Algebra worksheet — GCSE Foundation

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

2.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

3.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

4.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

5.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

6.Factorise fully 5x + 5y − 5

7.Solve x/4 + 1 = 3

8.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.

9.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

10.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

11.n = 3. Work out the value of (2n)².

12.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

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

14.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

15.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.