Algebra worksheet — GCSE Foundation

1.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

2.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

3.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

4.Factorise fully 5x + 5y − 5

5.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

6.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

7.Write down the gradient of the line with equation y = 6 + 4x.

8.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

9.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.

10.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

11.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

12.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

13.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

14.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

15.Work out the y-intercept of the graph of y = x² + 3x − 10.