Algebra worksheet — GCSE Foundation

1.Solve the inequality 4x + 1 > 2x + 9.

2.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

3.A square tile has an area of 144 cm². Work out the side length of the tile.

4.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

5.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

6.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

7.Which expression is equivalent to 6x − (2x − 5)?

8.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.

9.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

10.Which of these rules generates the sequence 6, 11, 16, 21, …?

11.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

12.Write down the expression that means the same as m² × m × 3.

13.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

14.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

15.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?