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AP Precalculus Curriculum

Unit 1: Polynomial and Rational Functions


In this unit, students will explore polynomial and rational functions. They will learn about rates of change, complex zeros, end behavior, transformations, and how to represent polynomial and rational expressions equivalently. Additionally, students will develop skills in constructing function models and applying them in various contexts.


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 Equivalent Representations of Polynomial and Rational Expressions

1.12 Transformations of Functions

1.13 Function Model Selection and Assumption Articulation

1.14 Function Model Construction and Application

Unit 2: Exponential and Logarithmic Functions


Unit 2 dives into exponential and logarithmic functions. Students will explore the properties, manipulations, and applications of these functions, as well as their relationship to arithmetic and geometric sequences, inverse functions, and solving equations and inequalities involving exponential and logarithmic expressions.


2.1 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


Unit 3 focuses on trigonometric and polar functions. Students will study periodic phenomena, trigonometric ratios, graphing trigonometric functions, inverse trigonometric functions, polar coordinates, and polar function graphs. They will also learn about rates of change in polar functions and how to solve trigonometric equations and inequalities.


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 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

Unit 4 explores functions involving parameters, vectors, and matrices. Students will study parametric functions, their applications in modeling planar motion, rates of change in parametric functions, implicitly defined functions, conic sections, vectors, vector-valued functions, matrices, linear transformations, and matrices as functions. Note: Unit 4 is not assessed on the AP® Precalculus exam.

4.1 Parametric Functions

4.2 Parametric Functions Modelling 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

4.8 Vectors

4.9 Vector-Valued Functions

4.10 Matrices

4.11 The Inverse and Determinant of a Matrix

4.12 Linear Transformations and Matrices

4.13 Matrices as Functions

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