What you'll learn

33 lessons in Precalculus

Logarithms & exponentialsComplex numbersConic sectionsFunction transformationsPolynomial & rational functionsSigma (Σ) and Pi (Π) notationArithmetic sequences & seriesGeometric series & convergencePolar coordinatesParametric equationsPartial fractionsInduction for summation formulasExponential growth & decay applicationsMatrices previewConic sections — focus and directrixMathematical induction examplesLimits intuitivelyProof: $\sqrt 2$ is irrationalProof: laws of logarithmsBounded sequencesVectors in 2D & 3DConjugate diameters & the auxiliary circleAsymptotes & the conjugate hyperbolaFocal properties & the polar equation of a conicEven & odd functionsEnd behavior & the leading-term testSystems of inequalities & linear programmingRotation of axes & the general conicDot & cross productsDeterminants & Cramer's ruleThe binomial theorem & general termLimits of sequences & infinite seriesCurve fitting & mathematical modeling

How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Precalculus exactly where it's useful.

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