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# Precalculus

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## We’ve updated this course!

We’ve recently made improvements to Precalc! We’ve improved the scope and the structure to be better aligned to the spirit of the Common Core! You are viewing the newer edition.

Learn more or access older editionWhat are the imaginary numbers?: Complex numbersWhat are the complex numbers?: Complex numbersThe complex plane: Complex numbersAdding and subtracting complex numbers: Complex numbersDistance and midpoint of complex numbers: Complex numbers

Multiplying complex numbers: Complex numbersComplex conjugates and dividing complex numbers: Complex numbersIdentities with complex numbers: Complex numbersAbsolute value and angle of complex numbers: Complex numbersPolar form of complex numbers: Complex numbersMultiplying and dividing complex numbers in polar form: Complex numbers

Introduction to matrices: MatricesRepresenting linear systems of equations with augmented matrices: MatricesElementary matrix row operations: MatricesRow-echelon form and Gaussian elimination: MatricesAdding and subtracting matrices: MatricesMultiplying matrices by scalars: MatricesProperties of matrix addition & scalar multiplication: MatricesMultiplying matrices by matrices: Matrices

Properties of matrix multiplication: MatricesMatrices as transformations: MatricesThe determinant of a 2x2 matrix: MatricesIntroduction to matrix inverses: MatricesFinding the inverse of a matrix using its determinant: MatricesPractice finding the inverses of 2x2 matrices: MatricesSolving equations with inverse matrices: MatricesModel real-world situations with matrices: Matrices

Introduction to conic sections: Conic sectionsThe features of a circle: Conic sectionsStandard equation of a circle: Conic sectionsExpanded equation of a circle: Conic sectionsCenter and radii of an ellipse: Conic sectionsFoci of an ellipse: Conic sections

Focus and directrix of a parabola: Conic sectionsIntroduction to hyperbolas: Conic sectionsFoci of a hyperbola: Conic sectionsHyperbolas not centered at the origin: Conic sectionsIdentifying conic sections from their equations: Conic sectionsChallenging conic section problems (IIT JEE): Conic sections

Basic probability: Probability and combinatoricsVenn diagrams and the addition rule: Probability and combinatoricsCompound probability of independent events using diagrams: Probability and combinatoricsCompound probability of independent events using the multiplication rule: Probability and combinatorics