Algebra worksheet — GCSE Foundation

1.Expand and simplify 2(a + 6) − 2(a − 7)

2.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

3.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

4.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.

5.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.

6.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.

7.A square tile has an area of 144 cm². Work out the side length of the tile.

8.Write down the gradient of the line with equation y = 7x − 2.

9.Which expression is equivalent to 2(x + 6)?

10.Solve 2x² = 18.

11.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

12.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

13.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

14.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

15.Simplify 2b − 1 + 2b − 4 + 2b