Algebra worksheet — GCSE Foundation

1.Solve the inequality 3x − 1 ≤ 11.

2.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.

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

4.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.

5.Which of these is a term, rather than a whole expression, an equation, or a formula?

6.Which of these is an equation, rather than an expression, a formula or an identity?

7.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

8.Make x the subject of the formula y = x/2 − 5.

9.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

10.y = 5x − 1. Work out the value of y when x = 3.

11.Solve 2x + 7 = x + 13

12.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

13.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

14.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

15.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.