Algebraic proof

Sample Algebraic proof questions

A few of the 70 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 12 marksGrade 3
   Two consecutive whole numbers are $n$ and $n+1$. The two numbers are added together. Show that the answer must be an odd number.
   Show the worked solution

   n + (n + 1) = 2n + 1. M1

   2n is always a multiple of 2, so it is always even.

   An even number plus 1 is always odd, so 2n + 1 must always be odd. A1
2. Question 2

What are the common mistakes in Algebraic proof?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Treats a single worked numeric example as sufficient proof, rather than a general algebraic proof

  Only checked one example pair (e.g. 3 + 4 = 7) rather than proving the result algebraically for all integers

• Drops the constant term when expanding brackets

  Added n + (n+1) + (n+2) but dropped the constant terms, giving 3n instead of 3n+3

• Completes the working but does not state the required conclusion

  Correctly expanded and combined all terms but never factored out the 2 or stated the conclusion that this proves the expression is always even.

Quick answers about Algebraic proof

How many Algebraic proof practice questions are there?

There are 70 self-marking GCSE Maths questions on Algebraic proof, written for AQA, Pearson, OCR across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.

Do I need an account to practise Algebraic proof?

No. You can start practising Algebraic proof straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.