Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 5x − (x + 3)?

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

3.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

4.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.

5.Solve 4x² − 9 = 0.

6.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.

7.Solve x² − 5x + 6 = 0 by factorising.

8.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

9.Solve the inequality 3x − 1 ≤ 11.

10.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

11.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

12.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

13.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

14.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

15.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.