# High School Common Core Algebra 2

• High School course based on the Common Core State Standards
• Third course in a traditional sequence of Algebra 1, Geometry and Algebra 2
• Full year Course
• This course is aligned to the Common Core State Standards and successful mastery of items within this course should prepare students for state tests covering CCSS Algebra 2

### Subject:

Author(s):
Andrew Bayliss - Sparta High School, Sparta, NJ
Joseph Morse - Winnetonka High School, North Kansas City, MO
Version:
1.0
Description:

The purpose of this course is to satisfy the Algebra II requirement of the Common Core Mathematics Standards. This upper level course fits into an overall program of mathematics studies with a rigorous academic core by extending what students have learned in the introductory-­level mathematics courses as well as introducing more advanced topics. These advanced topics include linear equations, inequalities, and systems, quadratic, polynomial, exponential, logarithmic, and Trigonometric functions, equations, and expressions.

The Problem Sets are divided into Units

• Unit 1 - Real numbers & Polynomial Expressions/Equations: Sets 01-05
• Unit 2 - Rational Expressions & Equations: Sets 06-08
• Unit 3 - Irrational Numbers & Radical Expressions/Equations: Sets 09-11
• Unit 4 - Relations and Functions: Sets 12-16
• Unit 5 - Quadratic Functions: Sets 17-20
• Unit 6 - Sequences & Series: Sets 21-22
• Unit 7 - Exponential Functions: Sets 23-25
• Unit 8 - Logarithmic Functions: Sets 26-28
• Unit 9, 10, & 11 - Trigonometry: Sets 29-32
• Unit 12 - Statistics: Sets 33-34
• Unit 13 - Probability: Sets 35
Problem Set:
Set name:
set01 Real Numbers and Review
Objectives:

The students will be able to

• Complete problems that involve identifying the types of numbers given.
• Determine the relationship between real numbers and expressions representing real numbers.
• Combine like terms.
• Operate on real numbers and simple variable expressions.
• Problems involving properties of real numbers like identifying multiplicative and additive inverses and identities.
• This set is review and does not address any of the Algebra 2 CCSS standards.
Set name:
set02 Linear Equations
Objectives:

Students will be able to:

• Solve linear equations and inequalities.
• Determine the relationship between expressions.
• Do word problems requiring the translation of words into equations.
• Do number problems, consecutive integer problems.
• Do area problems.
• Do age problems.
• Do rate of work problems.
• Be able to solve some literal equations.
• This set is review and does not address any of the Algebra 2 CCSS standards.
Set name:
set03 Operations on Polynomials
Objectives:

Students will be able to :

• Identify leading coefficient, degree and constant term in polynomials and monomials.
• Evaluate a polynomial at a given value
• Add, subtract, multiply and factor polynomials.
• Factor a polynomial of 4th degree that has a quadratic form.
• This set addresses CCSS A.APR.1
Set name:
Objectives:

Students will be able to:

• Solve quadratic equations by the square root method.
• Solve quadratic equations by factoring.
• Solve quadratic equations by completing the square.
• Solve quadratic equations by using a method of their choosing.
• Solve word problems involving quadratic equations.
• This set addresses CCSS A.CED.1 and A.REI.4.
Set name:
Objectives:

Students will be able to:

• This set addresses CCSS A.CED.1.

note: It is suggested that students have completed the set Solve_Quadratic Equations prior to working this set.

Set name:
set06 Simplify Rational Expressions
Objectives:

Students will be able to:

• Manipulate rational expressions.
• Cancel common factors.
• Multiply and divide rational numbers.
• Multiply and divide rational expressions.
• Evaluate a rational function for particular values using functional notation and find the domain of the function.
• This set addresses CCSS A.APR.8
Set name:
set07 Adding and Subtracting Rational Expressions
Objectives:

Students will be able to:

• Add or subtract rational expressions.
• Manipulate complex fractions.
• This set addresses CCSS A.APR.8
Set name:
set08 Solving Proportions and Applications
Objectives:
• Solving Proportions
• Applications using proportions
• Solving More Advanced Rational Equations
Set name:
set09 Irrational Numbers and Radical Expressions
Objectives:
• This set of homework problems involves irrational numbers and radical expressions.
• Manipulating radical expressions and operations on radical expressions is the main focus of the problems.
• Problem 12 uses the alternate form of the definition of the absolute value.
• This set addresses CCSS N.RN.3.
Set name:
set10 Multiplying and Dividing Radical Expressions
Objectives:

Students will be able to:

• Solve problems involving the operations of multiplication and division on radical expressions.
• Rationalize denominators.
• This set addresses CCSS N.RN.3.
Set name:
Objectives:
• This set of problems requires students to solve radical equations that involve quadratic methods and extraneous solutions.
• A few equations may have more than one radical.
• None of the equations require the quadratic formula to solve it.
• The set addresses CCSS A.REI.2.
Set name:
set12 Intro to Relations and Functions
Objectives:

Students will be able to:

• Determine if a graph represents a function.
• Use functional notation with equations.
• Use functional notation with graphs.
• Use functional notation with piecewise defined functions.
• This set addresses the CCSS F.IF.1 and F.IF.2.
Set name:
set13 Finding Domain and Range
Objectives:

Students will be able to:

• Find the domain and range of functions represented in graphs.
• Find the domain and range of functions represented in equations.
• Answer all domains and ranges using inequalities. The domain uses the variable "x", and the range uses the variable "y" within their respective inequalities.
• Solve problems that are applications that include the concept of domain, range, independent and dependent variables, interpreting functional notation and values within the application.
• This set addresses the CCSS F.IF.1 and F.IF.2.
Set name:
set14 Linear Relations and Functions
Objectives:

Students will be able to:

• Find the slope of a linear function.
• Find the y-intercept of a linear function.
• Transform linear functions.
• Graph linear functions.
• Write linear equations given various conditions.
• Find the slopes of parallel lines.
• Find the slopes of perpendicular lines.
• This set addresses CCSS F.IF.1.
Set name:
set15 Combining Functions
Objectives:

Students will be able to:

• Find a new function based upon some combination of two functions represented as tables.
• Find a new function based upon some combination of two functions represented as graphs.
• Find a new function based upon some combination of two functions represented as equations.
• Find the domain of the resulting relation.
• This set addresses CCSS F.IF.2.

Note: This set includes questions concerning composition, as well as algebraic combinations of relations.

Set name:
set16 Inverse Functions and Relations
Objectives:

Students will be able to:

• Find the inverse of a function algebraically.
• Find the inverse of a function by inverting a table.
• Find the inverse of a function by reflecting a graph over the line y=x.
• Understand the relationship between the a function and its inverse.
• Understand the difference between inverse and reciprocal.
• This set addresses CCSS F.BF.4.
Set name:
set17 Real Roots, Quadratic Form, Discriminant
Objectives:

Students will be able to:

• Understand the role of the discriminant.
Set name:
set18 Complex Numbers and Operations w/ Complex Numbers
Objectives:

Students will be able to:

• Use Complex Numbers
• Perform operations with Complex numbers
Set name:
set19 Complex Roots of Quadratic Functions
Objectives:

Students will be able to:

• Find the Complex Roots to a Quadratic Equation
• Find the Sum and Product of Roots of a Quadratic Equation
• Solve for Roots of Higher degree polynomials
Set name:
set20 Systems of Equations & Inequalities