Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 4(x − 2) + 10?

2.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

3.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

4.Which of these statements is an identity?

5.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

6.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

7.Which expression is equivalent to 2(x + 6)?

8.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

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

10.Solve 3x + 14 = 8x − 6

11.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

12.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

13.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

14.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

15.Which of these equations is equivalent to 5x − 2 = 3x + 8?