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
[The end of a onesemester fourcredit 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 "InverseReverse" Method
 The Zero Product Rule Method
 The Quadratic Formula
 GuessandCheck ("trial and error")
CHAPTER 2, FUNCTIONS AND GRAPHS
 2.1. Functions and Graphs
 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
 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
 CalculatorAided 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
 EndBehavior
 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 (halflife models)
 Compound Interest
 Base e
 Polynomial Approximations
 ChangeofBase
 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
 Reference Angles
 Solving Trigonometric Equations
 Other Trigonometric Functions
 Identities from RightTriangle Pictures
 Trigonometric Substitution
 7.3. More Identities
 The Sum and Difference Identities
 Double and HalfAngle Identities, Squared Identities
 7.4. Waves
 Describing Sine Waves
 Adding Sine Waves
 Applications
[This is the end of a onesemester fourcredit course at Montana State University.]
Homeschoolers might be interested in two additional chapters.
Return to the main page.