Algebra worksheet — GCSE Foundation

1.Which expression means the same as a × a × a?

2.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.

3.A vertical line passes through the point (4, 7). Write down the equation of this line.

4.Which of these points lies in the first quadrant?

5.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

6.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

7.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

8.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

9.n = 3. Work out the value of (2n)².

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

11.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

12.Simplify x + x + 4

13.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.

14.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.

15.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).