Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

2.Simplify 5a/6 − a/3

3.Work out the gradient of the straight line with equation 2x + y = 8.

4.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

5.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

6.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

7.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

8.p = 4. Work out the value of 2p³.

9.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

10.Solve x² − 6x = 0.

11.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

12.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

13.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

14.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

15.Solve 3x − 5 = 4.