Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

2.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.

3.Simplify 2a + 3b − a + 2b − b

4.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

5.Factorise fully 56x − 24

6.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

7.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

8.n = 3. Work out the value of (2n)².

9.Make x the subject of the formula y = (x − 4)/5.

10.Solve x² − 5x + 6 = 0 by factorising.

11.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

12.Solve x² + 3x − 10 = 0.

13.Work out the value of 3a − 2b when a = 5 and b = 4

14.Factorise fully 5x + 5y − 5

15.Write down the expression that means the same as (x + 7) ÷ 4.