Algebra worksheet — GCSE Foundation

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

2.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

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

4.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

5.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

6.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

7.Simplify 2b − 1 + 2b − 4 + 2b

8.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

9.Make p the subject of the formula n = p/3.

10.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

11.Solve 6x + 4 = 28

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

13.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

14.Write down the expression that means the same as m × m × m × n.

15.Solve x − 4 = −9