Algebra worksheet — GCSE Foundation

1.Expand 2(x − 13)

2.n = 3. Work out the value of (2n)².

3.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

4.Which of these equations is equivalent to 5x − 2 = 3x + 8?

5.Factorise fully 5x + 5y − 5

6.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

7.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

8.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

10.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

11.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.

12.Work out the value of 4p² − 3 when p = 2.5

13.The point A lies on the x-axis. Which statement about A must be true?

14.Solve 4(x − 3) = 2x + 6.

15.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.