Algebra worksheet — GCSE Foundation

1.Solve 5x + 2 = 17.

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

3.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

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

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

6.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

7.Make x the subject of the formula y = 3(x + 2).

8.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

9.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

10.Solve 6x + 4 = 28

11.Work out the value of a² − 2b when a = −3 and b = 4.

12.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

13.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

14.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.

15.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.