Algebra worksheet — GCSE Foundation

1.Solve 6x + 4 = 28

2.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

3.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?

4.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.

5.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?

6.a = 2 and b = 5. Work out the value of ab².

7.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

8.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

9.Factorise fully 12x² + 18x.

10.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

11.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

12.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

13.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

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

15.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.