Algebra worksheet — GCSE Foundation

1.Which of these equations describes a vertical line?

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

3.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

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

5.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

6.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

7.Which of these is an equation, rather than an expression, a formula or an identity?

8.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

9.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

10.Write down the expression that means the same as (x + 7) ÷ 4.

11.Make x the subject of the formula y = 4x − 3.

12.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

13.Work out the gradient of the straight line with equation 2x + y = 8.

14.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

15.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.