Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = 4(x − 6).

2.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.

3.Simplify 2b − 1 + 2b − 4 + 2b

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

5.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

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

7.Which of these is an inequality?

8.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

9.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

10.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?

11.Solve x − 4 = −9

12.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

13.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

14.Write down the expression that means the same as m² × m × 3.

15.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.