Mathletes’ Greatest Secrets Finally Revealed
Henry
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(Image credit: P. Cowie. Public Domain.)
Tip #1: Keep a formula notebook (see below). You'll find it useful, and so will archaeologists 3500 years later. |
I will be discussing this sort of contest (e.g. Sipnayan, Lord of the Math, et al) at once, as there are so many and doing them one at a time would needlessly prolong the series and bore you, my precious readers. There are also other contests that contain math among many subjects; if you’re performing well in the math-only contests, the math there should be manageable.
Back to math-only contests. These are usually organized by a student organization within the school, with varying levels of support from the resident math department.
Again as an NCR resident, most of my examples will be NCR contests. Contests elsewhere of this nature should hopefully not be too different.
Format
The most common format involves each school sending one or more teams of three students each. A typical contest day would consist of one screening/elimination round in the morning, followed by team semi-finals and finals in the afternoon/evening.
The elimination round is often an individual written test, with 15-25 short answer or multiple choice questions. For each team the scores are added up, and teams with a sufficiently high score (usually the top 20-30) continue to the semi-finals. Very often, the top individual scorer(s) in the elimination round are awarded separately. Of course, winning any individual award does not guarantee entrance into the team rounds.
Pre-final and final rounds are usually quiz-bee type; questions are announced orally, teams are given a time limit to submit answers, and correct answers are credited.
Examples and Quirks
Most of the contests of this class that I've encountered follow the above format exactly; others, however, have a signature twist. I'll outline some below:
UP Mathirang Mathibay turns the screening round into a group test with more problems than one average-strength student can attempt. Teams qualifying for the afternoon are pared down to the top three by a series of pre-final rounds, each bearing more point weight than the previous one. This is not trivial; since the last few questions are very heavy, a landslide lead is worthless if you flub the last question of the day.
AMS Sipnayan conducts the semi-finals in two batches; the top three from each batch proceeds to the finals. The batch into which a qualifying team goes into is completely random; this can be a bit of a problem in the case when all the particularly strong teams end up in the same batch. Moreover, the final round will almost always introduce some kind of game element. This means winning involves some element of luck and strategy apart from good solving skills.
Some contests of this type (SSHS Lord of the Math; GCC GMATIC) have separate quiz-bee style rounds for top-scoring individuals. This arrangement gives more shots at an award, but is itself a test of energy management; the whole affair can be very tiring.
Preparation
New contests are usually unpredictable: difficulty can range from dangerously easy to unreasonably difficult (see NOTE).
NOTE
Both extremes are bad because everybody would be getting the same score (perfect for the former, zero for the latter!).
For the ones that have been around for a while, (eg Sipnayan, Lord of the Math, GMATIC, Mathirang Mathibay et al) expect intermediate level problems. Accuracy is first priority, followed by speed. There will be a fair share of exotic problems, but I think quite easy to pick up the general themes. As is inevitable with student-made papers, sometimes unreasonably difficult problems turn up. Don’t let them bother you, and work on the problems you can do.
A good place to start would be AMC 8 or AMC 12 for easy questions and AIME for more challenging ones. Once you have exhausted these, take a look at UNC / USC contests - these are good for the oral rounds. Problems from Brilliant a few notches below Olympiad should be appropriate, but when practicing, please simulate time pressure! Check the track record of the contest, including previous year papers, to see how you manage your time in the eliminations. Remember: it will often be students who prepare the paper, and since a new crew takes over each time, they’ll be looking at the old papers too!
Tips
This applies to any contest where marking time is limited. It’s best to make it easy for the checker to mark answers, because they rarely have the time or the means to resolve unclear answers. This applies especially to the elimination round where the paper is one among hundreds, and it’s virtually impossible to appeal.
A very smart way for a contest to eliminate ambiguity is to calibrate the qualifying round questions so that all answers are integers from 0000 to 9999 (this is precisely what AIME does): for example, a question that originally asks for fraction $\frac{m}{n}$ in lowest terms will instead ask for $m+n$. This makes it completely clear if a contestant is correct or wrong, and lifts the difficulty from the grader to recognize multiple forms of the correct answer.
Unfortunately, this method hasn't seen popularity as of this writing.
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| You have to help your checkers out. (S)he wants to give you points. But (s)he will appreciate if you simply write $2$, instead of $\sqrt{\frac{1}{\pi}\sum_{n=0}^{\infty}\frac{\exp\left(n\pi\mathbf{i}\right)}{2n+1}}$. Believe me. |
A very smart way for a contest to eliminate ambiguity is to calibrate the qualifying round questions so that all answers are integers from 0000 to 9999 (this is precisely what AIME does): for example, a question that originally asks for fraction $\frac{m}{n}$ in lowest terms will instead ask for $m+n$. This makes it completely clear if a contestant is correct or wrong, and lifts the difficulty from the grader to recognize multiple forms of the correct answer.
Unfortunately, this method hasn't seen popularity as of this writing.
One cliched strategy is to put all the strong students in one team, so the school is guaranteed at least one slot in the afternoon rounds. While effective, it may not be the best arrangement for all cases (it deprives rookies of the much-needed experience of the pre-finals). It adds to the fun if teammates work well together and don’t play the blame game.
Intermediate level problems often involve arcane tactics, but in the oral round there’s no time to derive these on the spot, so it’s best to know some toolsets of techniques and formulae by heart. It is a good idea to keep them all in a small notebook you can review right before the test.
I’ve found it very stressful to encounter ambiguity in an elimination round question. Act quickly, but don’t expect too much; the judges and the problem setters may not necessarily be available, and even if they are, it will take time for your question to reach them, and for them to formulate a response (or cancel the question).
In the afternoon rounds this is less of a problem. On the other hand, especially for new contests, people may try to exploit a mechanics loophole; protesting these really can get quite nasty. In my opinion, the best course of action is to adhere to the spirit of healthy competition. Sometimes scandalizing the judges is not worth one or two points one can recover later, especially since one’s carrying the name of the school. It’s just a contest, after all.
Any developments regarding the usual school/university contest you'd like to share? Any burning realizations about the 'genre'? Do comment below!
Any developments regarding the usual school/university contest you'd like to share? Any burning realizations about the 'genre'? Do comment below!
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