Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 4(x − 2) + 10?

2.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

3.a = 3 and b = 5. Work out the value of a²b.

4.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?

5.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.

6.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

7.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

8.Work out the value of 4p² − 3 when p = 2.5

9.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

10.Expand and simplify (x − 3)²

11.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

12.Solve the inequality 5x − 3 > 2x + 9.

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.y = x + 10. Work out the value of y when x = 0.

15.A vertical line passes through the point (4, 7). Write down the equation of this line.