Level 4 – GCSE and A level maths full justification

This is an A level maths proof companion consisting of documents and videos where intuition or proofs are provided for all results in GCSE and A level maths 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. The proofs for statistics, as well as a technical detail about implicit differentiation, are included with the further maths proof companions in level 6 as those tend to be more complicated.

You would benefit from this if one of the following (or equivalent for a non‑British system) describes you:

• A level maths students seeking to go beyond the curriculum
• A level further maths students
• A level maths students interested in better understanding the material
• A level maths students interested to understand the “why” for results or formulas or methods that are not typically properly justified in A level textbooks or their exercises but still used in GCSEs or A level pure maths
• Students aiming for an A or an A* in A level maths
• Anyone considering pursuing maths at university
• Undergraduate maths students
• Maths teachers or prospective maths teachers (A level teachers in particular)

Note: In the document for this level there are 2 appendices. It is crucial that one reads both if they want to move on beyond level 5, since we later use results a ton from Appendix B especially.

Here is the document and videos for this level:

Open document for level 4