Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as m × m × m × n.

2.The point A is at (5, −3). In which quadrant does A lie?

3.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

4.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

5.Solve x² + 7x = 0.

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

7.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

8.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

9.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.

10.Work out the value of 3a − 2b when a = 5 and b = 4

11.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

12.Solve 3x − 5 = 4.

13.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

14.Which of these is a formula, rather than an expression, an equation, or an identity?

15.Solve the inequality 2(x − 1) ≤ 8.