Home > Assessment, Curriculum, GCSE, Maths, Teaching > Venn Diagrams, Algebra and the New GCSE

Venn Diagrams, Algebra and the New GCSE

I’m a fan of Venn Diagrams (and the more versatile, lesser know Euler Diagrams), and the uses they have when dealing with probability. I was glad to see then installed in their full glory to the new GCSE curriculum. They are an excellent way of displaying data, and they can give rise to some great questions which test a range of mathematical skills in a different (sometimes unfamiliar) context. While I was looking for the question mentioned in this post I came across this question:


It’s from the AQA higher SAMs and I absolutely love it. It looks simple from the outset, but it actually covers a number of topics. You need to have an understanding of Venn Diagrams, you need an understanding of Probability Theory and you need to be proficient in Algebra.

Algebra underpins everything in mathematics, and the biggest flaw in the current GCSE is that it allows people to gain a food pass without Algebraic proficiency. I think we need to see more questions like this, that mix topics and place algebra at the heart of the question, to ensure people leave the GCSE course with the skills needed to progress further in mathematics.

The question


I couldn’t help but explore it. My first thought was, “I need to find x”, this was fairly easily achieved using the fact that there are 120 coins. It’s just a case if forming and solving the equation.


Discounting the negative x, of course. Then it was just a case of substituting the values in and finding the probability from the Venn Diagram.


A lovely problem.

  1. December 17, 2014 at 6:57 pm

    Fabulous problem.

  2. December 17, 2014 at 7:18 pm

    Reblogged this on The Echo Chamber.

  3. flyingcoloursmaths
    December 17, 2015 at 8:32 am

    To play Devil’s Advocate, it’s a bit pseudocontexty for my tastes. I like the maths part of it to a degree, but don’t think a Venn diagram is any better than a table here.

    • December 17, 2015 at 8:42 am

      Aye, It’s certainly not necessary to use the Venn, but I love the question still.

  4. Abdul Azim
    December 8, 2016 at 9:32 pm

    Sorry, I got confused where did 34 come from

    • December 8, 2016 at 10:29 pm

      We are given that the coin is British, so falls in that circle which has 2x -2 elements (as there are x in the intersection and x-2 in that bit alone) as x = 18, 2x – 2 = 34.

  5. Abdul Azim
    December 8, 2016 at 9:33 pm

    Where did 34 come from?

  6. Gigi
    March 6, 2018 at 9:10 pm

    How did you access this paper?

  7. renordw
    October 22, 2018 at 3:23 am

    The answer should be x / (x+x(x-15))… the intersection over British coins, which is the probability that a British coin is both British and 20th Century.

    • renordw
      October 22, 2018 at 3:32 am

      Whoops. I was wrong.

  8. Amy David
    November 10, 2020 at 4:42 am

    Creately also have different types of Venn diagrams which can be used based on the requirement.https://creately.com/lp/venn-diagram-maker/

  1. December 22, 2014 at 8:09 am
  2. August 20, 2019 at 10:07 am

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