Algebra worksheet — GCSE Foundation

1.Solve 2x² − 32 = 0.

2.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

3.Which of these values of x is a solution of x² + 2x − 15 = 0?

4.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

5.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

6.Simplify 2b − 1 + 2b − 4 + 2b

7.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

8.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

9.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

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.Solve 2x − 2 = 2

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.x = 5. Work out the value of 3x² − 4.

14.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

15.Solve x² − 2x − 24 = 0.