Algebra worksheet — GCSE Foundation

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

2.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

3.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

4.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

5.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

6.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

7.Solve 2x + 1 = 9

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

9.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.

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

11.Make p the subject of the formula n = p/3.

12.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

13.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

14.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

15.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.