Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 7x − 3(2x − 6)?

2.a = 2 and b = 5. Work out the value of a²b.

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

4.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

5.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

6.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

7.A straight line has equation y = 5x. Work out the value of y when x = 3.

8.Solve 5x² − 15x = 0.

9.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

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

11.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

12.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

13.Work out the value of 5y + 9 when y = 0

14.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

15.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.