Algebra worksheet — GCSE Foundation

1.Solve 4(x − 3) = 2x + 6.

2.Write down the gradient of the line with equation y = 7x − 2.

3.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

4.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.

5.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

6.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

7.A number machine multiplies its input by 5. Work out the output when the input is −1.

8.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.

9.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

10.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.

11.Solve x² + 7x = 0.

12.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

13.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

14.Make c the subject of the formula k = 6c.

15.Simplify (5x² + 3x − 2) − (2x² − x + 5)