Algebra worksheet — GCSE Foundation

1.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

2.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

3.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

4.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

5.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

6.A curve has equation y = x² − 9. Which statement about its graph is correct?

7.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.

8.Solve x² − 100 = 0.

9.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

10.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

11.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

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

13.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

14.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

15.Make b the subject of the formula a = 5b.