Algebra worksheet — GCSE Foundation

1.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

2.Make b the subject of the formula a = 5b.

3.Which of these statements is an equation with exactly one solution?

4.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

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

7.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

8.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

9.Solve x² = 81.

10.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

11.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

12.Which of these equations gives a straight-line graph when plotted?

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

14.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

15.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.