Precalculus, Table of Contents

From the Preface:

"The goal of this course is to develop your ability to read, write, think, and do mathematics and to give you command of the facts and methods of algebra and trigonometry. It emphasizes everything you need to understand to be prepared for calculus.  

"A unique feature of this course is its emphasis on developing fluency in the abstract and symbolic language of algebra. That "foreign" language is extremely important because it is the most effective and efficient language in which to learn, understand, recall, and think mathematical thoughts."

CHAPTER 1, READING MATHEMATICS

• 1.1. Algebra
• 1.2. Order Matters!
• 1.3. Functions and Notation
• 1.4. Reading and Writing Mathematics
• 1.5. Graphs
• 1.6. Four Ways to Solve Equations Chapter 1 subsections

What goes on in each section? Section titles can't tell you all want to know, so subsection descriptions are included below. Also, here is a link for a prose description of the emphasis of each chapter and a bit of philosophy. Return to the main page.

CHAPTER 2, FUNCTIONS AND GRAPHS

• 2.1. Functions and Graphs
• 2.2. Composition and Decomposition
• 2.3. Relations and Inverses


• Chapter 2 subsections

CHAPTER 3, FUNDAMENTAL FUNCTIONS

• 3.1. Lines
• 3.2. Quadratics
• 3.3. Distance, Circles, and Ellipses
• 3.4. Graphical Factoring
• 3.5. Word Problems
• 3.6. More on Word Problems


• Chapter 3 subsections

[What goes on in each section? Section titles can't tell you all want to know, so subsection descriptions are included below.]

CHAPTER 4, POWERS

• 4.1. Powers and Polynomials
• 4.2. Polynomial Equations
• 4.3. Fractional Powers
• 4.4. Percents, Money, and Compounding
• 4.5. Rational Functions
• 4.6. Inequalities Chapter 4 subsections

CHAPTER 5, EXPONENTIAL AND LOGARITHMIC FUNCTIONS

• 5.1. Exponents and Logarithms
• 5.2. Base 2 and Base e
• 5.3. Applications
• 5.4. More Applications Chapter 5 subsections

CHAPTER 6, TRIGONOMETRY

• 6.1. Geometry for Trigonometry
• 6.2. Trigonometric Functions
• 6.3. Solving Triangles
• 6.4. Solving Figures Chapter 6 subsections

CHAPTER 7, TRIGONOMETRY FOR CALCULUS

• 7.1. Radians
• 7.2. Trigonometric Identities
• 7.3. More Identities
• 7.4. Waves Chapter 7 subsections

[The end of a one-semester four-credit course at Montana State University]
 

Return to the main page.

   
    Homeschoolers might be interested in two additional chapters.

Precalculus, Table of Contents  (somewhat expanded to include subsections. The shorter version is above).  

From the Preface: "A unique feature of this course is its emphasis on developing fluency in the abstract and symbolic language of algebra. That "foreign" language is extremely important because it is the most effective and efficient language in which to learn, understand, recall, and think mathematical thoughts." 

Chapter 1 is not typical. It emphasizes learning the symbolic language of algebra. It discusses what algebraic symbolism is for and how it is used to say what it says.
 

CHAPTER 1, READING MATHEMATICS

• 1.1. Algebra
  • Interpretation of Expressions, Operations and Identities
• 1.2. Order Matters!
  • Notation for Grouping
  • Parentheses For the Quadratic Formula
  • Guide to Pronunciation
• 1.3. Functions and Notation
  • functional "f(x)" notation
  • placeholders (dummy variables) 
• 1.4. Reading and Writing Mathematics
  • Placeholders (dummy variables) and unknowns
  • How to write Methods
  • Methods as Formulas
  • Methods as Identities
  • Methods as Relations between Equations
• 1.5. Graphs
  • Terminology of Graphs
  • Expressions and Graphs
  • Graphing with Calculators,
  • Selecting a Window
  • Limitations of Calculator Graphs
  • Graphing Expressions to Solve Equations,
  • Maximizing or Minimizing an Expression
  • Graphs Without Expressions
• 1.6. Four Ways to Solve Equations
  • The "Inverse-Reverse" Method
  • The Zero Product Rule Method
  • The Quadratic Formula
  • Guess-and-Check ("trial and error")

CHAPTER 2, FUNCTIONS AND GRAPHS

• 2.1. Functions and Graphs
  • Finding Windows
• 2.2. Composition and Decomposition
  • Composition and Inverses
  • Composition and Graphs
• 2.3. Relations and Inverses

CHAPTER 3, FUNDAMENTAL FUNCTIONS

• 3.1. Lines
  • Slope
  • Proportional
  • Parameters
  • Solving Linear Equations
  • Applications
  • Parallel and Perpendicular Lines
• 3.2. Quadratics
  • Symmetry
  • Location Changes, completing the square
  • The Quadratic Formula
  • Scale Changes
• 3.3. Distance, Circles, and Ellipses
  • Distance in the Plane
  • Circles
• 3.4. Graphical Factoring
  • The Factor Theorem
• 3.5. Word Problems
  • Build Your Own Formula
  • Evaluation and Solving
• 3.6.  More on Word Problems 
•  

CHAPTER 4, POWERS

• 4.1. Powers and Polynomials
  • Polynomials
  • Graphs of Polynomials
  • End Behavior
  • The Use of Polynomials, Approximation
• 4.2. Polynomial Equations
  • Solving Monomial Equations
  • Solving Polynomial Equations
  • Calculator-Aided Factoring Techniques
• 4.3. Fractional Powers
  • Fractional Powers
  • Square Root
• 4.4. Percents, Money, and Compounding
  • Composition of Functions
  • Money, Compound Interest
  • Average Rate of Change
• 4.5. Rational Functions
  • Solving Rational Equations
  • Graphs
  • Asymptotes
  • End-Behavior
  • Uses of Rational Functions
• 4.6. Inequalities
  • Interval Notation
  • Graphical Solutions
  • Absolute Values
  • Inequalities for Calculus
  • Solving Linear Inequalities
  • Zeros and Inequalities

CHAPTER 5, EXPONENTIAL AND LOGARITHMIC FUNCTION

• 5.1. Exponents and Logarithms
  • Scientific Notation
  • Exponents and Logarithms
  • Properties of Exponential Functions
  • Properties of Logarithms
• 5.2. Base 2 and Base e
  • Base 2 (doubling time models)
  • Exponential Growth
  • Base 1/2 (half-life models)
  • Compound Interest
  • Base e
  • Polynomial Approximations
  • Change-of-Base
• 5.3. Applications
  • Richter Scale
  • Decibels
  • Exponential Models
  • Growth of Money
• 5.4. More Applications
  • Power Models, Kepler's Laws
  •  

CHAPTER 6, TRIGONOMETRY

• 6.1. Geometry for Trigonometry
  • Solving a Triangle
  • Pythagorean Theorem
  • Ambiguous Cases, Recognizing the Cases
• 6.2. Trigonometric Functions
  • Sine, Inverse Sine
  • Solving Right Triangles
  • Cosine, Inverse Cosine
  • Tangent, Inverse Tangent
  • Reference Angles, Basic Facts
• 6.3. Solving Triangles
  • Area
  • The Law of Sines
  • The Law of Cosines
• 6.4. Solving Figures
  • Solving Triangles
  • More Complex Figures
  • Navigation

CHAPTER 7, TRIGONOMETRY FOR CALCULUS

• 7.1. Arc Length and Radians
  • Arc Length
  • Area of a Sector
• 7.2. Trigonometric Identities
  • From Unit-Circle Pictures
  • Reference Angles
  • Solving Trigonometric Equations
  • Other Trigonometric Functions
  • Identities from Right-Triangle Pictures
  • Trigonometric Substitution
• 7.3.  More Identities
  • The Sum and Difference Identities
  • Double- and Half-Angle Identities, Squared Identities
• 7.4. Waves
  • Describing Sine Waves
  • Adding Sine Waves
  • Applications

[This is the end of a one-semester four-credit course at Montana State University.]

    Homeschoolers might be interested in two additional chapters.

Return to the main page.