Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

2.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

3.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

4.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.

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.Simplify k + k + k + k + k.

7.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

8.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

9.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.

10.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

11.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

12.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

13.Write down the gradient of the line with equation y = 7x − 2.

14.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

15.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.