Algebra worksheet — GCSE Foundation

1.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

2.Make x the subject of the formula y = 5x + 3.

3.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

4.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

5.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

6.A square tile has an area of 144 cm². Work out the side length of the tile.

7.Expand 7(a + 8)

8.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

9.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

10.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

11.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

12.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

13.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

14.Expand 2(x + 12)

15.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.