Algebra worksheet — GCSE Foundation

1.y = 5x − 1. Work out the value of y when x = 3.

2.Which of these is an identity?

3.Factorise fully 56x − 24

4.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

5.Which of these is a formula, rather than an expression, an equation, or an identity?

6.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.

7.Simplify x + x + 4

8.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

9.Solve 6x + 4 = 28

10.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

11.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

12.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

13.Solve 2x + 7 = x + 13

14.Make x the subject of the formula y = 2x − 9.

15.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.