Algebra worksheet — GCSE Foundation

1.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

2.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

3.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

4.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.

5.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

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

7.Which of these is a formula?

8.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.

9.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

10.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

11.Expand 7(a + 8)

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

13.Make c the subject of the formula k = 6c.

14.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

15.Work out the gradient of the straight line with equation 3y = 12 − 6x.