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### Estimated Completion Time

2 segments / 32-36 weeks

### Overview

This course allows students to learn while having fun. Interactive examples help guide students’ journey through customized feedback and praise. Mathematical concepts are applied to everyday occurrences such as earthquakes, stadium seating, and purchasing movie tickets. Students investigate the effects of an equation on its graph through the use of technology. Students have opportunities to work with their peers on specific lessons.

Algebra 2 is an advanced course using hands-on activities, applications, group interactions, and the latest technology.

Note: content varies depending on course version. For currently enrolled students, please refer to the syllabus located in the course information area for curriculum specifics.

### Major Topics and Concepts

#### Segment IModule 1: Radical and Polynomial Operations

• 01.00 Introduction to Radical and Polynomial Operations
• 01.01 Rational Exponents
• 01.02 Properties of Rational Exponents
• 01.04 Radical and Polynomial Operations Mid-Module Check
• 01.05 Radical and Polynomial Operations Discussion-Based Assessment
• 01.06 Complex Numbers
• 01.07 Operations on Complex Numbers
• 01.08 Polynomial Operations
• 01.09 Radical and Polynomial Operations Review and Practice Test
• 01.10 Radical and Polynomial Operations Test

#### Module 2: Factoring and Quadratics

• 02.00 Introduction to Factoring and Quadratics
• 02.01 Greatest Common Factors and Special Products
• 02.02 Factoring by Grouping
• 02.03 Sum and Difference of Cubes
• 02.05 Completing the Square
• 02.07 Solving Quadratic Equations with Complex Solutions
• 02.09 Factoring and Quadratics Review and Practice Test
• 02.10 Factoring and Quadratics Discussion-Based Assessment
• 02.11 Factoring and Quadratics Test

#### Module 3: Solving Polynomials

• 03.00 Introduction to Solving Polynomials
• 03.01 Polynomial Long Division
• 03.02 Theorems of Algebra
• 03.03 Polynomial Transformations
• 03.04 Solving and Graphing Polynomials
• 03.05 Polynomial Identities and Proofs
• 03.06 Solving Polynomials Review and Practice Test
• 03.07 Solving Polynomials Discussion-Based Assessment
• 03.08 Solving Polynomials Test

#### Module 4: Rational Equations

• 04.00 Introduction to Rational Equations
• 04.01 Simplifying Rational Expressions
• 04.02 Discontinuities of Rational Expressions
• 04.03 Asymptotes of Rational Functions
• 04.04 Solving Rational Equations
• 04.05 Rational Equations Quiz
• 04.08 Segment One Exam Review
• 04.09 Rational Equations Discussion-Based Assessment
• 04.10 Segment One Exam

#### Segment IIModule 5: Exponential and Logarithmic Functions

• 05.00 Introduction to Exponential and Logarithmic Functions
• 05.01 Exponential Functions
• 05.02 Logarithmic Functions
• 05.03 Exponential and Logarithmic Functions Mid-Module Check
• 05.04 Exponential and Logarithmic Functions Discussion-Based Assessment
• 05.05 Graphing Exponential Functions
• 05.06 Graphing Logarithmic Functions
• 05.07 Exponential and Logarithmic Functions Review and Practice Test
• 05.08 Exponential and Logarithmic Functions Test

#### Module 6: Systems of Equations

• 06.00 Introduction to Systems of Equations
• 06.01 Solving Systems of Equations Algebraically
• 06.02 Solving Systems of Equations Graphically
• 06.03 Solving Systems of Nonlinear Equations
• 06.04 Graphing Systems of Nonlinear Equations
• 06.05 Systems of Equations Review and Practice Test
• 06.06 Systems of Equations Discussion-Based Assessment
• 06.07 Systems of Equations Test

#### Module 7: Sequences and Series

• 07.00 Introduction to Sequences and Series
• 07.01 Arithmetic Sequences and Series
• 07.02 Geometric Sequences
• 07.03 Geometric Series
• 07.04 Sigma Notation
• 07.05 Graphing Sequences and Series
• 07.06 Sequences and Series Review and Practice Test
• 07.07 Sequences and Series Discussion-Based Assessment
• 07.08 Sequences and Series Test

#### Module 8: Statistics

• 08.00 Introduction to Statistics
• 08.01 Events and Outcomes in a Sample Space
• 08.02 Independent Probability
• 08.03 Conditional Probability
• 08.04 Normal Distribution
• 08.05 Models of Populations
• 08.06 Using Surveys
• 08.07 Using Experiments
• 08.08 Statistics Review and Practice Test
• 08.09 Statistics Discussion-Based Assessment
• 08.10 Statistics Test

#### Module 9: Trigonometry

• 09.00 Introduction to Trigonometry
• 09.01 Introduction to the Unit Circle
• 09.02 Unit Circle and the Coordinate Plane
• 09.03 Trigonometric Functions with Periodic Phenomena
• 09.04 Pythagoras, Trigonometry, and Quadrants
• 09.05 Functions of All Types
• 09.06 Trigonometry Quiz
• 09.07 Segment Two Collaboration Component
• 09.08 Segment Two Exam Review
• 09.09 Trigonometry Discussion-Based Assessment
• 09.10 Segment Two Exam

## Career

Pyrotechnician

Open

3-4 Weeks

### Competency

Systems of Equations – Students will demonstrate an understanding of systems of equations by solving systems of linear and nonlinear equations through graphing, elimination, and substitution.

### Project

You are a Pyrotechnician. You were hired to design a small fireworks show at a stadium. You will be using 4 shells of fireworks to demonstrate the beginning of the show to the client. The client also wants to make sure that the fireworks explode above the stadium, so spectators on the outside can also enjoy the show.

## Career

Pharmacy Technician

Open

3-4 Weeks

### Competency

Radical Expressions – Students will demonstrate an understanding of radical expressions by simplifying radicals, adding, subtracting, multiplying and dividing radicals, simplifying expressions with rational exponents, simplifying complex numbers, and solving equations involving exponents and radicals

### Project

You are a pharmacy technician in a hospital. You will measure the dosage for Solu-Medrol for two children to take home as well as create the labels for the medication.

## Career

Roller Coaster Engineer

Open

3-4 Weeks

### Competency

Polynomial Functions – Students will demonstrate an understanding of polynomial functions by classifying, performing operations, identifying roots, graphing and interpreting graphs, and solving problems involving polynomials.

### Project

You are a Roller Coaster Engineer and are responsible for designing a new roller coaster for younger children in a small amusement park. In this project, you will learn about the behavior of polynomial functions so that you can graph a function for a roller coaster that is safe for the client’s customers.

## Career

Open

3-4 Weeks

### Competency

Quadratic Functions – Students will demonstrate an understanding of quadratic functions by writing and graphing quadratic functions, solving quadratic equations using zero product property, completing the square and quadratic formula, and using the discriminant to determine the number of solutions for a quadratic equation.

### Project

You are a road safety engineer and as a city employee have been asked to determine if the placement of reduced traffic speed limit signs allow enough time for vehicles traveling at the listed speed limit to react and then break before coming to traffic lights and stop signs.

## Career

Anthropologist

Open

3-4 Weeks

### Competency

Exponential and Logarithmic Functions – Students will demonstrate an understanding of exponential and logarithmic functions by simplifying exponential and logarithmic expressions, solving equations, and solving real-life problems.

### Project

You are an Anthropologist whose specialty is determining the age of artifacts using a radiocarbon dating process. You have been asked to use radiocarbon dating to verify the authenticity of various artifacts discovered during a recent dig at an archeological site. In this project, you will research and identify an archeological site to use in your project, pick realistic artifacts that might be found at that site, and then determine through radiocarbon exponential and logarithmic formulas if the artifacts are genuine to that site.

## Career

Landscaping Supervisor

Open

3-4 Weeks

### Competency

Rational Expressions – Students demonstrate an understanding of rational expressions by simplifying rational expressions using addition, subtraction, multiplication, and division, and solving equations involving rational expressions.

### Project

You are a Landscaping Supervisor. You feel there are not enough employees to take care of the clients’ yards and gardens in a timely manner and would like to hire an additional employee to help during the spring and summer seasons. The owner of the company you work for is not convinced an extra employee would have enough of an effect to offset the additional salary. Your task is to show, through the use of rational equations, how hiring this employee would be to the company’s advantage.

## Career

Financial Planner

Open

3-4 Weeks

### Competency

Sequences and Series – Students will demonstrate their understanding of sequences and series by using formulas to evaluate specific terms in a sequence, determine a partial sum of a sequence, determine sum of infinite series, and apply the use of sequences and series to solve non-routine problems.

### Project

You are a Financial Planner responsible for helping your clients make decisions about financial planning for their future and their retirement. The customers you are advising are undecided as to whether to continue depositing monthly savings into their checking account, which earns no interest but can be accessed anytime without penalty, or to deposit their money into an annuity which will earn interest but cannot be as easily accessed. Your task will be to present a comparison of future savings to help your customers make an informed decision about their future.

## Career

Market Research Analyst

Open

3-4 Weeks

### Competency

Event Probability – Student will demonstrate an understanding of calculating probability of events by analyzing survey data through descriptive and inferential statistics.

### Project

You are a Market Research Analyst. You have been hired by a company that is interested in collecting data about their customers before they decide which new product line to introduce into their stores. Your job will be to collect customer data, conduct an analysis of the data, and then report the results to the company.

## Career

Psychologist

Open

3-4 Weeks

### Competency

Unit Circle and Radians – Student will demonstrate an understanding of the Unit Circle and radian measures by graphing and analyzing trigonometric functions.

### Project

You are a psychologist You have a new patient who believes that biorhythm affects her performance physically, intellectually, and emotionally. This is a new field of psychology for you. To assist your patience better, you will construct your own biorhythm for your next session with her so that you can discuss hers.

### Competencies

Students will demonstrate an understanding of quadratic functions by factoring, graphing, and solving quadratic equations.
• Polynomials
Students will demonstrate an understanding of polynomial functions by performing operations on polynomials, graphing polynomials, and proving polynomial identities.
• Rational Expressions
Students demonstrate an understanding of rational expressions by simplifying rational expressions and solving rational equations.
• Exponential and Logarithmic Functions
Students will demonstrate an understanding of exponential and logarithmic functions by simplifying exponential and logarithmic expressions and graphing and solving exponential and logarithmic equations.
• Sequences and Series
Students will demonstrate an understanding of sequences and series by evaluating arithmetic and geometric sequences and series, using sigma notation to evaluate a series, and graphing sequences and series.
• Statistics
Students will demonstrate an understanding of statistics by explaining events and outcomes, calculating probability, and analyzing surveys and experiments.
• Systems of Equations
Students will demonstrate an understanding of systems of equations by solving linear and nonlinear systems of equations algebraically and graphically.
• Trigonometry
Students will demonstrate an understanding of trigonometry by solving problems using the Unit Circle, graphing trigonometric functions, solving problems involving trigonometric functions, and analyzing Pythagorean Identities.

Algebra 1

## Attend a virtual open house

We offer regular online open house webinars where VLACS staff members provide parents and students with an overview of our programs and answer questions about online learning.