Algebra worksheet — GCSE Foundation

1.Simplify 5x + 3y − 2x + y.

2.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

3.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

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.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

6.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

7.Solve 5x − 9 = 16

8.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.

9.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

10.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

11.Make x the subject of the formula y = 5x + 3.

12.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

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

14.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

15.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?