Algebra worksheet — GCSE Foundation

1.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

2.Factorise x² − 3x − 10.

3.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

4.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

5.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

6.Work out the value of a² − 2b when a = −3 and b = 4.

7.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

8.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

9.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.

10.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

11.Solve 3x + 14 = 8x − 6

12.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

13.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

14.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

15.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.