Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

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.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

4.Make x the subject of the formula y = 3(x + 2).

5.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

6.Expand 4(2x − 3).

7.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

8.Which of these is an inequality?

9.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

10.Work out the value of 3n − 2 when n = 1

11.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

12.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

13.y = x + 4. Work out the value of y when x = 3.

14.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

15.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.