Algebra worksheet — GCSE Higher

1.Work out the period of the graph of y = cos x, in degrees.

2.Factorise 3x² + 10x − 8.

3.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

4.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

5.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

6.Solve x² − 6x = 0.

7.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

8.Which expression is equivalent to 7x − 3(2x − 6)?

9.The graph of y = f(x) has a root (an x-intercept) at x = 5. Work out the x-coordinate of the corresponding root on the graph of y = f(x + 2).

10.A candidate solves the simultaneous equations y = x − 2 and y = x² − 4x + 2 by substitution. They write: "x − 2 = x² − 4x + 2, so x² − 3x + 4 = 0." Which of these is a correct comment on the candidate's working?

11.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

12.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

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

14.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).

15.Factorise fully 56x − 24