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Pre-Calculus Simplified
Learn Pre-Calculus step by step through the exactly same course Mr. McLogan taught inside of the classroom
Functions including identifying the domain and range, piecewise functions, operations such as composition and finding inverses
Polynomials including, graphing, solving, factoring, multiplicity, synthetic long division, long division and theorems
Rational Functions including vertical, horizontal and oblique asymptotes, finding holes, operations and complex fractions
Trigonometry including right triangles, six trigonometric functions, graphing and and evaluating trigonometric functions
Analytic Trigonometry including solving, simplifying, verifying, and evaluating trigonometric functions using trig identities
Applications of Trigonometry including law of sines/cosines, vectors, parametric and polar equations
Analytic Geometry including graphing and writing the equation of paraboloas, circles, ellipses, and hyperboolas
The limit including evaluating, general, left hand, right hand, and limits at infinity from a graph or equation
After spending years creating new lesson plans every day I decided to record my lesson so that my student and you could benefit from them, if you are sick, need a refresher, or just want to learn on your own.
In this I will break down the sections into a warmup or intro, notes, examples and then homework. You will have plenty of practice problems to try on your own, check your answers or watch me complete. In addition to the assinged work, you will also have online quizzes to test your skills after each section and topic.
In addition to online quizzes I also provide the full print out version of test and quizzes I gave to my students in addition to the semester and final exam review and actual tests.
While Pre-calculus courses can vary in this pre-calculus course I will cover Functions, Polynomials, Rational Expressions, Trigonometry, Analytic Trigonometry, Applications of Trigonometry, Analytic Geometry and the Limit. You will have everything you will need to know as either a refresher of pre-calculus or to move on to calculus. I hope you enjoy!!
Now you have everything you would need to learn or maybe even teach Pre-Calculus.
You Ready? Lets do this!
2.) Polynomials
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1.) IntroductionWelcome to Functions our first chapter in Pre-Calculus Simplified. Below you will see our Assignment Organizer, Checklist and Notes to download and/or print.
The assignment organizer is used within my class to record students completion of work in addition to add goals and reflect on the unit.
The checklist is provided to give context to the types of problems that students will need to know for each section
Lastly, the notes provide a condensed version of the notes that are provided within the chapter. Even though each section has detailed guided notes provided the condensed notes keep everything taught in the chapter in one place.
Assignment Organizer
Checklist
Notes
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1.) What You Need to Know
Before we get into the meat of this chapter, we want to make sure we remember some of the basics. This worksheet is designed to provide you will a successful foundation for our unit on functions.
Give it a shot and when you get stuck refer to the video or provided answers.
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1a.) Intro Characteristics of Functions
In this lesson we will explore the characteristics that make up functions. We will focus on the characteristics of functions based on their graphs. This is to include, domain and range, boundness, even and odd, discontinuities, increasing, decreasing constant intervals, extrema, and intercepts.
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1a.) Notes Characteristics of Functions
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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1a.) Examples Characteristics of Functions
In this lesson we will practice identifying the characteristics that make up functions. We will focus on the characteristics of functions based on their graphs. This is to include, domain and range, boundness, even and odd, discontinuities, increasing, decreasing constant intervals, extrema, and intercepts.
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1a.) Homework Characteristics of Functions
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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1a.) Quiz Characteristics of FunctionsIt is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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1b.) Intro Implied Domain
In this lesson we will explore how to determine the implied domain of a function. We will do this by focusing on two restrictions of functions. Not dividing by zero and not taking the square root of a negative number. We will work through problems where there are 1, 2, 3 or no restrictions on the domain.
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1b.) Notes Implied Domain
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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1b.) Examples Implied Domain
In this lesson we will practice how to determine the implied domain of a function. We will do this by focusing on two restrictions of functions. Not dividing by zero and not taking the square root of a negative number. We will work through problems where there are 1, 2, 3 or no restrictions on the domain.
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1b.) Homework Implied Domain
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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1b.) Quiz Implied Domain
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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1c.) Intro Transformation of Functions
In this lesson we will explore the basic transformations of functions such as stretch, compression, reflections, horizontal and vertical shifts. This transformations will be applied an identified to the 12 basic functions. Not only will we understand the transformation but how they impact the graph of each function as well as their domain and range.
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1c.) Notes Transformations of Functions
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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1c.) Examples Transformations of Functions
In this lesson we will practice identifying the basic transformations of functions such as stretch, compression, reflections, horizontal and vertical shifts. This transformations will be applied an identified to the 12 basic functions. Not only will we understand the transformation but how they impact the graph of each function as well as their domain and range.
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1c.) Homework Transformations of Functions
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation
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1c.) Quiz Transformations of Functions
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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1.) Quiz #1
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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1d.) Intro Piecewise Functions
In this lesson we will explore how to graph and evaluate piecewise functions. by graphing we will be able to understand the domain, range and discontinuities. We will further explore the types of piecewise functions that create jump, removable and infinite discontinuities. This will allow us to understand why and how to evaluate piecewise functions for any given value.
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1d.) Notes Piecewise Functions
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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1d.) Examples Piecewise Functions
In this lesson we will practice how to graph and evaluate piecewise functions. by graphing we will be able to understand the domain, range and discontinuities. We will further explore the types of piecewise functions that create jump, removable and infinite discontinuities. This will allow us to understand why and how to evaluate piecewise functions for any given value.
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1d.) Homework Piecewise Functions
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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1d.) Quiz Piecewise Functions
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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1e.) Intro Operations of Functions
In this lesson we will explore how to apply operations such as addition, subtraction, multiplication, division and composition between two functions and then identify how the domain has been impacted.
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1e.) Notes Operations of Functions
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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1e.) Examples Operations of Functions
In this lesson we will practice how to apply operations such as addition, subtraction, multiplication, division and composition between two functions and then identify how the domain has been impacted.
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1e.) Homework Operations of Functions
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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1e.) Quiz Operations of Functions
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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1f.) Intro Inverse of Functions
In this lesson we will explore how to determine the inverse of a function. We will focus on finding the inverse of linear, rational, cubic, quadratic, square root and cube root functions. The purpose behind finding the inverse is to understand the relationship between a function and it's inverse as well as to understand the relationship of the domain and range.
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1f.) Notes Inverse of Functions
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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1f.) Examples Inverse of Functions
In this lesson we will practice how to determine the inverse of a function. We will focus on finding the inverse of linear, rational, cubic, quadratic, square root and cube root functions. The purpose behind finding the inverse is to understand the relationship between a function and it's inverse as well as to understand the relationship of the domain and range.
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1f.) Homework Inverse of Functions
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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1f.) Quiz Inverse of Functions
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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1.) Quiz #2
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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1.) Review and Test
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
3.) Rational Functions
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2.) Introduction
You'll learn to write, graph and determine the zeros of a function so that you can solve any polynomial.
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2.) What You Need to Know
Before we get into the meat of this chapter, we want to make sure we remember some of the basics. This worksheet is designed to provide you will a successful foundation for our unit on Polynomials.
Give it a shot and when you get stuck refer to the video or provided answers.
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2a.) Intro Characteristics of Polynomials
Welcome to Characteristics of Polynomials. Learn how to identify the parts that make up a polynomial so that you can understand how to find those parts algebraically.
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2a.) Notes Characteristics of Polynomials
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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2a.) Examples Characteristics of Polynomials
In this lesson we will cover the characteristics that make up a polynomial. Specifically we will explore the zeros, end behavior, multiplicity and intercepts of polynomials. We will focus this lesson of determining the characteristics from equations in factored form and graphs.
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2a.) Homework Characteristics of Polynomials
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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2a.) Quiz Characteristics of Polynomials
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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2b.) Intro Binomial Expansion
Welcome to Binomial Expansion. Learn how to expand a binomial as well as complete the square so that you can better understand binomials raised to a power to represent a function.
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2b.) Notes Binomial Expansion
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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2b.) Examples Binomial Expansion
In this lesson we will cover how to expand a binomial raised to a power. We will do this by applying binomial expansion and Pascal's Triangle. In addition to expanding a binomial to identify the full expansion or a given term, we will learn how to create binomials by completing the square.
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2b.) Homework Binomial Expansion
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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2b.) Quiz Binomial Expansion
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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2c.) Intro Real Rational Zeros of Polynomials
Welcome to Real Rational Zeros of Polynomials. Learn how to find the real rational zeros of a polynomial algebraically so that you can build the essential skills for solving polynomials as well as understanding the zeros of a polynomial.
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2c.) Notes Real Rational Zeros of Polynomials
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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2c.) Examples Real Rational Zeros of Polynomials
Let's get to work. I can't do every type of example but hand selected these to give you the most value for the least amount of your time. You can always refer back to the guided notes if you need more examples but what I cover here will get you started.
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2c.) Homework Real Rational Zeros of Polynomials
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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2c.) Quiz Real Rational Zeros of Polynomials
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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2.) Quiz #1
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2d.) Intro Real Irrational Zeros of Polynomials
Welcome to Real Irrational Zeros of Polynomials. Learn how to find the real irrational zeros of a polynomial by using factoring, quadratic formula, synthetic and long division so you can apply the factor and remainder theorem.
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2d.) Notes Real Irrational Zeros of Polynomials
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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2d.) Examples Real Irrational Zeros of Polynomials
In this lesson, we will cover how to determine the irrational zeros of a polynomial. We will begin the lesson with finding the zeros by factoring but then pivot to using long and synthetic division to help determine all the zeros of a polynomial. We will conclude the lesson by introducing the factor and remainder theorem.
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2d.) Homework Real Irrational Zeros of Polynomials
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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2d.) Quiz Real Irrational Zeros of Polynomials
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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2e.) Intro Real Complex Zeros of Polynomials
Welcome to Real Complex Zeros of Polynomials. Learn how to find the complex zeros of a polynomial so that you can apply Fundamental Theorem of Algebra.
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2e.) Notes Real Complex Zeros of Polynomials
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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2e.) Examples Real Complex Zeros of Polynomials
In this lesson, we will cover how to determine the complex zeros of a polynomial. We will again begin by finding the zeros with factoring and then division. To round out the lesson as well as the chapter we will use the Rational Zero Test, Descartes Rule of Signs and the Fundamental Theorem of Algebra to better understand the lesson and overall concepts.
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2e.) Homework Real Complex Zeros of Polynomials
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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2e.) Quiz Real Complex Zeros of Polynomials
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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2.) Quiz #2 Print
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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2.) Quiz #2 Online
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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2.) Chapter Review and Old Tests
This chapter review includes not only a review to practice the content you have learned thus far but also old tests with answers for you to practice even more the types of problems you can expect.
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2.) Chapter Test Online
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
4.) Trigonometry
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3.) Introduction
You'll learn how to simplify, and graph rational functions so that you can solve rational equations.
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3.) What You Need to Know
Before we get into the meat of this chapter, we want to make sure we remember some of the basics. This worksheet is designed to provide you will a successful foundation for our unit on Rational Functions.
Give it a shot and when you get stuck refer to the video or provided answers.
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3a.) Intro Simplify Rational Expressions
Welcome to Simplify Rational Expressions! Learn how to simplify rational expressions so that you can identify the discontinuities as well as add, subtract, multiply and divide rational expressions.
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3a.) Notes Simplify Rational Expressions
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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3a.) Examples Simplify Rational Expressions
Let's get to work. I can't do every type of example but hand selected these to give you the most value for the least amount of your time. You can always refer back to the guided notes if you need more examples but what I cover here will get you started.
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3a.) Homework Simplify Rational Expressions
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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3a.) Quiz Simplify Rational Expressions
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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3b.) Intro Graph Rational Functions
Welcome to Graph Rational Functions! Learn how to graph rational functions so that you can identify the points and asymptotes of a rational function.
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3b.) Notes Graph Rational Functions
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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3b.) Examples Graph Rational Functions
Let's get to work. I can't do every type of example but hand selected these to give you the most value for the least amount of your time. You can always refer back to the guided notes if you need more examples but what I cover here will get you started.
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3b.) Homework Graph Rational Functions
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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3b.) Quiz Graph Rational Functions
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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3c.) Intro Solve Rational Equations
Welcome to Solve Rational Equations! Learn how to solve rational equations so that you are able to find and label extraneous solutions.
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3c.) Notes Solve Rational Equations
Print out the notes and/or guided notes and keep them by your side. They will be extremely helpful to refer to as I go through examples and you practice on your own.
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3c.) Examples Solve Rational Equations
Let's get to work. I can't do every type of example but hand selected these to give you the most value for the least amount of your time. You can always refer back to the guided notes if you need more examples but what I cover here will get you started.
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3c.) Homework Solve Rational Equations
Practice what you have learned with some examples both free response and multiple choice. You can work alone and check your answers with the provided worked out solutions or work out the problems with me by watching the video explanation.
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3c.) Quiz Solve Rational Equations
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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3.) Quiz #1 Print
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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3.) Quiz #1 Online
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
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3) Chapter Review and Old Tests
This chapter review includes not only a review to practice the content you have learned thus far but also old tests with answers for you to practice even more the types of problems you can expect.
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3.) Chapter Test Online
It is time to test your skills. Work through the following problems and check your understanding. Don't worry if you don't do well, you can take the assessment over and over until you get them right. Something I recommend anyways. Best of luck, you got this!
You can view and review the lecture materials indefinitely, like an on-demand channel.
Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!
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