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## January 23 – Dr. Andreescu – A Few Brain Teasers

Metroplex Math Circle will start its 2010 Spring season this Saturday with a lecture by Dr. Andreescu himself.  Dr. Andreescu’s problem sets are always entertaining and challenging.  However, as students prepare for the AMC 10 and 12 it is particularly helpful to learn from a former director of the AMC.

## First Annual UT Arlington Math Competition

UT Arlington will be hosting a Math Competition that should be of interest to many of our Math Circle participants.  Here are the details:

First Annual UT Arlington Math Competition

Saturday, February 6, 2010, 9:00 am – 12:00 pm
Pickard Hall, Room 110
The University of Texas at Arlington

Who Participates?
Both middle-school and high-school students are welcome to participate in the competition. There is no registration fee. If you plan to attend, please indicate so on your Calculus Bowl online registration form. If you plan not to attend the Calculus Bowl, but to participate in the UT Arlington Math Competition, please contact Dr. Dimitar Grantcharov (grandim@uta.edu, 817-272-1148).

What is the UT Arlington Math Competition?
The competition will contain two parts: one part with about 20 multiple-choice problems, and another part containing one essay-type problem. Calculators will not be allowed. The multiple-choice problems will be at a level of compatible to the American Mathematical Contest 10 (AMC 10), while the essay-type problem will be a bit more challenging. A few sample problems are provided below.

• Which of the following numbers is a perfect square?
(A) 98!99! (B) 98! 100! (C) 99! 100! (D) 99!101! (E) 101!101!
• A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?
• A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively. How many rounds will there be in the game?

What is the Math Battle?
The Math Battle is an exciting two-team problem-solving competition. Each of the two teams will receive a list of problems in advance. A jury and the teams will discuss the solutions of the problems in the afternoon.

Prizes?
The student with the highest score on the UT Arlington Math Competition will be awarded a \$100 gift card. The top five contestants will be awarded medals and trophies.

## November 17 – AMC 8

November 17th is the official date for the upcoming AMC 8.  This test is administered through many middle schools, but if yours does not, it is important to talk to your math teacher or principal now!

The AMC 8 gives invaluable practice for students who will later want to take the AMC 10 and 12.  The results of these high school level exams, administered in the Spring, are often required by the math and science departments of elite universities.

Here is some additional information from the AMC site:

The AMC 8 is a 25 question, 40 minute multiple choice examination in middle school mathematics designed to promote the development and enhancement of problem solving skills. This school year it will be held Tuesday , November 17 , 2009 . Click here for a current brochure.

The examination provides an opportunity to apply the concepts taught at the junior high level to problems which not only range from easy to difficult but also cover a wide range of applications. Many problems are designed to challenge students and to offer problem solving experiences beyond those provided in most junior high school mathematics classes. Calculators are not allowed starting in 2008. High scoring students are invited to participate in the AMC 10.

A special purpose of the AMC 8 is to demonstrate the broad range of topics available for the junior high school mathematics curriculum. This is done by competencies. The AMC 8 has the potential to increase the perceptions of the importance of problem solving activities in the mathematics curriculum by stimulating these activities both preceding and following the examination —specifically by studying the solutions manual.

Additional purposes of the AMC 8 are to promote excitement, enthusiasm and positive attitudes towards mathematics and to stimulate interest in continuing the study of mathematics beyond the minimum required for high school graduation. Developmentally, junior high school students are at a point where attitudes toward school and learning, and perceptions of themselves as learners of mathematics are solidified. It is important that they be provided opportunities that foster the development of positive attitudes towards mathematics and positive perceptions of themselves as learners of mathematics. The AMC 8 provides one such opportunity.

## USAMO Qualifiers

AMC recently announced the students invited to sit for the USA Mathematical Olympiad.  This is a tremendous accomplishment following exemplary performance on the AMC 10 or 12 and a high score on the AIME.  The qualifiers from Texas are:

Every student representing Texas at the USAMO deserves to be very proud.  However, Metroplex Math Circle is particularly proud that one of our most regular attendees is by far the youngest student on the national list.

Michael Ma, as a fourth grader received a perfect score on the AMC 10 and followed it up with a performance on the AIME that is beyond all but the best high school students.  MMC cannot claim the credit for this terrific success (that belongs to Michael and his family) but Michael does exemplify the hard work and talent that Dr. Andreescu seeks to identify and encourage.

## AMC 10/12B Honor Roll

Dr. Andreescu once again offered UT Dallas as a higher education site for this year’s AMC 10/12B.  We were very proud of all of the Metroplex Math Circle participates who took the test.  Following are the students who scored above 100 points (out of 120) on the AMC 10 and above 90 points on the AMC 12.

### AMC 10

RUSSELL HOUSTON  *
DANIEL HUANG  *
AMY CHYAO  *  (SA)
MICHAEL HWANG  *  (SA)
ERIK NGUYEN  *
JACOB CORDEIRO
NIHAL KODURI  (SA)
SANGJUN YOO
DOMINIC YURK
JOSHUA CAI

### AMC 12

ARNOLD LIAO   *
KEVIN CHANG  *
SIDDHANT MITTAL  *
YEJIN KIM
ARI GAO
ROBERT TUNG

* = AIME qualifier

(SA) = Metroplex Math Circle Student Advisor

Please join me in congratulating these students on their strong performance.  If you are a math circle participant who scored in this range on the 10/12A or at your own school please feel free to post in the comments below or e-mail your score to be recognized.  Students who would like to receive their scores from the 10/12B can e-mail djcordeiro@sbcglobal.net

## March 14th – Titu Andreescu – AIME Preparation

Dr. Titu Andreescu, former director of AMC and coach of the US IMO team will be giving a special lecture for those preparing for the American Invitational Mathematics Examination (AIME).   This will be a very challenging session befitting the caliber of the AIME examination.  However, students who did not qualify this year but are working on AMC 10 and 12 preparation should benefit from the unique insights and strategies that Dr. Andreescu will provide.

Here is some information about the AIME:

The AIME (American Invitational Mathematics Examination) is an intermediate examination between the AMC 10 or AMC 12 and the USAMO. All students who took the AMC 12 and achieved a score of 100 or more out of a possible 150 or were in the top 5% are invited to take the AIME. All students who took the AMC 10 and had a score of 120 or more out of a possible 150, or were in the top 1% also qualify for the AIME. For the 2008-2009 school year the date for the AIME I is Tuesday, March 17, 2009 and the AIME II is Wednesday, April 1, 2009.

The AIME is a 15 question, 3 hour examination in which each answer is an integer number from 0 to 999. The questions on the AIME are much more difficult and students are very unlikely to obtain the correct answer by guessing. As with the AMC 10 and AMC 12 (and the USAMO), all problems on the AIME can be solved by pre-calculus methods. The use of calculators is not allowed.

## NACLO 2009

Students who excel at math competitions like the AMC 10 and 12 might be interested in participating in the North American Computational Linguistics Olympiad coming up in February.   Similar to the USAMO, this national test is used to select a team to compete internationally in the International Linguistics Olympiad.

Like Math Circles and international problem solving competitions, these linguistics competitions have their origins in Eastern Europe.  They also appear to draw on many of the same problem solving and thinking talents of successful Math Olympians.    In this interview with Adam Hesterberg, a former MATHCOUNTS and USAMO winner, explains how he prepared for his win in last year’s ILO.

For those of us in the Metroplex area it appears that the University of North Texas in Denton will be offering the NACLO this year.

## Alcumus

Our very good friends at the Art of Problem Solving have worked very hard to develop a new online learning system called “Alcumus.”  Alcumus is a game that students can play to compete against themselves, compare their progress on the leader’s board and identify gaps or weaknesses in their math preparation.

Alcumus features over 1100 different problem representing a wide variety of subjects.  In addition, the Art of Problem Solving instructors have developed over 60 video tutorials to help students better understand the subjects they are likely to see on contests like AMC 8, AMC 10 and AMC 12.

Alcumus is currently free to members of the Art of Problem Solving community so login or create an account today.

## AMC Test Preparation – Recap

The October 18th Math Circle was very special.  Dr. Andreescu selected 15 problems to teach specific problem solving strategies to the students.  Some of the problems involved numbers small enough to be solved in a brute force method, but Dr. Andreescu explained a principal underlying each of the problems which would allow them to be solved within a fraction of the time with less risk of arithmetic mistakes.

If the lecture just gave the students 15 “tricks” for improving their AMC test scores it would have been worthwhile, but not nearly to the standards of Dr. Andreescu or Metroplex Math Circle.  Instead, Dr. Andreescu explained exactly how each rule was derived and gave the students the tools to generalize these ideas to other kinds of problems.

Between problems, Dr. Andreescu answered questions from students and parents about these critical tests.  A quick poll of this well-attended session showed that unfortunately many schools still do not offer the AMC 8.  Parents and students went away from this session with a mission to demand that their school systems take seriously these valuable and respected tests.