Algebra worksheet — GCSE Foundation

1.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

2.Factorise fully 56x − 24

3.Simplify (5x² + 3x − 2) − (2x² − x + 5)

4.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

5.Solve 2x − 2 = 2

6.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

7.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

8.Solve 3x − 5 = 4.

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

10.Work out the gradient of the straight line with equation y = (2x/5) − 3.

11.Solve 5x − 9 = 16

12.Factorise fully 12x² + 18x.

13.Work out the value of 3n − 2 when n = 1

14.Write down the expression that means the same as w ÷ 6.

15.p = 4. Work out the value of 2p³.