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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