Algebra worksheet — GCSE Foundation

1.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

2.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

3.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

4.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

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

6.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

7.Make x the subject of the formula y = 3(x + 2).

8.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.

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

10.Work out the value of 3x² − 4x when x = −2.

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

12.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.

13.Which of these is a formula?

14.Solve 2x² = 18.

15.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.