Algebra worksheet — GCSE Foundation

1.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

2.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

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

4.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

5.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

6.Solve x² − 2x − 24 = 0.

7.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

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

9.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

10.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.

11.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.

12.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

13.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

14.Solve 5x + 2 = 17.

15.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.