Algebra worksheet — GCSE Foundation

1.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

2.Work out the distance of the point (−6, 4) from the x-axis.

3.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

4.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

5.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

6.Make x the subject of the formula y = (x − 4)/5.

7.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

8.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

9.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

10.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

11.Which of these is an expression?

12.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

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

14.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.

15.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.