Algebra worksheet — GCSE Foundation

1.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

2.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

3.Solve 4(x − 3) = 2x + 6.

4.Simplify 2a + 3b − a + 2b − b

5.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

6.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.

7.Write down 0.2x with its coefficient written as a fraction in its simplest form.

8.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

9.Solve 4x + 3 = 19

10.Solve 2x² − 32 = 0.

11.Which of these rules generates the sequence 6, 11, 16, 21, …?

12.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

13.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

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

15.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.