Algebra worksheet — GCSE Foundation

1.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.

2.Solve 2x² = 18.

3.Solve 3(2x − 1) = 27

4.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.

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

6.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

7.Write down the coefficient of p in the expression 7 − 4p + 9q.

8.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.

9.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

10.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

11.Solve 3x + 14 = 8x − 6

12.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

13.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

14.Which expression means 'add 3 to n, then multiply the result by 4'?

15.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.