Ratio, proportion and rates of change worksheet — GCSE Higher

1.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.

2.Two numbers A and B are in the ratio 3:5. When 6 is added to B, the ratio of A to the new value of B is 1:2. Work out the value of A.

3.y is directly proportional to √x. When x = 4, y = 8. Construct the equation connecting x and y, then work out the value of y when x = 9.

4.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.

5.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.

6.Last week Priya worked 5 shifts of 7 hours. This week she worked 4 shifts of 8 hours. Write the number of hours she worked last week as a fraction of the number of hours she worked this week.

7.A map has a scale of 1 : 100 000. Two railway stations are 8 km apart in real life. Work out the distance between the stations on the map, in centimetres.

8.A recipe needs 1.2 kg of flour. Dan has 750 g of flour in his cupboard. Write the mass of flour the recipe needs as a fraction of the mass of flour Dan has. Give your answer in its simplest form.

9.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.

10.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.

11.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.

12.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.

13.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.

14.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.

15.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.