Algebra worksheet — GCSE Foundation

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

2.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

3.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

4.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

5.Work out the value of 2x² when x = −3

6.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

7.Factorise x² − 64.

8.y = 5 − 2x. Work out the value of x when y = 11.

9.Work out the value of m² + 3m when m = −2

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

11.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

12.Solve 5x + 2 = 17.

13.A number machine adds 5 to its input. Work out the output when the input is 0.

14.The point B has coordinates (−2, −2). In which quadrant is B?

15.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.