Venn Diagrams, Algebra and the New GCSE by @srcav

This is a re-blog post originally posted by Stephen Cavadino and published with kind permission.

The original post can be found here.

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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, those 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.

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.

Images supplied from Stephen Cavadino – Feature Image via



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