Algebra worksheet — GCSE Foundation

1.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

2.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.

3.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

4.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

5.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.

6.Write down 0.2x with its coefficient written as a fraction in its simplest form.

7.Solve 5x + 2 = 17.

8.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

9.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

10.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.

11.Work out the value of 3x² − 4x when x = −2.

12.Work out the y-intercept of the graph of y = x² + 3x − 10.

13.Expand 2(x − 13)

14.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

15.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.