Algebra worksheet — GCSE Foundation

1.Work out the value of n² − n when n = −3

2.Which of these equations gives a straight-line graph when plotted?

3.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.

4.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

5.Which of these equations describes a vertical line?

6.Work out the value of a² − 2b when a = −3 and b = 4.

7.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

8.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.

9.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

10.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

11.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

12.Solve x² − 2x − 24 = 0.

13.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

14.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.

15.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.