Algebra worksheet — GCSE Foundation

1.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

2.Solve x² − 2x − 24 = 0.

3.Write down the first four terms of the sequence with nth term 6n − 5.

4.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

5.Solve x² + 3x − 10 = 0.

6.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

7.A number machine adds 6 to its input. Work out the output when the input is −4.

8.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

9.Expand 2(x − 13)

10.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

11.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

12.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

13.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

14.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

15.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.