Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

2.Solve x² = 81.

3.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

4.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

5.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.

6.Solve 2x + 1 = 9

7.Solve the inequality 3x + 6 ≤ 0.

8.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.

9.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

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

11.Solve 3(2x − 1) = 27

12.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

13.Write down the expression that means the same as m × m × m × n.

14.Solve 3x − 5 = 4.

15.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?