R. Review
R.1 Expressions, Equations, and Functions: Writing and Evaluating Algebraic Expressions (p5)
R.1 Expressions, Equations, and Functions: Solving Equations (p9)
R.4 Solving Systems of Linear Equations and Inequalities: Graphing Linear Systems of Inequalities
Evaluate an Expression
Write an Expression
Mathematical Properties
Solving Linear Equations
Application: Airline Tickets
Application: Bicycle Race
Application: Boat and Current
Solving for a Variable
The Slope of a Line
The Slope-Intercept Form of a Line
Graphing Equations in Slope-Intercept Form
Finding the Equation with Slope and One Point Known
Finding an Equation from Two Points
Relations and Functions
Evaluating a Function
Graphs of Functions
Determining the Domain and Range from a Graph
Number of Solutions to Systems of Linear Equations
Solving a System of Equations Graphically
Solving by Elimination
Solving by Substitution
Application: Birds in a Breeze
Application: Coins in Your Pocket
Graphing Systems of Linear Inequalities
Interactive Problems: Systems of Inequalities
Multiplying Monomials
Multiplying Polynomials
The Parabola with the Vertex at the Origin
Vertex Form for a Parabola
1. Themes in Algebra II
1.1 Functions: Translating Functions (p52)
1.3 Working with Models: Linear Programming—Activity 1 (p68)
1.3 Working with Models: Linear Programming—Activity 2 (p68)
1.3 Working with Models: Linear Programming—Activity 3 (p68)
Shifting Function Graphs Vertically
Shifting Function Graphs Horizontally
Interactive Problems: Shifting Functions
Odd and Even Functions
2. Quadratics
2.7 Modeling with Quadratic Functions: Spreadsheet and Graphing Calculator (p114)
2.8 Parabolas at the Origin: The Directrix and Focus (p120)
2.8 Parabolas at the Origin: Shifting the Focus (p120)
2.8 Parabolas at the Origin: Enter the Focus and Directrix (p121)
Factoring Quadratic Trinomials
Special Product Patterns
Factoring the Difference of Squares
More Difficult Factoring Problems
Factoring by Grouping
Factoring a Trinomial with ax², a ≠ 1
Factoring the Sum or Difference of Cubes
More Difficult Factoring Problems
The Square Root Principle
The Zero-Product Property
Solving a Quadratic Equation Using the Square Root Principle
Using Quadratic Structure to Solve an Equation
Complete the Square
Complete the Square: a > 1
The Quadratic Formula
Adding and Subtracting Complex Numbers
Multiplying Complex Numbers
Complex Conjugates
Factoring and Complex Numbers
Finding the Discriminant
Graphing a Parabola Using Its Solutions
Geometric Definition of a Parabola
Graphing a Parabola at the Origin
Sample Problem: Determining the Equation of a Parabola
3. Polynomials
3.5 Finding Zeros Polynomial Functions: Graphing Polynomial Functions (p157)
Finding the Degree of Multivariable Polynomials
Evaluating Multivariable Polynomials
Long Division and Synthetic Division
3.3 Remainder and Factor Theorems The Remainder Theorem
The Factor Theorem
Sample Problems: The Factor Theorem
Solving Cubic Equations by Factoring Out a Common Factor
Solving Another Cubic Equation
Solving a Quartic Equation
Solving a Fifth-Degree Equation
Graphing Polynomial Functions
Interactive Problems: Graphing Polynomials
Finding Roots Using the Graph of a Polynomial
Using the Fundamental Theorem of Algebra
4. Rational Expressions
4.3 Rational Equations: Elvauating Rational Expressions and Equations—Two Beavers (p197)
4.3 Rational Equations: Evaluating Rational Expressions and Equations—One Beaver (p197)
Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Simplifying Complex Rational Expressions
Application: Focal Length
Adding and Subtracting Rational Expressions with a Common Denominator
Adding and Subtracting Rational Expressions with Different Denominators
Rational Expressions
Application: Rate Problems
Extraneous Solutions
Graph of Reciprocal Function
Translating the Reciprocal Function
Graphs of More Reciprocal Functions
Writing an Equation from a Graph
Application: Modeling Velocity
5. Powers and Radicals
5.5 Radical Function Graphs: Graphing a Square Root Function (p251)
Roots
Simplifying Radical Expressions
Product Rule
Multiplying and Simplifying Radicals
Quotient Rule for Radicals
Multiplying Radicals with Negative Radicands
Adding and Subtracting Like Radicals
Multiplying Binomial Radical Expressions
Rationalizing the Denominator
Summary: Simplifying Radical Expressions
Exponent Notation for Roots
Rules of Exponents and Fractional Exponents
Multiplying and Dividing Radicals with Different Indices but Same Radicand
Squaring Principle
Extraneous Solutions
Sample Problems: Radical Equations
Power Principle to Solve Equations
Graphing a Square Root Function
Graphing a Cube Root Function
Interactive Problems: Shifting Graphs
6. Exponential Functions
6.4 Inverse and Composite Functions: Inverse Functions—Activity 1 (p281)
6.4 Inverse and Composite Functions: Inverse Functions—Activity 2 (p281)
Evaluating Exponential Functions
Exponential Function Graphs and Writing an Exponential Expression as a Single Power
The Shapes of Exponential Function Graphs
Exponential Functions and the Percent Rate of Change
Proving That Percent Change Is Constant with an Exponential Function
Application: Interest Compounded Annually
Application: Interest Compounded Monthly
Finding an Equivalent Percent Rate
Restating an Exponential Decay Function in Terms of t
Application: Radioactive Decay
Combining Functions
Evaluating a Combined Function
Finding an Inverse Function
The Graph of a Function and Its Inverse
Deciding If a Function Has an Inverse Function
Composite Functions
7. Logarithmic Functions
7.1 Logarithms: Create Equivalent Exponential Equations (p296)
7.1 Logarithms: Restate Exponential Equations (p296)
7.1 Logarithms: Mixed Logarithmic Functions and Exponential Equations (p296)
Logarithmic Functions
Interactive Problems: Converting Between Exponential and Logarithmic Equations
Sample Problems: Evaluating Logarithms
Common Logarithms
Solving Logarithmic Equations
Mental Math: Logarithms
Graphing Exponential and Logarithmic Functions
7.3 Natural Logarithms and e Natural Logarithms
Sample Problems: Using the Natural Logarithm
e and Continuously Compounded Interest
Logarithmic Identities
Logarithmic Equations
Product Rule for Logarithms
Quotient Rule for Logarithms
Power Rule for Logarithms
Change-of-Base Formula
Solving Exponential Equations Using Logarithms
Application: Compound Interest
Application: Exponential Growth of Bacteria
Breaking Up Logarithmic Expressions
Combining Logarithms
Deriving the Product and Quotient Rules for Logarithms
8. Sequences and Series
8.1 Arithmetic Sequences: Shapes and Pattern—Activity 1 (p339)
8.1 Arithmetic Sequences: Shapes and Patterns—Activity 2 (p339)
8.1 Arithmetic Sequences: Shapes and Patterns—Activity 3 (p339)
8.1 Arithmetic Sequences: The Geometric Frog—Activity 1 (p339)
8.1 Arithmetic Sequences: The Geometric Frog—Activity 2 (p339)
8.3 Geometric Sequences: The Geometric Frog—Activity 3 (p339)
8.3 Geometric Sequences: The Geometric Frog—Activity 4 (p355)
8.3 Geometric Sequences: The Geometric Frog—Activity 5 (p356)
8.3 Geometric Sequences: Shapes and Patterns—Activity 4 (p357)
8.3 Geometric Sequences: Shapes and Patterns—Activity 5 (p357)
What Is a Sequence?
Arithmetic Sequences
Explicit Formula for the General Term, a^{n}
Sample Problems: Arithmetic Sequence
Application: Planning an Event
Graph of an Arithmetic Sequence
Arithmetic Series
Sigma Notation
Partial Sum of an Infinite Arithmetic Series
Application: Counting Logs
Geometric Sequences
Explicit Formula for the General Term of a Geometric Sequence
Sample Problems: Geometric Sequences
Sample Problems: What Type of Sequence?
Application: Enlarging a Photograph
Geometric Series and Partial Sums
Sample Problems: Determining a Partial Sum
Application: The Bouncing Ball
Infinite Geometric Series
Sample Problem: Infinite Geometric Series
Binomial Expansion
Sample Problems: Binomial Expansion
Factorial Notation
Binomial Coefficients
Sample Problems: Binomial Coefficients
9. Trigonometry
9.2 Trigonometric Functions: Right Triangles (p395)
9.3 Angles of Rotation and Trigonometric Functions: Converting Degrees and Radians (p415)
9.3 Angle Action: Finding Radian Measures (p415)
9.3 Angle Action: Finding More Challenging Radian Measures (p415)
9.3 Angle Action: Finding Radian Measures Greater Than One Rotation (p415)
9.4 Trigonometric Functions and the Unit Circle: The Unit Circle (p417)
9.5 Trigonometric Function Graphs: Matching Graphs (p428)
9.5 Trigonometric Function Graphs: Experimenting with Two Changes to a Function (p428)
9.5 Trigonometric Function Graphs: Experimenting with Translations (p431)
9.5 Trigonometric Function Graphs: Matching Graphs with Translations (p432)
Pythagorean Theorem
Types of Triangles
Applying Special Right Triangles
Application: Baseball Diamond
Sine, Cosine, and Tangent Ratios
Using a Calculator in Trigonometry
Working with Sine, Cosine, and Tangent
Sine, Cosine, and Tangent for Special Right Triangles
10. Probability
10.1 Introduction to Probablity: Three Coins Tossed (p465)
10.1 Introduction to Probablity: Four Coins Tossed (p465)
10.1 Introduction to Probablity: Six Coins Tossed (p465)
10.1 Introduction to Probablity: Sixteen Coins Tossed (p465)
10.1 Introduction to Probability: Millionaire Game Round 1 (p468)
10.2 Independent Events and the Multiplication Rule: Millionaire Game Round 2 (p472)
10.5 Normal Distribution: Six Coins Tossed (p499)
Graphing a Sample Space
Application: Modeling Populations Using Simulations