Algebra worksheet — GCSE Foundation

1.Solve 5x² − 15x = 0.

2.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

3.Write down 0.2x with its coefficient written as a fraction in its simplest form.

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.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

6.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

7.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

8.Work out the value of 2(x + 2) when x = −5

9.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

10.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

11.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.

12.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

13.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

14.Work out the value of a² − 2b when a = −3 and b = 4.

15.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.