Algebra worksheet — GCSE Foundation

1.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

2.Which of these statements is an equation with exactly one solution?

3.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

4.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

5.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?

6.Simplify 5x + 3y − 2x + y.

7.Solve the inequality x − 10 < −3.

8.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

9.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

10.Which of these equations describes a vertical line?

11.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

12.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

13.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

14.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

15.Factorise fully 56x − 24