Algebra worksheet — GCSE Foundation

1.Factorise fully 56x − 24

2.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

3.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

4.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

5.a = 3 and b = 5. Work out the value of a²b.

6.Which of these statements is an equation with exactly one solution?

7.Write down the number of terms in the expression 4x² − 7x + 3.

8.Solve 7x − 5 = 3x + 11

9.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

10.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

11.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

12.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

13.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.

14.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

15.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.