Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = 4x − 3.

2.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.

3.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

4.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

5.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

6.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

7.Solve 5(x + 3) = 40

8.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

9.a = 3 and b = 5. Work out the value of a²b.

10.Solve the inequality 3x + 6 ≤ 0.

11.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

12.Solve the inequality 2(x − 1) ≤ 8.

13.Simplify 5x + 3y − 2x + y.

14.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

15.Write down the gradient of the line with equation y = 6 + 4x.