Algebra worksheet — GCSE Foundation

1.A number machine adds 5 to its input. Work out the output when the input is 0.

2.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

3.Solve the inequality 5x − 3 > 2x + 9.

4.Simplify 5x + 3y − 2x + y.

5.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

6.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

7.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.

8.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

9.Work out the value of 2x² when x = −3

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

11.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

12.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

13.Solve the inequality 3x + 6 ≤ 0.

14.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

15.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.