Algebra worksheet — GCSE Foundation

1.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

2.Work out the value of 5a + 2 when a = 3

3.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

4.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.

5.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

6.Factorise fully 56x − 24

7.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

8.Solve 6x − 5 = 3x + 13.

9.Make b the subject of the formula a = 5b.

10.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

11.How many turning points does the graph of y = x² − 7x + 10 have?

12.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

13.Which of these statements is an identity?

14.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

15.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?