Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

2.Solve the inequality 3x + 6 ≤ 0.

3.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

4.Write down the expression that means the same as w ÷ 6.

5.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

6.Expand and simplify 2(a + 6) − 2(a − 7)

7.Simplify 5a/6 − a/3

8.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

9.A market stall's cost of hiring n tables is modelled by two formulas: Formula A: C = 3(2n + 5); Formula B: C = 6n + 15, where C is in pounds. A stallholder says the two formulas always give the same cost. Work out the cost given by each formula when n = 4, and use your results to decide whether the stallholder is correct.

10.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

11.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

12.Work out the value of 3n − 2 when n = 1

13.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

14.A point lies on the y-axis. What can be said about the x-coordinate of that point?

15.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.