Algebra worksheet — GCSE Foundation

1.Solve the inequality 2(3x − 1) ≥ 4x + 8.

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

3.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.

4.Which expression is equivalent to 3(2x − 5) + 4x?

5.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

6.Write down the expression that means the same as 3 × y × y.

7.Write down the expression that means the same as p + p + p + q.

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

9.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

10.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.

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

12.Solve the inequality 6x ≥ 18.

13.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

14.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

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