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.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

3.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

4.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

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

6.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

7.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

8.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

9.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

10.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

11.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

12.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

13.Solve the inequality 9 − 2x ≥ 1.

14.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

15.Which expression is equivalent to 6x − (2x − 5)?