Algebra worksheet — GCSE Foundation

1.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

2.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

3.Solve the inequality 4x + 1 > 2x + 9.

4.Solve (3x + 2)/5 = (x + 4)/3

5.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

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

7.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

8.Work out the value of 2(x + 2) when x = −5

9.Solve 5(x + 3) = 40

10.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

11.Solve 6x − 5 = 3x + 13.

12.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.

13.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

14.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

15.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.