Algebra worksheet — GCSE Foundation

1.Work out the gradient of the straight line with equation 2x + y = 8.

2.Which expression is equivalent to 0.5(4x + 6) − x?

3.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.

4.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?

5.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

6.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.

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

8.Simplify 5x + 3y − 2x + y.

9.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

10.Solve x² − 100 = 0.

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

12.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

13.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

14.The diagram shows the graph of a quadratic function. Which equation could it represent?

15.Solve 4x + 3 = 19