Algebra worksheet — GCSE Foundation

1.Factorise fully 12x² + 18x.

2.Make m the subject of the formula w = m − 8.

3.Solve 6x − 5 = 3x + 13.

4.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

5.In which quadrant does the point (−3, 0.5) lie?

6.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

7.Write down the gradient of the line with equation y = −x + 3.

8.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

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.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.

11.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

12.Solve 5x² − 15x = 0.

13.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

14.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.

15.Which expression means the same as a × a × a?