Algebra 2 Connections Book Cover

Algebra 2 Connections Book Cover

Algebra 2 Connections

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TABLE OF CONTENTS

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Chapter 1: Investigations and Functions
Opening 1.OP Chapter Opening
Section 1.1 1.1.1 Solving Puzzles in Teams
1.1.2 Using a Graphing Calculator to Explore a Function
1.1.3 Domain and Range
1.1.4 Points of Intersection in Multiple Representations
Section 1.2 1.2.1 Modeling a Geometric Relationship
1.2.2 Function Investigation
1.2.3 The Family of Linear Functions
1.2.4 Function Investigation Challenge
Closure 1.CL Chapter Closure

Chapter 2: Sequences and Equivalence
Opening 2.OP Chapter Opening
Section 2.1 2.1.1 Representing Exponential Growth
2.1.2 Rebound Ratio
2.1.3 The Bouncing Ball and Exponential Decay
2.1.4 Generating and Investigating Sequences
2.1.5 Generalizing Arithmetic Sequences
2.1.6 Using Multipliers to Solve Problems
2.1.7 Comparing Sequences and Functions
2.1.8 Sequences that Begin with n = 1
Section 2.2 2.2.1 Equivalent Expressions
2.2.2 Area Models and Equivalent Expressions
2.2.3 Solving by Rewriting
Closure 2.CL Chapter Closure

Chapter 3: Exponential Functions
Opening 3.OP Chapter Opening
Section 3.1 3.1.1 Investigating y = bx
3.1.2 Multiple Representations
3.1.3 More Applications of Exponential Growth
3.1.4 Exponential Decay
3.1.5 Graph to Rule
3.1.6 Completing the Web
Section 3.2 3.2.1 Curve Fitting and Fractional Exponents
3.2.2 More Curve Fitting
3.2.3 Solving a System of Exponential Functions Graphically
Closure 3.CL Chapter Closure

Chapter 4: Transformations of Parent Graphs
Opening 4.OP Chapter Opening
Section 4.1 4.1.1 Modeling Non-Linear Data
4.1.2 Parabola Investigation
4.1.3 Graphing a Parabola Without a Table
4.1.4 Mathematical Modeling with Parabolas
Section 4.2 4.2.1 Transforming Other Parent Graphs
4.2.2 Describing (h, k) for Each Family of Functions
4.2.3 Transforming the Absolute Value Parent Graph
4.2.4 Transforming Non-Functions
Section 4.3 4.3.1 Completing the Square
4.3.2 More Completing the Square
Closure 4.CL Chapter Closure

Chapter 5: Solving and Intersections
Opening 5.OP Chapter Opening
Section 5.1 5.1.1 Strategies for Solving Equations
5.1.2 Solving Equations and Systems Graphically
5.1.3 Finding Multiple Solutions to Systems of Equations
5.1.4 Using Systems of Equations to Solve Problems
Section 5.2 5.2.1 Solving Inequalities with One or Two Variables
5.2.2 Using Systems to Solve a Problem
5.2.3 Applications of Systems of Linear Inequalities
5.2.4 Using Graphs to Find Solutions
Closure 5.CL Chapter Closure

Chapter 6: Inverses and Logarithms
Opening 6.OP Chapter Opening
Section 6.1 6.1.1 Undo Rules
6.1.2 Using a Graph to Find the Inverse
6.1.3 Finding Inverses and Justifying Algebraically
Section 6.2 6.2.1 Finding the Inverse of an Exponential Function
6.2.2 Defining the Inverse of an Exponential Function
6.2.3 Investigating the Family of Logarithmic Functions
6.2.4 Transformations of Log Graphs
6.2.5 Investigating Compositions of Functions
Closure 6.CL Chapter Closure

Chapter 7: 3-D Graphing and Logarithms
Opening 7.OP Chapter Opening
Section 7.1 7.1.1 Creating a Three-Dimensional Model
7.1.2 Graphing Equations in Three Dimensions
7.1.3 Systems of Three-Variable Equations
7.1.4 Solving Systems of Three Equations with Three Unknowns
7.1.5 Using Systems of Three Equations for Curve Fitting
Section 7.2 7.2.1 Using Logarithms to Solve Exponential Equations
7.2.2 Investigating the Properties of Logarithms
7.2.3 Writing Equations of Exponential Functions
7.2.4 An Application of Logarithms
Section 7.3 7.3.1 Introduction to Matrices
7.3.2 Matrix Multiplication
7.3.3 Matrix Multiplication with a Graphing Calculator
7.3.4 Writing Systems as Matrix Equations
7.3.5 Using Matrices to Solve Systems of Equations
Closure 7.CL Chapter Closure

Chapter 8: Trigonometric Functions
Opening 8.OP Chapter Opening
Section 8.1 8.1.1 Introduction to Cyclic Models
8.1.2 Graphing the Sine Function
8.1.3 Unit Circle ↔ Graph
8.1.4 Graphing and Interpreting the Cosine Function
8.1.5 Defining a Radian
8.1.6 Building a Unit Circle
8.1.7 The Tangent Function
Section 8.2 8.2.1 Transformations of y = sin x
8.2.2 One More Parameter for a Cyclic Function
8.2.3 Period of a Cyclic Function
8.2.4 Graph ↔ Equation
Closure 8.CL Chapter Closure

Chapter 9: Polynomial Functions
Opening 9.OP Chapter Opening
Section 9.1 9.1.1 Sketching Graphs of Polynomial Functions
9.1.2 More Graphs of Polynomials
9.1.3 Stretch Coefficients for Polynomial Functions
Section 9.2 9.2.1 Introducing Imaginary Numbers
9.2.2 Complex Roots
9.2.3 More Complex Numbers and Equations
Section 9.3 9.3.1 Polynomial Division
9.3.2 Factors and Integral Roots
9.3.3 An Application of Polynomials
Closure 9.CL Chapter Closure

Chapter 10: Probability and Counting
Opening 10.OP Chapter Opening
Section 10.1 10.1.1 Probability and Expected Value
10.1.2 Conditional Probabilities
Section 10.2 10.2.1 The Fundamental Principle of Counting
10.2.2 Permutations
10.2.3 Combinations
10.2.4 Categorizing Counting Problems
10.2.5 Choosing Counting Methods
10.2.6 Some Challenging Probability Problems
Closure 10.CL Chapter Closure

Chapter 11: Conic Sections
Opening 11.OP Chapter Opening
Section 11.1 11.1.1 A Special Property of Parabolas
11.1.2 Constructing and Analyzing Parabolas
Section 11.2 11.2.1 Sections of a Cone
11.2.2 Multiple Perspective on Parabolas and Circles
11.2.3 Equations of Ellipses
11.2.4 Equation ↔ Graph for Ellipses
11.2.5 A New Conic Section
11.2.6 Equation ↔ Graph for Hyperbolas
Section 11.3 11.3.1 Identifying and Graphing Conic Sections
11.3.2 Graphing Form for Conic Sections
11.3.3 Quadratic Relations
11.3.4 Conic Sections Project
Closure 11.CL Chapter Closure

Chapter 12: Series
Chapter 12.1 12.1.1 Introduction to Arithmetic Series
12.1.2 More Arithmetic Series
12.1.3 General Arithmetic Series
12.1.4 Summation Notation and Combinations of Series
Section 12.2 12.2.1 Mathematical Induction
Section 12.3 12.3.1 Geometric Series
12.3.2 Infinite Series
Section 12.4 12.4.1 Pascal’s Triangle and the Binomial Theorem
12.4.2 Applying the Binomial Theorem
Section 12.5 12.5.1 The Number e
12.5.2 Calculating e and Using Natural Logarithms
Closure 12.CL Chapter Closure

Chapter 13: Analytic Trigonometry
Chapter 13.1 13.1.1 Evaluating Trigonometric Equations
13.1.2 Solutions to Trigonometric Equations
13.1.3 Inverses of Trigonometric Functions
13.1.4 Reciprocal Trigonometric Functions
Section 13.2 13.2.1 Trigonometric Identities
13.2.2 Proving Trigonometric Identities
13.2.3 Angle Sum and Difference Identities
Closure 13.CL Chapter Closure

Checkpoint Materials:
Checkpoint 1: Using the Slope-Intercept Form of a Line to Solve a System of Equations
Checkpoint 2: Solving Systems of Linear Equations in Two Variables
Checkpoint 3: Multiplying Polynomials
Checkpoint 4: Simplifying Expressions with Positive Exponents
Checkpoint 5: Factoring Quadratic Expressions
Checkpoint 6: Writing the Equation of a Line Given Two Points
Checkpoint 7: Finding the x- and y-intercepts of a Quadratic Function
Checkpoint 8: Finding the Slope of a Line through Two Points and the Distance Between the Points
Checkpoint 9: Using Function Notation and Identifying the Domain and Range
Checkpoint 10: Solving for One Variable in an Equation with Two or More Variables
Checkpoint 11: Integral and Rational Exponents
Checkpoint 12: Graphing Linear Inequalities
Checkpoint 13: Solving Rational Equations
Checkpoint 14: Completing the Square and Finding the Vertex for a Parabola
Checkpoint 15: Writing and Solving Exponential Equations
Checkpoint 16: Solving Absolute Value Equations and Inequalities
Checkpoint 17: Finding an Equation for the Inverse of a Function
Checkpoint 18: Solving a System of Equations in Three Variables

Glossary
Index
 
 

RESOURCE PAGES

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Chapter 1: Investigations and Functions
Chapter 2: Sequences and Equivalence
Chapter 3: Exponential Functions
Chapter 4: Transformations of Parent Graphs
Chapter 5: Solving and Intersections
Chapter 6: Inverses and Logarithms
Chapter 7: 3-D Graphing and Logarithms
Chapter 8: Trigonometric Functions
Chapter 9: Polynomial Functions
Chapter 10: Probability and Counting
Chapter 11: Conic Sections
Chapter 12: Series
Chapter 13: Analytic Trigonometry

PARENT GUIDE W/ EXTRA PRACTICE

Welcome to the Algebra 2 Connections Parent Guide with Extra Practice. The purpose of this guide is to assist you should your child need help with homework or the ideas in the course. We believe all students can be successful in mathematics as long as they are willing to work and ask for help when they need it. We encourage you to contact your child’s teacher if your student has additional questions that this guide or other resources do not answer.   Read More...


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General eTools
Chapter 1: Investigations and Functions
Chapter 2: Sequences and Equivalence
Chapter 3: Exponential Functions
Chapter 4: Transformations of Parent Graphs
Chapter 5: Solving and Intersections
Chapter 6: Inverses and Logarithms
Chapter 7: 3-D Graphing and Logarithms
Chapter 8: Trigonometric Functions
Chapter 9: Polynomial Functions
Chapter 10: Probability and Counting
Chapter 11: Conic Sections
Chapter 12: Series
Chapter 13: Analytic Trigonometry

SUPPORT MATERIALS

A2C: Algebra 2 Connections: Quick Reference Guide PDF
A2C: Algebra 2 Connections: Course Overview PDF

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