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- Real Numbers
- Number Lines
- Inequalities on a Number Line
- Sets and Symbols
- Order of Operations
- Algebra Expressions with Fraction Bars
- Algebra Expressions with Exponents
- Calculator Use with Algebra Expressions
- Numerical Expression Evaluation
- Numerical Expression Evaluation with Basic Operations
- Numerical Expression Evaluation with Grouping Symbols
- Expression Evaluation with Powers and Grouping Symbols
- Polynomial Expression Evaluation
- Definition of Variable
- Mathematical Expressions
- Expressions with One or More Variables
- Patterns and Expressions
- Words that Describe Patterns
- Single Variable Expressions
- Expressions for Real-Life Situations
- Checking Solutions
- Checking Solutions to Equations
- Checking Solutions to Inequalities
- Variable Expressions
- Addition and Subtraction Phrases as Expressions
- Multiplication and Division Phrases as Expressions
- Sums and Differences of Single Variable Expressions
- Products and Quotients of Variable Expressions
- Working with Real Numbers
- Axioms for Real Numbers
- Mixed Numbers in Applications
- Rational Numbers in Applications
- Distributive Property
- Expressions and the Distributive Property
- When to Use the Distributive Property
- Distributive Property to Evaluate Formulas with Decimals
- Opposites and Absolute Values
- Additive Inverses and Absolute Values
- Absolute Value
- Operations with Real Numbers
- Properties of Real Number Addition
- Properties of Real Number Multiplication
- Simplify Expressions
- Simplify Variable Expressions Involving Integer Addition
- Simplify Variable Expressions Involving Integer Subtraction
- Simplify Variable Expressions Involving Integer Multiplication
- Simplify Variable Expressions Involving Integer Division
- Simplify Sums or Differences of Single Variable Expressions
- Simplify Products or Quotients of Single Variable Expressions
- Simplify Variable Expressions Involving Multiple Operations

- Linear Equations
- Equations that Describe Patterns
- Sentences as Single Variable Equations
- Addition and Subtraction Phrases as Equations
- Multiplication and Division Phrases as Equations
- Single Variable Equations from Verbal Models
- Input-Output Tables
- Function Rules for Input-Output Tables
- Input-Output Tables for Function Rules
- Extend Numerical Patterns
- One-Step Equations and Inverse Operations
- Single Variable Addition Equations
- Single Variable Subtraction Equations
- Mental Math for Addition and Subtraction Equations
- Inverse Property of Addition in Decimal Equations
- Inverse Property of Addition in Fraction Equations
- One-Step Equations Transformed by Multiplication/Division
- Single Variable Multiplication Equations
- Single Variable Division Equations
- Mental Math for Multiplication/Division Equations
- Division to Solve Decimal Equations
- Multi-Step Equations
- Two-Step Equations and Properties of Equality
- Two-Step Equations from Verbal Models
- Two-Step Equations with Addition and Multiplication
- Two-Step Equations with Addition and Division
- Two-Step Equations with Subtraction and Multiplication
- Two-Step Equations with Subtraction and Division
- Solving Real-World Problems with Two-Step Equations
- Multi-Step Equations with Like Terms
- Equations with Decimals, Fractions, and Parentheses
- Equations with Fractions
- Equations with Decimals
- Distributive Property for Multi-Step Equations
- Solving Real-World Problems Using Multi-Step Equations
- Equations with Variables on Both Sides
- Applications of One-Step Equations
- Problem-Solving Models
- Comparison of Problem-Solving Models
- Trends in Data
- Guess and Check, Work Backward
- Scale and Indirect Measurement Applications
- Formulas for Problem Solving
- Dimensional Analysis
- Applications Using Linear Models
- Problem Solving Plan, Mental Math

- Linear Inequalities
- Inequalities that Describe Patterns
- Inequality Expressions
- Inequalities with Addition and Subtraction
- Inequalities with Multiplication and Division
- Inequalities with Multiplication
- Inequalities with Division
- Multi-Step Inequalities
- Inequalities with Like Terms
- Inequalities with the Distributive Property
- Compound Inequalities
- Union and Intersection of Sets
- Solutions to Compound Inequalities
- Absolute-Value Equations and Inequalities
- Absolute Value Equations
- Graphs of Absolute Value Equations
- Absolute Value Inequalities
- Graphs of General Absolute Value Equations with Technology
- Graphs of Absolute Value Inequalities
- Applications with Inequalities
- One-Step Inequalities

- Graphs and Functions
- Function Notation
- Domain and Range of a Function
- Functions that Describe Situations
- Points in the Coordinate Plane
- Ordered Pairs in Four Quadrants
- Coordinate Locations on a Map
- Graphs in the Coordinate Plane
- Functions on a Cartesian Plane
- Graphs of Functions based on Rules
- Function Rules based on Graphs
- Graphs of Inequalities in One Variable
- Linear and Non-Linear Function Distinction
- Linear and Non-Linear Patterns of Change
- Algebraic Functions
- Vertical Line Test
- Solving Open Sentences in Two Variables
- Function Notation and Linear Functions
- Graph of a Linear Equation in Two Variables
- Graphs of Linear Equations
- Horizontal and Vertical Line Graphs
- Intercepts by Substitution
- Intercepts and the Cover-Up Method
- Graphs of Linear Functions
- Applications of Linear Graphs
- Problem Solving with Linear Graphs
- Linear Inequalities in Two Variables
- Testing Solutions for Linear Inequalities in Two Variables
- Slope
- Rates of Change
- Slope of a Line Using Two Points
- Slope-Intercept Form
- Graphs Using Slope-Intercept Form
- Graphs of Linear Models of Direct Variation
- Forms of Linear Equations
- Standard Form of Linear Equations
- Slope-Intercept Form of Linear Equations
- Linear Equations in Point-Slope Form
- Write a Function in Slope-Intercept Form
- Comparing Equations of Parallel and Perpendicular Lines
- Equations of Parallel Lines
- Equations of Perpendicular Lines
- Families of Lines
- Determining the Equation of a Line
- Write an Equation Given the Slope and a Point
- Write an Equation Given Two Points
- Fitting Lines to Data
- Linear Interpolation and Extrapolation
- Problem Solving with Linear Models

- Systems of Equations and Inequalities
- Systems of Linear Equations in Two Variables
- Checking a Solution for a Linear System
- Graphs of Linear Systems
- Linear Systems with Addition or Subtraction
- Linear Systems with Multiplication
- Solving Systems by Multiplying One Equation
- Solving Systems by Multiplying Both Equations
- Comparing Methods for Solving Linear Systems
- Systems Using Substitution
- Consistent and Inconsistent Linear Systems
- Determining the Type of Linear System
- Applications of Linear Systems
- Graphs of Systems of Linear Inequalities in Two Variables
- Checking for Solutions to Systems of Linear Inequalities
- Systems of Linear Equations in Three Variables
- Mixture Problems
- Systems of Linear Inequalities
- Linear Programming

- Polynomials and Factoring
- Addition and Subtraction of Polynomials
- Addition of Polynomials
- Subtraction of Polynomials
- Polynomials in Standard Form
- Multiplication of Monomials by Polynomials
- Multiplication of Polynomials by Binomials
- Multiplying Polynomials
- Multiplying Binomials Mentally
- Factoring Completely
- Monomial Factors of Polynomials
- Special Products of Polynomials
- Factor Polynomials Using Special Products
- Factorization using Difference of Squares
- Factorization using Perfect Square Trinomials
- Factorization of Quadratic Expressions
- Factorization of Quadratic Expressions with Negative Coefficients
- Factoring when the Leading Coefficient Equals 1
- Factoring by Grouping
- Sum and Difference of Cubes
- Applications of Factoring
- Zero Product Principle
- Solving Problems by Factoring

- Rational Expressions
- Division of Polynomials
- Excluded Values for Rational Expressions
- Simplifying Rational Expressions
- Zero, Negative, and Fractional Exponents
- Negative Exponents
- Fractional Exponents
- Evaluating Exponential Expressions
- Operations with Rational Expressions
- Products and Quotients of Rational Expressions
- Multiplication of Rational Expressions
- Division of Rational Expressions
- Addition and Subtraction of Rational Expressions
- Applications of Adding and Subtracting Rational Expressions
- Sums and Differences of Rational Expressions with Unequal Denominators
- Adding and Subtracting Rational Expressions where One Denominator is the LCD
- Complex Fractions
- Percent Problems
- Rational Expressions in Equations and Problems
- Clearing Denominators in Rational Equations
- Solving Rational Equations using Cross-Multiplication
- Solving Rational Equations using the LCD
- Number Problems
- Ratio, Proportion, and Variation
- Rational Equations Using Proportions
- Proportions with Variable in the Numerator
- Proportions with Variable in the Denominator
- Direct Variation
- Applications Using Direct Variation
- Inverse Variation Models
- Graphs of Rational Functions
- Horizontal and Vertical Asymptotes
- Determining Asymptotes by Division
- Inverse Variation Problems
- Oblique Asymptotes
- Joint and Combined Variation
- Applications Using Rational Equations

- Square Roots and Irrational Numbers
- Properties of Rational Numbers versus Irrational Numbers
- Evaluation of Square Roots
- Evaluation of Perfect Square Roots
- Rational Square Roots
- Irrational Square Roots
- Estimation of Square Roots
- Pythagorean Theorem and its Converse
- Solving Equations Using the Pythagorean Theorem
- Applications Using the Pythagorean Theorem
- Distance Formula
- Midpoint Formula
- Expressions with Radicals
- Simplification of Radical Expressions
- Multiplication and Division of Radicals
- Raising a Product or Quotient to a Power
- Addition and Subtraction of Radicals
- nth Roots
- Radical Equations
- Equations with Radicals on Both Sides
- Applications Using Radicals
- Equations with Square Roots
- Radical Equations with Variables on Both Sides
- Graphs of Square Root Functions
- Shifts of Square Root Functions

- Quadratic and Exponential Equations and Functions
- Solutions Using the Discriminant
- Use Square Roots to Solve Quadratic Equations
- Square Root Applications
- Completing the Square
- Vertex Form of a Quadratic Equation
- Completing the Square when the Leading Coefficient Equals 1
- Quadratic Formula
- Discriminant
- Using Quadratic Equations to Solve Problems
- Comparing Methods for Solving Quadratics
- Graphing Quadratic and Other Polynomial Functions and Equations
- Quadratic Functions and Their Graphs
- Vertical Shifts of Quadratic Functions
- Use Vertex Form of Quadratics
- Graphs of Quadratic Functions in Intercept Form
- Graphing Calculator to Graph Quadratic Functions
- Transformations of Quadratic Functions
- Roots to Determine a Quadratic Function
- Quadratic Functions and Equations
- Use Graphs to Solve Quadratic Equations
- Polynomial Functions
- Exponential Properties and Functions
- Exponent Properties with Variable Expressions
- Exponential Properties Involving Products
- Exponential Properties Involving Quotients
- Exponent of a Quotient
- Exponential Terms Raised to an Exponent
- Solving Equations with Exponents
- Solving Equations with Fractional Exponents
- Scientific Notation
- Scientific Notation with a Calculator
- Comparison of Numbers in Scientific Notation
- Operations with Numbers in Scientific Notation
- Exponential Growth and Decay
- Exponential Growth
- Exponential Decay
- Geometric Sequences and Exponential Functions
- Applications of Exponential Functions
- Graphs of Exponential Functions
- Logarithms
- Linear, Exponential, and Quadratic Models
- Applications of Function Models
- Identification of Quadratic Models

- Matrices to Represent Data
- Matrix Algebra
- Adding and Subtracting Matrices
- Multiplying Matrices by a Scalar
- Matrix Multiplication
- Limitations of Matrix Multiplication
- Determinants
- Cramer's Rule
- Matrix Equations
- Solving a Matrix Equation
- Row Operations and Row Echelon Forms
- Augmented Matrices
- Writing and Solving a Matrix Equation for a Linear System
- Solving Linear Systems Using Matrices and Technology
- Inverse Matrices
- Applications of Matrices
- Partial Fraction Expansions

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