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AP®︎ Precalculus Study Guides

Prepare for your quiz, test, or the AP exam with comprehensive study guides that cover everything you need to know. Select a unit or topic to begin.

Unit 1: Polynomial and Rational Functions

All Topics
Complete Unit Review

Topic 1.1
Change in Tandem

Topic 1.2
Rates of Change

Topic 1.3
Rates of Change in Linear and Quadratic Functions

Topic 1.4
Polynomial Functions and Rates of Change

Topic 1.5
Polynomial Functions and Complex Zeros

Topic 1.6
Polynomial Functions and End Behavior

Topic 1.7
Rational Functions and End Behavior

Topic 1.8
Rational Functions and Zeros

Topic 1.9
Rational Functions and Vertical Asymptotes

Topic 1.10
Rational Functions and Holes

Topic 1.11
Equivalent Representations of Polynomial and Rational Expressions

Topic 1.12
Transformations of Functions

Topic 1.13
Function Model Selection and Assumption Articulation

Topic 1.14
Function Model Construction and Application

Unit 2: Exponential and Logarithmic Functions

All Topics
Complete Unit Review

Topic 2.1
Change in Arithmetic and Geometric Sequences

Topic 2.2
Change in Linear and Exponential Functions

Topic 2.3
Exponential Functions

Topic 2.4
Exponential Function Manipulation

Topic 2.5
Exponential Function Context and Data Modeling

Topic 2.6
Competing Function Model Validation

Topic 2.7
Composition of Functions

Topic 2.8
Inverse Functions

Topic 2.9
Logarithmic Expressions

Topic 2.10
Inverses of Exponential Functions

Topic 2.11
Logarithmic Functions

Topic 2.12
Logarithmic Function Manipulation

Topic 2.13
Exponential and Logarithmic Equations and Inequalities

Topic 2.14
Logarithmic Function Context and Data Modeling

Topic 2.15
Semi-log Plots

Unit 3: Trigonometric and Polar Functions

All Topics
Complete Unit Review

Topic 3.1
Periodic Phenomena

Topic 3.2
Sine, Cosine, and Tangent

Topic 3.3
Sine and Cosine Function Values

Topic 3.4
Sine and Cosine Function Graphs

Topic 3.5
Sinusoidal Functions

Topic 3.6
Sinusoidal Function Transformations

Topic 3.7
Sinusoidal Function Context and Data Modeling

Topic 3.8
The Tangent Function

Topic 3.9
Inverse Trigonometric Functions

Topic 3.10
Trigonometric Equations and Inequalities

Topic 3.11
The Secant, Cosecant, and Cotangent Functions

Topic 3.12
Equivalent Representations of Trigonometric Functions

Topic 3.13
Trigonometry and Polar Coordinates

Topic 3.14
Polar Function Graphs

Topic 3.15
Rates of Change in Polar Functions

Unit 4: Functions Involving Parameters, Vectors, and Matrices

All Topics
Complete Unit Review

Topic 4.1
Parametric Functions

Topic 4.2
Parametric Functions Modeling Planar Motion

Topic 4.3
Parametric Functions and Rates of Change

Topic 4.4
Parametrically Defined Circles and Lines

Topic 4.5
Implicitly Defined Functions

Topic 4.6
Conic Sections

Topic 4.7
Parametrization of Implicitly Defined Functions

Topic 4.8
Vectors

Topic 4.9
Vector-Valued Functions

Topic 4.10
Matrices

Topic 4.11
The Inverse and Determinant of a Matrix

Topic 4.12
Linear Transformations and Matrices

Topic 4.13
Matrices as Functions

Topic 4.14
Matrices Modeling Contexts

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