Algebra worksheet — GCSE Foundation

1.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

2.y = 5x − 1. Work out the value of y when x = 3.

3.Solve the inequality 2(x − 1) ≤ 8.

4.Expand 2(x − 13)

5.Which of these statements is an equation with exactly one solution?

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

7.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

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

9.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

10.Solve 4x − (2x − 6) = 18

11.A number machine adds 6 to its input. Work out the output when the input is −4.

12.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

13.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

14.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

15.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.