Textbook Sections

1.1 Introduction to Whole Numbers
1.2 Addition and Subtraction of Whole Numbers
1.3 Multiplication and Division of Whole Numbers
1.4 The Order of Operations Agreement

2.1 LCM and GCF
2.2 Introduction to Fractions
2.3 Addition and Subtraction of Fractions
2.4 Multiplication and Division of Fractions
2.5 Introduction to Decimals
2.6 Operations on Decimals
2.7 The Order of Operations Agreement

3.1 Introduction to Integers
3.2 Addition and Subtraction of Integers
3.3 Multiplication and Division of Integers
3.4 Operations with Rational Numbers
3.5 The Order of Operations Agreement

4.1 Evaluating Variable Expressions
4.2 Simplifying Variable Expressions
4.3 Translating Verbal Expressions into Variable Expressions

5.1 Introduction to Equations
5.2 General Equations: Part I
5.3 General Equations: Part II
5.4 Translating Sentences into Equations

6.1 Ratios and Rates
6.2 Proportion
6.3 Percent
6.4 The Basic Percent Equation

7.1 Introduction to Geometry
7.2 Plane Geometric Figures
7.3 Triangles
7.4 Solids (Objective A only)

5.1 Introduction to Equations
5.2 General Equations: Part I
5.3 General Equations: Part II
5.4 Translating Sentences into Equations
5.5 Mixture and Uniform Motion Problems

7.1 Introduction to Geometry (Review)
7.2 Plane Geometric Figures (Review)
7.3 Triangles (Review)
7.4 Solids (Review - Objective A only)

9.1 Addition and Subtraction of Polynomials
9.2 Multiplication of Monomials
9.3 Multiplication of Polynomials
9.4 Integer Exponents and Scientific Notation
9.5 Division of Polynomials

10.1 Common Factors
10.2 Factoring Polynomials of the form x^2 + bx + c
10.3 Factoring Polynomials of the form ax^2 + bx + c
10.4 Special Factoring
10.5 Solving Equations

11.1 Multiplication and Division of Rational Expressions

12.1 The Rectangular Coordinate System
12.2 Linear Equations in Two Variables
12.3 Intercepts and Slopes of Straight Lines
12.4 Equations of a Straight Line

13.1 Solving System of Linear Equations by Graphing
13.2 Solving System of Linear Equations by the Substitution Method
13.3 Solving System of Linear Equations by the Addition Method
13.4 Application Problems in Two Variables

2.5 Inequalities

3.4 Factoring: Greatest Common Factor and Common Binomial Factor
3.5 Factoring: Difference of Two Square and Sum or Difference of Two Cubes
3.6 Factoring Trinomials
3.7 Equations and Problem Solving

4.1 Simplifying Rational Expressions
4.2 Multiplying and Dividing Rational Expressions
4.3 Adding and Subtracting Rational Expressions
4.4 More on Rational Expressions and Complex Fractions
4.6 Fractional Equations

5.2 Roots and Radicals
5.3 Combining Radicals and Simplifying Radicals That Contain Variables
5.4 Products and Quotients Involving Radicals
5.5 Equations Involving Radicals
5.6 Merging Exponents and Roots

6.1 Complex Numbers
6.2 Quadratic Equations
6.3 Completing the Square
6.4 Quadratic Formula
6.5 More Quadratic Equations and Applications

7.1 Rectangular Coordinate System and Linear Equations (review)
7.2 Linear Inequalities in Two Variables
7.3 Distance and Slope (review)
7.4 Determining the Equation of a Line

8.1 Concept of a Function
8.2 Linear Functions and Applications
8.3 Quadratic Functions

2.3 Equations Involving Decimals and Problem Solving
2.5 Inequalities
2.6 More on Inequalities and Problem Solving
2.7 Equations and Inequalities Involving Absolute Value

4.6 Fractional Equations (review)
4.7 More Fractional Equations and Applications

5.5 Equations Involving Radicals

6.2 Quadratic Equations
6.3 Completing the Square
6.4 Quadratic Formula
6.5 More Quadratic Equations and Applications
6.6 Quadratic and Other Nonlinear Inequalities

7.1 Rectangular Coordinate System and Linear Equations
7.2 Linear Inequalities in Two Variables
7.4 Determining the Equation of a Line

8.1 Concept of a Function
8.2 Linear Functions and Applications
8.3 Quadratic Functions
8.4 More Quadratic Functions and Applications
8.5 Transformations of Some Basic Curves
8.6 Combining Functions

9.4 Graphing Polynomial Functions
9.5 Graphing Rational Functions

10.1 Exponents and Exponential Functions
10.2 Applications of Exponential Functions
10.3 Inverse Functions
10.4 Logarithms
10.5 Logarithmic Functions
10.6 Exponential Equations, Logarithmic Equations, and Problem Solving

11.1 Systems of Two Linear Equations in Two Variables
11.2 Systems of Three Linear Equations in Three Variables
11.3 Matrix Approach to solving Linear Systems

13.5 Systems Involving Nonlinear Equations

6.1 Angles and Their Measure
6.2 Trigonometric Functions: Unit Circle Approach
6.3 Properties of the Trigonometric Functions
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Phase Shift; Sinusoidal Curve Fitting (optional)

7.1 The Inverse Sine, Cosine, and Tangent Functions
7.2 The Inverse Trigonometric Functions (continued)
7.3 Trigonometric Equations
7.4 Trigonometric Identities
7.5 Sum and Difference Formulas
7.6 Double-angle and Half-angle Formulas
7.7 Product-to-Sum and Sum-to-Product Formulas

8.1 Right Triangle Trigonometry; Applications
8.2The Law of Sines
8.3 The Law of Cosines
8.4 Area of a Triangle

9.1 Polar Coordinates (optional)
9.3 The Complex Plane; De Moivre’s Theorem
9.4 Vectors
9.5 The Dot Product (optional)
9.6 Vectors in Space (optional)

3.1 Simple Interest
3.2 Compound and Continuous Compound Interest
3.3 Future Value of an Annuity; Sinking Funds
3.4 Present Value of an Annuity; Amortization

4.1 Review: Systems in Two Variables (optional)
4.2 Systems Augmented Matrices
4.3 Gauss Jordan Elimination
4.4 Matrices: Basic Operations

5.1 Inequalities in Two Variables
5.2 Systems of Linear Inequalities in Two Variables
5.3 Linear Programming in Two Dimensions

6.1 A Geometric Introduction to the Simplex Method
6.2 The Simplex Method
6.3 The Dual Problem

7.2 Sets
7.3 Basic Counting Principles
7.4 Permutations and Combinations

8.1 Samples Spaces, Events, and Probability
8.2 Union, Intersection, and Complement of Events
8.3 Conditional Probability, Intersection, Independence
8.4 Bayes’ Formula
8.5 Random Variable, Distribution, and Expected Value

11.1 Graphing Data
11.2 Measures of Central Tendency
11.3 Measures of Dispersion

2.1 Functions
2.2 Graphs and Transformations (optional)
2.3 Quadratic Equations (optional)
2.4 Polynomial and Rational Functions
2.5 Exponential Functions
2.6 Logarithmic Functions

3.1 Introduction to Limits
3.2 Infinite Limits and Limits at Infinity (optional)
3.3 Continuity
3.4 The Derivative
3.5 Basic Differentiation Properties
3.6 Differentials (optional)
3.7 Marginal Analysis in Business and Economics

4.1 The Constant e and Continuous Interest
4.2 Derivatives of Exp and Logarithmic Functions
4.3 Derivatives of Products and Quotients
4.4 The Chain Rule
4.5 Implicit Differentiation (optional)
4.6 Related Rates (optional)
4.7 Elasticity of Demand (optional)

5.1 First Derivative and Graphs
5.2 Second Derivative and Graphs
5.3 L’Hôpital’s Rule (optional)
5.4 Curve Sketching Techniques
5.5 Absolute Maxima and Minima
5.6 Optimization

6.1 Anti-derivatives and Indefinite Integrals
6.2 Integration by Substitution
6.3 Diff. Equations: Growth and Decay (optional)
6.4 The Definite Integral
6.5 The Fundamental Theorem of Calculus

7.1 Area between Curves
7.2 Applications in Business and Economics (optional)
7.3 Integration by Parts (optional)

8.1 Functions of Several Variables
8.2 Partial Derivatives

2.1 Symbols and Terminology
2.2 Venn Diagrams and Subsets
2.3 Set Operations and Cartesian Products
2.4 Surveys and Cardinal Numbers

3.1 Statements and Quantifiers
3.2 Truth Tables and Equivalent Statements
3.3 The Conditional and Circuits
3.4 The Conditional and Related Statements
3.5 Analyzing Arguments with Euler Diagrams
3.6 Analyzing Arguments with Truth Tables

9.1 Points, Lines, Planes, Angles
9.2 Curves, Polygons, and Circles
9.3 The Geometry of Triangles: Congruence, Similarity and Pythagorean Theorem
9.4 Perimeter, Area, Circumference
9.5 Volume and Surface Area

10.1 Counting by Systematic Listing
10.2 Using the Fundamental Counting Principle
10.3 Using Permutations and Combinations
10.5 Counting Problems Involving “Not” and “Or”

11.1 Basic Concepts of Probability
11.2 Events Involving “Not” and “Or”
11.3 Conditional Probability: Events Involving “And”

12.1 Visual Displays of Data
12.2 Measures of Central Tendency
12.3 Measures of Dispersion

Chapter 1 is mainly for reading and terminology.
1.1 Descriptive and Inferential Statistics
1.2 Variables and Type of Data
1.3 Data Collection
1.4 Observational and Experimental Studies
1.5 Uses and Misuses
1.6 Computers and Calculators

2.1 Organizing Data
2.2 Histograms, Frequency Polygons and Ogives
2.3 Other Types of Graphs
2.4 Paired Data and Scatter Plots

3.1 Measures of Central Tenancy
3.2 Measures of Variation
3.3 Measures of Position
3.4 Exploratory Data Analysis

4.1 Sample Spaces and Probability
4.2 The Addition Rules
4.3 The Multiplication Rules
4.4 Counting Rules
4.5 Probability and Counting Rules

5.1 Probability Distributions
5.2 Mean, Variance, Standard Deviation and Expectation
5.3 The Binomial Distribution

6.1 Normal Distributions
6.2 Applications of the Normal Distribution
6.3 The Central Limit Theorem

7.1 Confidence Intervals for the Mean Standard Deviation Known
7.2 Confidence Intervals for the Mean, Standard Deviation Unknown
7.3 Confidence Intervals for Proportions
7.4 Confidence Intervals for Variances and Standard Deviation

8.1 Hypothesis Testing Traditional
8.2 z Test for a Mean
8.3 t Test for a Mean
8.4 z Test for a Proportion
8.5 Chi-Squared Test for a Variance and Standard Deviation

10.1 Correlation
10.2 Regression

11.1 Test for Goodness of Fit
11.2 Tests Using Contingency Tables
11.3 Analysis of Variance (ANOVA)

1.1 An Introduction to Problem Solving
1.2 Pólya's Problem-Solving Principles
1.3 More Problem-Solving Strategies
1.4 Algebra as Problem-Solving Strategy
1.5 Additional Problem-Solving Strategies
1.6 Reasoning Mathematically

2.1 Sets and Operations on Sets
2.2 Sets, Counting, and the Whole Numbers
2.3 Addition and Subtraction of Whole Numbers
2.4 Multiplication and Division of Whole Numbers

3.1 Numeration Systems Past and Present
3.2 Non-decimal Positional Systems
3.3 Algorithms for Adding and Subtracting
3.4 Algorithms for Multiplication and Division
3.5 Mental Arithmetic and Estimation

4.1 Divisibility of Natural Numbers
4.2 Tests for Divisibility
4.3 Greatest Common Divisors Least Common Multiples

5.1 Representations of Integers
5.2 Addition and Subtraction of Integers
5.3 Multiplication and Division of Integers

6.1 Basic Concepts of Fractions and Rational Numbers
6.2 Addition and Subtraction of Fractions
6.3 Multiplication and Division of Fractions
6.4 The Rational Number System

7.1 Decimals and Real Numbers
7.2 Computations with Decimals
7.3 Proportional Reasoning
7.4 Percent

8.1 Algebraic Expressions, Functions, and Equations
8.2 Graphing Points, Lines, and Elementary Functions

9.1 Graphical Representation of Data
9.2 Measures of Central Tendency and Variability
9.3 Statistical Inference and Sampling

10.1 Empirical Probability
10.2 Principles of Counting
10.3 Permutations and Combinations
10.4 Theoretical Probability

11.1 Figures in the Plane
11.2 Curves and Polygons in the Plane
11.3 Figures in Space
11.4 Networks

12.1 The Measurement Process
12.2 Area and Perimeter
12.3 The Pythagorean Theorem
12.4 Surface Area and Volume

13.1 Rigid Motions and Similarity Transformations
13.2 Patterns and Symmetries
13.3 Tilings and Escher-like Design

14.1 Congruent Triangles
14.2 Constructing Geometric Figures
14.3 Similar Triangles

2.1 Functions
2.2 The Graph of a Function
2.3 Properties of Functions
2.4 Library of Functions; Piecewise-defined Functions

3.3 Quadratic Functions and Their Properties
3.4 Build Quadratic models from Verbal Descriptions and from Data

5.3 Exponential Functions
5.4 Logarithmic Functions
5.5 Properties of Logarithms
5.6 Logarithmic and Exponential Equations

6.1 Angles and Their Measure
6.2 Trigonometric Functions: Unit Circle Approach
6.3 Properties of the Trigonometric Functions
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Phase Shift; Sinusoidal Curve Fitting

7.1 The Inverse Sine, Cosine, and Tangent Functions
7.2 The Inverse Trigonometric Functions (continued)
7.3 Trigonometric Equations
7.4 Trigonometric Identities
7.5 Sum and Difference Formulas
7.6 Double-angle and Half-angle Formulas
7.7 Product-to-Sum and Sum-to-Product Formulas

8.1 Applications Involving Right Triangles
8.2 Law of Sines
8.3 Law of Cosines
8.4 Area of a Triangle

9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.4 Vectors
9.5 The Dot Product
9.6 Vectors in Space
9.7 The Cross Product

10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola

11.2 Systems of Linear Equations: Matrices
11.3 Systems of Linear Equations: Determinants
11.5 Partial Fraction Decomposition

12.1 Sequences
12.2 Arithmetic Sequences
12.3 Geometric Sequences; Geometric Series
12.4 Mathematical Induction
12.5 The Binomial Theorem

2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of the Limit
2.5 Continuity
2.6 Limits at Infinity
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function

3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Derivatives
3.6 Derivatives of Logarithmic Functions
3.7 Rates of Change in the Natural and Social Sciences

3.8 Exponential Growth and Decay (optional)
3.9 Related Rates
3.10 Linear Approximations (optional)
3.11 Hyperbolic Functions

4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of the Graph
4.5 Summary of Curve Sketching
4.7 Optimization Problems
4.9 Anti-derivatives

5.1 Areas and distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals

4.4 Indeterminate Forms

6.1 Areas Between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.4 Work

7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.7 Approximate Integration
7.8 Improper Integrals

10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Areas and Lengths in Polar Coordinates

11.1 Sequences
11.2 Series
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series
11.6 Absolute Convergence and the Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
11.9 Representations of functions as Power Series
11.10 Taylor and Maclaurin Series
11.11 Applications of Taylor Polynomials

10.1 Review, Curves Defined by Parametric Equations
10.2 Review, Calculus with Parametric Equations
10.3 Review, Polar Coordinates
10.4 Areas and Lengths in Polar coordinates

12.1 Three Dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Equations of Lines and Planes
12.6 Cylinders and Quadric Surfaces

13.1 Vector Functions and Space Curves
13.2 Derivatives and Integrals of Vector Functions
13.3 Arc Length and Curvature
13.4 Motion in Space: Velocity and Acceleration

14.1 Functions of Several Variables
14.2 Limits and Continuity
14.3 Partial Derivatives
14.4 Tangent Plane and Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient Vector
14.7 Maximum and Minimum Values
14.8 Lagrange Multipliers

15.1 Double Integrals over Rectangles
15.2 Iterated Integrals
15.3 Double Integrals over General Regions
15.4 Double Integrals over Polar Coordinates
15.5 Application of Double Integrals
15.6 Surface Area
15.7 Triple Integrals
15.8 Triple Integrals in Cylindrical Coordinates
15.9 Triple Integrals in Spherical Coordinates
15.10 Change of Variables in Multiple Integrals

16.1 Vector Fields
16.2 Line Integrals
16.3 The Fundamental Theorem of Line Integrals
16.4 Green's Theorem
16.5 Curl and Divergence
16.6 Parametric Surfaces and Their Areas
16.7 Surface Integrals
16.8 Stokes’ Theorem
16.9 The Divergence Theorem
16.10 Summary