Algebra worksheet — GCSE Foundation

1.Solve the inequality 9 − 2x ≥ 1.

2.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

3.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

4.Solve 2(x + 3) = 10

5.Solve x² − 100 = 0.

6.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

7.Solve 2x² − 32 = 0.

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

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

11.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

12.Simplify 2a + 3b − a + 2b − b

13.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

14.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

15.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.