Algebra worksheet — GCSE Foundation

1.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

2.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.

3.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

4.Which expression is equivalent to 0.5(4x + 6) − x?

5.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

6.Solve x² − 5x + 6 = 0 by factorising.

7.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

8.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

9.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

10.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

11.Write down the expression that means the same as w ÷ 6.

12.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

13.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

14.Work out the value of 3b − 4 when b = 6

15.Make a the subject of the formula b = 20 − a.