Algebra worksheet — GCSE Foundation

1.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

2.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.

3.Work out the value of 5m² + 3m when m = −2.4

4.Solve (3x + 2)/5 = (x + 4)/3

5.Work out the value of 3n − 2 when n = 1

6.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

7.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

8.Solve 4x + 3 = 19

9.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

10.Write down the gradient of the line with equation y = −x + 3.

11.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

12.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

13.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.

14.Work out the value of 3x² − 4x when x = −2.

15.Expand 2(x + 12)