Algebra worksheet — GCSE Foundation

1.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

2.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

3.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

4.Solve 6x + 4 = 28

5.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

6.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.

7.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.

8.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

9.Make b the subject of the formula a = 5b.

10.Solve 2(x + 3) = 10

11.Which of these is a formula?

12.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

13.Solve the inequality x + 5 < 12.

14.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.

15.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.