Algebra worksheet — GCSE Foundation

1.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

2.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

3.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

4.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

5.Factorise fully 5x + 5y − 5

6.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

7.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

8.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.

9.Which of these is a formula?

10.Write down the gradient of the line with equation y = 7x − 2.

11.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

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

13.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

14.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.

15.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.