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.
cavmaths 
Fabulous problem.
Reblogged this on The Echo Chamber.
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.
Aye, It’s certainly not necessary to use the Venn, but I love the question still.
Sorry, I got confused where did 34 come from
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.
Where did 34 come from?
How did you access this paper?
Via the websites the exam board
Do you still have the link as I’ve been trying to find it myself.
https://qualifications.pearson.com/en/qualifications/edexcel-gcses/mathematics-2015.html
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.
Whoops. I was wrong.
Creately also have different types of Venn diagrams which can be used based on the requirement.https://creately.com/lp/venn-diagram-maker/