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Precalculus

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Composite and inverse functions

Composing functions: Composite and inverse functionsModeling with composite functions: Composite and inverse functionsInvertible functions: Composite and inverse functions
Inverse functions in graphs and tables: Composite and inverse functionsVerifying inverse functions by composition: Composite and inverse functions

Trigonometry

Special trigonometric values in the first quadrant: TrigonometryTrigonometric identities on the unit circle: TrigonometryInverse trigonometric functions: TrigonometryLaw of sines: TrigonometryLaw of cosines: Trigonometry
Solving general triangles: TrigonometrySinusoidal equations: TrigonometrySinusoidal models: TrigonometryAngle addition identities: TrigonometryUsing trigonometric identities: Trigonometry

Complex numbers

The complex plane: Complex numbersDistance and midpoint of complex numbers: Complex numbersComplex conjugates and dividing complex numbers: Complex numbersIdentities with complex numbers: Complex numbers
Modulus (absolute value) and argument (angle) of complex numbers: Complex numbersPolar form of complex numbers: Complex numbersGraphically multiplying complex numbers: Complex numbersMultiplying and dividing complex numbers in polar form: Complex numbersThe fundamental theorem of algebra: Complex numbers

Rational functions

Reducing rational expressions to lowest terms: Rational functionsEnd behavior of rational functions: Rational functionsDiscontinuities of rational functions: Rational functions
Graphs of rational functions: Rational functionsModeling with rational functions: Rational functionsMultiplying and dividing rational expressions: Rational functionsAdding and subtracting rational expressions: Rational functions

Conic sections

Introduction to conic sections: Conic sectionsCenter and radii of an ellipse: Conic sectionsFoci of an ellipse: Conic sections
Introduction to hyperbolas: Conic sectionsFoci of a hyperbola: Conic sectionsHyperbolas not centered at the origin: Conic sections

Vectors

Vectors introduction: VectorsVector components: VectorsMagnitude of vectors: VectorsScalar multiplication: Vectors
Vector addition and subtraction: VectorsDirection of vectors: VectorsVector components from magnitude and direction: VectorsAdding vectors in magnitude and direction form: VectorsVectors word problems: Vectors

Matrices

Introduction to matrices: MatricesUsing matrices to represent data: MatricesMultiplying matrices by scalars: MatricesAdding and subtracting matrices: MatricesProperties of matrix addition & scalar multiplication: MatricesUsing matrices to manipulate data: MatricesMatrices as transformations of the plane: Matrices
Using matrices to transform the plane: MatricesTransforming 3D and 4D vectors with matrices: MatricesMultiplying matrices by matrices: MatricesProperties of matrix multiplication: MatricesRepresenting systems of equations with matrices: MatricesIntroduction to matrix inverses: MatricesFinding inverses of 2x2 matrices: MatricesSolving linear systems with matrices: Matrices

Probability and combinatorics

Venn diagrams and the addition rule: Probability and combinatoricsMultiplication rule for probabilities: Probability and combinatoricsPermutations: Probability and combinatoricsCombinations: Probability and combinatorics
Probability using combinatorics: Probability and combinatoricsProbability distributions introduction: Probability and combinatoricsTheoretical & empirical probability distributions: Probability and combinatoricsDecisions with probability: Probability and combinatoricsExpected value: Probability and combinatorics

Series

Mastery unavailable
Geometric series: SeriesGeometric series (with summation notation): SeriesThe binomial theorem: Series
Arithmetic series: Series

Limits and continuity

Mastery unavailable
Defining limits and using limit notation: Limits and continuityEstimating limit values from graphs: Limits and continuityEstimating limit values from tables: Limits and continuityDetermining limits using algebraic properties of limits: limit properties: Limits and continuityDetermining limits using algebraic properties of limits: direct substitution: Limits and continuityDetermining limits using algebraic manipulation: Limits and continuitySelecting procedures for determining limits: Limits and continuity
Determining limits using the squeeze theorem: Limits and continuityExploring types of discontinuities: Limits and continuityDefining continuity at a point: Limits and continuityConfirming continuity over an interval: Limits and continuityRemoving discontinuities: Limits and continuityConnecting infinite limits and vertical asymptotes: Limits and continuityConnecting limits at infinity and horizontal asymptotes: Limits and continuityWorking with the intermediate value theorem: Limits and continuity

Course challenge

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