Autorentext

Stephen Kokoska; Bruce Crauder; Benny Evans; Alan Noell

Klappentext

Precalculus for the AP® Course gives you a clear, AP®-aligned framework for helping students bridge foundational algebra and dynamic modeling while building the conceptual understanding and problem-solving skills they need throughout the course.

Organized to follow the AP® Precalculus Course and Exam Description (CED), the text provides a rigorous, approachable progression through course content, including Unit 4 topics and the Laws of Sines and Cosines. Students explore functions, identify mathematical patterns, and apply concepts through examples and problems designed to strengthen understanding.

Integrated AP® practice makes it easy to reinforce course skills throughout the year. AP® Practice and Review Problems at the section, chapter, and unit levels provide ongoing opportunities to apply learning, while a full-length AP® Practice Exam brings course concepts and skills together for exam preparation. Point-of-use margin features provide additional guidance on AP® Exam expectations, notation, technology, mathematical communication, and problem-solving strategies.

Stepped-Out Problem-Solving and Break It Down provide scaffolded support for working through challenging problems. Clear, structured examples model the problem-solving process step by step, helping students understand not only how to reach a solution but also how to reason through and communicate their mathematical thinking.

Inhalt

Chapter 0: Prerequisites

0.1 The Coordinate Plane: Lines and Circles

0.2 Linear Inequalities

0.3 Nonlinear Inequalities

Unit 1: Polynomial and Rational Functions

Chapter 1: Polynomial Functions

1.1 Function Essentials

1.2 Rates of Change

1.3 Rates of Change: Linear and Quadratic Functions

1.4 Rates of Change: Polynomial Functions

1.5 Polynomial Functions: Characteristics Related to Zeros

1.6 Polynomial Functions: End Behavior

Chapter 2: Rational Functions

2.1 Rational Functions: End Behavior

2.2 Rational Functions: Zeros

2.3 Rational Functions: Vertical Asymptotes

2.4 Rational Functions: Holes

2.5 Equivalent Representations of Polynomials and Rational Expressions

Chapter 3: Transformations and Modeling

3.1 Transformations of Functions

3.2 Function Models: Selection, Assumptions, Limitations

3.3 Function Models: Applications

Unit 2: Exponential and Logarithmic Functions

Chapter 4: Exponential Functions

4.1 Rates of Change: Arithmetic and Geometric Sequences, Linear and Exponential Functions

4.2 Exponential Functions: Characteristics and Properties

4.3 Exponential Function Models

4.4 Composition of Functions

Chapter 5: Logarithmic Functions

5.1 Inverse Functions

5.2 Logarithmic Functions: Characteristics and Properties

5.3 Exponential and Logarithmic Equations and Inequalities

5.4 Function Models: Logarithmic

5.5 Semi-Log Plots

Unit 3: Trigonometric and Polar Functions

Chapter 6: Trigonometry Part 1

6.1 Periodic Phenomena

6.2 Sine, Cosine, and Tangent Functions

6.3 Sine and Cosine Graphs

6.4 The Sine and Cosine Functions: Transformations

6.5 Sinusoidal Function Models

6.6 The Tangent Function

Chapter 7: Trigonometry Part 2

7.1 Inverse Trigonometric Functions

7.2 Trigonometric Equations and Inequalities

7.3 The Secant, Cosecant, and Cotangent Functions

7.4 Trigonometric Identities and Simplifications

7.5 Verifying Trigonometric Identities

Chapter 8: Polar Functions

8.1 The Polar Coordinate System

8.2 Polar Function Graphs

8.3 Rates of Change in Polar Functions

Unit 4: Functions Involving Parameters, Vectors, and Matrices

Chapter 9: Parametric Equations and Functions Defined Implicitly

9.1 Parametric Equations: Definitions and Graphs

9.2 Parametric Equations: Modeling Motion

9.3 Parametric Equations: Rates of Change

9.4 Parametric Equations: Circles and Lines

9.5 Functions Defined Implicitly

9.6 Conic Sections

9.7 Rewriting Equations in Parametric Form

Chapter 10: Vectors and Matrices

10.1 Vectors

10.2 Vector-Valued Functions

10.3 Matrices

10.4 The Determinant and the Inverse of a Matrix

10.5 Linear Transformations

10.6 Representation of Functions using Matrices

10.7 Matrix Models

Appendix

A.1 Law of Sines

A.2 Law of Cosines