Algebra II

Course Description

This is a college preparatory course that will build upon the basic foundations of Algebra I. The course deepens students' understanding of algebraic concepts while emphasizing problem-solving, critical thinking, and mathematical reasoning. Topics covered include polynomial operations, rational expressions, complex numbers, quadratic functions, systems of equations and inequalities, exponential and logarithmic functions, sequences and series, and matrices.

Students will explore both real and complex number systems and apply algebraic techniques to solve higher-level problems. The course will also integrate graphical, numeric, and algebraic methods, promoting a deeper conceptual understanding of functions and their properties.

Course Big Ideas

All functions can be investigated for the same basic features.
Different types of equations require different solution steps.
Operating with and understanding properties of numbers is vital to solving mathematical problems.
Problem solving techniques.

Course Essential Questions

What are the common features of all functions?
How do we investigate functions?
How do we solve equations?
How do we perform various operations with numbers and functions?

Course Competencies

Understand how to find the domain, range, intercepts, graphical representation, and key points for various functions.
Understand how to solve linear, quadratic, radical, rational, exponential, and logarithmic equations.
Understand the importance of analyzing functions.
Understand how to properly operate with different types of numbers and expressions.

Course Assessments

Skill Based Summative Unit Quizzes and Tests
Check for understanding Mini-Quizzes
Writing prompts

Course Units

Unit 1: Linear Functions

Standards

PA Common Core Mathematics Standards

CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data.
CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context.
CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems.
CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable.
CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships.
CC.2.2.HS.D.9 Use reasoning to solve equations, and justify the solution method.
CC.2.2.HS.D.10 Represent,solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

What steps do we take to solve linear equations?
How do we create the graph of a line?
How do we solve systems of equations?
How does solving inequalities differ from solving linear equations?
How does solving absolute value equations differ from solving linear equations?
How does the graph of an absolute value function differ from the graph of a linear function?

CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.
CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials.
CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable.
CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers.
CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.
CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems
CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.
CC.2.2.HS.C.4 Interpret the effects transformations have on functions, and find the inverses of functions.
CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems.

Graph a quadratic function in standard form.
Graph a quadratic function in vertex form.
Graph a quadratic function in intercept form.
Factor a quadratic expression.
Solve a quadratic equation with factoring.
Solve a quadratic equation with square roots.
Solve a quadratic equation with the quadratic formula.
Solve quadratic equations with imaginary solutions.
Operate with complex numbers.
Translate a quadratic function from one form to another.

CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.
CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials.
CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.
CC.2.2.HS.D.5 Use polynomial identities to solve problems.
CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers.
CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.

How can we represent and operate with very large or very small numbers?
How do we operate with polynomials?
What are our options for dividing polynomials, and how do we decide which method is best?
How do we evaluate polynomials?
How do we predict the end behavior of a polynomial?
How do we predict the shape of the graph of a polynomial function?
How do we factor polynomials of a higher degree?

CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents.
CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.
CC.2.2.HS.C.4 Interpret the effects transformations have on functions, and find the inverses of functions.
CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable.

Find the domain and range of a provided function or graph.
Evaluate expressions with rational exponents.
Find nth roots.
Simplify expressions using properties of rational exponents.
Simplify expressions involving radicals.
Perform operations on functions.
Find compositions of functions.
Find the inverse of relations and functions.
Verify inverse functions.
Graph radical functions.
Solve radical equations.

CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations.
CC.2.2.HS.C.4 Interpret the effects transformations have on functions, and find the inverses of functions.
CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems.
CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.
CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents.

CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays.
CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables.
CC.2.4.HS.B.6 Use the concepts of independence and conditional probability to interpret data.
CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model.