Algebra worksheet — GCSE Foundation

1.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.

2.a = 2 and b = 5. Work out the value of ab².

3.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.

4.Which expression is equivalent to 2(x + 6)?

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

6.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

7.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

8.Write down the expression that means the same as p + p + p + q.

9.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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

11.Solve 5x + 2 = 17.

12.Which of these rules generates the sequence 6, 11, 16, 21, …?

13.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

14.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

15.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.