Algebra worksheet — GCSE Foundation

1.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

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

3.Solve x² − 5x + 6 = 0 by factorising.

4.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

5.Expand 2(x − 13)

6.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

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

8.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

9.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

10.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

11.Work out the value of 5m² + 3m when m = −2.4

12.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

13.Which of these is a formula?

14.Solve 3(2x − 1) = 27

15.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.