Algebra worksheet — GCSE Higher

1.Which of these equations is equivalent to 5x − 2 = 3x + 8?

2.Write down the expression that means the same as (x + 7) ÷ 4.

3.Factorise x² − 3x − 10.

4.A tram sets off from a stop. Its velocity-time graph rises in a straight line from 0 m/s to 12 m/s over the first 8 seconds, then stays constant at 12 m/s for a further 10 seconds. Work out the total distance the tram travels in these 18 seconds, using the area under the graph.

5.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

6.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

7.The line y = 2x + 7 and the circle x² + y² = 4 are given. By finding the discriminant of the resulting quadratic, without solving it fully, work out how many points the line and the circle intersect at.

8.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

9.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

10.Work out the value of 3a − 2b when a = 5 and b = 4

11.Subtract, giving your answer as a single fraction in its simplest form: 4/(x − 1) − 2/(x + 3)

12.A square tile has an area of 144 cm². Work out the side length of the tile.

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

14.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

15.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.