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High School AP Precalculus

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Suggested Prerequisites

Algebra 1, Algebra 2, Geometry

Description

Engage in concepts that bridge current math knowledge and exciting new topics. The course centers on functions modeling dynamic behaviors. This research-based exploration of functions is designed to better prepare you for the next level of math classes. and provide a basis for other mathematics and science courses. As a result of examining functions from many perspectives, you will develop a conceptual understanding not only of specific function types but also of functions in general.

Module One: Mastering Polynomial Functions by Exploring Change

-determine the behavior of different function types

-denote end behavior using limit notation

-compare and analyze average rates of change

-identify key characteristics of different function types

-analyze transformations of different function types

-express functions in equivalent forms


Module Two: Mastering Rational and Piecewise Functions

-determine the behavior of rational functions

-compare and analyze average rates of change

-identify key characteristics of rational functions

-express rational functions in equivalent forms

-model data sets for multiple applications

-use technology to construct regression models

-describe and construct piecewise-defined functions


Module Three: Conquering Exponential Functions and Function Applications

-determine the behavior of exponential functions

-compare and analyze average rates of change

-identify key characteristics of exponential functions

-express exponential functions in equivalent forms

-analyze transformations of exponential functions

-model data sets for multiple applications

-use technology to construct regression models

-define and relate sequences to functions

-construct compositions of two or more functions

-construct and verify inverse functions

Module Four: Conquering Logarithmic Functions and Modeling

-rewrite logarithmic expressions as exponential expressions

-analyze transformations of logarithmic functions

-identify key characteristics of logarithmic functions

-solve equations and inequalities of logarithmic functions

-construct and verify inverse functions

-use technology to construct regression models

-apply and linearize functions modeled with semi-log plots


Module Five: Investigating Periodic Functions

-explore functions with periodic characteristics

-analyze transformations of trigonometric functions

-identify key characteristics of trigonometric functions

-use technology to construct sinusoidal regression models

-determine trigonometric function values using the unit circle


Module Six: Investigating Solutions of Trigonometric and Polar Functions

-solve equations and inequalities of trigonometric functions

-construct and verify inverse functions

-convert between trigonometric functions and their inverses 

-find solutions to describe trigonometric equations

-derive and verify trigonometric identities

-covert between rectangular and polar coordinates

-identify key characteristics of polar functions

-analyze and interpret average rates of change