Ratio, proportion and rates of change worksheet — GCSE Higher

1.The value of a delivery van, in £, is plotted against its age, in years, since it was bought. At age 2 years, the gradient of the tangent to the graph is −950. What does this tell you about the van at age 2 years?

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.The population of a town, P thousand, is plotted against time, t years, since 2020. A tangent to the graph at t = 6 has gradient 2.5. What does this gradient represent?

4.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.

5.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.

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.In a class, 50% of the students study French, 30% study Spanish and the rest study German. Write down the ratio of French : Spanish : German students, in its simplest form.

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

9.In a bag the ratio of red counters to blue counters is 7 : 4. Write the number of red counters as a fraction of the number of blue counters.

10.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.

11.It takes 2 identical pumps 10 hours to empty a flooded basement. Working at the same rate, work out how many hours 5 of these pumps would take to empty the same basement.

12.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.

13.Two mathematically similar rectangles have widths 5 cm and 10 cm. The perimeter of the smaller rectangle is 18 cm. Work out the perimeter of the larger rectangle.

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

15.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?