Ratio, proportion and rates of change worksheet — GCSE Higher

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

2.Maya is paid £105.30 for working 9 hours. Work out her rate of pay, in £ per hour.

3.Write 75p : £1.50 as a ratio of whole numbers in its simplest form.

4.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.

5.An online shop's total number of orders received is recorded at the end of each day for five consecutive days: Day 1, 1,284 orders; Day 2, 1,509 orders; Day 3, 1,830 orders; Day 4, 2,296 orders; Day 5, 2,510 orders. Work out between which two consecutive days the average rate of increase in orders was greatest.

6.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

7.A map has a scale of 1:25000. A road on the map is 6 cm long. Work out the real-life length of the road, giving your answer in kilometres.

8.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.

9.Triangle ABC is mathematically similar to triangle PQR, with AB corresponding to PQ and BC corresponding to QR. AB = 6 cm, BC = 8 cm and PQ = 12 cm. Work out the length of QR.

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

11.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.

12.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.

13.Priya invests £750 in a savings account that pays simple interest. After 3 years, the account contains £840. Work out the annual rate of simple interest.

14.Write 250 g : 2 kg as a ratio in its simplest form.

15.A patient is given a dose of 200 mg of a drug. Each hour, 30% of the drug remaining in the bloodstream is eliminated, and then a further dose of 50 mg is given. Using the recurrence D_{n+1} = 0.7D_n + 50, with D_0 = 200, work out the amount of drug in the bloodstream after 2 hours.