Math Lessons
Full lessons on the math behind the calculators, organized by domain and chapter.
Every calculator on this site does one job well, but a result you cannot reproduce by hand is hard to trust and impossible to check in an exam. These lessons cover the working underneath the tools: why a formula is shaped the way it is, where it comes from, and the steps to get the same answer on paper.
Each lesson follows the same pattern — the rule stated plainly, a worked derivation, several examples solved in full, the mistakes that cost the most marks, and a set of practice problems with hidden answers so you can test yourself before checking. All notation is typeset properly rather than written as plain text, and every lesson links to the matching practice problems when you want rep
Two courses are published so far. Algebra runs from the groundwork almost everything later assumes — exponent rules, radicals, polynomials, factoring and rational expressions in Preliminaries — through solving equations and inequalities, graphs and functions, polynomial, exponential and logarithmic functions, systems of equations, and sequences and series. Calculus begins Calculus 1 with a short review of functions, trigonometry and logarithms, then full chapters on limits and continuity and on derivatives. If you are unsure where to start, begin at the top of a course; the chapters are ordered so each lesson only relies on the ones before it.
nly relies on the ones before it.