# 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

**Unit 1: Expressions, Equations, and Inequalities**

- Create and recognize equivalent expressions involving radical and exponential forms of expressions.
- A2.REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.

**Unit 2: Functions, Equations, and Graphs**

- A2.IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2.IF.A.2 Translate between equivalent forms of functions.
- 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.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.
- A2.FM.A.1 Create functions and use them to solve applications of quadratic and exponential function modeling problems.

**Unit 3: Linear Systems**

- A2.REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.B.3 Create and solve systems of equations that may include nonlinear equations and inequalities.
- A2.FM.A.1 Create functions and use them to solve applications of quadratic and exponential function modeling problems.

**Unit 4: Quadratic Functions & Equations**

- A2.NQ.A.2 Create and recognize equivalent expressions involving radical
- and exponential forms of expressions.
- A2.NQ.A.3 Add, subtract, multiply and divide radical expressions.
- A2.NQ.B.5 Represent complex numbers.
- A2.NQ.B.6 Add, subtract, multiply and divide complex numbers.
- A2.REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.B.3 Create and solve systems of equations that may include nonlinear equations and inequalities.
- A2.APR.A.1 Extend the knowledge of factoring to include factors with complex coefficients.
- A2.APR.A.5 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the Polynomial.
- A2.IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems
- A2.IF.A.2 Translate between equivalent forms of functions.
- 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.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.
- A2.FM.A.1 Create functions and use them to solve applications of quadratic and exponential function modeling problems.

**Unit 5. Polynomials and Polynomial Functions**

- A2.NQ.A.2 Create and recognize equivalent expressions involving radical and exponential forms of expressions.
- A2.NQ.A.3 Add, subtract, multiply and divide radical expressions.
- A2.NQ.B.7 Know and apply the Fundamental Theorem of Algebra.
- A2.REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.B.3 Create and solve systems of equations that may include nonlinear equations and inequalities.
- A2.APR.A.1 Extend the knowledge of factoring to include factors with complex coefficients.
- A2.APR.A.2 Understand the Remainder Theorem and use it to solve Problems.
- A2.APR.A.3 Find the least common multiple of two or more polynomials.
- A2.APR.A.4 Add, subtract, multiply and divide rational expressions.
- A2.APR.A.5 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.
- A2.IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems
- A2.IF.A.2 Translate between equivalent forms of functions.
- 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.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.

**Unit 6: Radical Functions and Rational Exponents**

- A2.NQ.A.1 Extend the system of powers and roots to include rational Exponents.
- A2.NQ.A.3 Add, subtract, multiply and divide radical expressions.
- A2.NQ.A.4 Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.
- A2.REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.A.2 Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.
- A2.APR.A.1 Extend the knowledge of factoring to include factors with complex coefficients.
- A2.IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems (IF.B.5, IF.C.7-9)
- A2.IF.A.2 Translate between equivalent forms of functions.
- A2.BF.A.2 Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.

**Unit 7: Exponential and Logarithmic Functions**

- A2.NQ.A.2 Create and recognize equivalent expressions involving radical and exponential forms of expressions.
- 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.
- A2.SSE.A.4 Understand why logarithmic scales are used, and use them to solve problems.
- A2.IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems (IF.B.5, IF.C.7-9)
- A2.IF.A.2 Translate between equivalent forms of functions.
- A2.BF.A.2 Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.

**Unit 8: Rational Functions**

- A2.NQ.A.2 Create and recognize equivalent expressions involving radical and exponential forms of expressions.
- A2.NQ.A.3 Add, subtract, multiply and divide radical expressions.
- A2.NQ.A.4 Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.
- A2.REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.A.2 Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.
- A2.APR.A.1 Extend the knowledge of factoring to include factors with complex coefficients.
- A2.APR.A.4 Add, subtract, multiply and divide rational expressions.
- 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.

**Unit 9: Probability & Statistics**

- A2.DS.A.1 Analyze how random sampling could be used to make inferences about population parameters.
- A2.DS.A.2 Determine whether a specified model is consistent with a given data set.
- A2.DS.A.3 Describe and explain the purposes, relationship to randomization and differences, among sample surveys, experiments and observational studies.
- A2.DS.A.4 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 Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions
- A2.DS.A.6 Analyze decisions and strategies using probability concepts.
- A2.DS.A.7 Evaluate reports based on data.
- A2.DS.B.8 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 distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.