Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

2.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

3.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

4.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

5.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

6.A number machine multiplies its input by 3. The output is 15. Work out the input.

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

8.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

9.Factorise x² − 64.

10.Work out the distance of the point (−6, 4) from the x-axis.

11.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

12.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

13.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

14.Work out the value of 2(x + 2) when x = −5

15.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.