Algebra worksheet — GCSE Higher

1.Solve 3(2x − 1) = 27

2.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

3.A market trader builds a display of oranges in a rectangular block. The block is n oranges wide and 4 oranges longer than it is wide. The number of oranges needed is 5 when n = 1, 12 when n = 2, 21 when n = 3, 32 when n = 4, and 45 when n = 5. Work out an expression, in terms of n, for the number of oranges needed for a display of width n.

4.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?

5.The graph of y = 60 × (0.5)ˣ is sketched for x ≥ 0. Which statement correctly describes what happens to the curve as x increases?

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

7.Solve x² − 5x + 6 = 0 by factorising.

8.Which of these is a factor of 15x + 20?

9.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.

10.Simplify 5a/6 − a/3

11.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

12.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

13.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

14.Which of these is an identity?

15.f(x) = 3x − 2. Find f⁻¹(x).