Algebra worksheet — GCSE Foundation

1.Work out the y-intercept of the graph of y = x² + 3x − 10.

2.Make m the subject of the formula w = m − 8.

3.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

4.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

5.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

6.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

7.Solve 2x² = 18.

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

9.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

10.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

11.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

12.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

13.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.

14.Which expression means the same as 3 × a × b?

15.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?