Clemson Calculus Challenge Description

During the summer of 2002, mathematics faculty from the South Carolina Governor's School for Science and Mathematics (GSSM) suggested the Department of Mathematical Sciences at Clemson University organize a calculus-based mathematics competition for high school students. The GSSM teachers pointed out there were many mathematics contests for their students to enter, but none that concentrated on calculus exclusively. The Department of Mathematical Sciences was very eager to encourage excellence in the study of calculus at the high school level and agreed to provide such a contest: The Clemson Calculus Challenge (CCC ).

The inaugural CCC was held on April 5, 2003, with 54 participants from 11 schools. Over the years the CCC has grown, with the most recent CCC attracting over 170 students from 21 regional high schools. The Department of Mathematical Sciences and Clemson University look forward to the CCC ’s continued expansion.

The competitive portion of the CCC has two components: an individual examination given in the morning and a team competition that takes place in the afternoon. Awards for individual performance on the morning exam, team performance in the afternoon competition, and overall school performance are presented for first, second, and third place in each of the school divisions. In addition to the competitive components of the CCC , participants are exposed to some of the exciting research taking place at Clemson University via displays housed outside the competition rooms. There is also a short research presentation given by an invited speaker.

High schools are invited to bring a group of no more than twelve students to represent their institutions.

Morning Individual Exam

The morning exam is an individual exam that consists of forty multiple choice questions covering topics found in the Advanced Placement Calculus AB syllabus. The time allotted for the individual exam is ninety minutes. The use of calculators is not permitted on this exam.

The morning test is designed to progress from fairly straightforward questions to quite challenging problems. The first ten questions will cover general knowledge of the AP Calculus AB topics. The second ten questions will be more conceptual and may require combining knowledge from several areas of calculus. The next set of 10 questions will be “tricky,“ i.e., will have some twist needing a deeper understanding of calculus. The last ten questions will be the most challenging. There will be five multiple choice answers for each question, including the choice of “none of the above.”

Each individual test score will equal the number of correct responses minus one fourth the number of incorrect responses. A question that is not answered will neither contribute nor subtract from the exam score.

If there are ties for first, second or third places, the following rules will be applied sequentially to those tests with tied scores until the ties are broken:

smallest number of incorrect responses
weighted correct answers =
1*(no. of correct responses from problems 1-10)
+ 2*(no. of correct responses from problems 11-20)
+ 3*(no. of correct responses from problems 21-30)
+ 4*(no. of correct responses from problems 31-40)
sudden death: 3 free-response problems, graded by judges.

Afternoon Team Competition

A team may consist of two, three, or four members. However each school must enter the minimal number of teams possible from their school. For example, if a school brings eight students, this school must enter two 4-person teams. Schools with only one participant may have that student assigned to a “mixed” team for the afternoon competition. Mixed teams, i.e., teams composed of individuals from different schools, are eligible for team awards, but their team scores will not contribute toward their respective school scores.

Each team will sit at one table. The use of calculators is strictly prohibited during the team competition.

There will be six rounds of questions. Each round will be allocated ten minutes. At the beginning of each round, the round's question will be delivered to each team by the runner assigned to the team. All teams will begin work on the round's question simultaneously. A digital clock located at the front of the room will indicate the time remaining during the round. When a team has an answer, they raise their hand and a runner will immediately collect their answer and note the time remaining. The team's response will then be delivered to the graders, and if correct, the score for that question will be the “ceiling function” of the minutes remaining. For example, if a team submits a correct answer with 6:32 left on the clock, the team will receive a score of 7 for this round. A team that submits an incorrect response will receive a score of 0 for the round.

Each team score is the total of the points rewarded for the six rounds. Ties among the top team scores will be broken by a sudden death round. Only teams who remain present for the sudden death round are eligible to break the tie.

For each non-mixed team, a team-school score will be computed as the team score in the afternoon contest plus the average of the individual scores from the morning contest for the members of the team. Each school score will be determined as the maximum of the team-school scores for the teams representing the school. The team-score from a mixed team will not be used in determining a school score.

School Divisions

Schools of similar enrollment are assigned to one of several divisions. Prior to 2008, there were two divisions in the CCC . Because of the increase in the number of schools participation in the 2008 CCC , the number of divisions was increased to three. In the future, the number of school divisions will be determined by the amount of participating schools and their enrollments.

Awards

Following the afternoon competition, the award ceremony will take place. Awards will be presented to the top three finishers in each school division for the Individual Test Competition, the Team Competition, and the School Competition. We also expect to give several $500 Clemson University scholarships to winners of the Individual Test Competition. The scholarship recipients must attend Clemson University to collect the scholarship award.

Any challenges to grading of either the morning exam or the afternoon team competition rounds must made after the competition is over. The challenge must be written and be made by a team coach.

Research Presentations

Prior to the afternoon team competition, we will have a short lecture illustrating a current research area at Clemson University. The talk will relate to calculus and will be for a general audience. In addition to the talk, current Clemson students or faculty will have static displays located outside the examination rooms describing some of the ongoing research at Clemson University.

Sample Questions

We often get requests for copies of old contest exams. We do not give out old copies, but we do supply some sample questions that have been used in previous Challenges. The sample problems can be downloaded as a PDF file.

We are grateful to our sponsors:

College of Engineering Science Department of Mathematical Sciences