Algebra worksheet — GCSE Foundation

1.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

2.Which expression means 'add 3 to n, then multiply the result by 4'?

3.Solve 4(x − 3) = 2x + 6.

4.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

5.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

6.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.

7.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

8.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

9.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

10.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

11.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

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

13.Which expression is equivalent to 3(2x − 5) + 4x?

14.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

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