A2.1: Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.

A2.1.1: Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.

General Form of a Rational Function
Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Rational Functions

A2.1.2: Use function notation. Add, subtract, multiply, and divide pairs of functions.

Addition and Subtraction of Functions
Function Machines 1 (Functions and Tables)
Function Machines 3 (Functions and Problem Solving)

A2.1.3: Understand composition of functions and combine functions by composition.

Function Machines 1 (Functions and Tables)

A2.1.4: Graph relations and functions with and without graphing technology.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions

A2.1.5: Find the zeros of a function.

Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Roots of a Quadratic

A2.1.6: Solve an inequality by examining the graph.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Quadratic Inequalities
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

A2.1.7: Graph functions defined piece-wise.

Absolute Value with Linear Functions

A2.1.8: Interpret given situations as functions in graphs, formulas, and words.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions

A2.2: Students solve systems of linear equations and inequalities and use them to solve word problems. They model data with linear equations.

A2.2.1: Graph absolute value equations and inequalities.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Compound Inequalities

A2.2.2: Use substitution, elimination, and matrices to solve systems of two or three linear equations in two or three variables.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

A2.2.3: Use systems of linear equations and inequalities to solve word problems.

Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

A2.2.4: Find a linear equation that models a data set using the median fit method and use the model to make predictions.

Least-Squares Best Fit Lines
Solving Using Trend Lines

A2.3: Students solve quadratic equations, including the use of complex numbers. They interpret maximum and minimum values of quadratic functions. They solve equations that contain square roots.

A2.3.1: Define complex numbers and perform basic operations with them.

Points in the Complex Plane
Roots of a Quadratic

A2.3.2: Understand how real and complex numbers are related, including plotting complex numbers as points in the plane.

Points in the Complex Plane

A2.3.3: Solve quadratic equations in the complex number system.

Points in the Complex Plane
Roots of a Quadratic

A2.3.4: Graph quadratic functions. Apply transformations to quadratic functions. Find and interpret the zeros and maximum or minimum value of quadratic functions.

Addition and Subtraction of Functions
Exponential Functions
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Translating and Scaling Functions
Translations
Zap It! Game

A2.3.6: Solve equations that contain radical expressions.

Operations with Radical Expressions

A2.4: Students write equations of conic sections and draw their graphs.

A2.4.1: Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).

Circles
Ellipses
Hyperbolas
Parabolas

A2.4.2: Graph conic sections.

Circles
Ellipses
Hyperbolas
Parabolas
Zap It! Game

A2.5: Students use the binomial theorem, divide and factor polynomials, and solve polynomial equations.

A2.5.2: Divide polynomials by others of lower degree.

Dividing Polynomials Using Synthetic Division

A2.5.3: Factor polynomials completely and solve polynomial equations by factoring.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A2.6: Students use negative and fractional exponents. They simplify algebraic fractions and solve equations involving algebraic fractions. They solve problems of direct, inverse, and joint variation.

A2.6.1: Understand and use negative and fractional exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A2.6.4: Solve equations involving algebraic fractions.

Solving Algebraic Equations II

A2.6.6: Solve problems of direct, inverse, and joint variation.

Determining a Spring Constant
Direct and Inverse Variation

A2.7: Students graph exponential functions and relate them to logarithms. They solve logarithmic and exponential equations and inequalities. They solve word problems using exponential functions.

A2.7.1: Graph exponential functions.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

A2.7.4: Solve logarithmic and exponential equations and inequalities.

Exponential Functions

A2.8: Students define and use arithmetic and geometric sequences and series.

A2.8.1: Define arithmetic and geometric sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2.8.2: Find specified terms of arithmetic and geometric sequences.

Arithmetic Sequences
Geometric Sequences

A2.9: Students use fundamental counting principles to compute combinations, permutations, and probabilities.

A2.9.1: Understand and apply counting principles to compute combinations and permutations.

Binomial Probabilities
Permutations and Combinations

A2.9.2: Use the basic counting principle, combinations, and permutations to compute probabilities.

Binomial Probabilities
Permutations and Combinations

A2.10: Mathematical Reasoning and Problem Solving

A2.10.1: Use a variety of problem-solving strategies, such as drawing a diagram, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

Absolute Value Equations and Inequalities
Linear Inequalities in Two Variables
Modeling One-Step Equations
Solving Equations on the Number Line
Using Algebraic Equations

A2.10.4: Use the properties of number systems and the order of operations to justify the steps of simplifying functions and solving equations.

Solving Algebraic Equations II
Solving Equations on the Number Line

A2.10.5: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously. .

Solving Linear Systems (Standard Form)

A2.10.6: Use counterexamples to show that statements are false.

Conditional Statements