Algebra worksheet — GCSE Foundation

1.Write down the expression that means 5 more than half of n.

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

3.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.

4.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

5.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

6.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

7.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.

8.a = 2 and b = 5. Work out the value of a²b.

9.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

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

11.Solve x/4 + 1 = 3

12.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

13.A number machine adds 5 to its input. Work out the output when the input is 0.

14.Solve 3x − 5 = 4.

15.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.