Algebra worksheet — GCSE Foundation

1.Solve x² + 3x − 10 = 0.

2.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

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

4.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

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

6.Factorise fully 12x² + 18x.

7.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

8.Solve 3x − 5 = 4.

9.Make b the subject of the formula a = 5b.

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.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

12.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

13.Solve the inequality x − 10 < −3.

14.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.

15.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.