Table of Contents
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Course Contents
Faculty Resources
Module 0: Review
- Why It Matters: Review
- Introduction to Using the Order of Operations
- Simplify Expressions With the Order of Operations
- Use the Distributive Property to Simplify
- Introduction to Arithmetic With Fractions
- Adding and Subtracting Fractions
- Multiplying Fractions
- Dividing Fractions
- Putting It Together: Review
Module 1: Real Numbers and Algebraic Expressions
- Why It Matters: Real Numbers and Algebraic Expressions
- Introduction to Classifying and Defining Properties of Real Numbers
- Classify Real Numbers
- Use Properties of Real Numbers
- Evaluate Algebraic Expressions
- Introduction to Solving Multi-Step Linear Equations
- Multi-Step Equations
- Solve Equations with the Distributive Property
- Classify Solutions to Linear Equations
- Introduction to Problem Solving
- Set Up a Linear Equation to Solve an Application
- Solve an Application Using a Formula
- Putting It Together: Real Numbers and Algebraic Expressions
Module 2: Linear Inequalities
- Why It Matters: Linear Inequalities
- Introduction to Solving Single-Step and Multi-Step Inequalities
- Describe Solutions to Inequalities
- Solve Inequalities
- Introduction to Solving Compound Inequalities
- Describe Sets as Intersections or Unions
- Solve Compound Inequalities—OR
- Solve Compound Inequalities—AND
- Solve Absolute Value Inequalities
- Putting it Together: Linear Inequalities
Module 3: Graph Linear Equations and Inequalities
- Why It Matters: Graph Linear Equations and Inequalities
- Introduction to Graphing Linear Equations in Two Variables
- Graph Linear Equations
- Graph Using Intercepts
- Introduction to Graphing Linear Inequalities
- Graph an Inequality in Two Variables
- Solution Sets of Inequalities
- Putting it Together: Graph Linear Equations and Inequalities
Module 4: Functions and Function Notation
- Why It Matters: Functions and Function Notation
- Introduction to Functions and Their Notation
- Define a Function
- Function Notation
- Evaluate Functions
- Introduction to Graphs of Functions
- Graph Linear Functions
- Graph Quadratic Functions
- Graph Radical Functions
- Introduction to Domain and Range
- Identify a One-to-One Function
- Domain Restrictions
- Find Domain and Range From a Graph
- Putting it Together: Functions
Module 5: Linear Functions
- Why it Matters: Linear Functions
- Introduction to Characteristics of Linear Functions and Their Graphs
- Calculate and Interpret Slope
- Graph Linear Functions Using Slope and y-Intercept
- Transform Linear Functions
- Introduction to Equations of Linear Functions
- Write the Equation of a Linear Function Part I
- Write the Equation of a Linear Function Part II
- Model an Application With a Linear Function
- Introduction to Piecewise-Defined Linear Functions
- Define and Write Piecewise Functions
- Graph Piecewise Functions
- Putting it Together: Linear Functions
Module 6: Linear Systems
- Why It Matters: Systems of Equations and Inequalities
- Introduction to Solving Systems in Two Variables
- Solutions for Systems of Linear Equations
- Solve Systems by Substitution
- Solve Systems by Elimination
- Introduction to Systems of Equations in Three Variables
- Systems of Three Equations in Three Variables
- Inconsistent and Dependent Systems in Three Variables
- Applications of Linear Equations in Three Variables
- Introduction to Systems of Linear Inequalities
- Define Solutions to Systems of Linear Inequalities
- Graph Solutions to Systems of Linear Inequalities
- Applications of Systems of Linear Inequalities
- Putting it Together: Linear Systems
Module 7: Exponents
- Why It Matters: Exponents
- Introduction to Applying Exponent Rules
- Terms and Expressions with Exponents
- Product and Quotient Rules
- The Power Rule for Exponents
- Negative and Zero Exponent Rules
- Find the Power of a Product and a Quotient
- Introduction to Scientific Notation
- Writing Scientific Notation
- Multiply and Divide Numbers in Scientific Notation
- Problem Solving With Scientific Notation
- Putting It Together: Exponents
Module 8: Polynomials and Polynomial Functions
- Why It Matters: Polynomials
- Introduction to Algebraic Operations on Polynomials
- Define and Evaluate Polynomials
- Sums and Products of Polynomials
- Multiply a Trinomial and a Binomial
- Divide Polynomials Part I
- Divide Polynomials Part II
- Introduction to Polynomial Functions
- Define and Identify Polynomial Functions
- Graphs of Polynomial Functions
- Algebra of Polynomial Functions
- Putting it Together: Polynomials and Polynomial Functions
Module 9: Factoring
- Why It Matters: Factoring
- Introduction to Factoring Trinomials
- The Greatest Common Factor
- Factor a Trinomial with Leading Coefficient = 1
- Factor by Grouping
- Introduction to Special Cases
- Special Cases - Squares
- Special Cases - Cubes
- More Factoring Methods
- Introduction to Polynomial Equations
- Solve Polynomial Equations
- Projectiles
- Pythagorean Theorem
- Putting It Together: Factoring
Module 10: Rational Expressions and Equations
- Why It Matters: Rational Expressions and Equations
- Introduction to Operations With Rational Expressions
- Define and Simplify Rational Expressions
- Multiply and Divide Rational Expressions
- Add and Subtract Rational Expressions
- Complex Rational Expressions
- Introduction to Rational Equations and Their Applications
- Solve Rational Equations
- Proportions
- Variation
- Applications with Rational Equations
- Putting It Together: Rational Expressions and Equations
Module 11: Roots and Rational Exponents
- Why It Matters: Roots and Rational Exponents
- Introduction to Simplifying Roots and Rational Exponents
- Define and Evaluate Roots
- Radical Expressions and Rational Exponents
- Simplify Radical Expressions
- Introduction to Algebraic Operations with Radical Expressions
- Multiply and Divide Radical Expressions
- Add and Subtract Radical Expressions
- Multiple Term Radicals
- Rationalize Denominators
- Introduction to Equations with Radicals
- Solve Radical Equations
- Applications with Radical Equations
- Putting it Together: Roots and Rational Exponents
Module 12: Quadratic Equations and Complex Numbers
- Why It Matters: Quadratic Equations and Complex Numbers
- Introduction to Quadratic Equations
- Quadratic Equations
- Square Roots and Completing the Square
- The Quadratic Formula
- Introduction to Complex Numbers
- Imaginary and Complex Numbers
- Add and Subtract Complex Numbers
- Multiply and Divide Complex Numbers
- Introduction to Quadratic Equations with Complex Solutions
- Quadratic Equations With Complex Solutions
- The Discriminant
- Putting it Together: Quadratic Equations and Complex Numbers
Module 13: Exponential, and Logarithmic Functions
- Why It Matters: Exponential and Logarithmic Functions
- Introduction to Exponential Functions
- Define and Evaluate Exponential Functions
- Exponential Functions with Base e
- Graph Exponential Functions
- Introduction to Logarithmic Functions
- Composite and Inverse Functions
- Define Logarithmic Functions
- Evaluate Logarithms
- Graphs of Logarithmic Functions
- Putting it Together: Exponential and Logarithmic Functions
Module 14: Exponential and Logarithmic Equations
- Why It Matters: Exponential and Logarithmic Equations
- Introduction to Logarithmic Properties
- Product Rule for Logarithms
- Quotient and Power Rules for Logarithms
- Expand and Condense Logarithms
- Change of Base
- Introduction to Exponential and Logarithmic Equations
- Exponential Equations with Like Bases
- Exponential Equations with Unlike Bases
- Logarithmic Equations
- Applied Exponential and Logarithmic Equations
- Putting it Together: Exponential and Logarithmic Equations
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