Algebra worksheet — GCSE Foundation

1.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

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

3.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

4.a = 2 and b = 5. Work out the value of a²b.

5.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

6.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

7.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

8.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

9.Solve the inequality 9 − 2x ≥ 1.

10.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

11.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

12.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.

13.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

14.Which of these is a factor of 15x + 20?

15.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.