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AP® Precalculus

Free AP® Precalculus Tips, Study Guides, Review Resources & Test Strategies

Welcome to Albert’s collection of math topic reviews for teaching and reviewing AP® Precalculus. Teachers and students can explore our easy-to-follow guides below for use at home or in the classroom.

Introduction to the Course

Is AP® Precalculus hard? Will colleges take AP® Precalculus? How long is the AP® Precalculus exam? Find out answers to these questions and more below!

The articles below provide an overview of AP® Precalculus, covering everything from course expectations to study strategies. Whether you're wondering how challenging the course is, looking for practice tests, or seeking tips for free-response questions, these guides will help you prepare with confidence.

Subject icon for AP® Precalculus Overview

AP® Precalculus Overview

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AP® Precalculus Score Calculator

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AP® Precalculus Practice Tests

Subject icon for Is AP® Precalculus Hard?

Is AP® Precalculus Hard?

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AP® Precalculus Prerequisites

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How to Answer AP® Precalculus Free Response Questions

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The Ultimate List of AP® Precalculus Tips

Unit 1: Polynomial and Rational Functions

How can you transform the graph of a polynomial function? How to determine whether a function is a polynomial? What is instantaneous rate of change? How do you find a hole in a rational function?

The articles below explore essential topics related to polynomial and rational functions, from function transformations to zeros, end behaviors, and asymptotes. Whether you're analyzing rates of change or refining your algebraic skills, these resources will help you build a strong foundation in AP® Precalculus.

AP® Precalculus Unit 1 Review

1.1 Change in Tandem

1.2 Rates of Change

1.3 Rates of Change in Linear and Quadratic Functions

1.4 Polynomial Functions and Rates of Change

1.5 Polynomial Functions and Complex Zeros

1.6 Polynomial Functions and End Behavior

1.7 Rational Functions and End Behavior

1.8 Rational Functions and Zeros

1.9 Rational Functions and Vertical Asymptotes

1.10 Rational Functions and Holes

1.11.A Equivalent Representations of Polynomial and Rational Expressions

1.11.B Equivalent Representations of Polynomial and Rational Expressions

1.11.C Equivalent Representations of Polynomial and Rational Expressions

1.12 Transformations of Functions

1.13.A Function Model Selection and Assumption Articulation

1.13.B Function Model Selection and Assumption Articulation

1.14 Function Model Construction and Application

Unit 2: Exponential and Logarithmic Functions

Which graph represents an exponential function? How to find exponential function from two points? How do you know if a function has an inverse? How do you find the domain of a logarithmic function?

The articles below dive into key exponential and logarithmic function topics, from sequences and converting exponents to logarithms and function composition. Whether you're exploring arithmetic and geometric patterns, modeling with exponentials, or working with inverse and logarithmic functions, these guides will help you develop a deeper understanding of essential mathematical relationships.

2.1.A Change in Arithmetic and Geometric Sequences

2.1.B Change in Arithmetic and Geometric Sequences

2.2 Change in Linear and Exponential Functions

2.3 Exponential Functions

2.4 Exponential Function Manipulation

2.5 Exponential Function Context and Data Modeling

2.6 Competing Function Model Validation

2.7 Composition of Functions

2.8 Inverse Functions

2.9 Logarithmic Expressions

2.10 Inverses of Exponential Functions

2.11 Logarithmic Functions

2.12 Logarithmic Function Manipulation

2.13 Exponential and Logarithmic Equations and Inequalities

2.14 Logarithmic Function Context and Data Modeling

2.15 Semi-log Plots

Unit 3: Trigonometric and Polar Functions

How to graph sine and cosine? How to find the exact value of a trigonometric function? How to find period and amplitude? How to graph polar functions?

The articles below cover essential AP® Precalculus topics in trigonometry and periodic functions, from unit circle fundamentals to graphing sine, cosine, and tangent functions. Whether you're exploring transformations, inverse trig functions, or the connections between polar and rectangular coordinates, these guides will help you master the key concepts of trigonometric modeling and analysis.

3.1 Periodic Phenomena

3.2 Sine, Cosine, and Tangent

3.3 Sine and Cosine Function Values

3.4 Sine and Cosine Function Graphs

3.5 Sinusoidal Functions

3.6 Sinusoidal Function Transformations

3.7 Sinusoidal Function Context and Data Modeling

3.8.A The Tangent Function

3.8.B The Tangent Function

3.8.C The Tangent Function

3.9 Inverse Trigonometric Functions

3.10 Trigonometric Equations and Inequalities

3.11 The Secant, Cosecant, and Cotangent Functions

3.12 Equivalent Representations of Trigonometric Functions

3.13 Trigonometry and Polar Coordinates

3.14 Polar Function Graphs

3.15 Rates of Change in Polar Functions

Unit 4: Functions Involving Parameters, Vectors, and Matrices

What is a parametric function? How to parametrize a line? What is a unit vector? Is speed a vector or scalar? How to multiply matrices? How to add matrices?

The articles below explore key concepts in functions involving parametric equations, vectors, and matrices. Whether you're analyzing particle motion, working with conic sections, or mastering vector operations and transformations, these guides will help you build a strong understanding of advanced function modeling and algebraic techniques.

4.1 Parametric Functions

4.2 Parametric Functions Modeling Planar Motion

4.3 Parametric Functions and Rates of Change

4.4 Parametrically Defined Circles and Lines

4.5 Implicitly Defined Functions

4.6 Conic Sections

4.7 Parametrization of Implicitly Defined Functions

4.9 Vector-Valued Functions

4.11 The Inverse and Determinant of a Matrix

4.12 Linear Transformations and Matrices

4.13 Matrices as Functions

4.14 Matrices Modeling Contexts

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