Algebra worksheet — GCSE Foundation

1.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

2.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.

3.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

4.Solve 4x² − 9 = 0.

5.Factorise x² − 64.

6.Which of these is an inequality?

7.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

8.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

9.Solve the inequality 2(3x − 1) ≥ 4x + 8.

10.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

11.Which expression means the same as 3 × a × b?

12.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

13.Write down the expression that means 5 more than half of n.

14.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

15.Solve 3x − 1 = 8