Algebra worksheet — GCSE Foundation

1.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

2.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

3.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.

4.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

5.Work out the value of a² − 2b when a = −3 and b = 4.

6.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

7.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

8.Simplify 2a + 3b − a + 2b − b

9.Simplify 5a/6 − a/3

10.y = x + 4. Work out the value of y when x = 3.

11.Make c the subject of the formula k = 6c.

12.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

13.A square tile has an area of 144 cm². Work out the side length of the tile.

14.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

15.Expand and simplify 2(a + 6) − 2(a − 7)