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.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

3.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.

4.Work out the distance of the point (−6, 4) from the x-axis.

5.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

6.Work out the coordinates of the reflection of (6, −3) in the y-axis.

7.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

8.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

9.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?

10.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

11.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

12.Solve 5x + 2 = 17.

13.Solve the inequality 4x + 1 > 2x + 9.

14.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

15.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.