Algebra worksheet — GCSE Foundation

1.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.

2.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

3.a = 3 and b = 5. Work out the value of a²b.

4.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

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

6.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

7.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

8.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

9.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

10.Solve the inequality 5x − 3 > 2x + 9.

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

12.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

13.Work out the value of n² − n when n = −3

14.Work out the gradient of the straight line with equation 3y = 12 − 6x.

15.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?