Algebra worksheet — GCSE Foundation

1.Solve 5(x + 3) = 40

2.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.

3.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).

4.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

5.The diagram shows the graph of a function. Which equation could it represent?

6.Work out the value of 3a − 2b when a = 5 and b = 4

7.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

8.Solve 5x + 2 = 17.

9.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

10.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

11.Which of these equations gives a straight-line graph when plotted?

12.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

13.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

14.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

15.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.