Ratio, proportion and rates of change worksheet — GCSE Higher

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

2.A shop's takings were £4500 in May. In June the takings fell by £900. Write the June takings as a fraction of the May takings, in its simplest form.

3.The ratio of the amount Noah has saved to the amount Grace has saved is 4:5. Noah has saved £200. Work out how much they have saved altogether.

4.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.

5.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.

6.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.

7.Two quantities x and y are in direct proportion. When x = 8, the value of y is 20. Work out the value of y when x = 14.

8.Write the ratio 0.75 : 2 as a ratio of whole numbers in its simplest form.

9.£1 is worth 1.25 US dollars. Write the ratio of pounds to dollars in its simplest form, using whole numbers.

10.In a fruit drink, cranberry juice and apple juice are mixed in the ratio 3:7. Write the amount of apple juice as a fraction of the amount of cranberry juice, in its simplest form.

11.A coach journey of 240 km takes 3 hours. For this fixed distance the average speed needed is inversely proportional to the time taken. Work out the average speed needed to complete the same journey in 2 hours.

12.In a fruit drink, 3/8 of the total volume is orange juice and the rest is apple juice. Write down the ratio of orange juice to apple juice, in its simplest form.

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

14.The height of a ball, in metres, above the ground is plotted against time, in seconds, after it is thrown. The tangent to the graph at t = 1.5 seconds has gradient 2. Which of these four statements about the ball at t = 1.5 seconds is correct?

15.The volume of water in a paddling pool, in litres, is plotted against the time since the tap was turned on, in minutes. What are the units of the gradient of a tangent to this graph?