Algebra worksheet — GCSE Higher

1.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

2.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

3.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

4.Solve 2x² − 32 = 0.

5.Solve the inequality x² + 6x + 9 > 0.

6.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

7.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

8.Solve the inequality 3x − 1 ≤ 11.

9.f(x) = 2x + 1. Work out the value of x for which f⁻¹(x) = 5.

10.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.

11.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

12.Which expression means 'y squared, multiplied by 3'?

13.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

14.Work out the value of a² − 2b when a = −3 and b = 4.

15.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.