Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

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

3.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

4.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.

5.Simplify 5x + 3y − 2x + y.

6.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

7.Work out the value of a² − 2b when a = −3 and b = 4.

8.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

9.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

10.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

11.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.

12.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

13.Solve 2(x + 3) = 10

14.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

15.A point lies on the y-axis. What can be said about the x-coordinate of that point?