Algebra worksheet — GCSE Foundation

1.Work out the value of 4p² − 3 when p = 2.5

2.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

3.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

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

5.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

6.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

7.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

8.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.

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

10.Write down the gradient of the line with equation y = −x + 3.

11.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

12.Solve 4x + 3 = 19

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

14.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

15.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).