Algebra worksheet — GCSE Foundation

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

2.Which of these numbers is a cube number?

3.Solve the inequality x + 5 < 12.

4.Simplify x + x + 4

5.Which of these quadratic graphs does NOT cross the x-axis at all?

6.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

7.Expand 2(x − 13)

8.A number machine multiplies its input by 5. Work out the output when the input is −1.

9.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.

10.Solve 4(x − 3) = 2x + 6.

11.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

12.Make x the subject of the formula y = 2x − 9.

13.Expand and simplify (x − 3)²

14.Solve x² − 6x = 0.

15.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.