Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

2.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

3.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

4.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

5.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

6.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

7.Solve 4(x − 3) = 2x + 6.

8.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

9.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.

10.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

11.Solve 5x − 9 = 16

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

13.Write down the gradient of the line with equation y = 6 + 4x.

14.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

15.Solve the inequality 4x + 1 > 2x + 9.