Algebra worksheet — GCSE Foundation

1.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

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.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

4.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

5.Solve 6x + 4 = 28

6.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

7.Solve 5x − 9 = 16

8.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

9.Which of these values of x is a solution of x² + 2x − 15 = 0?

10.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

11.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.

12.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

13.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

14.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

15.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.