Algebra worksheet — GCSE Foundation

1.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

2.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.

3.Solve x² − 2x − 24 = 0.

4.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

5.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

6.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

7.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

8.Solve 5x − 9 = 16

9.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

10.Work out the value of m² + 3m when m = −2

11.Which expression is equivalent to 0.5(4x + 6) − x?

12.Solve 3x + 14 = 8x − 6

13.Solve x² = 81.

14.Which expression is equivalent to 5x − (x + 3)?

15.Simplify k + k + k + k + k.