Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

2.Which of these is a formula?

3.Write down the gradient of the line with equation y = 6 + 4x.

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

5.y = 5 − 2x. Work out the value of x when y = 11.

6.Solve 5x − 9 = 16

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

8.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

9.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

10.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

11.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

12.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.

13.Solve 5(x + 3) = 40

14.Solve 6x − 5 = 3x + 13.

15.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.