Algebra worksheet — GCSE Foundation

1.x = 5. Work out the value of 3x² − 4.

2.A number machine adds 6 to its input. Work out the output when the input is −4.

3.Which of these numbers is a cube number?

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

5.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.

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

7.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

8.Which expression is equivalent to 4(x − 2) + 10?

9.p = 4. Work out the value of 2p³.

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

11.Expand 7(a + 8)

12.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

13.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

14.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

15.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.