# College Algebra

MTH 173YC Academy’s College Algebra course provides a comprehensive introduction to the foundations of mathematics typically taught in a traditional college algebra course. This course develops problem‐solving strategies and establishes a foundation for higher levels of mathematics. After exploring a variety of functions and understanding how they are used to model complex phenomena, students will feel empowered with the real-world skills to succeed in math, science, business, and programming.

## Course Outline

Click the + icon in each module to see its contents.

## Outcomes/Objectives

Click on each tab to view its contents.

### Module #1

**Algebra Foundations**

- Multiples
- Basic Exponent Rules
- Combining Exponent Rules
- Scientific Notation

### Module #3

**Graphing Essentials**

- Solving Inequalities
- Compound Inequalities
- Coordinate Plane

### Module #5

**Functions**

- Relations and Functions
- Rates of Change and Graph Behavior
- Shifts and Reflections of Functions
- Compressions and Stretches of Functions
- Function Operations
- Composition of Functions

### Module #7

**Factoring Polynomials**

- Factoring Using GCF and Grouping
- Factoring Trinomials: Part 1
- Factoring Special Product Trinomials
- Factoring Trinomials: Part 2
- General Strategy for Factoring Polynomials

### Module #9

**Solving and Graphing Quadratics**

- Completing the Square
- Quadratic Formula
- Graphing a Parabola
- Graphing Quadratic Functions Using Transformations

### Module #11

**Polynomial Functions**

- Power and Polynomial Functions
- Graphing Polynomial Functions
- Dividing Polynomials
- Real Zeros of Polynomial Functions

### Module #13

**Exponential Functions**

- Exponential Functions
- Interest, Growth, and Decay
- Graphs of Exponential Functions

### Module #15

**Analytic Geometry (Conics)**

- The Circle
- The Parabola
- The Ellipse
- The Hyperbola
- Solving Systems of Nonlinear Equations

### Module #2

**Expressions and Equations**

- Basic Polynomial Operations
- Multiplying Polynomials and Special Products
- Solving Equations
- Intermediate Solving Linear Equations
- Basic Polynomial Operations

### Module #4

**Linear Equations and Systems**

- Slope and Lines
- Find the Equation of Line
- System of Equations: Graphs and Substitution
- Systems of Equations: Elimination and Comparing Methods

### Module #6

**Sequences and Series**

- Sequences and Sequence Notation
- Arithmetic Sequences
- Geometric Sequences
- Series and Series Notation

### Module #8

**Quadratic Equation Essentials**

- Radical and Rational Operations
- Square Root Property
- Solutions of Quadratics Using Factoring

### Module #10

**Matrices**

- Matrix Operations
- Solving Systems of Equations Using Matrices
- Solving Systems of Linear Equations With Three Variables
- Cramer’s Rule

### Module #12

**Rational Functions**

- Simplifying, Multiplying, and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Rational Functions
- Inverses and Radical Functions

### Module #14

**Logarithmic Functions**

- Logarithmic Functions
- Graphs of Logarithmic Functions
- Logarithm Rules
- Solving Logarithmic and Exponential Equations

- Course Outcome #1
- Course Outcome #2
- Course Outcome #3
- Course Outcome #4
- Course Outcome #5
- Course Outcome #6
- Course Outcome #7
- Course Outcome #8

The student will evaluate and explain the structure and properties of matter including identifying the function and role of atoms, the periodic table, and nuclear energy as it relates to matter.

*Bloom’s level 4*

Solve equations and inequalities.

*Bloom’s level 3*

Analyze the effect of transformations and operations on functions.

*Bloom’s level 4*

Select and apply the appropriate strategies to determine the slope, y-intercept, coordinates, and equation of a line or system of equations.

*Bloom’s level 2*

Factor, solve, and graph quadratic equations using multiple strategies for each.

*Bloom’s level 3*

Select appropriate strategies to solve systems of equations with three variables.

*Bloom’s level 1*

Compare and apply similar techniques to graph polynomial, rational, and radical functions.

*Bloom’s level 4*

Combine properties and equation solving strategies to evaluate and graph exponential and logarithmic functions, circles, ellipses, parabolas, and hyperbolas.

*Bloom’s level 3*

## Course Outline

Click the + icon in each module to see its contents.

### Module #1

**Algebra Foundations**

- Multiples
- Basic Exponent Rules
- Combining Exponent Rules
- Scientific Notation

### Module #3

**Graphing Essentials**

- Solving Inequalities
- Compound Inequalities
- Coordinate Plane

### Module #5

**Functions**

- Relations and Functions
- Rates of Change and Graph Behavior
- Shifts and Reflections of Functions
- Compressions and Stretches of Functions
- Function Operations
- Composition of Functions

### Module #7

**Factoring Polynomials**

- Factoring Using GCF and Grouping
- Factoring Trinomials: Part 1
- Factoring Special Product Trinomials
- Factoring Trinomials: Part 2
- General Strategy for Factoring Polynomials

### Module #9

**Solving and Graphing Quadratics**

- Completing the Square
- Quadratic Formula
- Graphing a Parabola
- Graphing Quadratic Functions Using Transformations

### Module #11

**Polynomial Functions**

- Power and Polynomial Functions
- Graphing Polynomial Functions
- Dividing Polynomials
- Real Zeros of Polynomial Functions

### Module #13

**Exponential Functions**

- Exponential Functions
- Interest, Growth, and Decay
- Graphs of Exponential Functions

### Module #15

**Analytic Geometry (Conics)**

- The Circle
- The Parabola
- The Ellipse
- The Hyperbola
- Solving Systems of Nonlinear Equations

### Module #2

**Expressions and Equations**

- Basic Polynomial Operations
- Multiplying Polynomials and Special Products
- Solving Equations
- Intermediate Solving Linear Equations
- Basic Polynomial Operations

### Module #4

**Linear Equations and Systems**

- Slope and Lines
- Find the Equation of Line
- System of Equations: Graphs and Substitution
- Systems of Equations: Elimination and Comparing Methods

### Module #6

**Sequences and Series**

- Sequences and Sequence Notation
- Arithmetic Sequences
- Geometric Sequences
- Series and Series Notation

### Module #8

**Quadratic Equation Essentials**

- Radical and Rational Operations
- Square Root Property
- Solutions of Quadratics Using Factoring

### Module #10

**Matrices**

- Matrix Operations
- Solving Systems of Equations Using Matrices
- Solving Systems of Linear Equations With Three Variables
- Cramer’s Rule

### Module #12

**Rational Functions**

- Simplifying, Multiplying, and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Rational Functions
- Inverses and Radical Functions

### Module #14

**Logarithmic Functions**

- Logarithmic Functions
- Graphs of Logarithmic Functions
- Logarithm Rules
- Solving Logarithmic and Exponential Equations

## Outcomes/Objectives

Click on each tab to view its contents.

- Course Outcome #1
- Course Outcome #2
- Course Outcome #3
- Course Outcome #4
- Course Outcome #5
- Course Outcome #6
- Course Outcome #7
- Course Outcome #8

The student will evaluate and explain the structure and properties of matter including identifying the function and role of atoms, the periodic table, and nuclear energy as it relates to matter.

*Bloom’s level 4*

Solve equations and inequalities.

*Bloom’s level 3*

Analyze the effect of transformations and operations on functions.

*Bloom’s level 4*

Select and apply the appropriate strategies to determine the slope, y-intercept, coordinates, and equation of a line or system of equations.

*Bloom’s level 2*

Factor, solve, and graph quadratic equations using multiple strategies for each.

*Bloom’s level 3*

Select appropriate strategies to solve systems of equations with three variables.

*Bloom’s level 1*

Compare and apply similar techniques to graph polynomial, rational, and radical functions.

*Bloom’s level 4*

Combine properties and equation solving strategies to evaluate and graph exponential and logarithmic functions, circles, ellipses, parabolas, and hyperbolas.

*Bloom’s level 3*

## Outcomes/Objectives

Click on each tab to view its contents.

- Course Outcome #1
- Course Outcome #2
- Course Outcome #3
- Course Outcome #4
- Course Outcome #5
- Course Outcome #6
- Course Outcome #7
- Course Outcome #8

The student will evaluate and explain the structure and properties of matter including identifying the function and role of atoms, the periodic table, and nuclear energy as it relates to matter.

*Bloom’s level 4*

Solve equations and inequalities.

*Bloom’s level 3*

Analyze the effect of transformations and operations on functions.

*Bloom’s level 4*

Select and apply the appropriate strategies to determine the slope, y-intercept, coordinates, and equation of a line or system of equations.

*Bloom’s level 2*

Factor, solve, and graph quadratic equations using multiple strategies for each.

*Bloom’s level 3*

Select appropriate strategies to solve systems of equations with three variables.

*Bloom’s level 1*

Compare and apply similar techniques to graph polynomial, rational, and radical functions.

*Bloom’s level 4*

Combine properties and equation solving strategies to evaluate and graph exponential and logarithmic functions, circles, ellipses, parabolas, and hyperbolas.

*Bloom’s level 3*

## Course Outline

Click the + icon in each module to see its contents.

### Module #1

**Algebra Foundations**

- Multiples
- Basic Exponent Rules
- Combining Exponent Rules
- Scientific Notation

### Module #2

**Expressions and Equations**

- Basic Polynomial Operations
- Multiplying Polynomials and Special Products
- Solving Equations
- Intermediate Solving Linear Equations
- Basic Polynomial Operations

### Module #3

**Graphing Essentials**

- Solving Inequalities
- Compound Inequalities
- Coordinate Plane

### Module #4

**Linear Equations and Systems**

- Slope and Lines
- Find the Equation of Line
- System of Equations: Graphs and Substitution
- Systems of Equations: Elimination and Comparing Methods

### Module #5

**Functions**

- Relations and Functions
- Rates of Change and Graph Behavior
- Shifts and Reflections of Functions
- Compressions and Stretches of Functions
- Function Operations
- Composition of Functions

### Module #6

**Sequences and Series**

- Sequences and Sequence Notation
- Arithmetic Sequences
- Geometric Sequences
- Series and Series Notation

### Module #7

**Factoring Polynomials**

- Factoring Using GCF and Grouping
- Factoring Trinomials: Part 1
- Factoring Special Product Trinomials
- Factoring Trinomials: Part 2
- General Strategy for Factoring Polynomials

### Module #8

**Quadratic Equation Essentials**

- Radical and Rational Operations
- Square Root Property
- Solutions of Quadratics Using Factoring

### Module #9

**Solving and Graphing Quadratics**

- Completing the Square
- Quadratic Formula
- Graphing a Parabola
- Graphing Quadratic Functions Using Transformations

### Module #10

**Matrices**

- Matrix Operations
- Solving Systems of Equations Using Matrices
- Solving Systems of Linear Equations With Three Variables
- Cramer’s Rule

### Module #11

**Polynomial Functions**

- Power and Polynomial Functions
- Graphing Polynomial Functions
- Dividing Polynomials
- Real Zeros of Polynomial Functions

### Module #12

**Rational Functions**

- Simplifying, Multiplying, and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Rational Functions
- Inverses and Radical Functions

### Module #13

**Exponential Functions**

- Exponential Functions
- Interest, Growth, and Decay
- Graphs of Exponential Functions

### Module #14

**Logarithmic Functions**

- Logarithmic Functions
- Graphs of Logarithmic Functions
- Logarithm Rules
- Solving Logarithmic and Exponential Equations

### Module #15

**Analytic Geometry (Conics)**

- The Circle
- The Parabola
- The Ellipse
- The Hyperbola
- Solving Systems of Nonlinear Equations

## Lesson Features

Each of our lessons is designed as self-contained learning environment that provides all the context, explanation, and resources you need to learn about a specific topic. We give you the information you need in a format that helps you apply it in your daily life.

#### Context

Knowing why a topic matters and how it applies to your experience is an important part of learning anything. That’s why we make sure you have the proper context for the information we give you.

#### Video Overview

Every TEL Library lesson features a video overview of the information being presented. Our videos provide helpful text callouts and a downloadable transcript.

#### Readings

We provide two different readings that elaborate information related to the lesson topic. The first gives you essential, objective information while the second offers a deeper look at a specific sub-topic or a view of different perspectives.

#### Check Your Knowledge

Developing a clear understanding of a topic generally requires that you spend time reflecting on the meaning or impact of its concepts and information. We facilitate this reflection with polls designed to help you create connections to the topic.

#### Glossary

It’s easy to get tripped up on unfamiliar terms when you’re trying to learn something new. We’ve developed in-line glossary definitions of key terms to help make lessons easier to read and understand.

#### Toolbox Resources

We know that our lessons are simply a starting point for many learners. That’s why we provide a toolbox with related web resources for each lesson so that you can continue your learning journey on a specific topic.