Cover
Title Page
Dedication
Copyright
About the Author
Table of Contents
How to Use This Book
Barron’s Essential 5
Introduction
Unit Outline
Exam Format
Scoring of the Exam
Using Your Graphing Calculator on the AP Exam
Prior Knowledge
Unit 1: Polynomial and Rational Functions
1. Rates of Change
1.1 Relations and Functions
1.2 Rates of Change
1.3 Rates of Change in Linear Functions
1.4 Rates of Change in Quadratic Functions
Multiple-Choice Questions
Answer Explanations
2. Polynomial Functions
2.1 Polynomial Functions and Rates of Change
2.2 Real and Complex Zeros of Polynomial Functions
2.3 Polynomial Functions and End Behavior
2.4 Graphs of Polynomial Functions
2.5 Equivalent Representations of Polynomial Expressions
2.6 Polynomial Inequalities
Multiple-Choice Questions
Answer Explanations
3. Rational Functions
3.1 Equivalent Representations of Rational Expressions: Long Division
3.2 Rational Functions and Zeros
3.3 Rational Functions and Vertical Asymptotes
3.4 Rational Functions and Holes
3.5 Rational Functions and End Behavior
3.6 Graphs of Rational Functions
3.7 Rational Inequalities
Multiple-Choice Questions
Answer Explanations
4. Parent Functions
4.1 Graphs and Properties of Basic Functions
4.2 Transformations of Functions
4.3 Function Model Selection, Construction, and Application
4.4 Composition of Functions
4.5 Inverse Functions
Multiple-Choice Questions
Answer Explanations
Unit 2: Exponential and Logarithmic Functions
5. Exponential Functions
5.1 Exponential Functions
5.2 Exponential Function Manipulation
5.3 Exponential Function Context and Data Modeling
5.4 Competing Function Model Validation
Multiple-Choice Questions
Answer Explanations
6. Sequences
6.1 Arithmetic Sequences
6.2 Geometric Sequences
6.3 Change in Linear and Exponential Functions
Multiple-Choice Questions
Answer Explanations
7. Logarithmic Functions
7.1 Logarithmic Expressions
7.2 Inverses of Exponential Functions
7.3 Logarithmic Functions
7.4 Logarithmic Function Manipulation
7.5 Exponential and Logarithmic Equations and Inequalities
7.6 Logarithmic Function Context and Data Modeling
7.7 Semi-log Plots
Multiple-Choice Questions
Answer Explanations
Unit 3: Trigonometric and Polar Functions
8. Trigonometric Functions
8.1 Periodic Phenomena
8.2 Sine, Cosine, and Tangent
8.3 Sine and Cosine Function Values
8.4 Sine and Cosine Function Graphs
8.5 Sinusoidal Functions
8.6 Sinusoidal Function Transformations
8.7 Sinusoidal Function Context and Data Modeling
8.8 The Tangent Function
8.9 Inverse Trigonometric Functions
8.10 Trigonometric Equations and Inequalities
8.11 The Secant, Cosecant, and Cotangent Functions
8.12 Equivalent Representations of Trigonometric Functions
Multiple-Choice Questions
Answer Explanations
9. Polar Functions
9.1 Trigonometry and Polar Coordinates
9.2 Polar Function Graphs
9.3 Rates of Change in Polar Functions
Multiple-Choice Questions
Answer Explanations
Unit 4: Functions Involving Parameters, Vectors, and Matrices
10. Parametric Functions
10.1 Parametric Functions
10.2 Parametric Functions Modeling Planar Motion
10.3 Parametric Functions and Rates of Change
10.4 Parametrically Defined Circles and Lines
10.5 Implicitly Defined Functions
10.6 Conic Sections
10.7 Parameterization of Functions
Multiple-Choice Questions
Answer Explanations
11. Vectors
11.1 Algebraic and Graphical Properties of Vectors
11.2 Vector-Valued Functions
Multiple-Choice Questions
Answer Explanations
12. Matrices
12.1 Matrix Operations
12.2 The Inverse and Determinant of a Matrix
12.3 Linear Transformations and Matrices
12.4 Matrices as Functions
12.5 Matrices Modeling Context
Multiple-Choice Questions
Answer Explanations
Practice Tests
Practice Test 1
Answer Explanations
Practice Test 2
Answer Explanations
Glossary of Key Terms