This is a compilation of AoPS posts that I feel are useful in some fashion. Some of them are mine, not because I feel they are necessarily the most useful posts around, but because I think they're generally useful nonetheless and they have the benefit of my complete agreement with their author (I also need to make reference to them on occasion, so it's helpful for me to have them in one place). Many others are posts that made a big impression on me throughout my contest career - you'll note that many of these posts are by v_Enhance, who is undoubtedly the leading authority on these matters (even if he protests this point). Others contain useful mathematical information, such as problem sets or articles about particular techniques. Finally, some simply contain oft-requested factual information, such as qualification processes.

I began collecting these posts as a simple matter of convenience: I'm often asked the same questions by many different people, and having posts handy to point them towards saves us all a lot of time - not to mention that many of these posts make the point far better than I could articulate. But when collecting the answers to questions I'm frequently asked, I realized that there is simply far more quality material on this website than people think to ask about. My goal in this compilation is to provide a centralized source of some - but certainly not all, as I could not hope to do justice to all the quality material on this website with a single compilation - of this quality content, and I hope that readers will get the answers to questions they haven't even thought about yet.

Mock tests I wrote or wrote in conjunction with others:

• 2015 Mock ARML
• 2015 Mock AMC
• 2014 Mock MATHCOUNTS (note: largely written for comedic effect; overly difficult)
• 2014 Mock AIME
• 2014 Mock AMC (intentionally difficult)
• 2013 Mock AIME (ASIA TEAM)
• 2012 Mock AIME (note: this, along the below test, is the only one on this list that I was not the main contributor to - which likely explains its high quality)
• 2012 Mock AMC (note: this, along the above test, is the only one on this list that I was not the main contributor to - which likely explains its high quality)
• I wrote a 2012 Mock MATHCOUNTS, but apparently unwisely uploaded it to 4shared (I have no idea where I got that idea from), which evidently does not save uploads for very long. If anyone happens to have a copy, please let me know
• 2011 Mock MATHCOUNTS
• 2010 Mock MATHCOUNTS (roughly Chapter-State level)

Other posts I've made that are useful in some way:

• How do I prepare for AIME?. An AIME-level "study guide" that basically intends to be an "AIME syllabus". First draft; hopefully will get around to version 2 at some point.
• Response to: "Test day tips?". Quick link to number sense/computation tests, which I used throughout middle and high-school competitions to "wake up" on the mornings of.
• Response to: "Power round solutions". BCA's solutions to the 2014 PUMaC Power Round, for which official solutions are not available.
• "QEDMonthly Issue 2". The second edition of the (now defunct) QEDMonthly magazine, which I authored along with a few friends. I simply didn't have the time or inclination to continue with this project, but the existing material is still solid (and perhaps someday I'll revive the concept).
• "Learn how to learn". Probably my most useful posts; describes how to efficiently practice (the focus is on MATHCOUNTS due to that being the question asked, but the post applies in a more general way).
• "QEDMonthly Issue 1". The first edition of the (now defunct) QEDMonthly magazine, which I authored along with a few friends. I simply didn't have the time or inclination to continue with this project, but the existing material is still solid (and perhaps someday I'll revive the concept).
• Response to: "CD strategies". Advice on performing well at MATHCOUNTS countdown.
• MATHCOUNTS Tips. A few general tips for MATHCOUNTS, many of which scale to other competitions as well.

Other posts I'm saving for ease of reference, in order to reply to FAQs more quickly (these are more meta-oriented posts than posts that are useful for competitions):

• Response to: "AMC Rant". Response to statements of the type "math competitions are useless", "math competitions have nothing to do with real math", "math competitors only know stupid tricks", etc.
• Response to: "What is your typical school day like?". Response to questions of the type "why do people homeschool", "why are you homeschooled", "doesn't homeschooling hurt socialization", etc.
• Response to: "Telling a high school teacher that he cannot teach math". Description of my single year in high school, and advice on dealing with suboptimal educational situations.
• Response to: "Alternate American competitions". (Intentionally) snarky response to people who are so concerned with finding optimal practicing methods that they don't actually do any practice, or those who complain incessantly about a disliked contest format. Inspired by the classic pair of posts by the master. Remarkably adaptable to a variety of situations.

Mock competitions by other users (not necessarily in chronological order; I just added high-quality ones as I came across them). Note that this is a very small sampling of mock tests out there; I chose the ones that I was impressed by:

• 2015 Mock AIME I. Written by Binomial-Theorem and djmathman, well known for creating very high quality contests.
• Mock MATHCOUNTS competition. Written by Th3Numb3rThr33, Benq, donot, AKAL3, and RadioActive. I'd definitely call this closer to state than chapter, but this is one of the few remarkably high quality mock MATHCOUNTS tests.
• Crowd-sourced mock MATHCOUNTS. Written by the community at large. This isn't included here so much because of the final result, which I will freely admit I'm not entirely thrilled with (most mock MATHCOUNTS tests tend to be way overboard on difficulty, and this one falls victim to the same issue), but for the rather novel concept: crowd-sourcing a mock competition. This seems like an idea that, with proper development, has a lot of potential.
• Mock AMC 10 2014-2015. Written by AlcumusGuy. The difficulty curve is a little wonky here, though less so than is usually for a mock test, but the problems are of quite high quality. Slightly harder than an AMC 10; could conceivably be rebranded as an AMC 12.
• Triple Mock AIME. Written by mcdonalds106_7, Iggy Iguana, and fractals. These are way more difficult than you should expect from the actual AIME, which makes it good preparation for those already looking at 10+ scores. If you're not there yet, though, there are more difficulty-appropriate ones you should look at first.
• Northeastern WOOTers Mock AIME I and II. First one written by codyj, djmathman, and yugrey, second written by ABCDE and codyj; both organized by ahaanomegas.
• MWMT. Operated by MSTang. This has been of excellent quality in the past, and a new "season" is about to start. Definitely well-worth checking out.
• (Not a post, but useful anyway) In the same vein, CleverMath is a relative newcomer to the math scene, but it seems like an excellent resource that's well worth getting used to doing. Unfortunately you'll have to start off in the lowest division, so there'll be a few weeks of cleaning up some easier problems, but the weekly set of fairly high-quality problems is worth it.

Useful general posts from other users (again, not necessarily in chronological order):

• Response to: "Silly mistakes" (by v_Enhance). A great look at how a top mathlete handles a contest, and addresses the question of avoiding silly mistakes in the process.
• How do I prepare for the AMCs? (by AkshajK). Not the greatest article ever (especially in terms of formatting and ordering of content), but still an excellent one-stop resource if you're not sure what to do next.
• Stop looking for the "right" training (by v_Enhance). The above post is a good collection of resources, but don't forget the main point of this post: what you do is far less important than how you're doing it.
• Response to: "USA(J)MO index" (by MSTang). A useful flowchart of the USA(J)MO qualification rules. This post, along with the below one, should answer most of the qualification questions around AMC season.
• Response to: "MOP Qualification" (by Wolstenholme). A quick explanation of how the MOP cutoff rules work. This post, along with the above one, should answer most of the qualification questions around AMC season.
• Response to: "Favorite Problem(s)?" (by v_Enhance). An excellent explanation of what makes a good problem a good problem (though of course there is room for subjectivity). Especially excellent reading for aspiring problem-writers.

Useful math posts from other users (again, not necessarily chronological):

• Olympiad Combinatorics book (by Pascal96). This is very much a work in progress (and unfortunately appears to have been largely abandoned), but the existing content is excellent and this is a resource not enough people are aware of.
• Not a post, but everything on v_Enhance's website is incredible material for olympiad-level preparation, as well as understanding how advanced mathletes think about and approach problems in general. His blog also contains a lot of mini-articles (though many are quite advanced) that are worth reading even if you don't 100% understand what's going on.
• Barycentric coordinates in Olympiad geometry (by Mewto55555 and v_Enhance). This is on the above website, but is significant enough to mention twice. You can thank this post for the sharp uptake of geometry difficulty, as well as the cult following it's attracted. Almost mandatory reading at these for olympiad-level participants.
• Cyclotomic Polynomials in Olympiad Number Theory (by dinoboy). Another great Olympiad-level article with a lot of applications, including several connections that are definitely not immediately obvious.
• Olympiad number theory through challenging problems (by Binomial-Theorem). An excellent introduction into the basics of Olympiad number theory. Unfortunately this is slightly dated now as Olympiad number theory seems to have largely died off, but this is still excellent reading for you AIME/JMO-level people.
• One hundred geometry problems - bridging the olympiad gap (by djmathman). In today's contest climate, one of the major downsides to geometry is that it's geometry. Another, albeit far less important, issue is that there exist few resources for "mid-level" geometry. This article helps bridge that gap through a well-selected set of problems.
• Response to: "AIME level geometry book" (by v_Enhance). A quick syllabus of AIME-level geometry, to complement the above problem set.
• AIME level practice problem set (by djmathman). A nice collection of 40 problems (10 per subject) from AIME-level competitions not named AIME. Definitely worth doing when you "run out" of AIME problems and/or want a different flavor.

Please don't take offense if you think you made a particularly useful post that didn't appear here; more than likely, I'm simply not familiar with the post and didn't think to include it here. If you know of (or authored) a post that you think deserves to be in this compilation, let me know and I'll consider adding it in. Also, if any of the factual information above (authorship etc.) is in error, let me know and I'll correct it ASAP.