# Algebra II

Algebra II continues the study of algebra, the representation of quantities using variables and mathematical operations to show relationships. Students will represent relationships and functions with linear equations and explore relationships of direct and indirect variation. Students will explore quadratic functions and perform operations with complex numbers. Polynomials and their properties will be explored and graphed. Students will explore exponential relationships, logarithmic functions, and probabilities.

**Credits:** 1.0 (0.5 per semester)

**Estimated Completion Time:** 2 semesters/18-36 weeks

**State Course Number:** 115810

Honors

Credit Acquisition

Credit Recovery

NCAA Approved

Semester 1

Unit 1: Inverse Functions and Function Transformations

- Concept 1: Explore Inverse Functions
- A2.IF.A.1: Use and interpret functions; Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2.BF.A.1: Create new functions from existing functions; Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).
- A2.BF.A.2: Create new functions from existing functions; Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.

- Concept 2: Explore Function Transformation
- A2.IF.A.1: Use and interpret functions; Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2.BF.A.3: Create new functions from existing functions; Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.

Unit 2: Solve Absolute Value Equations and Inequalities

Concept 1: Solve Absolute Value Equations and Inequalities

- A2.BF.A.3: Create new functions from existing functions; Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.
- A2.REI.A.1: Solve equations and inequalities; Create and solve equations and inequalities, including those that involve absolute value.

Unit 3: Exponents

- Concept 1: Represent Exponential Functions
- A2.REI.B.3: Create and solve systems of equations that may include non-linear equations and inequalities.
- A2.IF.A.1: Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2.BF.A.3: Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.

- Concept 2: Explore Function Transformation
- A2.REI.B.3: Create and solve systems of equations that may include non-linear equations and inequalities.
- A2.BF.A.1: Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).
- A2.IF.A.1: Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.

Unit 4: Logarithms

- Concept 1: Discover and Analyze Logarithms
- A2.BF.A.2: Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.
- A2.IF.A.1: Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2,SSE.A.3: Use properties of logarithms to solve equations or find equivalent expressions.

- Concept 2: Apply Logarithmic Functions
- A2.SSE.A.1: Develop the definition of logarithms based on properties of exponents.
- A2.SSE.A.2: Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations.
- A2.SSE.A.3: Use properties of logarithms to solve equations or find equivalent expressions.

Unit 5: Real and Complex Solutions

- Concept 1: Analyze Radical Functions
- A2.IF.A.1: Use and interpret functions; Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2.REI.A.1: Solve equations and inequalities; Create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.A.2: Solve equations and inequalities; Solve rational equations where numerators and denominators are polynomials where extraneous solutions may result.
- A2.NQ.A.4: Extend and use relationship between rational exponents and radicals; Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.
- A2.BF.A.1: Create new functions from existing functions; Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).
- A2.BF.A.2: Create new functions from existing functions; Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.
- A2.BF.A.3: Create new functions from existing functions; Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections, and dilations.
- A2.APR.A.5: Perform operations on polynomials and rational expressions; Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.

- Concept 2: Determine Complex Quadratic Roots
- A2.NQ.B.5: Use complex numbers; Represent complex numbers.
- A2.NQ.B.6: Use complex numbers; Add, subtract, multiply, and divide complex numbers.
- A2.REI.A.1: Solve equations and inequalities; Create and solve equations and inequalities, including those that involve absolute value.

**Semester 2**

Unit 6: Multivariate Equations and Inequalities

- Concept 1: Investigate Linear Systems
- A2.FM.A.1: Use functions to model real-world problems; Create functions and use them to solve applications of quadratic and exponential function modeling problems.
- A2.REI.B.3: Solve general systems of equations and inequalities; Create and solve systems of equations that may include non-linear equations and inequalities.

- Concept 2: Solve NonLinear Systems
- A2.FM.A.1 Use functions to model real-world problems; Create functions and use them to solve applications of quadratic and exponential function modeling problems.
- A2.REI.B.3: Solve general systems of equations and inequalities; Create and solve systems of equations that may include non-linear equations and inequalities.

Unit 7: Polynomial Expressions and Equations

- Concept 1: Operate with Polynomials
- A2.APR.A.1: Perform operations on polynomials and rational expressions; Extend the knowledge of factoring to include factors with complex coefficients.
- A2.APR.A.2: Perform operations on polynomials and rational expressions; Understand the Remainder Theorem and use it to solve problems.
- A2.APR.A.3: Perform operations on polynomials and rational expressions; Find the least common multiple of two or more polynomials.
- A2.APR.A.5: Perform operations on polynomials and rational expressions; Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.

- Concept 2: Explore Polynomial Factors:
- A2.APR.A.2: Perform operations on polynomials and rational expressions; Understand the Remainder Theorem and use it to solve problems.
- A2.APR.A.4: Perform operations on polynomials and rational expressions; Add, subtract, multiply, and divide rational expressions.

- Concept 3: Analyze Polynomial Functions:
- A2.APR.A.1: Perform operations on polynomials and rational expressions; Extend the knowledge of factoring to include factors with complex coefficients.
- A2.APR.A.5: Perform operations on polynomials and rational expressions; Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.
- A2.IF.A.2: Use and interpret functions: Translate between equivalent forms of functions.

Unit 8: Rational Expressions and Equations

- Concept 1: Develop Rational Expressions and Equations
- A2.APR.A.1: Perform operations on polynomials and rational expressions: Extend the knowledge of factoring to include factors with complex coefficients
- A2.APR.A.4: Perform operations on polynomials and rational expressions: Add, subtract, multiply and divide rational expressions.
- A2.NQ.A.3: Extend and use the relationship between rational exponents and radicals: Add, subtract, multiply, and divide radical expressions

- Concept 2: Radical Expressions
- A2.NQ.A.1: Extend and use the relationship between rational exponents and radicals: Extend the system of powers and roots to include rational exponents.
- A2.NQ.A.3: Extend and use the relationship between rational exponents and radicals: Add, subtract, multiply, and divide radical expressions.
- A2.APR.A.1: Perform operations on polynomials and rational expressions: Extend the knowledge of factoring to include factors with complex coefficients

- Concept 3: Solving Rational Equations
- A2.REI.A.1: Solve equations and inequalities: Create and solve equations and inequalities, including those that involve absolute value
- A2.REI.A.2: Solve equations and inequalities: Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result
- A2.REI.B.3: Solve general systems of equations and inequalities: Create and solve systems of equations that may include nonlinear equations and inequalities
- A2.NQ.A.3: Extend and use the relationship between rational exponents and radicals: Add, subtract, multiply, and divide radical expressions
- A2.NQ.A.4: Extend and use the relationship between rational exponents and radicals: Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.
- A2.APR.A.1: Perform operations on polynomials and rational expressions: Extend the knowledge of factoring to include factors with complex coefficients

Unit 9: Rational Functions

- Concept 1: Represent Rational Functions
- A2.REI.A.1: Solve equations and inequalities: create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.B.3: Solve general systems of equations and inequalities: create and solve systems of equations that may include non-linear inequalities.
- A2.IF.A.1: Use and interpret functions: Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2.BF.A.2: Create new functions from existing functions: Derive inverses of functions, and compose the inverses with the original function to show that the functions are inverses.

- Concept 2: Compare Rational Functions
- A2.REI.A.1: Solve equations and inequalities: create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.B.3: Solve general systems of equations and inequalities: create and solve systems of equations that may include non-linear inequalities.
- A2.BF.A.2: Create new functions from existing functions: Derive inverses of functions, and compose the inverses with the original function to show that the functions are inverses.

Unit 10: Data Modeling

- Concept 1: Collect, Analyze, and Interpret Statistical Date:
- A2.DS.A.1: Make inferences and justify conclusions: Analyze how random sampling could be used to make inferences about population parameters.
- A2.DS.A.2: Make inferences and justify conclusions: Determine whether a specific model is consistent with a given data set.
- A2.DS.A.3: Make inferences and justify conclusions: Describe and explain the purposes, relationship to randomization and differences, among sample surveys, experiments and observational studies.
- A2.DS.A.4: Make inferences and justify conclusions: Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.
- A2.DS.A.5: Make inferences and justify conclusions: Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.
- A2.DS.A.6: Make inferences and justify conclusions: Analyze decisions and strategies using probability concepts.
- A1.DS.A.7: Make inferences and justify conclusions: Evaluate reports based on data.
- A2.DS.B.8: Fit a data set to a normal distribution: Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.
- A2.DS.B.9: Fit a data set to a normal distribution: Fit a data set to a distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.