Algebra worksheet — GCSE Foundation

1.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.

2.Which expression means 'y squared, multiplied by 3'?

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

4.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

5.Expand and simplify 2(a + 6) − 2(a − 7)

6.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

7.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

8.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

9.Simplify x + x + 4

10.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

11.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.

12.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

13.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?

14.Solve the inequality 3x + 6 ≤ 0.

15.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.