Algebra worksheet — GCSE Foundation

1.Which of these is a formula, rather than an expression, an equation, or an identity?

2.Which of these numbers is a cube number?

3.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

4.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

5.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

6.Solve 3x − 5 = 4.

7.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

8.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

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

10.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

11.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

12.Work out the gradient of the straight line with equation 3y = 12 − 6x.

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

14.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.

15.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.