Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

2.In which quadrant does the point (−3, 0.5) lie?

3.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

4.Solve (2x + 1)/3 = 5

5.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.

6.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

7.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

8.Work out the value of 5a + 2 when a = 3

9.Which of these is a formula?

10.Work out the coordinates of the reflection of (6, −3) in the y-axis.

11.Write down the expression that means 5 more than half of n.

12.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

13.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

14.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

15.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.