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Which AOPS Contest Math book? Vol 1 or Vol 2?


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Any recommendations for which AOPS Contest Math book to get for a student who has just completed the AOPS Intro series (Intro to Alg, NT, C&P, Geo) and has done reasonably well on AMC8 in the past (But not very well on AMC 10)?  Will Volume 1 be too basic, or will there still be good things to learn? Will Vol 2 be too hard?  This would be for the student to work through on their own for fun, not as part of a class.  

Trying not to overbuy 🙂--- Thanks in advance !

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20 hours ago, WTM said:

Any recommendations for which AOPS Contest Math book to get for a student who has just completed the AOPS Intro series (Intro to Alg, NT, C&P, Geo) and has done reasonably well on AMC8 in the past (But not very well on AMC 10)?  Will Volume 1 be too basic, or will there still be good things to learn? Will Vol 2 be too hard?  This would be for the student to work through on their own for fun, not as part of a class.  

Trying not to overbuy 🙂--- Thanks in advance !

My ds used Volume 1 for Mathcounts, AMC 8, and AMC 10(problems 1-20) He is using Volume 2 for AMC 10 for problems 20-25 level, AMC 12 and AIME. 
Volume one is used for AoPS middle school math contest and Volume 2 is used for High school math contest class at their Academy.

Edited by SDMomof3
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I would actually say Volume 1. 

I've been working through a LOT of contests with my tutoring students recently, and I really can't remember the last time I saw something that wasn't in Volume 1 before the AIME. Practically all of the AMC 10 questions have solutions using ideas in one of the introductory books and in Volume 1. 

But I will also say that the best way to study for AMC contests is to do AMC contests. When I work with the kids who are missing problems, it's very rarely the issue with the content. The issue is more like... they get freaked out by unfamiliar questions, or they simply don't know how to start questions, or they haven't learned a certain useful trick because they haven't quite used it enough.

Basically, doing well at contests requires knowing the material inside and out, and I haven't actually found that going through the AoPS curriculum quite does that for you. So going through contest problems and getting stuck is a really good way to go. And I imagine doing the same thing with Volume 1 will help, too. 

If you're really aiming at the last 5 problems on the AMC 10/12, my answer may be different. Just my experience so far. 

Edited by Not_a_Number
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Here's a Quora answer that agrees with me 😉 . 

https://www.quora.com/How-much-of-AOPS-vol-2-should-I-know-to-qualify-for-AIME

I'm mostly posting this here because I've actually had some pushback to this opinion. I've had people state that Volume 2 is used for high school contests, and that Volume 1 is only for middle school contests. It's good to see that I'm not the only one who disagrees with that stance. 

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22 hours ago, WTM said:

Any recommendations for which AOPS Contest Math book to get for a student who has just completed the AOPS Intro series (Intro to Alg, NT, C&P, Geo) and has done reasonably well on AMC8 in the past (But not very well on AMC 10)?  Will Volume 1 be too basic  

Trying not to overbuy 🙂--- Thanks in advance !

If you don't want to overbuy and your student has already studied the regular AoPS curriculum, then I think both books are skippable.  Both were published first, before all the other curriculum books and are redundant with those.  If he's already studied AoPS NT, CP, Algebra and Geometry, then volumes 1 and 2 will both have low ROI.  

6 hours ago, Not_a_Number said:

But I will also say that the best way to study for AMC contests is to do AMC contests. When I work with the kids who are missing problems, it's very rarely the issue with the content. The issue is more like... they get freaked out by unfamiliar questions, or they simply don't know how to start questions, or they haven't learned a certain useful trick because they haven't quite used it enough.

 

If you're really aiming at the last 5 problems on the AMC 10/12, my answer may be different. Just my experience so far. 

I agree with NaN, the best thing to do to prepare is to study old exams, focusing on learning from the problems your student couldn't solve. 

Advise him to take care that he answers he marks are correct with high probability.  When you look at the qualifying AIME scores, they vary a lot now, from mid 80s to to 120, so it's hard to strategize.  But if you want to aim for a score of at least 110, that will mean 17 correct and 8 blank for a score of 114.  Scoring 14 correct and 3 incorrect brings you score down to 96.     

He should check and double check for silly mistakes before attempting more difficult problems that take away more testing time.  

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For my kids, Vol 1 worked well after they'd mastered basic algebra and geometry & while they were writing the AMC 8 and 10/12 exams. They were starting to qualify for AIME at that point and were scoring about 4 to 6 on that test.  I'm on vacation now, so I don't have the books available to check, but I think that it's volume 1 that has some very useful material on tackling contest problems in geometry problems which are often tricky for kids. And as others have pointed out, the last few problems on the 10/12 exams in a category of their own!

We did Vol 2 in place of textbook math for the kids' precalculus year, since I could never find a precalculus text that appealed to me. AoPS textbooks weren't written yet, so they weren't an option.

Volume 2 has some very challenging material, and I enjoyed working through it alongside them. The kids were taking intermediate and olympiad level AoPS classes online at that point, and were scoring well on the AIME. One of them was starting to qualify for USAMO (as they did 3 times in high school) and this was one of our resource books that helped for that level.

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21 minutes ago, Kathy in Richmond said:

Volume 2 has some very challenging material, and I enjoyed working through it alongside them. The kids were taking intermediate and olympiad level AoPS classes online at that point, and were scoring well on the AIME. One of them was starting to qualify for USAMO (as they did 3 times in high school) and this was one of our resource books that helped for that level.

Yeah, when I look through the Table of Contents for Volume 2, I see things I think of Olympiad-level or Problems 10-15 on the AIME level, not AMC 10 level. 

Not everything is like that, but a lot of it is. 

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34 minutes ago, daijobu said:

Advise him to take care that he answers he marks are correct with high probability.  When you look at the qualifying AIME scores, they vary a lot now, from mid 80s to to 120, so it's hard to strategize.  But if you want to aim for a score of at least 110, that will mean 17 correct and 8 blank for a score of 114.  Scoring 14 correct and 3 incorrect brings you score down to 96.     

He should check and double check for silly mistakes before attempting more difficult problems that take away more testing time.  

You're assuming gender here, and I would guess you're assuming incorrectly 😉 . 

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Thank you, all! So much to learn. I didn’t know how the AMCs were structured. Is there anything online that talks about which problems are easier, which are harder, and scoring strategies?

https://www.maa.org/math-competitions/amc-10-american-mathematics-contest-10

this page doesn’t seem to talk about the different levels Of difficulty for the questions, or the scoring…



DD doesn’t have an overt  goal of doing better on the AMCs. She wants to do these kinds of problems for fun. She did a bunch of old AMCs last year just for kicks. I haven’t pushed her to try to “do well on the test,” because then it’s my goal, not hers, and it’s not as much fun for her anymore. I’m not sure if or when I should encourage her to study these problems for the sake of improving her test performance. I guess that is a more philosophical question. I’m curious to hear how you guys think about that. 
 

DD is in this stage where if we (DH and I)  are the ones pushing, she can sometimes become an iron wall of passive resistance. 😂 

Sounds like volume 1 is the right place to start.

 

Edited by Porridge
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1 hour ago, WTM said:

Thank you, all! So much to learn. I didn’t know how the AMCs were structured. Is there anything online that talks about which problems are easier, which are harder, and scoring strategies?

https://www.maa.org/math-competitions/amc-10-american-mathematics-contest-10

this page doesn’t seem to talk about the different levels Of difficulty for the questions, or the scoring…

They are basically in increasing order. The later in the test, the harder. Basically all contests are structured that way. 

It's not perfect, of course, because human beings sometimes misjudge how hard a question is, but on average that's the idea. 

 

1 hour ago, WTM said:

DD doesn’t have an overt  goal of doing better on the AMCs. She wants to do these kinds of problems for fun. She did a bunch of old AMCs last year just for kicks. I haven’t pushed her to try to “do well on the test,” because then it’s my goal, not hers, and it’s not as much fun for her anymore. I’m not sure if or when I should encourage her to study these problems for the sake of improving her test performance. I guess that is a more philosophical question. I’m curious to hear how you guys think about that. 

Hmmmm. It really depends how that goes for you guys, I suppose. Right now, DD9 is far more motivated by me suggesting that we work to improve her scores than she is by me giving her random questions, so we're working on getting her AMC 8 score up so she can actually place on some list or another this year. But then she's not nearly as motivated by simply solving questions -- she's not motivated by puzzles and doesn't much like being frustrated. 

 

1 hour ago, WTM said:

DD is in this stage where if we (DH and I)  are the ones pushing, she can sometimes become an iron wall of passive resistance. 😂 

Hah. Yes, I know EXACTLY what you mean about the passive resistance. I would personally do a lot to avoid that, lol. But if you did want her to do well, I suppose you could try to motivate her in some other way... I don't know what motivates her, though. My DD9 is quite competitive (we're a competitive family in general!), so she's definitely motivated by winning. But I don't know if your DD is. 

It also depends whether you want her to do well, I suppose 🙂 . I always figure that getting some high scores on these contests opens doors, and the math comes easy enough for DD9 that it always seems like a shame to not work on it. 

 

1 hour ago, WTM said:

Sounds like volume 1 is the right place to start.

I'd say so, if you absolutely need to work from a book. But you can always just work from old contests, too. That's what I've been doing with my tutoring students. And that's what I did myself back in the day. I didn't have very many books. 

Edited by Not_a_Number
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33 minutes ago, Not_a_Number said:

They are basically in increasing order. The later in the test, the harder. Basically all contests are structured that way. 

Thanks - yes I assumed the q’s got harder as the test progressed, but wasn’t sure if there were actually numerical breakdowns of number of one type of problem vs another.

 

34 minutes ago, Not_a_Number said:

I'd say so, if you absolutely need to work from a book. But you can always just work from old contests, too. That's what I've been doing with my tutoring students. And that's what I did myself back in the day. I didn't have very many books. 

I ordered volume 1 and I’m also going to print all the old tests and put them in a binder and “strew” it in the house 🙂 . I think she did 4 old tests last year but I don’t remember which years.

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2 minutes ago, WTM said:

Thanks - yes I assumed the q’s got harder as the test progressed, but wasn’t sure if there were actually numerical breakdowns of number of one type of problem vs another.

No, I don't think there are really numerical breakdowns. I can tell you approximately how they break down, but it's not precise. 

 

2 minutes ago, WTM said:

I ordered volume 1 and I’m also going to print all the old tests and put them in a binder and “strew” it in the house 🙂 . I think she did 4 old tests last year but I don’t remember which years.

I don't know if you're at all interested in preparing her, but if you wind up being so, I'd leave a few for actual timed practice tests. Those are much more useful for test prep. 

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On 8/2/2021 at 6:20 PM, WTM said:

Thanks - yes I assumed the q’s got harder as the test progressed, but wasn’t sure if there were actually numerical breakdowns of number of one type of problem vs another.

The last 6-8 questions are harder than the rest. For example, for this year, since the prep time has been cut short due to the new schedules, I asked my DS to only focus on the last 8 questions on older exams to increase his exposure to harder problems.

There is a lot of repetition between the AOPS (Vol I and II) books and the textbooks. This is because the texts cover the same topics as well, so it is a good test prep strategy to choose those topics in the AOPS Vol I book that your DD needs more review on and focus on them. Also, Alcumus is a good source for the Algebra component for the prep as there are some tricky problems for Int Alg on Alcumus.

Edited by mathnerd
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