Understanding Algebra Course Differences

What's the difference between Algebra 1, Algebra 2, College Algebra, and Pre-Calculus? If you look online through different textbooks or courses, you'll notice there's a tremendous amount of overlap. So what I'm going to do in this video is talk about what each course covers, talk about why there's different definitions for these courses, and I'll explain what you can do if you're a self-studier. So what courses should you take, and then what courses should you skip? All right, just so we can all be on the same page, I'm going to be using some free textbooks here. So I'm going back to the openstacks.org website. I'll leave a link for you in the description, but this is the one that I talked about previously. So go over to subjects, and then you're going to go to math. I'm just going to show you all the textbooks I'm going to be using for today's discussion. So just sliding down here, we have college algebra. So I'm going to be working with this college algebra 2E, then coming down to where it says developmental math, I'm going to be working with elementary algebra 2E, intermediate algebra 2E. I'm not going to work with... pre-algebra 2e, but you can grab it if you want. You'll be able to use the same thought process to look through that book. And then for pre-calculus, I'm going to take the pre-calculus 2e. Now, in terms of getting the book, you can just grab this right here and see where it says download a PDF. You can do it like that and just go to your file. And that's basically all you need to do. Now, this will allow you to read it on your device. If you want to download it to your device, come up here where it says download and just click that right there. All right, what I'm going to do to start things out is talk about the difference between Algebra 1 which is also called elementary algebra, and then Algebra 2, which is also called intermediate algebra. So I'm going to be using a textbook approach for this. What we're going to find is that all the topics that are taught in Algebra 1 are going to come up again in Algebra 2. It's just that you're going to go through them more quickly in Algebra 2. And in Algebra 2, you're going to go further than you did in Algebra 1. I'm going to go over here and start with just a table of contents and reading through that with you. So let's just first establish what's in Algebra 1. and different textbooks will have different topics. But this textbook right here, I'm going to say, is 95% similar to the other textbooks you would find. So it's not going to be an issue of which textbook you're using. So the first chapter in any Algebra 1 textbook, it's going to be Foundations, or you could say a Review chapter. These are just the things you learned before you get into Algebra. So what did you learn in elementary school? Operations with whole numbers, integers, decimals, fractions, things like that. Once you're done with this review, now the Algebra is going to start. So here you have a chapter on solving linear equations and inequalities. Then you have math models. So that's just word problems. In other words, that's where we take the solving a linear equation in one variable, also solving a linear inequality in one variable, and we look at application problems or word problems. Then we get down to graphs. So this is where we talk about graphing a linear equation into variables. We come to systems of linear equations. We get to operations with polynomials. We get to factoring polynomials. rational expressions and equations. We get to roots and radicals. And then we finish up with quadratic equations. If I go to my Algebra 2 textbook and I go to my table of contents, you're going to notice that it's pretty much the same thing as I just saw in Algebra 1. It's just that they're adding topics and the topics that they previously covered, they're going through very quickly. In other words, you have the same foundations here. So it's just a review of things that you need. And then you're coming to, again, solving linear equations. Okay, if we come over here, this was the second chapter, so solving linear equations and inequalities. What you'll notice is that if you focus in on this, if you want to read this on your own, notice that for 2.1, you have use a general strategy to solve linear equations. They're going to assume that you know something about solving a linear equation one variable, because in algebra one, they took one, two, three, four, and this one would be included there too. So five lesson plans to teach what's in one lesson plan here. If you go through this, you're thinking about... in algebra one, well, I've never seen anything before, so I've got to go slow. I've got to develop the concept over a long period of time. I'm going to start with solving equations using the subtraction and addition properties of equality. Then I'm going to go to using the division and multiplication properties of equality. Then I'm going to solve equations with variables and constants on both sides. Then I'm going to get to a general strategy, and then I'm going to talk about solving equations with fractions or decimals. Again, that's one, two, three, four, five lesson plans there that gets put into one in algebra two. So Algebra 2 covers every single thing that's in Algebra 1. It just goes through those foundational concepts more quickly. They do not give you the time that you need if you're a newcomer. You have to already know that stuff because you're rolling through things now. And then if you look at some additional things that they have here, they've added solve compound inequalities. They've also added solve absolute value inequalities. So these are things that are new for Algebra 2. They're typically not taught in Algebra 1. And you would not be able to make a textbook by putting just these things in here because you need the basis of being able to solve a linear inequality. You need that stuff in there for reference. As you continue through the book, you're going to see, again, you have graphs and functions. So here you have graphs. And if you come down here, you have systems of linear equations. And this is systems of linear equations. Here you have solve systems of linear equations by graphing, then substitution, then elimination. If you come to where it says systems of linear equations in algebra 2, that's all rolled into one lesson plan, 4.1, solve systems of linear equations in two variables. If you click on that, you're going to see that they're going to do graphing, substitution, and elimination all in one lesson plan now because they assume that you've already seen it before in Algebra 1. Then coming back, they're going to talk about some new things. They're going to talk about solving systems of equations with three variables. That is not covered in this Algebra 1 course. It typically is not. They're also going to introduce using matrices, using determinants, and I think they did talk about systems of linear inequalities. Yeah, so they do have that there. And then coming down, Again, you can go through this on your own and see all the things that they're adding. In other words, all we're saying is that when you look at this course versus the other one, it contains everything that was in that course. They're just adding on to it. And you'll also see that after quadratic equations and functions, now you're getting into some new topics. So exponential logarithmic functions, that's not in there. You have conic sections. You have sequences, series, and then the binomial theorem. All right, now let's talk about the difference between college algebra and precalculus. So this is one that causes a lot of confusion. And if you think about college algebra first... This is us just taking Algebra 1 and Algebra 2 and then just going further. So just like we started with Algebra 2 and I showed you it contained all the topics from Algebra 1, we just went further. Well, it's the same thing with College Algebra. This is going to be a very comprehensive course, so it contains everything from Algebra 1, Algebra 2, and you're going to see all the topics from Precalculus with the exception of a few topics that require trigonometry. So in my opinion, this is actually a terrible name for this book. It shouldn't be called College Algebra. It should just be called Algebra. In the same way that when you get a calculus book, it's just called calculus. They don't split it up into calculus 1, calculus 2, and calculus 3. We do that in the school system. You typically use the same book for calc 1, 2, and 3. A lot of people use the James Stewart book or the Larson book, but it doesn't say anywhere that we're leaving calculus 1 and entering calculus 2 or we're leaving calculus 2 and entering calculus 3. The book is just called calculus. So this book right here, a good title would just be algebra because it contains everything. It's a comprehensive book. But when we think about pre-calculus, this is where things get confusing because pre-calculus... contains algebra and trigonometry mixed. Some people refer to pre-calculus as the algebra from college algebra, starting with functions and moving forward. But pre-calculus really is just algebra mixed with trigonometry. So if we come down and we compare the table of contents for college algebra to pre-calculus, again, you're going to see that it's pretty much the same thing. This college algebra book does contain more algebra in it just because it's putting in the stuff from algebra one and algebra two, whereas the pre-calculus book will typically leave some of that stuff out. Not all of it, but some of it. So here you have your prerequisites. That's a lot of stuff from algebra one and two. You have equations and inequalities, and then you get to functions. So at the point where you get to functions, you're pretty much matching up perfectly with the precalculus. So you have functions, then linear functions. Here's your linear functions. Polynomial rational functions. Here's your polynomial rational functions. Exponential logarithmic functions. Here's your exponential logarithmic functions. Systems of equations and inequalities. Of course, you have trigonometry here. So here, here, here, and here. But after the trigonometry is done, you have a matching again. So system of equations and inequalities, systems of equations and inequalities. inequalities. Then you have your analytic geometry, analytic geometry, sequences, probability, and counting theory, sequences, probability, and counting theory. Then you have an additional thing in pre-calculus, which is introduction to calculus. So that's where you talk about limits and derivatives. But I'm just talking about the algebra between the college algebra course and the pre-calculus course. You'll notice that it's basically the same after functions. So if you wanted something that was very comprehensive in terms of algebra, that covered everything from algebra one, algebra two, and pre-calculus, you want to use a college algebra book. Again, that's a terrible name for that book. It shouldn't be called college algebra. It should just be called algebra. The reason it's called college algebra is because every university in the country has a course that's called college algebra that uses that book. Unfortunately, that's where it gets its title from. But a better title would just be algebra, covering everything. This pre-calculus here would be good for somebody who wants to learn all the algebra, I would say, excluding algebra one, because a lot of that stuff is left out, with trigonometry. So if you're doing a self-study, what I would do is I would plan on skipping two of these courses. So I would say that I would start with Algebra 1 because that's the foundation. Things go slow there. You have time to develop your skills. And then after that, I would skip Algebra 2 and I'd probably skip College Algebra. If I was looking to go into advanced math, if I was looking to go as far as I could, I would just get into Precalculus right away. So I would just take two courses there. Again, this is for somebody who's self-studying. If you were taking this in a classroom, well, your teacher knows what you already covered. And a lot of times they just skip a lot of the stuff. That's why you get a lot of disagreement from people online where they say, no, Algebra 2 covers only these topics, not according to the textbook. Again, that's based on you taking it in a classroom where your teacher looks at the textbook and says, no, you covered this in Algebra 1, I'm going to skip it. We're basing things off the textbook, that's our reference. And if you have any questions for me, just post a comment and I'm happy to answer.

So what courses should you take, and then what courses should you skip? All right, just so we can all be on the same page, I'm going to be using some free textbooks here. So I'm going back to the openstacks.org website. I'll leave a link for you in the description, but this is the one that I talked about previously.

So go over to subjects, and then you're going to go to math. I'm just going to show you all the textbooks I'm going to be using for today's discussion. So just sliding down here, we have college algebra. So I'm going to be working with this college algebra 2E, then coming down to where it says developmental math, I'm going to be working with elementary algebra 2E, intermediate algebra 2E.

I'm not going to work with... pre-algebra 2e, but you can grab it if you want. You'll be able to use the same thought process to look through that book. And then for pre-calculus, I'm going to take the pre-calculus 2e. Now, in terms of getting the book, you can just grab this right here and see where it says download a PDF.

You can do it like that and just go to your file. And that's basically all you need to do. Now, this will allow you to read it on your device. If you want to download it to your device, come up here where it says download and just click that right there.

All right, what I'm going to do to start things out is talk about the difference between Algebra 1 which is also called elementary algebra, and then Algebra 2, which is also called intermediate algebra. So I'm going to be using a textbook approach for this. What we're going to find is that all the topics that are taught in Algebra 1 are going to come up again in Algebra 2. It's just that you're going to go through them more quickly in Algebra 2. And in Algebra 2, you're going to go further than you did in Algebra 1. I'm going to go over here and start with just a table of contents and reading through that with you.

So let's just first establish what's in Algebra 1. and different textbooks will have different topics. But this textbook right here, I'm going to say, is 95% similar to the other textbooks you would find. So it's not going to be an issue of which textbook you're using. So the first chapter in any Algebra 1 textbook, it's going to be Foundations, or you could say a Review chapter.

These are just the things you learned before you get into Algebra. So what did you learn in elementary school? Operations with whole numbers, integers, decimals, fractions, things like that.

Once you're done with this review, now the Algebra is going to start. So here you have a chapter on solving linear equations and inequalities. Then you have math models. So that's just word problems.

In other words, that's where we take the solving a linear equation in one variable, also solving a linear inequality in one variable, and we look at application problems or word problems. Then we get down to graphs. So this is where we talk about graphing a linear equation into variables. We come to systems of linear equations. We get to operations with polynomials.

We get to factoring polynomials. rational expressions and equations. We get to roots and radicals.

And then we finish up with quadratic equations. If I go to my Algebra 2 textbook and I go to my table of contents, you're going to notice that it's pretty much the same thing as I just saw in Algebra 1. It's just that they're adding topics and the topics that they previously covered, they're going through very quickly. In other words, you have the same foundations here. So it's just a review of things that you need.

And then you're coming to, again, solving linear equations. Okay, if we come over here, this was the second chapter, so solving linear equations and inequalities. What you'll notice is that if you focus in on this, if you want to read this on your own, notice that for 2.1, you have use a general strategy to solve linear equations.

They're going to assume that you know something about solving a linear equation one variable, because in algebra one, they took one, two, three, four, and this one would be included there too. So five lesson plans to teach what's in one lesson plan here. If you go through this, you're thinking about... in algebra one, well, I've never seen anything before, so I've got to go slow. I've got to develop the concept over a long period of time.

I'm going to start with solving equations using the subtraction and addition properties of equality. Then I'm going to go to using the division and multiplication properties of equality. Then I'm going to solve equations with variables and constants on both sides.

Then I'm going to get to a general strategy, and then I'm going to talk about solving equations with fractions or decimals. Again, that's one, two, three, four, five lesson plans there that gets put into one in algebra two. So Algebra 2 covers every single thing that's in Algebra 1. It just goes through those foundational concepts more quickly.

They do not give you the time that you need if you're a newcomer. You have to already know that stuff because you're rolling through things now. And then if you look at some additional things that they have here, they've added solve compound inequalities. They've also added solve absolute value inequalities.

So these are things that are new for Algebra 2. They're typically not taught in Algebra 1. And you would not be able to make a textbook by putting just these things in here because you need the basis of being able to solve a linear inequality. You need that stuff in there for reference. As you continue through the book, you're going to see, again, you have graphs and functions. So here you have graphs.

And if you come down here, you have systems of linear equations. And this is systems of linear equations. Here you have solve systems of linear equations by graphing, then substitution, then elimination. If you come to where it says systems of linear equations in algebra 2, that's all rolled into one lesson plan, 4.1, solve systems of linear equations in two variables.

If you click on that, you're going to see that they're going to do graphing, substitution, and elimination all in one lesson plan now because they assume that you've already seen it before in Algebra 1. Then coming back, they're going to talk about some new things. They're going to talk about solving systems of equations with three variables. That is not covered in this Algebra 1 course.

It typically is not. They're also going to introduce using matrices, using determinants, and I think they did talk about systems of linear inequalities. Yeah, so they do have that there.

And then coming down, Again, you can go through this on your own and see all the things that they're adding. In other words, all we're saying is that when you look at this course versus the other one, it contains everything that was in that course. They're just adding on to it. And you'll also see that after quadratic equations and functions, now you're getting into some new topics. So exponential logarithmic functions, that's not in there.

You have conic sections. You have sequences, series, and then the binomial theorem. All right, now let's talk about the difference between college algebra and precalculus. So this is one that causes a lot of confusion. And if you think about college algebra first...

This is us just taking Algebra 1 and Algebra 2 and then just going further. So just like we started with Algebra 2 and I showed you it contained all the topics from Algebra 1, we just went further. Well, it's the same thing with College Algebra.

This is going to be a very comprehensive course, so it contains everything from Algebra 1, Algebra 2, and you're going to see all the topics from Precalculus with the exception of a few topics that require trigonometry. So in my opinion, this is actually a terrible name for this book. It shouldn't be called College Algebra. It should just be called Algebra. In the same way that when you get a calculus book, it's just called calculus.

They don't split it up into calculus 1, calculus 2, and calculus 3. We do that in the school system. You typically use the same book for calc 1, 2, and 3. A lot of people use the James Stewart book or the Larson book, but it doesn't say anywhere that we're leaving calculus 1 and entering calculus 2 or we're leaving calculus 2 and entering calculus 3. The book is just called calculus. So this book right here, a good title would just be algebra because it contains everything. It's a comprehensive book.

But when we think about pre-calculus, this is where things get confusing because pre-calculus... contains algebra and trigonometry mixed. Some people refer to pre-calculus as the algebra from college algebra, starting with functions and moving forward.

But pre-calculus really is just algebra mixed with trigonometry. So if we come down and we compare the table of contents for college algebra to pre-calculus, again, you're going to see that it's pretty much the same thing. This college algebra book does contain more algebra in it just because it's putting in the stuff from algebra one and algebra two, whereas the pre-calculus book will typically leave some of that stuff out.

Not all of it, but some of it. So here you have your prerequisites. That's a lot of stuff from algebra one and two. You have equations and inequalities, and then you get to functions.

So at the point where you get to functions, you're pretty much matching up perfectly with the precalculus. So you have functions, then linear functions. Here's your linear functions. Polynomial rational functions.

Here's your polynomial rational functions. Exponential logarithmic functions. Here's your exponential logarithmic functions.

Systems of equations and inequalities. Of course, you have trigonometry here. So here, here, here, and here.

But after the trigonometry is done, you have a matching again. So system of equations and inequalities, systems of equations and inequalities. inequalities. Then you have your analytic geometry, analytic geometry, sequences, probability, and counting theory, sequences, probability, and counting theory.

Then you have an additional thing in pre-calculus, which is introduction to calculus. So that's where you talk about limits and derivatives. But I'm just talking about the algebra between the college algebra course and the pre-calculus course.

You'll notice that it's basically the same after functions. So if you wanted something that was very comprehensive in terms of algebra, that covered everything from algebra one, algebra two, and pre-calculus, you want to use a college algebra book. Again, that's a terrible name for that book.

It shouldn't be called college algebra. It should just be called algebra. The reason it's called college algebra is because every university in the country has a course that's called college algebra that uses that book. Unfortunately, that's where it gets its title from. But a better title would just be algebra, covering everything.

This pre-calculus here would be good for somebody who wants to learn all the algebra, I would say, excluding algebra one, because a lot of that stuff is left out, with trigonometry. So if you're doing a self-study, what I would do is I would plan on skipping two of these courses. So I would say that I would start with Algebra 1 because that's the foundation.

Things go slow there. You have time to develop your skills. And then after that, I would skip Algebra 2 and I'd probably skip College Algebra. If I was looking to go into advanced math, if I was looking to go as far as I could, I would just get into Precalculus right away. So I would just take two courses there.

Again, this is for somebody who's self-studying. If you were taking this in a classroom, well, your teacher knows what you already covered. And a lot of times they just skip a lot of the stuff. That's why you get a lot of disagreement from people online where they say, no, Algebra 2 covers only these topics, not according to the textbook.

Again, that's based on you taking it in a classroom where your teacher looks at the textbook and says, no, you covered this in Algebra 1, I'm going to skip it. We're basing things off the textbook, that's our reference. And if you have any questions for me, just post a comment and I'm happy to answer.

Transcript for:Understanding Algebra Course Differences

Transcript for:
Understanding Algebra Course Differences