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.Which expression is equivalent to 5x − (x + 3)?

3.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

4.Factorise fully 56x − 24

5.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

6.Which of these points lies in the first quadrant?

7.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

8.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

9.Which expression is equivalent to 3(2x − 5) + 4x?

10.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

11.Make x the subject of the formula y = 4(x − 6).

12.Solve 4x − (2x − 6) = 18

13.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

14.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

15.Make b the subject of the formula a = 5b.