Algebra worksheet — GCSE Foundation

1.Solve x² = 81.

2.Which expression means the same as a × a × a?

3.Which expression is equivalent to 3(2x − 5) + 4x?

4.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.

5.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

6.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

7.Solve x² − x − 12 = 0.

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

9.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.

10.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

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

12.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

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

14.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

15.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?