Ratio, proportion and rates of change worksheet — GCSE Higher

1.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

2.A smoothie recipe combines 350 cm³ of mango juice with 650 cm³ of orange juice. Work out the total volume of the smoothie in litres.

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

4.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?

5.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.

6.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.

7.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.

8.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.

9.A shop's number of online orders is proportional to its number of in-store orders. Last month there were 45 in-store orders and 180 online orders. Write the ratio of online orders to in-store orders, in its simplest form.

10.The tangent to a curve at the point where x = 4 has equation y = 3x − 2. Work out the instantaneous rate of change of y with respect to x at x = 4.

11.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.

12.A process is modelled by the recurrence P_{n+1} = 0.6P_n + 40. As n increases, P_n approaches a long-run value L, which satisfies L = 0.6L + 40. Solve this equation to find L.

13.A cordial drink is made by mixing cordial concentrate and water in the ratio 1 : 6. Freya says that a 700 ml jug of this drink contains 100 ml of concentrate. Is she correct? Give a reason for your answer.

14.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.

15.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.