Algebra worksheet — GCSE Foundation

1.Solve 5x − 9 = 16

2.A point lies on the y-axis. What can be said about the x-coordinate of that point?

3.Solve x² − x − 12 = 0.

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

5.Which expression is equivalent to 3(2x − 5) + 4x?

6.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

7.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

8.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

9.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.

10.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

11.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

12.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

13.Factorise x² − 3x − 10.

14.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.

15.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?