Algebra worksheet — GCSE Foundation

1.Solve x² − 6x = 0.

2.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

3.Write down the first four terms of the sequence with nth term 6n − 5.

4.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

5.Make b the subject of the formula a = 5b.

6.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

7.Solve the inequality x − 10 < −3.

8.n = 3. Work out the value of (2n)².

9.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.

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

11.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

12.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.

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

14.Simplify k + k + k + k + k.

15.Which of these quadratic graphs does NOT cross the x-axis at all?