Algebra worksheet — GCSE Higher

1.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

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

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

4.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

5.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.

6.Solve 2x² = 18.

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

8.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

9.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

10.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

11.A distance-time graph is a straight line from (0, 0) to (4, 100), where time is in hours and distance is in kilometres. Work out the gradient of the line.

12.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?

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.The diagram shows the graph of a quadratic function. Which equation could it represent?

15.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.