Algebra worksheet — GCSE Foundation

1.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

2.A straight line has equation y = 5x. Work out the value of y when x = 3.

3.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

4.a = 2 and b = 5. Work out the value of a²b.

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

6.Simplify k + k + k + k + k.

7.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

8.Which expression means 'y squared, multiplied by 3'?

9.Solve (3x + 2)/5 = (x + 4)/3

10.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

11.Which of these statements is an equation with exactly one solution?

12.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.

13.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

14.Simplify x + x + 4

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