Algebra worksheet — GCSE Higher

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

2.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.

3.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

4.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

5.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.

6.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

7.f(x) = 3x − 2. Find f⁻¹(x).

8.Solve 2x² − 7x + 3 = 0.

9.Solve (2x + 1)/3 = 5

10.Write down the first four terms of the sequence with nth term 6n − 5.

11.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

12.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

13.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

14.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

15.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.