A2.AAPR: Arithmetic with Polynomials and Rational Expressions

A2.AAPR.1: Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

A2.AAPR.3: Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior. Write a polynomial function of least degree corresponding to a given graph. (Limit to polynomials with degrees 3 or less.)

Graphs of Polynomial Functions
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

A2.ACE: Creating Equations

A2.ACE.1: Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Inequalities
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

A2.ACE.2: Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales.

Absolute Value Equations and Inequalities
Circles
Compound Interest
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

A2.ACE.3: Use systems of equations and inequalities to represent constraints arising in real-world situations. Solve such systems using graphical and analytical methods, including linear programing. Interpret the solution within the context of the situation. (Limit to linear programming.)

Linear Inequalities in Two Variables
Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

A2.ACE.4: Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

Area of Triangles
Solving Formulas for any Variable

A2.AREI: Reasoning with Equations and Inequalities

A2.AREI.2: Solve simple rational and radical equations in one variable and understand how extraneous solutions may arise.

Radical Functions

A2.AREI.4: Solve mathematical and real-world problems involving quadratic equations in one variable.

A2.AREI.4.b: Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

A2.AREI.11: Solve an equation of the form f(x) = g(x) graphically by identifying the x- coordinate(s) of the point(s) of intersection of the graphs of y = f (x) and y = g(x).

Absolute Value Equations and Inequalities
Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

A2.ASE: Structure and Expressions

A2.ASE.1: Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions.

Compound Interest
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Translating and Scaling Functions
Using Algebraic Expressions

A2.ASE.2: Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions II
Exponents and Power Rules
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Trigonometric Expressions
Solving Algebraic Equations II
Using Algebraic Expressions

A2.ASE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A2.ASE.3.b: Determine the maximum or minimum value of a quadratic function by completing the square.

Quadratics in Vertex Form

A2.ASE.3.c: Use the properties of exponents to transform expressions for exponential functions.

Dividing Exponential Expressions
Exponents and Power Rules

A2.FBF: Building Functions

A2.FBF.1: Write a function that describes a relationship between two quantities.

A2.FBF.1.a: Write a function that models a relationship between two quantities using both explicit expressions and a recursive process and by combining standard forms using addition, subtraction, multiplication and division to build new functions.

Addition and Subtraction of Functions
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2.FBF.1.b: Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations.

Addition and Subtraction of Functions

A2.FBF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2.FBF.3: Describe the effect of the transformations kf (x), f(x) + k, f(x + k), and combinations of such transformations on the graph of y = f (x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

A2.FIF: Interpreting Functions

A2.FIF.3: Define functions recursively and recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic Sequences
Geometric Sequences

A2.FIF.4: Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.

Absolute Value with Linear Functions
Compound Interest
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Introduction to Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

A2.FIF.5: Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Logarithmic Functions
Radical Functions
Rational Functions

A2.FIF.6: Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context.

Cat and Mouse (Modeling with Linear Systems)
Slope

A2.FIF.7: Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases.

Absolute Value with Linear Functions
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
Zap It! Game

A2.FIF.8: Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function.

A2.FIF.8.b: Interpret expressions for exponential functions by using the properties of exponents.

Compound Interest
Exponential Functions

A2.FIF.9: Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal.

General Form of a Rational Function
Graphs of Polynomial Functions
Linear Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form

A2.FLQE: Linear, Quadratic, and Exponential

A2.FLQE.1: Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by a constant percent rate per unit interval.

A2.FLQE.1.b: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Compound Interest
Exponential Growth and Decay

A2.FLQE.2: Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables.

Absolute Value with Linear Functions
Arithmetic Sequences
Arithmetic and Geometric Sequences
Compound Interest
Exponential Functions
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

A2.FLQE.5: Interpret the parameters in a linear or exponential function in terms of the context.

Arithmetic Sequences
Compound Interest
Exponential Growth and Decay
Introduction to Exponential Functions

A2.NCNS: Complex Number System

A2.NCNS.1: Know there is a complex number 𝑖 such that i² = −1, and every complex number has the form a + bi with a and b real.

Points in the Complex Plane
Roots of a Quadratic

A2.NCNS.7: Solve quadratic equations in one variable that have complex solutions.

Points in the Complex Plane
Roots of a Quadratic