Ratio, proportion and rates of change worksheet — GCSE Higher

1.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.

2.A coach journey is 372 miles in total. After a stop, the coach has travelled 217 miles. Write the distance still to travel as a fraction of the total journey. Give your answer in its simplest form.

3.40% of a number is 12 more than 25% of the same number. Work out the number.

4.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.

5.Two taxi firms show their charges on straight-line graphs, with the cost in pounds on the vertical axis and the distance in miles on the horizontal axis. Firm A's line passes through (0, 4) and (5, 14). Firm B's line passes through (0, 6) and (5, 21). Work out which firm charges more per mile.

6.y is directly proportional to x. When x = 8, y = 20. Work out the value of y when x = 12.

7.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.

8.Write £3.60 : £2.40 as a ratio in its simplest form.

9.A mobile phone tariff is shown on a straight-line graph with the monthly cost, C pounds, on the vertical axis and the amount of data used, g gigabytes, on the horizontal axis. The line passes through (0, 10) and (8, 26). Work out the gradient and say what it represents.

10.The temperature of a chemical reaction, in °C, is modelled by T = 80 − 6t + 0.5t², where t is the time in minutes after the reaction starts. Which of these four statements about the reaction between t = 2 and t = 6 minutes is correct?

11.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.

12.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.

13.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.

14.A charity collects donations from adults and children in the ratio 5:2. Altogether, £238 is collected. Work out how much more the adults donate than the children.

15.A curve has equation y = x² + 2x. Work out the average rate of change of y with respect to x over the interval from x = 1 to x = 4.