1. Read each problem carefully and multiple times
I cannot stress this point enough. This is the single most important part of MATHCOUNTS for a great number of students, myself included. Misreading the problem is likely one of the leading causes, if not the leading cause, of incorrect answers. Personally, I would have made Nationals in 7th grade had I read some key words correct ("smallest" instead of "largest", "first" instead of "last", etc.). I also would likely have made National CD had I managed to read "Positive" on the final Target question.
2. Manage your time
This falls second on the list of importance, just below misreading. Note that poor time management will likely hamper your ability to read carefully (and multiple times), which will likely lead to even more time wasted. Know when to "give up" on a problem in favor of easier questions. They're all worth the same.
3. Do all the questions
Difficulty is extremely difficult to gauge (heh) in general, but even more so when the problems are all roughly the same difficulty level. Don't be intimidated by the question number - many times a #26 will be a giveaway question, while #14 will be one of the more difficult problems. You should aim to at least read through all of the questions (carefully!) and to make a serious attempt on most of them.
4. Organize your work
In MATHCOUNTS, you will likely spend a lot of time checking your answers, something that will be much harder to do if your paper is messy and disorganized. The method that you choose will be up to you, but my recommended method is to either section off your paper before the test begins, or to section off your paper as you complete problems. Write down all non-trivial steps - you'll use these for reference. You should include computation, either to the side or in the problem, as this is where you'll do most of your checking.
5. Do problems multiple ways
Most problems will have several valid approaches to the answer. In most cases, one approach will immediately jump out to you, and you will follow it to the answer. A great way to check your answer is to do the problem in another way, even if it's just slightly different. For example, if you do 5(3+5) as 5*3+5*5 and 5*8, you'll be significantly less likely to make a computation error. Similarly, if use similar triangles and Power of a Point, getting the same answer, you can be
reasonably sure your answer is correct (but if they're different, time to find out why!). When using a second method, you shouldn't know what answer you're trying to achieve - you may consciously or subconsciously force yourself to get that answer.
6. Make assumptions
This is a very dangerous, but potentially rewarding technique. Mostly used for time-saving (and especially in CD), what looks like it's true usually is. Rely on your intuition - it's usually a very powerful tool. A combination of practice and experience gives you an intuition that can easily outweigh the time needed for a rigorous solution. This isn't to say guess; rather to make educated guesses.
For example, take 2011 Chapter Target #8. From experience, I was able to immediately guess that the b in was 2 ( is highly associated with 45-degree angles and squares), which immediately led to (there's no other possible answer that makes it between 0 and 1). This gives the correct answer of 3 without any effort, on a relatively difficult problem (for chapter).
Disclaimer: Only use this technique when necessary. If you have time, focus on checking problems you used this method on FIRST, before checking others.
7. Don't check in order
It's usually a waste of time to check from #1 to #30 in that order. You'll end up using your precious time checking problems that are almost certainly correct instead of checking those that need it. Make a mark on your paper next to the question number signifying that you are unsure of your answer. Make a seperate mark if you arrived at the answer without a rigorous solution (see tip 6). Focus on checking these first. After that, focus on checking problems that you aren't 100% sure of, then go to the easier problems. I also made notes of problems that were essentially just computation, because I always made computational errors on early problems. You may decide that you need marks for certain issues that you typically encounter, which is also fine.
8. CD - Buzz in before you know the answer
Another dangerous but rewarding technique, only do so if you know you can get the answer within 3 seconds. For example, if you know that the answer is 15*16, that would be a good time to buzz in. Countdown is also an important time to utilize tip 6 - use your intution! With only 45 second per problem, and the "race" element, you need to be very fast in order to pick up your points. For example, this question: If , compute n, from the 2011 State CD
round, was one that I instantly recognized as a question I could solve within 3 seconds (btw, so did my opponent). I instantly buzzed in (before I knew the answer!), gave the correct answer of 5, and ended up winning my next match to make Nationals. Had I not buzzed in when I did, my opponent would have (he was going for his buzzer as well), and I would have missed out. In this case, the extra few milliseconds were incredibly important.
9. Take it easy
Finally, don't dwell on your results, good or bad, however cliche that sounds. Poor results do not really indicate much in a competition like MATHCOUNTS, where the difference between a national winner and a person just missing out on State CD is generally very small. It comes down to tiny speed tricks that makes one person just a little bit faster than the other guy, which can be enough. I know it won't feel like it at the time, but you're the lucky ones. As middle schoolers, you have so much time left to improve, both math-wise and competition-wise (yes, they can be seperate things). If you get 11th written at State (which I did in 7th grade), or 5th CD (which my friend did last year at States
[because I beat him]), you'll be originally crushed, but in the end, it really makes so little difference. Both me and my friend do decently at math now, despite our... failures at MATHCOUNTS. There's a lot more to life than it.