Algebra worksheet — GCSE Foundation

1.Work out the value of 3x² − 4x when x = −2.

2.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

3.Solve 3x − 5 = 4.

4.The graph of y = (x − 4)(x + 1) crosses the x-axis. Which pair gives the correct roots and reasoning?

5.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

6.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

7.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

8.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

9.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

10.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

11.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

12.Work out the value of n² − n when n = −3

13.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

14.Work out the value of 5a + 2 when a = 3

15.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.