Algebra worksheet — GCSE Foundation

1.a = 3 and b = 5. Work out the value of a²b.

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

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

4.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

5.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.

6.Solve 2x + 1 = 9

7.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

8.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.

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

10.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

11.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

12.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

13.Make x the subject of the formula y = (x − 4)/5.

14.The point B has coordinates (−2, −2). In which quadrant is B?

15.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.