Algebra worksheet — GCSE Foundation

1.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

2.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

3.A number machine adds 6 to its input. Work out the output when the input is −4.

4.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.

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

6.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

7.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.

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

9.Make x the subject of the formula y = 4x − 3.

10.Work out the gradient of the straight line with equation 3y = 12 − 6x.

11.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

12.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

13.Solve x² − 2x − 24 = 0.

14.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

15.Write down the expression that means the same as (x + 7) ÷ 4.