Algebra worksheet — GCSE Foundation

1.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

2.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

3.n = 3. Work out the value of (2n)².

4.Solve 2x² = 18.

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

6.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

7.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

8.Factorise x² − 64.

9.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

10.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

11.Which expression means 'triple c, then add double d'?

12.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

13.A number machine multiplies its input by 5. Work out the output when the input is −1.

14.a = 3 and b = 5. Work out the value of a²b.

15.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.