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.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

3.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

4.Solve 2x + 1 = 9

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

6.Solve 2(x + 3) = 10

7.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

8.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

9.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

10.Factorise fully 12x² + 18x.

11.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

12.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

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

14.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

15.In the expression 5x² − 3x + 7, which of these is a single term of the expression?