Algebra worksheet — GCSE Foundation

1.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

2.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

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.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

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

6.Solve 4x² − 9 = 0.

7.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

8.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

9.x = 5. Work out the value of 3x² − 4.

10.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

11.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

12.Solve the inequality 9 − 2x ≥ 1.

13.Write down the expression that means the same as m × m × m × n.

14.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

15.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.