2008 Competition Format and Sample Problems
Please take a few minutes to read the full explanation of the 2008 Competition Rules.
Individual Competition:
Each of the Junior-Varsity and Varsity individual competitions consist of
two separate
exams: the first is a one-hour, 20-question, multiple-choice examination
and a second 120-minute examination that emphasizes written proof as well
as problem solving. There will be 5 questions on each of the proof exams.
Team Competition:
The Junior-Varsity and Varsity team competitions will also consist of two
parts: the same morning multiple choice exam and an individual ciphering
event. A weighted average of the top four members of a team (60%
multiple choice and 40% ciphering) will be used to determine the team
score. A team
is defined as four or more students from the same high school in the
junior-varsity OR varsity competition; two examples,
- If six students come from ABC High School, with three varsity and three junior varsity competitors, then ABC does not have any 4-person teams.
- If 27 students come from XYZ High school, with many in each division, then XYZ has entered one JV and one V team that consist of the top four scores of its members within the appropriate divisions.
Multiple-Choice Exam:
The multiple-choice exam will be graded for correctness only and will have results posted soon after the test is over. The top 40-50 students in the Varsity examination and the top 20-25 students on the Junior-Varsity examination will be declared semi-finalists and be invited to take the proof examination.
Ciphering Exam:
The ciphering exam will consist of ten problems (different problems for JV and V) given to all students where students will be given a problem face down, and then after being told to start, have two minutes to complete the problem. Scoring will be based strictly on correctness and depend on the time interval submitted -- students holding up a correct answer within two minutes (time announced at 1:50 and 2:00) will be awarded 5 points and between two and three minutes (time announced at 2:50 and 3:00) will be awarded 3 points. You should notice that it would be slightly to your advantage to get the correct answer in the later time interval to two problems than in the first time interval for one problem. Answers that are not held up within the first three minutes will not be collected, strictly enforced.
Testing Procedure: READ THIS!!!!
All students will be required to sign an honor code statement affirming that they have not and will not cheat on any of the exams or competitions at the HSMC. In consideration of fairness, all students will have the same amount of time to work on exams -- if a student continues to work on either the multiple-choice exam or the proof exam after "pencils down" is called, they may be disqualified from the entire competition. As an extreme example, if somehow you forgot to write your name on your exam and do so after "pencils down," you may be disqualified -- writing anything on the exam papers after "pencils down" must be done with the express consent and in the direct presence of the head proctor.
Parents and teachers will only be allowed in the testing rooms for the ciphering competition.
Prizes:
Prizes will be awarded for each portion of the competition: the top-prize scholarships will be awarded entirely for performances on the written examination, with scores on the multiple-choice exam and elegance of proof used to break ties. The team awards will be given to the high school who posts the highest average score of its top four competitors.
Examples of similar examinations are posted below:
The Multiple-choice exam is similar in spirit to those given out annually by the University of Tennessee, Knoxville, or the University of Maryland, College Park. Please find here a sample exam with questions pulled from different sources: Sample test.
We expect the JV-level students to be familiar with basic concepts in geometry and algebra, whereas the Varsity-level students should be comfortable with ideas up to calculus: basic combinatorics, number theory, and probability.
The second examinations will be proof-based; for sample proof-type problems, please look at the Fermat II exams given by the University of Tennessee, and the Bay Area Math Olympiad held at Berkeley:
Please note that no calculators, straight edges, protractors, compasses, or other instruments will be allowed on any of the exams. You will be provided with everything you need (good old fashioned pencil and paper).
Rules and Regulations:
Scoring of the exams and the rules of the competition will be overseen by a panel of judges consisting of three Georgia Tech mathematics faculty members and two students. The panel of judges reserves the sole right to adjudicate any questions of rules or regulations and will do so in the good faith of fair competition and the honor of mathematics at Georgia Tech.