Algebra worksheet — GCSE Foundation

1.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

2.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

3.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.

4.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

5.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

6.Make x the subject of the formula y = 5x + 3.

7.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

8.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

9.Expand 2(x − 13)

10.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

11.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

12.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

13.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

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

15.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.