NOTE: This level proves all gaps from earlier levels. In a few cases, this means that this level will be a difficulty spike compared to levels 1-5. If you are less comfortable with following complex mathematical theory or proofs, you may find this level difficult. In that case if you don't mind waiting to see some proofs, an alternative progression path that does not have prerequisite clashes is to do level 6.1, then level 6.2 but excluding chapter 3, and the first 7 chapters of level 6.3, then levels 7.1, 7.2 and 7.3 (to gain some general mathematical maturity), then go back and read the rest of level 6, then read level 7.4.
This is an A level further maths proof companion consisting of documents and videos where intuition or proofs are provided for all results in A level further maths pure and statistics modules and A level maths statistics modules used as black boxes, some of which you may not have even realized required justification—when that happens, I explain why justification is needed. Many steps often skipped over in textbooks are justified in this level.
You would benefit from this if one of the following (or equivalent for a non‑British system) describes you:
Here are the documents and videos for this level.
How to use this: Do not expect any direct proofs of A level results in Level 6.2, rather note that results and definitions from chapters 1-5 and 6.1 are used in the proof of the Central Limit Theorem given in level 6.3, and that results and definitions from chapter 1 and chapters 5-7 are used in the proof of Chi Squared Tests given in level 6.3.
Open the level 6 technical results document (Level 6.2)