Algebra worksheet — GCSE Foundation

1.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

2.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

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

4.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

5.Write down the coefficient of p in the expression 7 − 4p + 9q.

6.Work out the value of 5y + 9 when y = 0

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

8.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

10.Work out the value of (x − 4)/2 + 3 when x = 10

11.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.

12.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

13.Work out the value of 3n − 2 when n = 1

14.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

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