Precalculus

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Table of Contents

Chapter 1 – FUNCTIONS AND THEIR GRAPHS

1.1 Lines in the Plane
1.2 Functions
1.3 Graphs of Functions
1.4 Shifting, Reflecting, and Stretching Graphs
1.5 Combinations of Functions
1.6 Inverse Functions
1.7 Linear Models and Scatter Plots

Chapter 2 – POLYNOMIAL AND RATIONAL FUNCTIONS

2.1 Quadratic Functions
2.2 Polynomial Functions of Higher Degree
2.3 Real Zeros of Polynomial Functions
2.4 Complex Numbers
2.5 The Fundamental Theorem of Algebra
2.6 Rational Functions and Asymptotes
2.7 Graphs of Rational Functions
2.8 Quadratic Models

Chapter 3 – EXPONENTIAL AND LOGARITHMIC FUNCTIONS

3.1 Exponential Functions and Their Graphs
3.2 Logarithmic Functions and Their Graphs
3.3 Properties of Logarithms
3.4 Solving Exponential and Logarithmic Equations
3.5 Exponential and Logarithmic Models
3.6 Nonlinear Models

Chapter 4 – TRIGONOMETRIC FUNCTIONS

4.1 Radian and Degree Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications and Models

Chapter 5 – ANALYTIC TRIGONOMETRY

5.1 Using Fundamental Identities
5.2 Verifying Trigonometric Identities
5.3 Solving Trigonometric Equations
5.4 Sum and Difference Formulas
5.5 Multiple-Angle and Product-to-Sum Formulas

Chapter 6 – ADDITIONAL TOPICS IN TRIGONOMETRY

6.1 Law of Sines
6.2 Law of Cosines
6.3 Vectors in the Plane
6.4 Vectors and Dot Products
6.5 Trigonometric Form of a Complex Number

Chapter 7 – LINEAR SYSTEMS AND MATRICES

7.1 Solving Systems of Equations
7.2 Systems of Linear Equations in Two Variables
7.3 Multivariable Linear Systems
7.4 Matrices and Systems of Equations
7.5 Operations with Matrices
7.6 The Inverse of a Square Matrix
7.7 The Determinant of a Square Matrix
7.8 Applications of Matrices and Determinants

Chapter 8 – SEQUENCES, SERIES, AND PROBABILITY

8.1 Sequences and Series
8.2 Arithmetic Sequences and Partial Sums
8.3 Geometric Sequences and Series
8.4 Mathematical Induction
8.5 The Binomial Theorem
8.6 Counting Principles
8.7 Probability

Chapter 9 – TOPICS IN ANALYTIC GEOMETRY

9.1 Circles and Parabolas
9.2 Ellipses
9.3 Hyperbolas
9.4 Rotation and Systems of Quadratic Equations
9.5 Parametric Equations
9.6 Polar Coordinates
9.7 Graphs of Polar Equations
9.8 Polar Equations of Conics

Chapter 10 – ANALYTIC GEOMETRY IN THREE DIMENSIONS

10.1 The Three-Dimensional Coordinate System
10.2 Vectors in Space
10.3 The Cross Product of Two Vectors
10.4 Lines and Planes in Space

Chapter 11 – LIMITS AND AN INTRODUCTION TO CALCULUS

11.1 Introduction to Limits
11.2 Techniques for Evaluating Limits
11.3 The Tangent Line Problem
11.4 Limits at Infinity and Limits of Sequences
11.5 The Area Problem

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