Math 105: Precalculus Algebra
About the Course
Topics covered in this precalculus algebra course range from basic mathematical modeling to an introduction to derivatives. You'll learn to solve various types of equations and inequalities both symbolically and graphically.
The experienced, knowledgeable instructors for this precalculus algebra course have developed several video lessons for you to view. Each category, such as complex numbers or geometry basics, is divided into several chapters, allowing the concepts to be presented more in depth. Each lesson also gives you the opportunity to test your knowledge through quizzes and practice exams.
|Mathematical Modeling||Write and solve equations that relate a 2-dimensional figure's side lengths, perimeter and area. Write and solve real-life models, such as cost determination and d=rt. Evaluate economic equilibrium and profit functions from linear models. Find minimum and maximum values of quadratic models.|
|Linear Equations & Inequalities||Graph and write linear equations. Use point-slope formula to find the equation of a line. Graph 1- and 2-variable inequalities. Use a system of equations.|
|Quadratic Functions||Factor quadratic equations. Complete the square. Solve quadratic equations by factoring or by using the quadratic formula. Graph quadratic inequalities and systems of quadratic inequalities and identify the regions that satisfy the inequalities or systems.|
|Rational Expressions & Functions||Add, subtract, multiply and divide rational expressions. Solve rational equations. Graph rational functions that consist of polynomials of various degrees. Identify asymptotes, domain and range algebraically and graphically.|
|Polynomial Functions of a Higher Degree||Add, subtract, multiply and divide polynomials. Identify and evaluate polynomials in quadratic form. Factor polynomials using the remainder, factor and rational zero theorems as well as synthetic division. Determine how many solutions a polynomial has based on the degree of the polynomial. Write a polynomial equation using given zeros of a function and the concept of complex conjugate pairs.|
|Absolute Value Equations & Inequalities||Evaluate absolute value expressions. Solve and graph absolute value equations and inequalities.|
|Complex Numbers||Add, subtract, multiply and divide complex numbers. Graph complex numbers on the complex plane. Solve quadratics with complex numbers as the solution.|
|Geometry Basics||Determine the area and circumference of a circle. Graph circles. Rewrite a general second-degree equation in standard form. Use the distance and midpoint formulas.|
|Functions Overview||Graph basic functions. Determine the domain and range of a function. Write and graph power functions. Graph square root and cube root functions. Graph and find the domain of piecewise functions. Shift graphs on a plane.|
|Function Operations||Add, subtract, multiply and divide functions. Graph functions of functions. Understand how the domain and range of one function affects the domain and range of another function. Graph inverse functions. Identify 1-to-1 functions algebraically and graphically. Recognize the relationship between domain and range of a 1-to-1 function and its inverse.|
|Graph Symmetry||Detect symmetry graphically, numerically and algebraically. Define even and odd functions algebraically and identify them graphically.|
|Exponential & Logarithmic Functions||Translate an exponential function horizontally and vertically. Define the natural base and graph natural base functions. Evaluate logarithms. Rewrite logarithmic equations in exponential form and vice versa. Graph a logarithmic function and identify its vertical asymptote, domain and range. Solve logarithmic and exponential equations. Use the change-of-base formula to evaluate logarithmic expressions. Calculate rate and exponential growth.|
|Introduction to the Derivative||Learn about velocity and rate of change as well as slopes and rate of change.|
100% developed This course is fully developed. You can use the lessons in this course to study for exams and supplement your learning right now.
All Videos in Mathematical Modeling
- 1. Writing & Evaluating Algebraic Expressions for Two-Dimensional Geometric Figures: Lesson & Quiz
- 2. Writing & Evaluating Real-Life Linear Models: Process & Examples
- 3. Applying Systems of Linear Equations to Breakeven Point: Steps & Example
- 4. Applying Systems of Linear Equations to Market Equilibrium: Steps & Example
- 5. Using Quadratic Models to Find Minimum & Maximum Values: Definition, Steps & Example
All Videos in Linear Equations & Inequalities
- 1. What is a Linear Equation?
- 2. Linear Equations: Intercepts, Standard Form and Graphing
- 3. Abstract Algebraic Examples and Going from a Graph to a Rule
- 4. Graphing Undefined Slope, Zero Slope and More
- 5. How to Write a Linear Equation
- 6. Equation of a Line Using Point-Slope Formula
- 7. What is an Inequality?
- 8. How to Graph 1- and 2-Variable Inequalities
- 9. Graphing Inequalities: Practice Problems
- 10. What is a System of Equations?
- 11. How Do I Use a System of Equations?
All Videos in Quadratic Functions
- 1. What is a Parabola?
- 2. Parabolas in Standard, Intercept, and Vertex Form
- 3. How to Factor Quadratic Equations: FOIL in Reverse
- 4. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient
- 5. How to Complete the Square
- 6. Completing the Square Practice Problems
- 7. How to Solve a Quadratic Equation by Factoring
- 8. How to Use the Quadratic Formula to Solve a Quadratic Equation
- 9. How to Solve Quadratics with Complex Numbers as the Solution
- 10. Graphing & Solving Quadratic Inequalities: Examples, Lesson & Quiz
- 11. Graphing a System of Quadratic Inequalities: Examples, Lesson & Quiz
All Videos in Rational Expressions and Functions
- 1. How to Multiply and Divide Rational Expressions
- 2. Multiplying and Dividing Rational Expressions: Practice Problems
- 3. How to Add and Subtract Rational Expressions
- 4. Practice Adding and Subtracting Rational Expressions
- 5. How to Solve a Rational Equation
- 6. Horizontal and Vertical Asymptotes
- 7. Graphing Rational Functions That Have Linear Polynomials: Steps & Examples
- 8. Graphing Rational Functions That Have Polynomials of Various Degrees: Steps & Examples
- 9. Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range
All Videos in Polynomial Functions of a Higher Degree
- 1. How to Add, Subtract and Multiply Polynomials
- 2. Factoring Polynomials Using Quadratic Form: Steps, Rules & Examples
- 3. How to Divide Polynomials with Long Division
- 4. How to Use Synthetic Division to Divide Polynomials
- 5. Remainder Theorem & Factor Theorem: Definition & Examples
- 6. Dividing Polynomials with Long and Synthetic Division: Practice Problems
- 7. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division
- 8. Fundamental Theorem of Algebra: Explanation and Example
- 9. Using Rational & Complex Zeros to Write Polynomial Equations: Lesson & Quiz
All Videos in Absolute Value Equations & Inequalities
- 1. What is an Absolute Value?
- 2. How to Evaluate Absolute Value Expressions
- 3. How to Solve an Absolute Value Equation
- 4. Solving Absolute Value Practice Problems
- 5. How to Graph an Absolute Value and Do Transformations
- 6. Graphing Absolute Value Equations: Dilations and Reflections
- 7. How to Solve and Graph an Absolute Value Inequality
- 8. Solving and Graphing Absolute Value Inequalities: Practice Problems
All Videos in Functions Overview
- 1. What is a Function: Basics and Key Terms
- 2. Functions: Identification, Notation & Practice Problems
- 3. Graphing Basic Functions
- 4. What Is Domain and Range in a Function?
- 5. What is a Power Function? - Definition, Equations, Graphs & Examples
- 6. What is a Radical Function? - Definition, Equations & Graphs
- 7. Discontinuities in Functions and Graphs
- 8. How to Graph Piecewise Functions
- 9. How to Find the Domain of Piecewise Functions
- 10. Transformations: How to Shift Graphs on a Plane
All Videos in Function Operations
- 1. How to Add, Subtract, Multiply and Divide Functions
- 2. How to Compose Functions
- 3. Applying Function Operations Practice Problems
- 4. Compounding Functions and Graphing Functions of Functions
- 5. Domain & Range of Composite Functions: Definition & Examples
- 6. Inverse Functions
- 7. Understanding and Graphing the Inverse Function
- 8. One-to-One Functions: Definitions and Examples
All Videos in Graph Symmetry
All Videos in Exponential and Logarithmic Functions
- 1. What Is an Exponential Function?
- 2. Exponential Growth vs. Decay
- 3. Transformation of Exponential Functions: Examples, Lesson & Quiz
- 4. Using the Natural Base e: Definition, Lesson & Quiz
- 5. What is a Logarithm?
- 6. How to Evaluate Logarithms
- 7. Writing the Inverse of Logarithmic Functions: Lesson & Quiz
- 8. Exponentials, Logarithms & the Natural Log
- 9. Basic Graphs & Shifted Graphs of Logarithmic Functions: Definition & Examples
- 10. Logarithmic Properties
- 11. Practice Problems for Logarithmic Properties
- 12. How to Solve Logarithmic Equations
- 13. Using the Change-of-Base Formula for Logarithms: Definition & Example
- 14. How to Solve Exponential Equations
- 15. Calculating Rate and Exponential Growth: The Population Dynamics Problem
Education Portal's 53 instructors bring a diverse array of experience and expertise to each course. From teaching philosophy in Athens, Greece, to exploring the mystery of genetics, each instructor is uniquely qualified to bring students the best online learning experience possible. Meet them now!
If you have a general question about Education Portal, please contact customer support.