Algebra worksheet — GCSE Foundation

1.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

2.Work out the distance of the point (−6, 4) from the x-axis.

3.Which of these quadratic graphs does NOT cross the x-axis at all?

4.Solve x² − 6x = 0.

5.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

6.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

7.Work out the value of 2x² when x = −3

8.Make x the subject of the formula y = x/2 − 5.

9.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.

10.Which expression is equivalent to 6x − (2x − 5)?

11.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

12.A number machine adds 5 to its input. Work out the output when the input is 0.

13.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

14.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

15.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.