1: Arithmetic with Polynomials and Rational Expressions

1.1: 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

2: Creating Equations

2.1: 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.

Compound Inequalities
Linear Inequalities in Two Variables
Solving Equations on the Number Line
Solving Two-Step Equations

2.2: 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
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

2.3: 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

3: Reasoning with Equations and Inequalities

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

Radical Functions

3.2: Solve mathematical and real-world problems involving quadratic equations in one variable.

3.2.1: Use the method of completing the square to transform any quadratic equation in 𝑥𝑥 into an equation of the form (x − h)² = k that has the same solutions. Derive the quadratic formula from this form.

Roots of a Quadratic

3.2.2: 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.

Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

3.3: 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).

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

4: Structure and Expressions

4.1: 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
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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

Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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

4.3.1: Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Zap It! Game

5: Building Functions

5.1: Write a function that describes a relationship between two quantities.

5.1.1: 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

5.1.2: 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
Function Machines 1 (Functions and Tables)
Function Machines 3 (Functions and Problem Solving)

5.2: 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

5.3: 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
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

6: Interpreting Functions

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

Arithmetic Sequences
Geometric Sequences

6.2: 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 1 (Functions and Tables)
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
Radical Functions

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

Introduction to Functions
Logarithmic Functions
Radical Functions

6.4: 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

6.5: 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.

Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Introduction to Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions

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

6.6.1: Interpret expressions for exponential functions by using the properties of exponents.

Compound Interest
Exponential Functions

6.7: 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

7: Linear, Quadratic, and Exponential

7.1: 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

7.2: Interpret the parameters in a linear or exponential function in terms of the context.

Arithmetic Sequences
Compound Interest
Introduction to Exponential Functions

8: Complex Number System

8.1: 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