Math by First Principles

Middle & high-school math · self-study

Learn math from first principles

Most math courses give you formulas and ask you to practice them. Here, we show you where those formulas come from. Ideas are built step by step from things you already know, so the rules make sense instead of feeling arbitrary.

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Why proofs
Because math is easier when the rules make sense. Instead of asking you to memorize formulas, we show where they come from and why they work, so you can understand them and use them in problems you have not seen before.
How lessons work
Each lesson starts with the problem an idea helps solve, then builds the idea step by step from what you already know. Worked examples, quick checkpoints, and common mistakes help you understand it before you move on. If a step needs explaining, we explain it.
Practice
Each lesson has three core sets of 12 practice questions that gradually get harder, plus two more sets for extra practice. Every question includes a full worked solution you can reveal when you need it. Work at your own pace, with no timer or score pressure. No account is required, and your answers are saved in your browser.

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Available subjects

How the subjects connect

See where to start and what comes next.

Pre-Algebra Algebra I Geometry and Algebra II Precalculus Calculus AB Calculus BC Statistics and Probability Pre-Algebra Algebra I Geometry and Algebra II Precalculus Calculus AB Calculus BC Statistics and Probability

Geometry and Algebra II can be taken in either order. Statistics and Probability does not require Precalculus or Calculus.

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How content is reviewed

Lessons are developed with AI assistance and reviewed for accuracy, clarity, consistency, and correct answers before publication.

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