Algebra worksheet — GCSE Foundation

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

2.Solve the inequality 5x − 3 > 2x + 9.

3.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

4.Solve 5x − 9 = 16

5.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

6.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

7.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

8.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

9.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

10.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

11.Work out the value of (x − 4)/2 + 3 when x = 10

12.Solve the inequality 2(x − 1) ≤ 8.

13.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

14.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

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