Algebra worksheet — GCSE Foundation

1.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.

2.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

3.Work out the gradient of the straight line with equation y = (2x/5) − 3.

4.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

5.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.

6.Which of these is an inequality?

7.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

8.Factorise fully 56x − 24

9.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

10.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

11.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

12.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

13.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

14.A number machine adds 6 to its input. Work out the output when the input is −4.

15.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.