What is "Algebra 2" in the AoPS texts?

[daijobu]

I've been asked to teach "Algebra 2", and I want to use the AoPS textbooks.   Which chapters in Intro to Algebra and/or Intermediate Algebra would I need to cover at minimum?  Thank you!  

[dancingmama]

Intro to Algebra 11 to the end of the book iirc. But it's not exactly what would normally be covered and it's considered Honors level.

[Soror]

WTM Academy uses Intro to Alg. Chp. 11-22 for Alg. 2

 

It seems I've read on the forum that people add in some topics but I can't remember details right now.

[daijobu]

Will I need to add any chapters from the Intermediate Algebra textbook to make it a complete course?  

[Mike in SA]

It really is difficult to slice & dice AoPS this way.  There is content in the Intermediate book going up to about ch 14 (radicals) that you probably should cover.  However, there is content in early chapters (eg, Vieta's formulas) that is not normally covered in any algebra 2 course.  You could consider it a "College Algebra" course, because it goes so deep.

 

I seem to recall Kathy in Richmond posting a detailed sequence of what should be included in a prior post, but I couldn't find it.  I do know that the "second half" of Introduction will meet California's UC requirements, fwiw.  Odd thing is they consider Intermediate as equivalent to algebra 2 as well, which is nowhere close to reality.

 

If it were me, I'd look at the precalculus book I planned to use, and look for content in the first 75% of Intermediate that is not covered in the precalc book, and include some coverage of those topics.  ETA: Assuming here that AoPS Precalc is not your target precalc book.  If it is, then plan on doing more Intermediate as the first half of precalculus, and do the trig from AoPS as the second half. 

 

 

Edited August 10, 2017 by Mike in SA

[Soror]

Alright- I did some digging because I need the info for ds and I couldn't remember exactly what I had read. I'm adding links and copying and pasting so I can hopefully find it a little easier the next time I look. Ds likes AoPS but is not a fast worker so I've been researching to find out exactly what he needs and what we can safely cut out and still be prepared.

 

This is a link to another thread where regentrude talks about what is needed for Alg. 2

EL: for algebra 2, I believe polynomials are usually covered, which would be ch. 6-9 in Intermediate Algebra.

Also, ch. 13 on exponentials and logarithms which are only briefly touched on in Intro, and ch. 14 on radicals.

Ch. 1-4 in Intermediate are review from Intro.

 

This thread gives details on what to use from Int. & Pre. Calc for Pre-Calc. from Kathy in Richmond- 

College algebra is in the Intermediate Alg text, and Trig is in the Precalculus text. But he doesn't have to complete those two volumes in their entirety in order to do precalculus. The material is wonderful and certainly worthwhile if you have the time, but it goes far beyond what we usually see in a precalc class.

With a good algebra 2 background, he could probably go quickly through the first 4 chapters of Int Alg, then move on to chapters 5 through 16. Then he could cover Chs 1 to 7 and 9 to 11 of Precalculus.

My 'bare bones' precalculus suggestion would be as follows: (This is for a kid who wants to cover what's usually done in precalculus in a text such as Foerster, but who wants an AoPS flavor & doesn't have two years to go through these volumes. Even so, this course outline would still be well beyond Foerster in depth and difficulty.) Do the exercises in each section and the Chapter Reviews. Starred problems and the end of chapter Challenging Problems could be sampled, but don't feel you have to do them all (it's not possible ).

Intermediate algebra textbook:
Ch 1 - 4: review
Ch 5 - 6: all
Ch 7.1 - 7.5
Ch 9.1 - 9.2
Ch 10.1 - 10.5
Ch 11.3 -11.4
Ch 13.1 -13.3, 13.5-6
Ch 14.1
Ch 15.1 - 15.3
Ch 16.1 - 16.3

Precalculus textbook:
Ch 1 - 2
Ch 3.1 - 3.4
Ch 4 - 7
Ch 9 - 11

Anything extra beyond that would be icing on the cake (and the skipped sections are the ones I consider my favorites:), but I understand time constraints).

 

 

 

Edited August 10, 2017 by soror

[chiguirre]

I'd take a look at WTMA's syllabus. Trinqueta did their class last year and covered the second half of Intro plus work in class on division of polynomials, exponential and logarithmic functions, basic trig functions and vectors. It was the first year they offered the class so they may have made changes this year based on that experience.

[skimomma]

This has been a source of continual confusion for me.

 

As outlined in the above posts, is "Algebra 2" considered a full credit?  As in would "normally" be taken after geometry and before pre-calc in a regular high school a la 1995?  

 

We plan to use AoPS all the way through because dd likes the approach.  She is doing geometry this year and completed the entire intro to algebra book last year.  But the time it takes is overwhelming.  I may have to cull parts in future years.  I guess I just assumed each book was a regular full high school credit following something resembling the regular high school math sequence, just perhaps a little out of order on certain topics.  But every time I read these threads I worry that I am asking too much of a bright-but-not-mathy kid.

[regentrude]

We plan to use AoPS all the way through because dd likes the approach.  She is doing geometry this year and completed the entire intro to algebra book last year.  But the time it takes is overwhelming.  I may have to cull parts in future years.  I guess I just assumed each book was a regular full high school credit following something resembling the regular high school math sequence, just perhaps a little out of order on certain topics.  

 

None of the other texts took my kids nearly as much time to complete as Intro to Algebra!

 

No, AoPS is not regular high school material. As stated on their website "Our texts offer broader, deeper, and more challenging instruction than other curricula."

 

This said, I simply called Intro to Algebra "Algebra 1" on the transcript and Intermediate Algebra "Algebra 2", even though the topics don't match up with "traditional" curricula. For a homeschool, it made no sense to me to agonize over how to call things - a different situation than the OP.

 

Even if you use the chapter suggestions linked in pp, this will still be work above and beyond what a regular high school math class covers.

[skimomma]

None of the other texts took my kids nearly as much time to complete as Intro to Algebra!

 

No, AoPS is not regular high school material. As stated on their website "Our texts offer broader, deeper, and more challenging instruction than other curricula."

 

This said, I simply called Intro to Algebra "Algebra 1" on the transcript and Intermediate Algebra "Algebra 2", even though the topics don't match up with "traditional" curricula. For a homeschool, it made no sense to me to agonize over how to call things - a different situation than the OP.

 

Even if you use the chapter suggestions linked in pp, this will still be work above and beyond what a regular high school math class covers.

 

That is very good to know about the intro to algebra book!  Phew.  

 

I knew it was "broader, deeper, and more challenging" but assumed that I could still call each book a single credit with some sort of title that somewhat resembled the normal high school progression.  It sounds like that is still the case.  Dd will just be getting a little extra and I may be able to cull some chapters in the intermediate algebra book if necessary.

[daijobu]

Yes, this isn't for my own transcript or for my own kids.  I've been approached by another mom that she wants her kids to take "Algebra 2" this year.  I will only use AoPS because that's what I'm comfortable with and she's fine with that.  (I'll probably skip the challenge problems depending on the skills of the students.)  But I want to make sure I cover everything I need to.  Thank you for the above directions.  I'll check those chapters and topics missing from the Intro book and add them at the end of the year.    

[Julie of KY]

I think just completing the Intro to algebra book is mostly algebra 2 and is more than kids locally get for algebra 2.

 

The topics I'd consider adding if they are not covered in precalc are basic matrices, parabolas, ellipses, hyperbolas. I would not advise using the Intermediate book for an average kid. What I'd probably do is pick up a basic algebra 2 book and see if it covers anything you are not covering with AoPS.

[daijobu]

I just receive a response from AoPS to this question.  Here is their response:

 

Chapters 10-22 of the Introduction to Algebra textbook should cover almost all of the topics you need. Although what's covered in Algebra 2 courses/textbooks can vary, the other topics I've typically seen included in Algebra 2 classes are conic sections (which are covered in Intermediate Algebra) and basic vectors and matrices (these are covered in depth in our Precalculus book).

 

Hence, you could supplement Introduction to Algebra with Chapter 5 of Intermediate Algebra and the parts of Chapters 9 and 10 of Precalculus. I'm fairly certain most Algebra 2 courses/texts don't cover vectors and matrices at great length – a quick google search for Algebra 2 syllabi suggests that it'd be fine to cover the definitions of vectors and matrices, matrix adding/subtracting/multiplying, inverse matrices, and determinants. You could most likely find an Algebra 2 syllabus from a local school posted online if you want to see which particular topics they cover.

 

If you want to double check that your students are ready to start at Chapter 10 of Introduction to Algebra – since I've seen at least one Algebra 2 syllabus that included topics covered in early chapters – you can give them the "Are You Ready?" pre-test for our Introduction to Algebra B course, which also starts with Chapter 10 of Introduction to Algebra. Furthermore, depending on how much their Algebra 1 course/text covered, note that they might be able to move more quickly through some sections of Chapters 10 and 11 than they will through the rest of the text. For example, most Algebra 1 classes cover basic quadratic equations or factorizations like the difference of squares.