Levels 2, 3 and 5 are meant to simulate what you would learn from GCSE and A level textbooks. The contents are meant for you to read to get an idea of what you need to know, or to skim if you think you already know it just to fill in gaps and pitfalls, but you should study it more formally alongside this if you go through the documents and don't feel you have done it in school or basically know it. These are basically quick revision notes and not meant to be a full textbook to learn from. Proofs for some things in here are deferred to levels 4 (for pure) and 6 (for stats). In many textbooks some of the proofs given in this level are provided but are oversimplified and not always fully correct (I point out common pitfalls as I go).
Latest expected release date for Level 3: April 2026.
Table of Contents for level 3.1 [Expand]
Page 1 - Working with surds, rationalizing the denominator
Page 1 - Solving "pseudo-quadratics"
Page 2 - Limits
Page 3 - Introduction to differentiation
Page 6 - Exponential graphs
Page 7 - Logarithms, definition of e
Page 9 - The product rule
Page 9 - The chain and quotient rules
Page 10 - Definition of higher order derivatives
Page 10 - Definition of the absolute value
Page 10 - Introduction to integration
Page 14 - More differentiation stuff
Page 15 - Polynomial long division
Page 16 - Partial fraction decomposition
Page 17 - Vectors
Page 18 - More graphs of stuff
Page 22 - Equation for a circle, radians, trigonometric identities and equations
Page 26 - The binomial theorem
Page 27 - Series and the generalized binomial theorem