Algebra worksheet — GCSE Foundation

1.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

2.Which of these equations is equivalent to 5x − 2 = 3x + 8?

3.Solve x² − 100 = 0.

4.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

5.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?

6.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

7.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

8.Solve 5x² − 15x = 0.

9.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

10.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

11.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.

12.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

13.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

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

15.Solve x² − x − 12 = 0.