Algebra worksheet — GCSE Foundation

1.Solve the inequality 2(3x − 1) ≥ 4x + 8.

2.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

3.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

4.Factorise fully 12x² + 18x.

5.The diagram shows the graph of a function. Which equation could it represent?

6.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.

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

8.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

9.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

10.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

11.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

12.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

13.Simplify x + x + 4

14.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

15.Which expression is equivalent to 4(x − 2) + 10?