Algebra worksheet — GCSE Foundation

1.Write down the number of terms in the expression 4x² − 7x + 3.

2.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

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

4.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

5.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

6.Write down the expression that means the same as m² × m × 3.

7.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

8.y = 3x − 2. Work out the value of y when x = 4.

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

10.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

11.Write down the first four terms of the sequence with nth term 6n − 5.

12.Which expression is equivalent to 0.5(4x + 6) − x?

13.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

14.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.

15.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.