Algebra worksheet — GCSE Foundation

1.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

2.Which of these values of x is a solution of x² + 2x − 15 = 0?

3.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

4.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

5.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

6.Write down the expression that means the same as m² × m × 3.

7.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

8.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.

9.Solve x/4 + 1 = 3

10.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

11.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

12.Which of these statements is an equation with exactly one solution?

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

14.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

15.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.