Algebra worksheet — GCSE Foundation

1.A number machine adds 6 to its input. Work out the output when the input is −4.

2.Solve 2x + 1 = 9

3.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

4.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

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

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

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

9.Work out the value of n² − n when n = −3

10.Make x the subject of the formula y = 5x + 3.

11.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

12.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

13.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

14.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

15.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.