Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

2.Simplify 2a + 3b − a + 2b − b

3.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

4.Work out the gradient of the straight line with equation y = (2x/5) − 3.

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

6.Solve the inequality 3x + 6 ≤ 0.

7.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

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.Which of these equations gives a straight-line graph when plotted?

10.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

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

12.Which expression is equivalent to 2(x + 6)?

13.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.

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 gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.