Saturday, April 17, 2010

Information for USAMO-takers

Albany Area Math Circle is honored and proud to have five USA Math Olympiad (USAMO) qualifiers this year:

Andrew Ardito
Matthew Babbitt
Dave Bieber
Schuyler Smith
Felix Sun

For their benefit, and the benefit of other USAMO takers across the country, I am listing some information designed to be helpful.

The italicized information below comes from page 14 of the USAMO Teachers' Manual, which all students should read carefully before taking the USAMO. I have also boldfaced especially important information.

USA(J)MO 2010 Teacher Manual
MAA American Mathematics Competitions USA Mathematical Olympiad
S-II – Instructions to be Read by USA(J)MO Participants

1. The space in the upper right-hand corner of your answer sheets is for your Student Number. You and your USA(J)MO proctor will be informed by mail of your assigned student number. The number at the top center is the Problem Number. Do NOT write your name or school anywhere on the answer sheets; all your papers must be anonymous at the time of the grading.

Write only your Student Number and Problem Number (in a similar location) on any additional papers you hand in.

2. There are six equally weighted problems, for which you will be allowed a total of nine hours. You will be allowed 4.5 hours on Tuesday, April 27, 2010 (
12:30pm –5:00pm EDT or equivalent in your time zone) for Problems 1, 2 and 3, and 4.5 hours on Wednesday, April 28, 2010 (12:30pm–5:00pm EDT or equivalent in your time zone) for Problems 4, 5 and 6. Each problem should be started on the corresponding numbered answer sheet. You may write on only the front of the sheet. During each session, carefully look over all the problems. Then work on those which you can work well or start well.

Concurrently, be aware of the total time you allocate to each problem.

3. You will be scored on your method of attack, clarity of reasoning, evidence of ingenuity, inventiveness, and general insight.
In order to obtain full credit, all the claims in your solution must be PROVED. When in doubt, you should include details rather than leave them out. Examination of special cases or generalizations may lead to fruitful ideas on how to begin a problem, and partial credit may be given for constructive progress toward a solution. An unusually elegant proof or a carefully stated non-trivial extension with proof may play a role in breaking an eventual tie.

4. Your papers should be CLEAR, CONCISE, COMPLETE, and
written DARKLY, keeping in mind it is a faxed copy being graded, not the original! This includes MATHEMATICAL CLARITY, GOOD ENGLISH and LEGIBILITY. Points will be deducted for inadequate or poorly written explanations, as well as for incorrect mathematics. Therefore, use scratch paper freely before writing the solutions you submit, and submit ONLY the final work you wish to have graded. Solutions written in languages other than English will not be graded. Please leave a 1” margin on all sides of the Answer Sheet and on any additional pages and write DARKLY and LEGIBLY, so your faxed copy can be easily read. A #2 lead pencil, black ink pen or marker fax best.

5. NO notes, headphones, cell phones, ipods, books, slide rules, mathematical tables, calculators or calculator watches are allowed during the exam.
The only instruments permitted are writing and drawing instruments (ruler, compass, protractor, graph paper, carbon paper). Students learning English as a second-language, who are taking the USA(J)MO for the first time are permitted to use a non-technical translation dictionary during the exam. However, the proctor must examine and keep the dictionary in his or her possession for the 24 hours preceding the USA(J)MO. Your solutions must be faxed to 303-374-6339 immediately at 5:00pm EDT or equivalent in your time zone each day.

6. The USA(J)MO will be administered in two sessions.
Students should come prepared with a sack lunch and/or snacks because there is no lunch break during the exam (exceptions will be made for restroom breaks). Your proctor is required to be present during the entire course of the exam for your papers to be valid, but is not permitted to answer any questions about the test. You are not allowed to talk to any other student while the exam is in progress. If you feel that a problem is not stated clearly, note this on your answer sheet and try to make a non-trivial restatement of the problem. Then try to solve the restated problem.

7. You will start the exam when your proctor gives the signal. When the proctor announces after each session that 4.5 hours are up, immediately cease writing. Double-check that your Student Number on your answer sheets matches with the one assigned by mail. Next, immediately hand all Answer Sheets to the USA(J)MO Proctor (even if some sheets are blank) to be faxed to the AMC office.

8. You may keep the problem sheets. Additional copies, a set of solutions, and the results (including your score interval) will be mailed to your Exam Manager after Wednesday, May 12, 2010.

9. The USA(J)MO is graded more strictly than most school examinations, so it is typical for students to overestimate the scores they will receive. The decisions of the graders are final and may not be appealed.

Clarity of exposition is essential: the burden of proof is on you to demonstrate that you understand the mathematical ideas you are using. Remember that the USAMO graders are human beings--they can't read your mind! Your work will not get the credit it deserves unless you have written it up in a clear and well-organized manner than allows the USAMO graders to follow the logic of your reasoning.

Richard Rusczyk and Mathew Crawford have posted an excellent guide on How to Write a Solution on the Art of Problem Solving website. You are strongly advised to read and/or re-read that guide before the USAMO. Their article includes many excellent cautionary notes of things NOT to do and good examples of how to improve the clarity of your presentation, to make sure your work gets the credit it deserves.

You should also be aware that USAMO grading is exceptionally rigorous.

Unlike a typical school essay exam, in which teachers may be struggling to give the benefit of the doubt for partial credit wherever possible, USAMO graders are notoriously stingy.

Each question is worth a maximum of 7 points, so the total number of points theoretically available is a 42. But even though it's a very strong group of students taking the contest each year, 0's are very frequent, even among students who thought they had "solved" one or more problems.

Zuming Feng, the Head Coach of the US International Math Olympiad team and academic director of the Math Olympiad Summer Program has posted the following advice on the Art of Problem Solving AMC discussion forum:

To be deducted (and usually) by lots of points): real math errors in logic, and real mistakes in calculations, unclear reasoning between the steps, claiming facts with no proofs (facts are sometimes restating the core parts of original the problems, etc.) Most of the time, we put your solution into two categories: top down (7-, which means you have all the ideas, in correct order, to solve the problem) or bottom up (0+, which means you are missing main ideas to solve the problem), it is very hard to get to 2 points if the solution is in the second category.

An additional resource: Thomas Jefferson High School's math team leaders have generously posted their advice on preparing for USA Math Olympiad at the links listed below:
TJ USAMO Practice: Proofs
TJ USAMO Practice: Inequalities
TJ USAMO Practice: Induction
TJ USAMO Practice Test
TJ USAMO Practice: Cyclic Quadrilaterals
TJ USAMO Practice: Pigeonhole
TJ USAMO Practice: Geometry practice
TJ USAMO Practice: Functional equations

Richard Rusczyk and other high scorers on past USAMOs have provided lots of great advice in their AOPS math jam linked here.

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