Chapter 1: Preliminary InformationSection 1-1:
Sets of Numbers
Section 1-2:
The Field Axioms
Section 1-3:
Variables and Expressions
Section 1-4:
Polynomials
Section 1-5:
Equations
Section 1-6:
Inequalities
Section 1-7:
Properties Provable from the Axioms
Section 1-8:
Chapter Review and Test
Chapter 2: Functions and RelationsSection 2-1:
Graphs of Equations with Two Variables
Section 2-2:
Graphs of Functions
Section 2-3:
Functions in the Real World
Section 2-4:
Graphs of Functions and Relations
Section 2-5:
Chapter Review and Test
Chapter 3: Linear FunctionsSection 3-1:
Introduction to Linear Functions
Section 3-2:
Properties of Linear Function Graphs
Section 3-3:
Other Forms of the Linear Function Equation
Section 3-4:
Equations of Linear Functions from Their Graphs
Section 3-5:
Linear Functions as Mathematical Models
Section 3-6:
Chapter Review and Test
Chapter 4: Systems of Linear Equations and InequalitiesSection 4-1:
Introduction to Linear Systems
Section 4-2:
Solution of Systems of Linear Equations
Section 4-3:
Second-Order Determinants
Section 4-4:
f(x) Terminology, and Systems as Models
Section 4-5:
Linear Equations with Three or More Variables
Section 4-6:
Systems of Linear Equations with Three or More Variables
Section 4-7:
Solution of Second-Order Systems by Augmented Matrices
Section 4-8:
Solution of Higher Order Systems by Augmented Matrices
Section 4-9:
Higher-Order Determinants
Section 4-10:
Systems of Linear Inequalities
Section 4-11:
Linear Programming
Section 4-12:
Chapter Review and Test
Chapter 5: Quadratic Functions and Complex NumbersSection 5-1:
Introduction to Quadratic Functions
Section 5-2:
Graphs of Quadratic Functions
Section 5-3:
x-Intercepts, and the Quadratic Formula
Section 5-4:
Imaginary and Complex Numbers
Section 5-5:
Evaluating Quadratic Functions
Section 5-6:
Equations of Quadratic Functions from their Graphs
Section 5-7:
Quadratic and Linear Functions as Mathematical Models
Section 5-8:
Chapter Review and Test
Section 5-9:
Cumulative Review: Chapter 1 through 5
Chapter 6: Exponential and Logarithmic FunctionsSection 6-1:
Introduction to Exponential Functions
Section 6-2:
Exponentiation for Positive Integer Exponents
Section 6-3:
Properties of Exponentiation
Section 6-4:
Exponentiation for Rational Exponents
Section 6-5:
Powers and Radicals without Calculators
Section 6-6:
Scientific Notation
Section 6-7:
Exponential Equations Solved by Brute Force
Section 6-8:
Exponential Equations Solved by Logarithms
Section 6-9:
Logarithms with Other Bases
Section 6-10:
Properties of Logarithms
Section 6-11:
Proofs of Properties of Logarithms
Section 6-12:
Inverses of Functions-The Logarithmic Functions
Section 6-13:
The Add-Multiply Property of Exponential FunctionsSection 6-14:
Exponential and Other Functions as Mathematical Models
Section 6-15:
Chapter Review and Test
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Chapter 7: Rational Algebraic FunctionsSection 7-1:
Introduction to Rational Algebraic Functions
Section 7-2:
Rational Functions Graphs-Discontinuities and Asymptotes
Section 7-3:
Special Products and Factoring
Section 7-4:
More Factoring and Graphing
Section 7-5:
Long Division of Polynomials
Section 7-6:
Factoring Higher Degree Polynomials- The Factor Theorem
Section 7-7:
Products and Quotients of Rational Expressions
Section 7-8:
Sums and Differences of Rational Expressions
Section 7-9:
Graphs of Rational Algebraic Functions Again
Section 7-10:
Fractional Equations and Extraneous Solutions
Section 7-11:
Variation FunctionsSection 7-12:
Chapter Review and Test
Chapter 8: Irrational Algebraic FunctionsSection 8-1:
Introduction to Irrational Algebraic Functions
Section 8-2:
Graphs of Irrational Functions
Section 8-3:
Radicals, and Simple Radical Form
Section 8-4:
Radical Equations
Section 8-5:
Variation Functions with Non-Integer Exponents
Section 8-6:
Functions of More Than One Independent Variable
Section 8-7:
Chapter Review and Test
Section 8-8:
Cumulative Review, Chapter 6, 7, and 8
Chapter 9: Quadratic Relations and SystemsSection 9-1:
Introduction to Quadratic Relations
Section 9-2:
Circles
Section 9-3:
Ellipses
Section 9-4:
Hyperbolas
Section 9-5:
Parabolas
Section 9-6:
Equations from Geometrical Definitions
Section 9-7:
Quadratic Relations - xy Term
Section 9-8:
Systems of Quadratics
Section 9-9:
Chapter Review and Test
Chapter 10: Higher Degree Functions and Complex NumbersSection 10-1:
Introduction to Higher Degree Functions
Section 10-2:
Complex Number Review
Section 10-3:
Quadratic Equations from their Solutions-Complex Number Factors
Section 10-4:
Graphs of Higher Degree Functions-Synthetic Substitution
Section 10-5:
Descartes' Rule of Signs and the Upper Bound Theorem
Section 10-6:
Higher Degree Functions as Mathematical Models
Section 10-7:
Chapter Review and Test
Chapter 11: Sequences and SeriesSection 11-1:
Introduction to Sequences
Section 11-2:
Arithmetic and Geometric Sequences
Section 11-3:
Arithmetic and Geometric MeansSection 11-4:
Introduction to Series
Section 11-5:
Arithmetic and Geometric Series
Section 11-6:
Convergent Geometric Series
Section 11-7:
Sequences and Series as Mathematical Models
Section 11-8:
Factorials
Section 11-9:
Introduction to Binomial SeriesSection 11-10:
The Binomial FormulaSection 11-11:
Chapter Review and Test
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Exercise 18
Exercise 19
Exercise 20
Exercise 21
Chapter 12: Probability, Data Analysis, and Functions of a Random VariableSection 12-1:
Introduction to ProbabilitySection 12-2:
Words Associated with Probability
Section 12-3:
Two Counting PrinciplesSection 12-4:
Probabilities of Various Permutations
Section 12-5:
Probabilities of Various Combinations
Section 12-6:
Properties of Probability
Section 12-7:
Functions of a Random Variable
Section 12-8:
Mathematical Expectation
Section 12-9:
Statistics and Data AnalysisSection 12-10:
Chapter Review and TestSection 12-11:
Cumulative Review, Chapter 9 through 12
Page 635:
ProblemsPage 635:
Do These Quickly
Exercise 1
Exercise 2
Exercise 3
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Chapter 13: Trigonometric and Circular FunctionsSection 13-1:
Introduction to Periodic Functions
Section 13-2:
Measurement of Arcs and Rotations
Section 13-3:
Definitions of Trigonometric and Circular Functions
Section 13-4:
Approximate Values of Trigonometric and Circular Functions
Section 13-5:
Graphs of Trigonometric and Circular Functions
Section 13-6:
General Sinusoidal Graphs
Section 13-7:
Equations of Sinusoids from their Graphs
Section 13-8:
Sinusoidal Functions as Mathematical Models
Section 13-9:
Inverse Circular Functions
Section 13-10:
Evaluation of Inverse Relations
Section 13-11:
Inverse Circular Relations as Mathematical Models
Section 13-12:
Chapter Review and Test
Chapter 14: Properties of Trigonometric and Circular FunctionsSection 14-1:
Three Properties of Trigonometric Functions
Section 14-2:
Trigonometric Identities
Section 14-3:
Properties Involving Functions of More than One Argument
Section 14-4:
Multiple-Argument Properties
Section 14-5:
Half-Argument Properties
Section 14-6:
Sum and Product Properties
Section 14-7:
Linear Combination of Cosine and Sine with Equal Arguments
Section 14-8:
Simplification of Trigonometric Expressions
Section 14-9:
Trigonometric Equations
Section 14-10:
Chapter Review and Test
Page 805:
Problems
Page 805:
Do These Quickly
Chapter 15: Triangle ProblemsSection 15-1:
Right Triangle Problems
Section 15-2:
Oblique Triangles-Law of Cosines
Section 15-3:
Area of a Triangle
Section 15-4:
Oblique Triangles-Law of Sines
Section 15-5:
The Ambiguous Case
Section 15-6:
General Solution of Triangles
Section 15-7:
Vectors
Section 15-8:
Vectors-Resolution into Components
Section 15-9:
Real-World Triangle Problems
Section 15-10:
Chapter Review and Test
Section 15-11:
Cumulative Review, Chapter 13 through 15
Page 867:
Do These Quickly
Page 868:
Problems
Section Appendix A:
Operations with Matrices
Section Appendix B:
Mathematical Induction
Section Appendix C:
An Exploration of Functions
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 18
Exercise 19
Exercise 20
Exercise 21
Exercise 22
Exercise 23
Exercise 24
Exercise 25
Exercise 26
Exercise 27
Exercise 28
Exercise 29
Exercise 30
Exercise 31
Exercise 32
Exercise 33
Exercise 34
Exercise 35
Exercise 36
Exercise 37
Exercise 38
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