Algebra worksheet — GCSE Foundation

1.Solve x² − 6x = 0.

2.Write down the expression that means the same as m² × m × 3.

3.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

4.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

5.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

6.Simplify 2b − 1 + 2b − 4 + 2b

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

8.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

9.Factorise fully 5x + 5y − 5

10.Write down the expression that means the same as w ÷ 6.

11.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.

12.Which of these is an identity?

13.Which expression is equivalent to 0.5(4x + 6) − x?

14.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

15.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?