Algebra worksheet — GCSE Foundation

1.Which expression means the same as 3 × a × b?

2.Solve 2x² − 32 = 0.

3.Work out the value of 4p² − 3 when p = 2.5

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

5.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

6.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

7.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

8.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

9.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

10.A square tile has an area of 144 cm². Work out the side length of the tile.

11.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

12.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

13.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

14.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

15.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.