<p>Hey all, I have a question for those who know about/are involved with high school math competitions (i.e. AMC).</p>
<p>Basically, my brother (just graduated 7th grade) is really interested in math. Although I never took the AMC tests (didn't know about them until after high school), I was looking at a few previously administered tests this week and showed them to my brother. He worked on the AMC 12 (B) from 2009 for a while and correctly answered 12 of the 25 questions (without guessing, since I told him how the scoring works/that you're penalized for guessing randomly).</p>
<p>Anyway, I was posting here because he asked me what he could do now (if anything -- he's 13, by the way) to learn more of the concepts/tricks/ideas that are tested on these types of competitions. He was frustrated that he couldn't answer more correctly, but for a lot of the questions he simply hasn't had the instruction to be able to solve them. (Or are the second half of the questions very obscure applications of math principles that can't/generally aren't taught in school?)</p>
<p>Any ideas what I should tell him? Should he do anything now to learn more (advanced) math? If so, what? I would hate to stifle his thirst for knowledge, although at the same time it is the summer and he is only 13. But he is naturally inquisitive and loves to learn, and since I wasn't sure what to tell him, I figured I'd post here and see what people thought! Opinions?</p>
<p>Oh, and he is going to ask his guidance counselor (whom he knows well) to register for the AMC 8 next year for his middle school. :)</p>
<p>wow, he’s only 13 and he’s smarter than most of the 12th graders who take the tests. my advice is to go on [Art</a> of Problem Solving](<a href=“http://artofproblemsolving.com%5DArt”>http://artofproblemsolving.com) and read the aops books. with preparation you could easily have a future usamo qualifier on your hands.</p>
It’s a combination of things - some of the problems require a solid understanding of precalc like is taught in school. Beyond that, the hardest problems often require intuition or other methods that won’t be taught in a standard course. The AMC was always my weakest test, comparatively, because I don’t do incredibly under heavily timed conditions and am more prone to make a foolish calculation error than in later rounds. One does not need to get them all right to get a good score, and if he has some mathematical intuition (which his score right now seems to imply), then just learning precalculus should boost his score.</p>
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This depends on many things. If having him learn more “standard” math just means he’ll be even more bored in the future because there’s no way to accelerate himself further, to do so is probably a mistake. He has plenty of time ahead of him to learn the material, and generally (not always, though) he’ll learn it more thoroughly in a classroom than on his own. In addition, the questions he got right were likely also on the AMC 10, since they share many questions. However, the AMC 10 does not require as much of a math background. In addition, it’s easier to qualify for higher rounds just to see what sorts of questions one can solve by taking the AMC 10. Stifling his desire to learn may not be a good thing, but it’s also worth thinking to the future. Have you discussed this with your parents?</p>
<p>I haven’t spoken with my parents about this, per se, although they know that he did really well on the practice AMC I showed him.</p>
<p>If the books on the AoPS website weren’t so expensive, I would order one of them (volume 1 perhaps), but $40-50 is a bit much, for me at least. Maybe I can persuade my dad to buy it for my brother to look through, if people have had success with it.
As you touched on, though, he’d probably learn the concepts better in school. But who knows what he can comprehend through his own self-study. I don’t think it could be detrimental…</p>
<p>So, I’m really not sure what to do. Just let it be? I don’t know enough about AMC/math in general to really coach him… I suppose I could look at old practice tests and see if he knows/can learn the concepts of the medium-to-hard questions.</p>
<p>I know the AMC/AIME/etc are useful tests to take, and he loves math, so I’m gonna try to figure out something for him.</p>
<p>Any recommendations (including AMC 10 vs 12)?</p>
<p>I haven’t spoken with my parents about this, per se, although they know that he did really well on the practice AMC I showed him.</p>
<p>If the books on the AoPS website weren’t so expensive, I would order one of them (volume 1 perhaps), but $40-50 is a bit much, for me at least. Maybe I can persuade my dad to buy it for my brother to look through, if people have had success with it.
As you touched on, though, he’d probably learn the concepts better in school. But who knows what he can comprehend through his own self-study. I don’t think it could be detrimental…</p>
<p>So, I’m really not sure what to do. Just let it be? I don’t know enough about AMC/math in general to really coach him… I suppose I could look at old practice tests and see if he knows/can learn the concepts of the medium-to-hard questions.</p>
<p>I know the AMC/AIME/etc are useful tests to take, and he loves math, so I’m gonna try to figure out something for him.</p>
<p>Any recommendations (including AMC 10 vs 12)?</p>
<p>I second the recommendation on the Art of Problem Solving books, the original two volumes anyways. They’re a really good investment, and teaches concepts much better, deeper and in more breadth than any standard school textbook–they’re written by math competition people for math competition people. Their forum is also a good tool. Another book I’d recommend is Mathematical Circles, by Dmitri Fomin, which is perfect for introducing a middle schooler to proofs and many useful ideas that are not taught in school, like graph theory, game theory, combinatorics, pigeonhole, invariants, number theory and inequalities. Both have tons of problems, and just working on problems is the best way to learn.</p>
<p>And get him to do competitions. AMC 8 and Mathcounts are decent competitions, but he can also take the AMC 10 and 12 officially at a local high school or some universities.</p>
<p>AoPS has a lot of free things on the website that’s pretty useful. They have a forum where people post problems and stuff, and they also have copies of a lot of AMCs and other contests too, with solutions too look at. They have chatrooms sessions every once in a while (“Math Jams”) that talk about different topics, and they also have general stuff about Intel competitions and an admissions counselor from MIT had one one time too. And the also have a online game set up mostly for preparing for MathCounts, but I think they use AMC problems as part of the game, so that’s pretty good too.</p>
<p>And outside of that, you can borrow books from the library if they have stuff, some areas have Math Circles which are pretty nice too.</p>
<p>Okay, I’ll definitely look into the AoPS books!</p>
<p>By the way, is there a list of high schools/universities that administer the AMC 10/12? I don’t know of any in my area. I tried to find a list on the Internet but wasn’t successful. I’m sure he’d be interested in taking the AMC 10 (preferable to 12?) if he had the opportunity to do so.</p>
<p>I think one of the problems is that I don’t know what area of math/math topic to focus on. Do the AMC tests, specifically the AMC 10, generally test the same type/format of questions? If so, perhaps I could get the AoPS book(s) and have my brother focus on, for now, just those topics which would be covered on AMC 10. Anyone know if the exam follows a regular format of problem types?</p>
<p>Not really. It’s a lot of the same fundamental ideas, methods and theorems, but the problems try to apply them in novel and interesting ways. It’s not like the SAT where you can basically become familiar with every type of problem, but you aren’t supposed to.</p>
<p>Of course the only university in my state that administers the AMC tests is over 300 miles away. It’s fine though, he can just take the AMC 8 next school year (assuming his counselor gives him the green light) and then start with the real deal the following year. I’m sure 2010’s AMC tests will be available on the AoPS website, so he can always try and solve them from there.</p>
<p>And my parents are really enthusiastic and are footing the bill for the first volume AoPS book, so my brother is really excited! Hopefully the book is solid, and can teach him some of new and basic concepts that he hasn’t learned in school year.</p>
<p>That’s probably true because they have less math to work with - it can’t assume anything beyond algebra 1 and geometry.</p>
<p>Just note that the cutoff score for AIME is higher for the AMC 10 than the 12 because the problems are easier, while getting a perfect score on the 8 (used to, at least) qualifies you to take the 10 and attempt to qualify for AIME.</p>
<p>Hm… Well, on the AMC website, under AMC 8, it says that “high scoring students are invited to participate in the AMC 10.” Not very definitive, what “high scoring” is, but that’s alright.
I also don’t know if that means that those students who did well on the AMC 8 and are invited to participate in the AMC 10 have the potential to qualify for AIME?</p>
<p>And thanks for the help, shravas! I’ll be sure to focus on geometry with my brother, and make sure he knows all the silly geometry-related rules. AoPS volume 1 is on its way to my house, so hopefully there’s a geometry section that he especially focus on.</p>
<p>Tha AMC 10 and 12 are open to all students in 10th and 12th grade and below. You do not need to qualify for them. The reason AMC 8 high scorers are invited to take the 10/12 is because the AMC believes taking the 10/12 will be a good experience for them.</p>