Algebra worksheet — GCSE Foundation

1.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

2.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

3.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

4.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

5.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

6.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

7.Which of these equations is equivalent to 5x − 2 = 3x + 8?

8.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

9.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

10.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

11.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

12.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.

13.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

14.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

15.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?