2006 Princeton University Mathematics Competition

The 2006 Princeton University Mathematics Competition was the first Princeton University Mathematics Competition. Approximately 200 students took the competition.

General Rules
1. There are 5 types of individual tests, in the topics of Algebra, Geometry, Number Theory, Calculus, and Advanced Topics. Each student will take exactly one of these tests. 2. There are 10 short-answer questions for each individual, and each test takes 60 minutes. 3. No more than 2 students on a full team can take the same individual test. 4. Half-teams must consist of one student taking each individual test. 5. The first 5 questions are worth 2 points each, while the last 5 questions are worth 3 points each. 6. There are 5-minute and 1-minute warnings for each test.

General Rules
1. The test consists of 10 short-answer questions and lasts 30 minutes. 2. The first five problems are worth 8 points each and the last five problems are worth 12 points. 3. There is no partial credit for any answer. 4. There are 5-minute and 1-minute warnings.

General Rules
1. The power round consists of an "interesting application" of an advanced concept. 2. The competition is proof-based, lasts 60 minutes, and is worth a total of 110 points. 3. The power round has several parts. Results from past problems may be used for a current problem, even if the result from the previous problem was failed to be proven. A source of problem is required. 4. There are 5-minute and 1-minute warnings. 5. Only one side of the official solution paper is written on.

Power Round Topics

 * Characteristic functions of intervals
 * Polynomials
 * Rational functions
 * Almost-refinability

General Rules
1. Each full team is broken into two groups of five students each. 2. Each of the students in each group receives a different problem. 3. When a student in relay positions 1, 2, 3, or 4 solves his/her problem, the answer is written on an Official Relay Passing slip, and passed to the right. 4. No means of communication is allowed during this section, except through the Official Relay Passing Slip, and the only thing that can be written on that is the final answer, or lines to avoid ambiguity (for example to distinguish between a 6 or a 9). 5. There is no limit as to how many times a student can pass back an answer. 6. Relay positions 2, 3, 4, and 5 will have problems that require the use of the answer from the previous question. 7. When the person in position 5 gets his/her answer, it is filled out on an Official Answer Slip, and is the only answer that gets considered for credit. 8. A relay lasts 12 minutes, and proctors accept answers from the person in position 5 at the 6-minute and the 12-minute mark. 9. If an answer submitted at 6 minutes is correct, and no answer is submitted after that, 10 points is awarded. If an answer is submitted at 12 minutes, all previous answers are discarded by the proctor, and if is correct, 5 points are awarded.