Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

2.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

3.Which expression is equivalent to 0.5(4x + 6) − x?

4.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.

5.A number machine multiplies its input by 3. The output is 15. Work out the input.

6.p = 4. Work out the value of 2p³.

7.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

8.Write down the expression that means 5 more than half of n.

9.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.

10.Solve 6x + 4 = 28

11.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

12.Work out the value of 3a − 2b when a = 5 and b = 4

13.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

14.Solve (2x + 1)/3 = 5

15.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.