Algebra worksheet — GCSE Foundation

1.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

2.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.

3.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

4.Factorise fully 56x − 24

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

6.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

7.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

8.Simplify p + p + p.

9.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

10.Make b the subject of the formula a = 5b.

11.Work out the value of n² − n when n = −3

12.Solve 3x − 5 = 4.

13.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

14.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

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