Algebra worksheet — GCSE Foundation

1.p = 4. Work out the value of 2p³.

2.Solve the inequality 5 − x ≤ 2.

3.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.

4.Make x the subject of the formula y = (x − 4)/5.

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

6.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

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 fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

9.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

10.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

11.A square has sides of length y cm. Write down an expression for the perimeter of the square.

12.The point A is at (5, −3). In which quadrant does A lie?

13.n = 3. Work out the value of (2n)².

14.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

15.Which expression means the same as 3 × a × b?