Algebra worksheet — GCSE Foundation

1.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.

2.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

3.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

4.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

5.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

6.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

7.Write down the first four terms of the sequence with nth term 6n − 5.

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

9.Which of these is an expression?

10.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

11.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

12.Which expression means 'add 3 to n, then multiply the result by 4'?

13.In which quadrant does the point (−3, 0.5) lie?

14.Which expression is equivalent to 7x − 3(2x − 6)?

15.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.