Algebra worksheet — GCSE Foundation

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

2.The point B has coordinates (−2, −2). In which quadrant is B?

3.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

4.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

5.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

6.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

7.Solve 4x + 3 = 19

8.Solve x² + 7x = 0.

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

10.Which of these statements is an equation with exactly one solution?

11.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

12.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

13.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.

14.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

15.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.