Algebra worksheet — GCSE Foundation

1.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

2.a = 2 and b = 5. Work out the value of a²b.

3.a = 2 and b = 5. Work out the value of ab².

4.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.

5.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

6.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

7.Make a the subject of the formula b = 20 − a.

8.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

9.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

10.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

11.Make m the subject of the formula w = m − 8.

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

13.Write down 0.2x with its coefficient written as a fraction in its simplest form.

14.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.

15.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?