Algebra worksheet — GCSE Higher

1.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

2.Which of these quadratic graphs does NOT cross the x-axis at all?

3.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

4.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

5.A circular pond has equation x² + y² = 20, with lengths in metres from the centre of the garden. A straight path runs along the line y = 2x, entering the pond and leaving it again. Work out the coordinates of the two points where the path meets the edge of the pond.

6.Work out the value of 3x² − 4x when x = −2.

7.Solve the inequality 5x − 3 > 2x + 9.

8.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.

9.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

10.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

11.Work out the value of n² − n when n = −3

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

13.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

14.Solve 2x² − 7x + 3 = 0.

15.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.