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Mathematics III (2018 edition)

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Unit 1: Functions

Combining functionsComposing functionsModeling situations by combining & composing functionsShifting functions

Stretching functionsIntroduction to inverses of functionsFinding inverse functionsVerifying that functions are inversesDetermining whether a function is invertible

Unit 2: Polynomials

Binomial theoremUnderstanding the binomial theoremAdvanced polynomial factorization methodsProving polynomial identitiesPolynomial identities with complex numbersQuadratic equations with complex numbers

Fundamental theorem of AlgebraFinding zeros of polynomialsZeros of polynomials and their graphsEnd behavior of polynomial functionsGraphs of polynomialsIntroduction to symmetry of functionsSymmetry of polynomial functions

Unit 3: Radical relationships

Square-root equationsExtraneous solutions of radical equationsCube-root equations

Domain of radical functionsGraphs of radical functions

Unit 4: Rational relationships

Simplifying rational expressionsMultiplying & dividing rational expressionsAdding & subtracting rational expressionsNested fractionsRational equations

Direct and inverse variationEnd behavior of rational functionsDiscontinuities of rational functionsGraphs of rational functionsModeling with rational functions

Unit 5: Exponentials & logarithms

Introduction to logarithmsThe constant e and the natural logarithmProperties of logarithmsChange of base formula for logarithms

Exponential equations: logarithmsSolving exponential modelsGraphs of exponential functionsGraphs of logarithmic functionsLogarithmic scale (optional)

Unit 6: Trigonometry

Law of sinesLaw of cosinesSolving general trianglesIntroduction to radiansUnit circle definition of sine, cosine, & tangentGraphs of sine, cosine, & tangentBasic trigonometric identities

Trigonometric values of special anglesPythagorean identityIntroduction to amplitude, midline, & extrema of sinusoidal functionsFinding amplitude & midline from formulaPeriod of sinusoidal functionsGraphing sinusoidal functionsConstructing sinusoidal functions

Unit 7: Advanced equations & functions

Solving equations by graphingSystems of quadratic equationsInterpreting the symmetry of algebraic models

Interpreting the end behavior of algebraic modelsInterpreting the periodicity of algebraic modelsComparing features of functions

Unit 8: Series

Basic sigma notationFinite arithmetic seriesFinite geometric series

Finite geometric series applications

Unit 9: Study Design

Samples and surveysObservational studies and experiments

Unit 10: Binomial probability

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Binomial probability

Unit 11: Normal distributions

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Normal distributions

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