Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as 3 × y × y.

2.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

3.Solve the inequality 9 − 2x ≥ 1.

4.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

5.Solve 4x² − 9 = 0.

6.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

7.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

8.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

9.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.

10.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

11.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

12.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.

13.Simplify k + k + k + k + k.

14.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

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