Algebra worksheet — GCSE Foundation

1.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

2.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

3.Solve the inequality 3x + 6 ≤ 0.

4.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

5.Which of these is an equation, rather than an expression, a formula or an identity?

6.Which of these rules generates the sequence 6, 11, 16, 21, …?

7.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

8.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

9.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

10.Make p the subject of the formula n = p/3.

11.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

12.Work out the value of 3n − 2 when n = 1

13.Solve x² + 7x = 0.

14.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

15.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.