Study guides that explain the why.

Each guide walks a whole course, one idea at a time: what the method is, why it works, and the mistakes that cost marks.

Middle school
Pre-algebra study guide

Pre-algebra is where arithmetic becomes structural. Instead of computing one answer, you learn the rules that let you rearrange numbers safely, which is exactly what algebra then does with letters.

High school
Algebra 1 study guide

Algebra 1 is one idea applied repeatedly: whatever you do to one side of an equation, do to the other. Everything else. Lines, systems, inequalities, is that idea plus notation.

High school
Algebra 2 study guide

Algebra 2 widens the catalogue of functions. The skill being trained is recognising which family a problem belongs to, because each family has its own standard first move.

High school
Geometry study guide

Geometry trains deduction. Each result follows from earlier results, so the fastest way to improve is to learn which theorem licenses which conclusion rather than memorising diagrams.

High school
Trigonometry study guide

Trigonometry starts as triangle measurement and becomes the mathematics of anything that repeats. The unit circle is the bridge between those two views, so time spent there pays back everywhere.

High school / college
Pre-calculus study guide

Pre-calculus is function literacy. Calculus asks how functions change, so this course makes sure you can describe a function's domain, shape, asymptotes and inverse before differentiating it.

College
Calculus 1 study guide

Calculus 1 answers two questions: how fast is this changing, and how much has accumulated. Derivatives answer the first, integrals the second, and the fundamental theorem shows they are inverse operations.

High school / college
Statistics study guide

Statistics moves from describing a sample to making claims about a population. Every formula in the second half exists to quantify how much that leap might be wrong.