What is Beyond A Level Mathematics Project?

Beyond A Level Mathematics #0

I have been complaining about the course design of A Level Mathematics and Further Mathematics for quite a long time. The A Level syllabus is not “friendly enough” for students who are interested in pure mathematics. For example, it teaches you the “algorithm” to work out the inverse of a matrix but never tells you why it is correct; it teaches you how to find the derivative of a function without strictly define the limit of a function. I understand that most of the questions I ask can be answered in some undergraduate courses. And this is part of the reason why I choose to do an undergraduate degree in maths. But I think the curiosity of maths should never be restricted by the syllabus. I cannot wait until university lectures. I want to solve them now.

I believe some young mathematicians may have a similar feeling, but there will not be many of them. As far as I know, most students who choose to do A Level Maths and Further Maths are neither interested in a maths career nor the maths subject itself. They only need that A or A* to get an offer from an Economics or Computer Science department. At least in my college, I don’t have any schoolmates to “discuss” maths problems. My friends do come to me to ask some maths questions, but I am more like a biological mark scheme generator instead of a discusser in that situation.

Finally, I come up with the idea of maintaining a project to record all of my questions and my answers to these questions based on the A Level Maths and Further Maths. I don’t expect this project to be an influential one, but if you accidentally find it, I hope you enjoy it!

The Beyond A Level Mathematics (BAM) project aims to answer some mathematical questions that A Level Maths and Further Maths students interested in but are not covered in the textbook.

The “beyond” does not mean that there will be a lot of content out of the A Level syllabus. There will still be a little of them because just too few things are covered within the syllabus. Instead, “beyond” means more mathematical thinkings and ideas are required to explore those topics. The BAM project is fully based on A Level Maths and Further Maths syllabus and will try very hard to avoid undergraduate content.

Why avoiding undergraduate content?
I have tried to write notes for undergraduate content before and find that at the end, I just wrote a trash Analysis or Linear Algebra textbook. So if you interested in those topics, go ahead and read a real textbook, or maybe consider doing a maths degree.

The BAM project should be treated as an extension to the A Level Maths and Further Maths. The content will stick to the textbook strictly. I am using the textbook from OCR, if you are studying under a different exam board, the Rewind section may not work for you, but the content itself is independent and does not rely on any specific exam board.

The content in BAM starts from a single topic from the A Level textbook. And it extends very fast to cover several different topics. For example, BAM-1 How to prove π is an irrational number? starts from proving by contradiction and extend to the definition of $pi$, binomial expansion, calculus and more. BAM-2 What is Poisson Distribution? starts from the Poisson distribution and covers things like binomial distribution, the Maclaurin series, calculus and more. A typical post starts from a basic introduction to the topic and the question we want to solve. Then, there will have a STEP-type question designed to guide you exploring the question yourself. The STEP-type question is followed by a detailed explaination to the topic which also provides an indirect solution to the question. Some extension reading materials will list at the end. You can leave your ideas in the comment area at the bottom of the page.

Most human beings do not read mathematical blogs for entertainment, so I don’t expect thousands and millions of readers. But if you are one of the following types of people, you might find these posts quite interesting.

  • Six form students who are very interested in mathematics and may decide to study maths in university.

Notice that the blog will involve all content in A Level Maths and Further Maths. So it assumes you have done all these already. But normal schools take two years to finish teaching all AS and A Level content. That’s why you need to be “very interested in maths” and self-studies most of the content in advance.

  • Maths teachers who want some extra teaching materials or maths problems and ideas for their students.

Similarly, you need to keep in mind that the blog will not follow your teaching progress and assume all A Level content.

For students

  • I recommend you to read it on an iPad or PC with a large screen, or print it out and read it on paper. The mobile experience is not guaranteed, and there are no easy articles that you can read on your phone while queuing for lunch. Pen and paper are needed because there may have small or large questions for you to solve.
  • Work through it.
  • Have a brief look at extra readings, find interested ones to keep moving on.
  • Leave a comment if you have any questions or just have something in your mind to share with others.

For teachers

  • Extra reading materials for your students.
  • Super curriculum. (reorganize it and explore the topic with students in lesson)

All posts are licensed under CC BY-NC 4.0.

It is free for education. There is no worry to print the posts out and distribute them to your students.

Commercial uses are restricted. You cannot sell it.

You can still donate by BTC to support me if you have too much money to spend.


There are four ways that you can contribute to this project.

  1. Subscribe, read and comment

The site provides subscriptions with RSS. Use RSS services such as Feedly to subscribe and get notifications when updates.

  1. Recommend it to your maths teacher or your schoolmates who are also interested in pure mathematics.
  2. Suggest new ideas for BAM

Choose the New idea for Project Beyond A Level Mathematics template to submit new ideas at GitHub issues.

  1. Report typos and errata

Choose the Report typos and errata template to report any typos or errata you find at GitHub issues.

Currently, you cannot submit your own articles. But all the development can be seen as draft pull requests. You can see the draft of new posts and suggest advice here GitHub pull requests.

There are many ways to save the posts offline.

  • You can build and run the website on your local server by following this guide.
  • You can use the Print to PDF function in your browser. (Not recommended. May cause some issues.)
  • You can use some browser screenshot extension to save the page.
  • You can click the “Read markdown” link at the botton left of each post and render it yourself.

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