## 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:

1. Demonstrate an understanding of operations with numbers

2. Manipulate algebraic expressions involving real and complex numbers

3. Solve linear and nonlinear equations and inequalities

4. Solve systems of linear equations and inequalities.

5. Solve, translate and model linear equations

6. Solve, translate and model quadratic equations

7. Solve, translate and model exponential equations

8. Solve, translate and model rational equations

9. Solve, translate and model radical equations

10. Solve, translate and model higher-order polynomial equations and inequalities

11. Solve problems presented in context

12. Represent, characterize and solve problems that involve quadratic functions

13. Represent, characterize and solve problems that involve higher-order polynomial

14. Represent, characterize and solve problems that involve simple rational functions

15. Represent, characterize and solve problems involving exponential functions and logarithmic functions.

16. Demonstrate an understanding of combinations and inverses of functions.

## Algebra II

**1- Introduction **

1- Introduction

2- Completing Math Assessments

3- Algebra II On The Web

4- Understanding Plagiarism

5- Pretest

Assignment: Pretest

6- MLA Formatting Word 2007

7- MLA Documentation updates

8- MLA Citation

9- MLA Incorporating Sources

**2- Integer Exponents **

1- Definition of Exponents

2- Zero and One

3- Negative Exponents

4- Grouping

5- Multiplying Like Bases

6- Dividing Like Bases

7- Exponents Raised to a Power

8- Simplifying Expressions

9- Simplifying Expressions, Continued

Handout: Integer Exponents Worksheet

Assignment: Integer Exponents

**3- Scientific Notation **

1- Scientific Notation

2- Scientific Notation, Continued

Quiz: Writing Scientific Notation

3- Multiplying with Scientific Notation

4- Dividing with Scientific Notation

Handout: Operations with Scientific Notation Worksheet

Assignment: Operations with Scientific Notation

**4- Radicals **

1- Definition of Square Root

2- Definition of Nth Root

3- Simplifying Radical Expressions

Handout: Simplifying Radical Expressions Worksheet

Assignment: Simplifying Radical Expressions

4- Adding & Subtracting Radical Expressions

5- Multiplying Radical Expressions

6- Dividing Radical Expressions

Handout: Operations With Radical Expressions Worksheet

Assignment: Operations With Radicals Expressions

**5- Rational Exponents **

1- Rational Exponents

2- Simplifying Rational Exponents

3- Operations with Rational Exponents

Handout: Rational Exponents Worksheet

Assignment: Rational Exponents

**6- Polynomials **

1- Defining Terms

2- Standard Form

3- Types of Polynomials

4- Combining Like Terms

5- Multiplying Polynomials

6- Monomial

7- Binomial Squared

8- Product of Sum and Difference

9- Polynomial

10- Binomial Cubed

Handout: Basic Polynomial Operations Worksheet

Assignment: Basic Polynomial Operations

**7- Factoring Polynomials **

1- Factoring Polynomials

2- Identify the GCF

3- Factoring a Polynomial

4- Example

5- Factoring Trinomials

6- Example 5

7- Example 6

8- Factoring Trinomials of the Form

9- Example 7

10- Example 8

11- Prime Polynomials

12- Factoring a Perfect Square

13- Factoring a Difference of Two Squares

14- Factoring Sum of Two Cubes

15- Factoring Difference of Two Cubes

16- Factoring Strategy

17- Example 16-17

18- Example 18-19

19- Example 20

Handout: Factoring Polynomials Worksheet

Assignment: Factoring Polynomials

**8- Simplifying Rational Expressions**

1- Rational Expressions

2- Principle Rational Expressions

3- Excluded Value

4- Example 3

Handout: Simplifying Rational Expressions Worksheet

Assignment: Simplifying Rational Expressions

**9- Multiplying and Dividing Rational Expressions **

1- Multiply/Divide Rational Expressions

2- Example 1

3- Example 2

4- Dividing Rational Expressions

5- Example 4

Handout: Multiplying & Dividing Rational Expressions Worksheet

Assignment: Multiplying & Dividing Rational Expressions

**10- Adding and Subtracting Rational Expressions **

1- Adding or Subtracting Rational Expressions

2- Example 1

3- Example 2

4- Least Common Denominator

5- Example 3

6- Example 4

Handout: Adding & Subtracting Rational Expressions Worksheet

Assignment: Adding & Subtractracting Rational Expressions

**11- Complex Rational Expressions**

1- Complex Fraction

2- Example 1

3- Example 2

4- Method II

5- Example 4

Handout: Complex Rational Expressions Worksheet

Assignment: Complex Rational Expressions

**12- Complex Numbers**

1- Complex Number

Handout: Complex Adding and Subtracting

Assignment: Complex Adding and Subtracting

2- Multiplying Complex Numbers

3- Example 3

4- Dividing Complex Numbers

5- Example 5

6- Example 6

Handout: Complex Multiply and Divide

Assignment: Complex Multiply and Divide

7- Principle Square Root

8- Example 9

9- Example 10 – 11

**13- Test Chapter 2-12**

1- Test on Chapters 2-12

Handout: Test #1

Assignment: Test #1

**14- Linear Equation in One Variable**

1- Equations

2- Properties of Equality

3- Multiplication and Division

4- Solving a Linear Equation

5- Examples 5-6

6- Identity

7- Conditional Equation

Handout: Solving Linear Equations

Assignment: Solving Linear Equations

**15- Equations with Rational Expressions**

1- Solving Rational Equations

2- Example 1

3- Examples 2-3 Removing the fractions

Handout: Rational Equations

Assignment: Rational Equations

**16- Formulas and Applications **

1- Translating English Phrases to Algebraic Expressions

2- Formulas & Applications Examples 1-2

3- Formulas and Applications Examples 3-4

Worksheet: Translating Verbal & Algebraic Expressions

4- Four Steps to Problem Solving

5- Numeric Word Problems

6- Understanding the problem

7- Consecutive Integers

8- Integers Example 8-9

9- Rectangle Problem

10- Percent Problems

11- Solving Formulas for Specific Variables

Handout: Word Problems

Assignment: Word Problems

Worksheet: Solving Formulas for Variables

**17- Quadratic Equations**

1- Quadrartic Characteristics

2- Quadratic Equation

3- Solving Quadric Equations by Factoring

4- Quadratic example 1-2

5- Quadratic Formula Example 3

6- Square Root Method

7- Square Root Method example 5 & 6

8- Quadratic Equations by Completing the Square

9- Example 7 Quadric Equation

10- Quadratic Equation Example 8

11- Solving by Quadratic Formula

12- Example 10 Solving Quadratic Equations by Quadratic Formula

13- Discriminant

14- Finding the Discriminant

15- Find the Discriminant (cont)

Handout: Solving Quadratics

Assignment: Solving Quadratics

**18- Solving Polynomial Equations by Factoring**

1- Factoring Polynomial Equations

2- Polynomial Equations solved by Factoring Examples

3- 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 **

1- Solving Radical Equations

2- Radical Equation Examples

3- Radical Equations (examples) cont

4- Equations that have Rational an Exponent

5- 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 **

1- Solving Equations in Quadratic Form

2- Quadratic Equation Example

3- Quadratic Equation Examples(cont)

4- Quadratic Equations Example 3

Handout: Equations that are Quadratic in Form

Assignment: Equations that are Quadratic in Form

**21- Absolute Value Equations**

1- Absolute Value

2- Solving an Absolute Value Equation

3- Absolute Value Equations (cont)

4- Absolute Value Equation Example

Handout: Solving Absolute Value Equations

Assignment: Solving Absolute Value Equations

**22- Linear Inequalities **

1- Inequality Signs

2- Interval Notation

3- Open/Closed Interval

4- Combining Open/Closed Intervals

5- Add/Sub Property for Inequalities

6- Multiplication/Division Properties for Inequalities

7- Strategy for Solving a Linear Inequality

8- Strategy for Solving a Linear Inequality(cont)

9- Solving a Compound Inequality

10- Solving an Absolute Value Inequality

11- Solving in Interval Notation

12- Solve in Interval Notation (cont)

Handout: Linear Inequalities

Assignment: Linear Inequalities

**23- Quadratic/Rational Inequalities **

1- Quadratic Inequalities

2- Quadratic inequalities in Standard form(example)

3- Quadratic Inequalities(example 2)

4- Test Point Method

5- Test Point Method Example

6- Test Point method example(cont)

Handout: Quadratic Inequalities

Assignment: Quadratic Inequalities

**24- Mid-Term**

1- Test on Chapters 14-23

Handout: Test #2

Assignment: Test #2

2- Midtest

Assignment: Midtest

**25- Slope of a Line**

1- Slope Formula

2- Slope of a Line

Worksheet: Slope

**26- Equations of Lines **

1- X and Y Intercepts

2- Point/Slope Form of an Equation

3- Slope/Intercept Equation of a Line

4- Slope/Intercept examples

Handout: Equations of Lines

Assignment: Equations of Lines

**27- Graphing Lines **

1- Slope

2- Slope/Intercept Equation of a Line

3- Graphing A Line Using the y-intercept and Slope

4- Slope and Y-intercept examples

5- Slope intercept examples

6- Vertical/Horizontal Lines

Handout: Graphing Lines

Assignment: Graphing Lines

**28- Parallel and Perpendicular Lines**

1- Parallel Lines and Their Slopes

2- Perpendicular Lines/Their Slopes

3- Point/Slope Form of an Equation

Handout: Parallel and Perpendicular

Assignment: Parallel and Perpendicular

**29- Circles**

1- Equation of a Circle

2- Equation of Circles (examples)

3- General Form of an Equation of a Circle

4- General Form of Equation(examples)

5- General Form of Equations Examples(Cont)

Handout: Circles

Assignment: Circles

**30- Introduction to Functions**

1- Functions

2- Functions (examples)

3- Function Notation

4- Constant Function

5- Compound Function

6- Find the Domain

Handout: Intro to Functions

Assignment: Intro to Functions

**31- Operations with Functions**

1- Operations with Functions

2- Composite Function

3- Composite Functions (cont)

Handout: Composition of Functions

Assignment: Composition of Functions

**32- Graphs of Functions, Part I**

1- Transformations & Variation

2- Graphs of Functions

3- Graphs of Functions (examples)

4- Graphing Examples

5- Graphing Examples(cont)

Handout: Graphs of Functions, Part 1

Assignment: Graphs of Functions, Part 1

**33- Graphs of Functions, Part II **

1- Graphing Functions Part 2

2- Graphs of Functions (examples)

3- Vertical Line Test

4- Increasing

5- Decreasing

6- Constant

7- Restricted Intervals

8- Even Function

9- Odd Function

10- Greatest Integer Function

11- Graphing Polynomials

Handout: Graph Behavior

Assignment: Graph Behavior

**34- Test Chapters 25-33**

1- Test on Chapters 25 – 33

Handout: Test #3

Assignment: Test #3

**35- Polynomial Division**

1- Descartes Rule of Signs and Rational Roots

2- Dividing Polynomials

3- 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**

1- Exponential & Log Characteristics

2- Solving Basic Exponential

3- Solving with Logs

Handout: Exponential & Logs

Assignment: Exponential & Logs

**37- Solving Systems of Equations **

1- Solve Systems of Equations: Graphically

Handout: Solve Systems of Equations Graphically

Assignment: Solve Systems of Equations Graphically

2- Solve Systems of Equations: Algebraically

Handout: Solve Systems of Equations Algebraically

Assignment: The Break-Even Point

Assignment: Solve Systems of Equations Algebraically

3- Solve Systems of Inequalities: Graphically

Handout: Solve Systems of Inequalities Graphically

Assignment: Solve Systems of Inequalities Graphically

4- Solve Systems of Equations in Three Variables

Assignment: Solve Systems of Equations in Three Variables

**38- Sequences and Series **

1- Sequences

2- Arithmetic Sequence

3- Arithmetic Series

4- Sigma Notation

5- Geometric Sequence

6- Geometric Series

Handout: Sequence & Series

Assignment: Sequence & Series

**39- Final Exam **

1- Test on Chapters 35-38

Handout: Test #4

Assignment: Test #4

2- Post-test

Assignment: Post-test

**40- Course Evaluation **

Handout: Course Evalulation

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