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For more information, please see full course syllabus of Pre Calculus

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### Introduction to Precalculus

• Depending on the school or institution providing this course, this class can go by a wide variety of different names:
• Pre-Calculus
• Math Analysis
• Trigonometry
• Algebra III
• Geometry II
• College Algebra
Still, all these names imply the same basic set of concepts: those that are essential for science classes and form the necessary foundation for calculus if you decide to continue in math. This is what we'll cover throughout these lessons.
• Each lesson introduces the concepts, works out the ideas involved, explains how to use them, and then gives a wide variety of examples. We'll also regularly work through word problems.
• This course was designed for a wide variety of students:
• Those who are taking one of the previously mentioned classes and who want some extra help.
• People working on the material but who aren't taking a formal class at a school.
• Anyone who needs a refresher on the concepts, whether it's for science class or another math class.
In short, anyone who needs help with the concepts contained in this course. Because the lessons combine an understanding of the material with step-by-step working through examples, this course is great for students with diverse needs.
• When watching the lessons, try to watch the whole lesson. While it can be tempting to skip straight to the examples, you'll gain a lot more understanding if you make sure the concepts make sense before working problems.
• It's very important to understand ideas that have come up in previous math classes. Very often, students have trouble not because what they're currently learning is confusing, but because they didn't fully understand past concepts. If this is true for you, use Educator.com to review the material that keeps giving you trouble. It will help a lot in the long run.
• For everyone, make sure you watch these two lessons first:
• Lesson #2: Sets, Elements, and Numbers
• Lesson #7: Idea of a Function
The ideas contained in those lessons are extremely important, but some teachers don't do a very good job explaining them. As such, I want to make sure you understand them as soon as possible.
• If you find yourself struggling with word problems, check out the lesson
• Lesson #6: Word Problems
• If you've had a lot of difficulty with previous math classes, the first seven lessons after this one form a review of important concepts:
• Lesson #2: Sets, Elements, and Numbers
• Lesson #3: Variables, Equations, and Algebra
• Lesson #4: Coordinate Systems
• Lesson #5: Midpoint, Distance, the Pythagorean Theorem, and Slope
• Lesson #6: Word Problems
• Lesson #7: Idea of a Function
• Lesson #8: Graphs
The ideas in these lessons form a foundation for much of the course. If you can make sense of them, you'll be in a good position for understanding what comes later on.
• At the very end of the course is an appendix dedicated to learning how to use graphing calculators. It's got a lot of useful stuff, so check it out. We'll go over a bunch of free options as well, so it's useful even if you don't own a graphing calculator right now.

### Introduction to Precalculus

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Title of the Course 0:06
• Different Names for the Course
• Precalculus
• Math Analysis
• Trigonometry
• Algebra III
• Geometry II
• College Algebra
• Same Concepts
• How do the Lessons Work? 0:54
• Introducing Concepts
• Apply Concepts
• Go through Examples
• Who is this Course For? 1:38
• Those Who Need eExtra Help with Class Work
• Those Working on Material but not in Formal Class at School
• Those Who Want a Refresher
• Try to Watch the Whole Lesson 2:20
• Understanding is So Important 3:56
• What to Watch First 5:26
• Lesson #2: Sets, Elements, and Numbers
• Lesson #7: Idea of a Function
• Lesson #6: Word Problems
• What to Watch First, cont. 6:46
• Lesson #2: Sets, Elements and Numbers
• Lesson #3: Variables, Equations, and Algebra
• Lesson #4: Coordinate Systems
• Lesson #5: Midpoint, Distance, the Pythagorean Theorem and Slope
• Lesson #6: Word Problems
• Lesson #7: Idea of a Function
• Lesson #8: Graphs
• Graphing Calculator Appendix 7:40
• What to Watch Last 8:46
• Let's get Started! 9:48

### Transcription: Introduction to Precalculus

Hi--welcome to Educator.com?0000

For our first lesson, we are going to have a quick introduction to the course.0002

What is this course called? Depending on the school you attend, this course goes by a wide variety of different names:0005

Precalculus, Math Analysis...it might be called Math Analysis with Trigonometry, or simply Trigonometry...0011

It might be called Precalculus and Trigonometry; it could be called Algebra III; it might be called Geometry II;0017

it might be called Algebra III and Geometry II; it might be called College Algebra (if you are in a college course);0022

it might be called College Algebra with Trigonometry; and it might be called something different from all of these.0028

It has a lot of names, sadly; but still, all of these different names imply basically the same set of concepts.0033

Those that are essential for science classes, and those that form the necessary foundation for calculus, if you decide to continue in math--0039

those are all the concepts that this course on Educator.com will work through.0046

So, how do the lessons work? Each lesson starts off by introducing the concepts.0051

We will make sense of the ideas involved, and we will say how they connect to what we have previously learned.0055

After we have a sense for what we are working on, we will learn how to apply these new concepts,0059

whether it is through new formulas or methods for solving problems, or just a new way of thinking.0064

We will come to understand how to use it.0069

Not only will we learn how to use the concepts, though; we will also learn why they work, and why they make sense,0071

so we can do more than just do problems; we can also actually understand what is going on and work on later concepts with that.0077

Finally, we will end each lesson by working through a wide variety of examples, so we can see the concepts in action.0084

Plus, most lessons will contain at least one word problem to help us see how to apply math in the real world.0091

Who is this course for? In short, anyone who needs help with the concepts contained in this course.0097

This course was designed and created with many different types of students in mind.0102

It is for those who are taking one of those previously mentioned classes, and they just want some extra help.0106

It is also for people working on the material, but who aren't taking a formal class at a school,0111

and anyone who just needs a refresher on the concepts, whether it is for a science class or another math class that they are taking.0116

Because the lessons combine an understanding of the material with step-by-step working through examples,0122

this course is great for students with diverse needs; it can help a whole bunch of different people, because it really teaches the whole thing.0127

When watching lessons, some students will just skip straight to the examples and only watch enough so that they can do their homework.0135

I want to urge you against doing this.0141

While this can work for getting homework done in the short term, it quickly falls apart in the long term.0144

So much of math builds upon previous ideas.0150

If you don't really understand what is happening now, understanding later concepts will be extremely difficult.0153

Because so many things are built "stair-step" after another, if you don't really understand what is happening today,0161

you might be able to get through the homework; but getting through other work in a couple of months0166

is going to become really, really difficult; it might become almost impossible.0170

The best thing you can do for your future understanding is to focus on more than just doing homework problems.0173

Watch the whole lesson, and make sure that the concepts are truly clear to you.0180

You really want to have an understanding of everything that is going on, not just how to do problems.0185

This helps, not just today, but later as well: this gives you the ability to understand what is going to happen in a few months or a few years.0190

And of course, if you already understand the concepts, and you just want some guidance on doing the problems, by all means, skip away.0198

But if you don't quite understand what is going on--you don't really see how the concepts work--0204

try to watch the whole lesson, because that will give you a much better understanding of how those examples work.0208

It is like the difference between teaching someone to fish and just handing them a fish.0213

You can either teach them a skill for the rest of their life, that they can use as long as they need it; or you can just feed them today.0217

If you end up only going to the examples, you are able to eat today, but you won't necessarily be able to "eat" in the long term.0223

And I want to teach you as much as I can, so you can really understand, and eventually be fine without needing any outside help.0229

In the same way, it is so important to understand the ideas that have come up in previous math classes.0236

We will do a fair bit of review in this course, but occasionally that will not be quite enough sometimes.0242

I have taught many students who understand the material that they are currently working on,0247

but they keep missing problems, because they don't fully understand past concepts--things that they learned previously.0252

They understand the new stuff--all of the new stuff that they are working on makes sense.0259

They get the ideas; they can do the problems; but these old ideas, like canceling negatives,0262

or working with fractions--things like that--just keep coming up, and they mess them up,0267

and they end up not being able to get problems right, not because they don't understand the big, new, complicated idea,0270

but because they don't understand this old, little thing that they never quite fully worked out back then.0276

If you find yourself having similar problems, go back and re-learn whatever is giving you trouble.0280

You have access to all of Educator.com here; that is a great resource.0285

You have all of this material in other courses at hand, so that you can easily review whatever ends up giving you trouble now.0289

If you notice that you keep missing the same kinds of problems--you keep making some mistake with some specific thing--0296

search it on Educator.com and try to re-learn that portion.0301

Once you have that under your belt, you will be able to stop making mistakes on that, and you won't have to worry about those things catching you.0304

It is not necessarily all about not understanding what is happening today.0310

You might understand perfectly what is going on and the things you are learning right now.0313

But because of this one little thing that you didn't fully understand previously, it keeps tripping you up.0316

But if you go back and re-learn it, you will be in a great position.0321

For everyone, I highly, highly recommend starting by watching the two lessons here:0325

Lesson #2 (Sets, Elements, and Numbers), and Lesson #7 (Idea of a Function).0330

The concepts in these two show up all over math, and some teachers don't do a very good job of explaining them, sadly.0336

Since they are so important and so common, I want to make sure that they make sense to you as soon as possible.0346

So, I really want you to have a chance to watch these early on, so that the later things that build on these ideas make as much sense to you as possible.0352

Also, if you have difficulty with word problems, check out the fifth lesson (unsurprisingly name "Word Problems").0361

It is not a terribly creative title, but "Word Problems" is this lesson that will help you see how to understand word problems and how to approach them.0367

It will build this framework for approaching all word problems.0374

That is something that you can start using on anything where you are having difficulty seeing how to set it up.0377

If you don't have time to watch any of these right now, that is perfectly OK.0381

Just try to come back and watch them in the next couple of weeks.0386

These ideas are crucial, and it will make a lot of things easier later on, once you have a good understanding of them.0390

It is not something you have to get done instantly.0396

But by having it done as soon as you can, you will end up being able to understand later things much more easily.0399

If you have had difficulty in previous math classes--if math class has been a little difficult for you--0405

you might want to watch the first seven lessons, because they form a review of important concepts:0409

Lesson #2 is Sets, Elements, and Numbers; #3 is Variables, Equations, and Algebra.0414

4 is Coordinate Systems; 5 is Midpoint, Distance, the Pythagorean Theorem, and Slope.0420

6 is Word Problems (I guess that should have been the sixth lesson previously; sorry about that).0425

Lesson #7 is Idea of a Function; and Lesson #8 is Graphs.0431

The ideas in these lessons form a foundation for much of the course.0435

If you can make sense of them, you will be in a good position for understanding what comes later on.0439

So, you really want to make sure that these ideas make sense to you,0443

because if they don't quite make sense to you right now, later stuff is going to be really hard.0446

But we will do a lot of review in these beginning review pieces, so that they will give you the chance to really understand what happens later on.0450

At the end of this course, there is an appendix all about graphing calculators and graphing programs.0459

But just because it comes last, just because it comes at the end of the course, doesn't mean you should wait to watch that.0464

You should watch it as soon as you have the chance--as soon as you are interested in it.0469

By this stage in your mathematics career, you might be considering purchasing a graphing calculator, or you might already own one.0473

The appendix will help you get started.0479

It has recommendations for buying one; it goes over the basics of use; and it explores some of the more advanced abilities for graphing calculators.0481

And even if you don't want to buy a graphing calculator--even if you know for sure that you are not going to buy a graphing calculator0488

(you just don't feel like spending the money), I recommend checking out the first lesson in the appendix.0494

We start that lesson by looking at a bunch of free options.0498

And it can really help to know that these things are available, and that you can have them on any computer really, really easily.0502

Having access to a graphing calculator, something that you can graph with, can make a lot of problems a whole lot easier.0507

It helps you really quickly build up an intuition that just doing these things by hand can't get you very quickly.0512

So, I really recommend checking out that first lesson; see some of the free options, even if you aren't interested in buying a graphing calculator.0517

Finally, what do you want to watch at the very end of the course?0524

At the end of this course is a short section that gives a preview of calculus.0527

Some math classes at various schools will work through this section, but others will simply skip it.0531

Either way, if you eventually plan on continuing to calculus, I recommend watching it at some point.0537

Being exposed to the ideas of calculus before actually being in a class--0543

before actually making it to a calculus class--can really help things click into place later.0549

Plus, calculus is really cool! I think calculus is really interesting to learn about.0554

You will probably want to watch it once you have worked through most of the rest of the course, though,0558

since it builds on previous ideas (so it is useful to have that foundation already there before you watch it).0561

And of course, you should still feel totally free to watch this, even if you don't plan to take calculus.0567

I think this stuff is really interesting, and it gives you a chance to watch this stuff0572

and be able to understand something that you might not get exposed to otherwise.0576

I think calculus is really cool, so if you are a little bit interested, even if you don't think you will take calculus,0580

you might want to check it out, because it is really cool stuff.0584

All right, that finishes it for this time--we are done with our housekeeping.0587

Now that you have a sense of how the course works, let's dive into it!0590

I hope you enjoy this course and learn a lot.0592

I put a lot of effort into this to give you the best understanding of the concepts that I possibly could.0594

I am looking forward to teaching it--all right, let's go!0598

I will see you at Educator.com later; goodbye!0601