Algebra worksheet — GCSE Foundation

1.A point lies on the y-axis. What can be said about the x-coordinate of that point?

2.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.

3.Make x the subject of the formula y = 4x − 3.

4.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

5.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

6.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

7.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

8.Work out the distance of the point (−6, 4) from the x-axis.

9.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

10.Simplify 5a/6 − a/3

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

12.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

13.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

14.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

15.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x