Algebra worksheet — GCSE Foundation

1.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.

2.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

3.Solve 6x + 4 = 28

4.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

5.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

6.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?

7.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

8.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.

9.Make c the subject of the formula k = 6c.

10.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

11.Make x the subject of the formula y = 5x + 3.

12.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

13.Solve the inequality 3x − 1 ≤ 11.

14.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

15.Which of these is a factor of 15x + 20?