Algebra worksheet — GCSE Foundation

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

2.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

3.Expand 7(a + 8)

4.Factorise x² − 64.

5.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

6.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

7.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

8.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

9.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

10.Solve 5x − 9 = 16

11.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

12.Make x the subject of the formula y = (x − 4)/5.

13.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

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

15.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.