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High School Algebra II course Outline

1.0 Credit

This course begins with a review of Algebra I topics and introduces the following new topics: matrices, complex numbers, exponential and logarithmic functions, conic sections, higher degree polynomial functions, sequences and series, and trigonometry. This course is required for students who are planning to attend most post-secondary institutions.

Algebra II is a continuation of the algebraic processes begun in Algebra I. This course includes solving equations, inequalities, matrices, graphing, functions, powers, roots, logarithms, complex numbers, polynomials, quadratic relations, sequences, series, probability and statistics. Appropriate technology is integrated into the curriculum.

Students will work with both scientific and graphing calculators throughout this Algebra 2 course. It is strongly recommended that you have at least a scientific calculator to use when completing your work. If you don’t have access to a scientific and/or graphing calculator, many are available for free online.

The Algebra II course will cover a range of algebraic topics. The over-arching topics include Operations on Numbers and Expressions, Equations and Inequalities, Polynomial and Rational Functions, Exponential Functions and Function Operations and Inverses.

By the end of the course you should be able to:

• onstrate an understanding of operations with numbers
• Manipulate algebraic expressions involving real and complex numbers
• Solve linear and nonlinear equations and inequalities
• Solve systems of linear equations and inequalities.
• Solve, translate and model linear equations
• Solve, translate and model quadratic equations
• Solve, translate and model exponential equations
• Solve, translate and model rational equations
• Solve, translate and model radical equations
• Solve, translate and model higher-order polynomial equations and inequalities
• Solve problems presented in context
• Represent, characterize and solve problems that involve quadratic functions
• Represent, characterize and solve problems that involve higher-order polynomial
• Represent, characterize and solve problems that involve simple rational functions
• Represent, characterize and solve problems involving exponential functions and logarithmic functions.
• Demonstrate an understanding of combinations and inverses of functions.

Algebra II

1- Introduction

• Introduction
• Completing Math Assessments
• Algebra II On The Web
• Understanding Plagiarism
• Pretest
• Assignment: Pretest
• MLA Formatting Word 2007
• MLA Documentation updates
• MLA Citation
• MLA Incorporating Sources

2- Integer Exponents

• Definition of Exponents
• Zero and One
• Negative Exponents
• Grouping
• Multiplying Like Bases
• Dividing Like Bases
• Exponents Raised to a Power
• Simplifying Expressions
• Simplifying Expressions, Continued
• Handout: Integer Exponents Worksheet
• Assignment: Integer Exponents

3- Scientific Notation

• Scientific Notation
• Scientific Notation, Continued
• Quiz: Writing Scientific Notation
• Multiplying with Scientific Notation
• Dividing with Scientific Notation
• Handout: Operations with Scientific Notation Worksheet
• Assignment: Operations with Scientific Notation

• Definition of Square Root
• Definition of Nth Root
• Simplifying Radical Expressions
• Handout: Simplifying Radical Expressions Worksheet
• Assignment: Simplifying Radical Expressions
• Multiplying Radical Expressions
• Dividing Radical Expressions
• Handout: Operations With Radical Expressions Worksheet
• Assignment: Operations With Radicals Expressions

5- Rational Exponents

• Rational Exponents
• Simplifying Rational Exponents
• Operations with Rational Exponents
• Handout: Rational Exponents Worksheet
• Assignment: Rational Exponents

6- Polynomials

• Defining Terms
• Standard Form
• Types of Polynomials
• Combining Like Terms
• Multiplying Polynomials
• Monomial
• Binomial Squared
• Product of Sum and Difference
• Polynomial
• Binomial Cubed
• Handout: Basic Polynomial Operations Worksheet
• Assignment: Basic Polynomial Operations

7- Factoring Polynomials

• Factoring Polynomials
• Identify the GCF
• Factoring a Polynomial
• Example
• Factoring Trinomials
• Example 5
• Example 6
• Factoring Trinomials of the Form
• Example 7
• Example 8
• Prime Polynomials
• Factoring a Perfect Square
• Factoring a Difference of Two Squares
• Factoring Sum of Two Cubes
• Factoring Difference of Two Cubes
• Factoring Strategy
• Example 16-17
• Example 18-19
• Example 20
• Handout: Factoring Polynomials Worksheet
• Assignment: Factoring Polynomials

8- Simplifying Rational Expressions

• Rational Expressions
• Principle Rational Expressions
• Excluded Value
• Example 3
• Handout: Simplifying Rational Expressions Worksheet
• Assignment: Simplifying Rational Expressions

9- Multiplying and Dividing Rational Expressions

• Multiply/Divide Rational Expressions
• Example 1
• Example 2
• Dividing Rational Expressions
• Example 4
• Handout: Multiplying & Dividing Rational Expressions Worksheet
• Assignment: Multiplying & Dividing Rational Expressions

10- Adding and Subtracting Rational Expressions

• Adding or Subtracting Rational Expressions
• Example 1
• Example 2
• Least Common Denominator
• Example 3
• Example 4
• Handout: Adding & Subtracting Rational Expressions Worksheet
• Assignment: Adding & Subtractracting Rational Expressions

11- Complex Rational Expressions

• Complex Fraction
• Example 1
• Example 2
• Method II
• Example 4
• Handout: Complex Rational Expressions Worksheet
• Assignment: Complex Rational Expressions

12- Complex Numbers

• Complex Number
• Handout: Complex Adding and Subtracting
• Assignment: Complex Adding and Subtracting
• Multiplying Complex Numbers
• Example 3
• Dividing Complex Numbers
• Example 5
• Example 6
• Handout: Complex Multiply and Divide
• Assignment: Complex Multiply and Divide
• Principle Square Root
• Example 9
• Example 10 – 11

13- Test Chapter 2-12

• Test on Chapters 2-12
• Handout: Test #1
• Assignment: Test #1

14- Linear Equation in One Variable

• Equations
• Properties of Equality
• Multiplication and Division
• Solving a Linear Equation
• Examples 5-6
• Identity
• Conditional Equation
• Handout: Solving Linear Equations
• Assignment: Solving Linear Equations

15- Equations with Rational Expressions

• Solving Rational Equations
• Example 1
• Examples 2-3 Removing the fractions
• Handout: Rational Equations
• Assignment: Rational Equations

16- Formulas and Applications

• Translating English Phrases to Algebraic Expressions
• Formulas & Applications Examples 1-2
• Formulas and Applications Examples 3-4
• Worksheet: Translating Verbal & Algebraic Expressions
• Four Steps to Problem Solving
• Numeric Word Problems
• Understanding the problem
• Consecutive Integers
• Integers Example 8-9
• Rectangle Problem
• Percent Problems
• Solving Formulas for Specific Variables
• Handout: Word Problems
• Assignment: Word Problems
• Worksheet: Solving Formulas for Variables

• Solving Quadric Equations by Factoring
• Quadratic example 1-2
• Quadratic Formula Example 3
• Square Root Method
• Square Root Method example 5 & 6
• Quadratic Equations by Completing the Square
• Example 7 Quadric Equation
• Quadratic Equation Example 8
• Solving by Quadratic Formula
• Example 10 Solving Quadratic Equations by Quadratic Formula
• Discriminant
• Finding the Discriminant
• Find the Discriminant (cont)
• Handout: Solving Quadratics
• Assignment: Solving Quadratics

18- Solving Polynomial Equations by Factoring

• Factoring Polynomial Equations
• Polynomial Equations solved by Factoring Examples
• Polynomial Equations solved by Factoring Examples(cont)
• Handout: Solve Polynomial Equations by Factoring
• Assignment: Solve Polynomial Equations by Factoring

19- Radical Equations Involving Rational Exponents

• Solving Radical Equations
• Radical Equation Examples
• Radical Equations (examples) cont
• Equations that have Rational an Exponent
• Equations with Rational Exponents (cont)
• Handout: Radical Equations
• Handout: Equations with Rational Exponents
• Assignment: Radical Equations
• Assignment: Equations with Rational Exponents

20- Equations that are Quadratic in Form

• Solving Equations in Quadratic Form
• Quadratic Equation Example
• Quadratic Equation Examples(cont)
• Quadratic Equations Example 3
• Handout: Equations that are Quadratic in Form
• Assignment: Equations that are Quadratic in Form

21- Absolute Value Equations

• Absolute Value
• Solving an Absolute Value Equation
• Absolute Value Equations (cont)
• Absolute Value Equation Example
• Handout: Solving Absolute Value Equations
• Assignment: Solving Absolute Value Equations

22- Linear Inequalities

• Inequality Signs
• Interval Notation
• Open/Closed Interval
• Combining Open/Closed Intervals
• Add/Sub Property for Inequalities
• Multiplication/Division Properties for Inequalities
• Strategy for Solving a Linear Inequality
• Strategy for Solving a Linear Inequality(cont)
• Solving a Compound Inequality
• Solving an Absolute Value Inequality
• Solving in Interval Notation
• Solve in Interval Notation (cont)
• Handout: Linear Inequalities
• Assignment: Linear Inequalities

• Quadratic inequalities in Standard form(example)
• Quadratic Inequalities(example 2)
• Test Point Method
• Test Point Method Example
• Test Point method example(cont)
• Handout: Quadratic Inequalities
• Assignment: Quadratic Inequalities

24- Mid-Term

• Test on Chapters 14-23
• Handout: Test #2
• Assignment: Test #2
• Midtest
• Assignment: Midtest

25- Slope of a Line

• Slope Formula
• Slope of a Line
• Worksheet: Slope

26- Equations of Lines

• X and Y Intercepts
• Point/Slope Form of an Equation
• Slope/Intercept Equation of a Line
• Slope/Intercept examples
• Handout: Equations of Lines
• Assignment: Equations of Lines

27- Graphing Lines

• Slope
• Slope/Intercept Equation of a Line
• Graphing A Line Using the y-intercept and Slope
• Slope and Y-intercept examples
• Slope intercept examples
• Vertical/Horizontal Lines
• Handout: Graphing Lines
• Assignment: Graphing Lines

28- Parallel and Perpendicular Lines

• Parallel Lines and Their Slopes
• Perpendicular Lines/Their Slopes
• Point/Slope Form of an Equation
• Handout: Parallel and Perpendicular
• Assignment: Parallel and Perpendicular

29- Circles

• Equation of a Circle
• Equation of Circles (examples)
• General Form of an Equation of a Circle
• General Form of Equation(examples)
• General Form of Equations Examples(Cont)
• Handout: Circles
• Assignment: Circles

30- Introduction to Functions

• Functions
• Functions (examples)
• Function Notation
• Constant Function
• Compound Function
• Find the Domain
• Handout: Intro to Functions
• Assignment: Intro to Functions

31- Operations with Functions

• Operations with Functions
• Composite Function
• Composite Functions (cont)
• Handout: Composition of Functions
• Assignment: Composition of Functions

32- Graphs of Functions, Part I

• Transformations & Variation
• Graphs of Functions
• Graphs of Functions (examples)
• Graphing Examples
• Graphing Examples(cont)
• Handout: Graphs of Functions, Part 1
• Assignment: Graphs of Functions, Part 1

33- Graphs of Functions, Part II

• Graphing Functions Part 2
• Graphs of Functions (examples)
• Vertical Line Test
• Increasing
• Decreasing
• Constant
• Restricted Intervals
• Even Function
• Odd Function
• Greatest Integer Function
• Graphing Polynomials
• Handout: Graph Behavior
• Assignment: Graph Behavior

34- Test Chapters 25-33

• Test on Chapters 25 – 33
• Handout: Test #3
• Assignment: Test #3

35- Polynomial Division

• Descartes Rule of Signs and Rational Roots
• Dividing Polynomials
• Remainder Theorem
• Handout: Long and Synthetic Division
• Handout: Division and Roots
• Assignment: Long and Synthetic Division
• Assignment: Division and Roots

36- Exponential and Logarithmic Function

• Exponential & Log Characteristics
• Solving Basic Exponential
• Solving with Logs
• Handout: Exponential & Logs
• Assignment: Exponential & Logs

37- Solving Systems of Equations

• Solve Systems of Equations: Graphically
• Handout: Solve Systems of Equations Graphically
• Assignment: Solve Systems of Equations Graphically
• Solve Systems of Equations: Algebraically
• Handout: Solve Systems of Equations Algebraically
• Assignment: The Break-Even Point
• Assignment: Solve Systems of Equations Algebraically
• Solve Systems of Inequalities: Graphically
• Handout: Solve Systems of Inequalities Graphically
• Assignment: Solve Systems of Inequalities Graphically
• Solve Systems of Equations in Three Variables
• Assignment: Solve Systems of Equations in Three Variables

38- Sequences and Series

• Sequences
• Arithmetic Sequence
• Arithmetic Series
• Sigma Notation
• Geometric Sequence
• Geometric Series
• Handout: Sequence & Series
• Assignment: Sequence & Series

39- Final Exam

• Test on Chapters 35-38
• Handout: Test #4
• Assignment: Test #4
• Post-test
• Assignment: Post-test

40- Course Evaluation

• Handout: Course Evalulation
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