AP Precalculus

Duration

10 Months

Prerequisites

Algebra 1, Geometry, and Algebra 2

Requirements

As a result of examining functions from many perspectives, students develop a conceptual understanding not only of specific function types but also of functions in general. Furthermore, as AP Precalculus may be the last mathematics course of a student's secondary education, the course is structured to provide a comprehensive experience rather than exclusively focusing on preparation for future courses.

Course Summary

AP Precalculus centers on functions modeling dynamic behaviors. This research-based exploration of functions is designed to better prepare students for college-level calculus and provide a basis for other mathematics and science courses. In this course, students study the value of polynomial and rational functions, exponential and logarithmic functions, trigonometric and polar functions, and supplemental topics

MAJOR TOPICS AND CONCEPTS

Major Topics and Concepts:

Segment One

  • Determine and evaluate the behavior of different function types, including end behavior using the mathematical notation of a limit.
  • Compare and analyze rates of change, including the change in the average rate of change for linear and quadratic functions.
  • Identify key characteristics of different function types.
  • Recognize and determine complex and real zeros of functions.
  • Determine the effects of transformations on different function types.
  • Analyze rational functions.
  • Determine and analyze vertical asymptotes and holes in the domain of rational functions.
  • Express functions in equivalent forms.
  • Model data sets for geometric and real-world applications.
  • Construct a model, including using technology to construct a regression function model.
  • Describe and construct piecewise-defined functions.
  • Define, apply, and relate arithmetic and geometric sequences to linear and exponential functions respectively.
  • Compare models to decide which is the most appropriate.
  • Construct the composition of two or more functions.
  • Construct and verify inverse functions.

Segment Two 

  • Rewrite and evaluate logarithmic expressions as exponential expressions.
  • Apply properties of inverse functions to logarithmic and exponential functions.
  • Determine the effects of transformations on different function types.
  • Identify key characteristics of different function types.
  • Solve equations and inequalities of different function types.
  • Construct and verify inverse functions.
  • Construct a model, including using technology to construct a regression function model.
  • Write, apply, and linearize functions modeled with semi-log plots.
  • Determine the sine, cosine, and tangent of an angle from the unit circle defined in radians.
  • Construct sinusoidal function models.
  • Convert between trigonometric functions and their inverse functions graphically, numerically, analytically, and verbally.
  • Produce general solutions to describe trigonometric equations.
  • Derive and verify trigonometric identities.
  • Covert between rectangular coordinates, polar coordinates, and complex numbers.
  • Determine how changes in input and output values correspond to changes in angle and radius measure, respectively.
  • Determine and interpret the average rate of change in a polar function.
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AP Precalculus