work out the total mass of pastry the baker can make.

13.Write 45 minutes : 2 hours as a ratio in its simplest form.

14.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.

15.A map has a scale of 1 : 50 000. Two villages are 4 cm apart on the map. Work out the real distance between the villages, in kilometres.