Algebra worksheet — GCSE Foundation

1.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

2.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

3.Which expression is equivalent to 7x − 3(2x − 6)?

4.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

5.Expand 2(x + 12)

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

7.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

8.Solve 4(x − 3) = 2x + 6.

9.Solve the inequality 6x ≥ 18.

10.Solve x² − 6x = 0.

11.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

12.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

13.Write down 0.2x with its coefficient written as a fraction in its simplest form.

14.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

15.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.