Algebra 2B - Greenways Academy
Syllabus
Algebra 2B Course Overview Algebra is a branch of mathematics that uses symbols in place of numbers to describe and generalize relationships. In Algebra 2B, you will begin with a study of trigonometry, how the sides and angles of a triangle are related. You will examine trigonometric functions and graphs in the context of the unit circle. You will also extend your understanding of lines by classifying systems of linear equations. In prior courses, you solved inequalities by graphing. Here, you will solve systems of inequalities including quadratic and absolute value inequalities that contain restrictions on the variable. You will finish Algebra 2B by applying statistics and probability to make complex decisions. You’ll reach decisions based on representative sampling from a population and the creation and evaluation of statistical models.
Course Goals By the end of this course, you will be able to do the following:
Examine and graph trigonometric functions using the unit circle as the basis. Apply the basic trigonometric identities. Classify a system of linear equations as parallel, intersecting, or coincident. Graph the solution set to inequalities in one variable. Graph the solution set to quadratic and absolute value inequalities. Perform operations on functions and investigate transformations of functions. Use the binomial formula to figure probability. Make inferences about a population based on a random sample. Evaluate the validity of a statistical model. Solve for probabilities in complex situations and use the solution to make fair decisions. Evaluate reports based on data.
Math Skills Two semesters of Algebra 1 and course Algebra 2A are prerequisites for Algebra 2B. Before beginning this course, you should be able to do the following:
Evaluate, simplify, and perform operations on rational expressions. Identify non-permissible values for variables in a rational expression. Analyze and graph polynomial functions. Plot complex numbers in the complex number plane. Solve quadratic equations in the complex number system.
1 © 2013 EDMENTUM, INC.
Solve equations involving radicals and the power function.
General Skills To participate in this course, you should be able to do the following:
Complete basic operations with word processing software, such as Microsoft Word or Google Docs. Understand the basics of spreadsheet software, such as Microsoft Excel or Google Spreadsheets, but having prior computing experience is not necessary. Perform online research using various search engines and library databases. Communicate through email and participate in discussion boards.
For a complete list of general skills that are required for participation in online courses, refer to the Prerequisites section of the Plato Student Orientation document, found at the beginning of this course.
Credit Value Algebra 2B is a 0.5-credit course.
Course Materials
Notebook Pencils Graphing calculator, recommend TI-83 or equivalent Computer with Internet connection and speakers or headphones Microsoft Word or equivalent Microsoft Excel or equivalent
Course Pacing Guide This course description and pacing guide is intended to help you keep on schedule with your work. Note that your course instructor may modify the schedule to meet the specific needs of your class.
Unit 1: Trigonometric Functions Summary This unit focuses on trigonometric functions and graphs. You will use trigonometric identities to solve problems involving angles and their measures. Day
Activity/Objective
Type
1 day:
Syllabus and Plato Student Orientation Review the Plato Student Orientation and Course Syllabus at
Course Orientation
1
2
the beginning of this course. 3 days: 2–4 4 days: 5–8 1 day: 9
Angles and Their Measures
Lesson
Examine angles and their measures. Trigonometric Functions and the Unit Circle Examine trigonometric functions using a unit circle. The Binomial Formula and Probability
Lesson
Examine the binomial formula and its use in probability.
3 days:
Trigonometric Functions
10–12
Examine trigonometric functions.
4 days:
Trigonometric Graphs
13–16
Examine trigonometric graphs.
4 days:
Basic Trigonometric Identities
17–20
Examine and apply the basic trigonometric identities.
4 days:
Unit Activity and Discussion—Unit 1
Lesson
Lesson
Lesson
21–24 1 day:
Lesson
Unit Activity Discussion
Posttest—Unit 1
Assessment
25
Unit 2: Modeling with Functions Summary In this unit, you will learn how a graph is a powerful tool used to solve a variety of equations and inequalities. You’ll use graphs to solve systems of linear equations and systems of inequalities in one variable. Some inequalities will have restrictions on the variable such as the absolute value inequality. You’ll close the unit by performing operations on functions and solving practical problems involving exponential and logarithmic functions.
Day 1 day: 26 1 day: 27
Activity/Objective Solving Linear Systems of Equations: Graphs
Type Lesson
Use the graphing method to solve systems of two linear equations. Classifying Linear Systems
Lesson
Classify a system of linear equations as parallel, intersecting, or coincident.
2 days:
Solving Linear Systems of Inequalities: Graphs
28–29
Solve a system of inequalities by graphing. 3
Lesson
2 days:
Solving Linear Systems of Equations: Substitution
30–31
Solve a system of equations by graphing.
1 day:
Graphing Linear Inequalities in 1 Variable
32 1 day: 33
Graphing with Restrictions on the Variable
Lesson
Graph the solution sets to absolute value inequalities in one variable. Graphing Solution Sets of Associated Inequalities
34–35
Graph the solution sets of quadratic inequalities in one variable and other unions of solution sets.
2 days:
Operations on Functions
36–37
Add, subtract, multiply, and divide pairs of functions.
1 day:
Solving Problems: Exponential and Logarithmic
Lesson
Lesson
Lesson
Solve problems that involve exponential or logarithmic functions.
4 days:
Transformation of Functions
39–42
Investigate transformations of functions.
4 days:
Unit Activity and Discussion—Unit 2
Lesson
43–46 1 day:
Lesson
Graph the solution sets to inequalities in one variable.
2 days:
38
Lesson
Unit Activity Discussion
Posttest—Unit 2
Assessment
47
Unit 3: Inferences and Conclusions from Data Summary In this unit, you’ll use statistics and probability to make decisions. You’ll understand the purposes of sample surveys, experiments, and observational studies. You’ll make judgments based on a representative sample of a population and decide if a statistical model is consistent with results from a given data-generating process. You will make complex decisions based on probability that goes beyond basic counting rules. Day
Activity/Objective
4 days:
Normal Distributions
48–51
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.
4 days:
Making Inferences Based on Statistics
52–55
Understand statistics as a process for making inferences about population parameters based on a random sample
Type Lesson
4
Lesson
from that population. 4 days:
Evaluating the Validity of a Statistical Model
56–59
Decide if a specified model (such as a simulation) is consistent with results from a given data-generating process.
4 days:
Using Statistics in Surveys, Experiments, and Studies
60–63
Recognize the purposes of and differences among sample surveys, experiments, and observational studies.
4 days:
Analyzing a Survey
64–67
Use data from a sample survey to estimate a population mean or proportion and develop a margin of error through the use of simulation models for random sampling.
4 days:
Fair Decisions with Random Variables
68–71
Solve for probabilities in complex situations that go beyond counting rules and use these probabilities to make fair decisions.
4 days:
Evaluating Reports Based on Data
72–75
Evaluate reports based on data.
4 days:
Statistically Comparing Two Treatments
76–79
Use data from a randomized experiment to compare two treatments and use simulations to decide if differences between parameters are significant.
4 days:
Complex Decisions Using Probability
80–83
Analyze decisions and strategies in complex situations, using probability concepts that go beyond counting rules.
4 days:
Unit Activity and Discussion—Unit 3
Lesson
Lesson
Lesson
Lesson
84–87 1 day:
Lesson
Lesson
Lesson
Unit Activity Discussion
Posttest—Unit 3
Assessment
88 1 day:
Semester Review
89 1 day:
End-of-Semester Exam
Assessment
90
5
Algebra 2B Course Overview Algebra is a branch of mathematics that uses symbols in place of numbers to describe and generalize relationships. In Algebra 2B, you will begin with a study of trigonometry, how the sides and angles of a triangle are related. You will examine trigonometric functions and graphs in the context of the unit circle. You will also extend your understanding of lines by classifying systems of linear equations. In prior courses, you solved inequalities by graphing. Here, you will solve systems of inequalities including quadratic and absolute value inequalities that contain restrictions on the variable. You will finish Algebra 2B by applying statistics and probability to make complex decisions. You’ll reach decisions based on representative sampling from a population and the creation and evaluation of statistical models.
Course Goals By the end of this course, you will be able to do the following:
Examine and graph trigonometric functions using the unit circle as the basis. Apply the basic trigonometric identities. Classify a system of linear equations as parallel, intersecting, or coincident. Graph the solution set to inequalities in one variable. Graph the solution set to quadratic and absolute value inequalities. Perform operations on functions and investigate transformations of functions. Use the binomial formula to figure probability. Make inferences about a population based on a random sample. Evaluate the validity of a statistical model. Solve for probabilities in complex situations and use the solution to make fair decisions. Evaluate reports based on data.
Math Skills Two semesters of Algebra 1 and course Algebra 2A are prerequisites for Algebra 2B. Before beginning this course, you should be able to do the following:
Evaluate, simplify, and perform operations on rational expressions. Identify non-permissible values for variables in a rational expression. Analyze and graph polynomial functions. Plot complex numbers in the complex number plane. Solve quadratic equations in the complex number system.
1 © 2013 EDMENTUM, INC.
Solve equations involving radicals and the power function.
General Skills To participate in this course, you should be able to do the following:
Complete basic operations with word processing software, such as Microsoft Word or Google Docs. Understand the basics of spreadsheet software, such as Microsoft Excel or Google Spreadsheets, but having prior computing experience is not necessary. Perform online research using various search engines and library databases. Communicate through email and participate in discussion boards.
For a complete list of general skills that are required for participation in online courses, refer to the Prerequisites section of the Plato Student Orientation document, found at the beginning of this course.
Credit Value Algebra 2B is a 0.5-credit course.
Course Materials
Notebook Pencils Graphing calculator, recommend TI-83 or equivalent Computer with Internet connection and speakers or headphones Microsoft Word or equivalent Microsoft Excel or equivalent
Course Pacing Guide This course description and pacing guide is intended to help you keep on schedule with your work. Note that your course instructor may modify the schedule to meet the specific needs of your class.
Unit 1: Trigonometric Functions Summary This unit focuses on trigonometric functions and graphs. You will use trigonometric identities to solve problems involving angles and their measures. Day
Activity/Objective
Type
1 day:
Syllabus and Plato Student Orientation Review the Plato Student Orientation and Course Syllabus at
Course Orientation
1
2
the beginning of this course. 3 days: 2–4 4 days: 5–8 1 day: 9
Angles and Their Measures
Lesson
Examine angles and their measures. Trigonometric Functions and the Unit Circle Examine trigonometric functions using a unit circle. The Binomial Formula and Probability
Lesson
Examine the binomial formula and its use in probability.
3 days:
Trigonometric Functions
10–12
Examine trigonometric functions.
4 days:
Trigonometric Graphs
13–16
Examine trigonometric graphs.
4 days:
Basic Trigonometric Identities
17–20
Examine and apply the basic trigonometric identities.
4 days:
Unit Activity and Discussion—Unit 1
Lesson
Lesson
Lesson
21–24 1 day:
Lesson
Unit Activity Discussion
Posttest—Unit 1
Assessment
25
Unit 2: Modeling with Functions Summary In this unit, you will learn how a graph is a powerful tool used to solve a variety of equations and inequalities. You’ll use graphs to solve systems of linear equations and systems of inequalities in one variable. Some inequalities will have restrictions on the variable such as the absolute value inequality. You’ll close the unit by performing operations on functions and solving practical problems involving exponential and logarithmic functions.
Day 1 day: 26 1 day: 27
Activity/Objective Solving Linear Systems of Equations: Graphs
Type Lesson
Use the graphing method to solve systems of two linear equations. Classifying Linear Systems
Lesson
Classify a system of linear equations as parallel, intersecting, or coincident.
2 days:
Solving Linear Systems of Inequalities: Graphs
28–29
Solve a system of inequalities by graphing. 3
Lesson
2 days:
Solving Linear Systems of Equations: Substitution
30–31
Solve a system of equations by graphing.
1 day:
Graphing Linear Inequalities in 1 Variable
32 1 day: 33
Graphing with Restrictions on the Variable
Lesson
Graph the solution sets to absolute value inequalities in one variable. Graphing Solution Sets of Associated Inequalities
34–35
Graph the solution sets of quadratic inequalities in one variable and other unions of solution sets.
2 days:
Operations on Functions
36–37
Add, subtract, multiply, and divide pairs of functions.
1 day:
Solving Problems: Exponential and Logarithmic
Lesson
Lesson
Lesson
Solve problems that involve exponential or logarithmic functions.
4 days:
Transformation of Functions
39–42
Investigate transformations of functions.
4 days:
Unit Activity and Discussion—Unit 2
Lesson
43–46 1 day:
Lesson
Graph the solution sets to inequalities in one variable.
2 days:
38
Lesson
Unit Activity Discussion
Posttest—Unit 2
Assessment
47
Unit 3: Inferences and Conclusions from Data Summary In this unit, you’ll use statistics and probability to make decisions. You’ll understand the purposes of sample surveys, experiments, and observational studies. You’ll make judgments based on a representative sample of a population and decide if a statistical model is consistent with results from a given data-generating process. You will make complex decisions based on probability that goes beyond basic counting rules. Day
Activity/Objective
4 days:
Normal Distributions
48–51
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.
4 days:
Making Inferences Based on Statistics
52–55
Understand statistics as a process for making inferences about population parameters based on a random sample
Type Lesson
4
Lesson
from that population. 4 days:
Evaluating the Validity of a Statistical Model
56–59
Decide if a specified model (such as a simulation) is consistent with results from a given data-generating process.
4 days:
Using Statistics in Surveys, Experiments, and Studies
60–63
Recognize the purposes of and differences among sample surveys, experiments, and observational studies.
4 days:
Analyzing a Survey
64–67
Use data from a sample survey to estimate a population mean or proportion and develop a margin of error through the use of simulation models for random sampling.
4 days:
Fair Decisions with Random Variables
68–71
Solve for probabilities in complex situations that go beyond counting rules and use these probabilities to make fair decisions.
4 days:
Evaluating Reports Based on Data
72–75
Evaluate reports based on data.
4 days:
Statistically Comparing Two Treatments
76–79
Use data from a randomized experiment to compare two treatments and use simulations to decide if differences between parameters are significant.
4 days:
Complex Decisions Using Probability
80–83
Analyze decisions and strategies in complex situations, using probability concepts that go beyond counting rules.
4 days:
Unit Activity and Discussion—Unit 3
Lesson
Lesson
Lesson
Lesson
84–87 1 day:
Lesson
Lesson
Lesson
Unit Activity Discussion
Posttest—Unit 3
Assessment
88 1 day:
Semester Review
89 1 day:
End-of-Semester Exam
Assessment
90
5
