Ratio, proportion and rates of change worksheet — GCSE Higher

1.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?

2.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?

3.Simplify the ratio 12 : 18 : 30 to its simplest form.

4.A shop sells rope by the metre. 3 m costs £7.50 and 5 m costs £11.00. Does this data show that the cost is directly proportional to the length of rope bought? Choose the correct verdict and reason.

5.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.

6.Before a charity campaign, donations were £6400 per month. Donations grew by 8% in the first year after the campaign, and then fell by 3% in the second year as interest faded. Work out the amount donated per month at the end of the second year, to the nearest pound.

7.Two numbers are in the ratio 3 : 7. Their sum is 60. Work out the positive difference between the two numbers.

8.A loan of £3000 has interest added at 2% each month, and then a fixed repayment of £200 is made. This is modelled by the recurrence B_{n+1} = 1.02B_n − 200, where B_n is the balance after n months and B_0 = 3000. Work out the balance after 2 months.

9.A car travels for 3 hours at an average speed of 80 km/h and then for 1 hour at an average speed of 40 km/h. Work out the average speed for the whole journey.

10.A machine is bought for £8500. Its value depreciates by 6% each year. Work out the value of the machine after 3 years, to the nearest pound.

11.A hiker's distance from the start of the trail, in kilometres, is plotted against time, in minutes, since she set off. At t = 45 minutes she stops to rest, so her distance from the start is neither increasing nor decreasing at that instant. Which statement about the tangent to the distance–time graph at t = 45 minutes is correct?

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

13.A charity fun run raises money through entry fees and donations. Entry fees raise £1,260, which is 60% of the total amount raised. Work out how much money was raised through donations.

14.Write 350 ml : 1.4 l as a ratio in its simplest form.

15.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.