Thursday, November 8, 2012

Math Competitions Problem Solutions


July, 2019
Math in Music 2 video: 
https://youtu.be/9HRARNpyhxo
Edited "Math in Music" article:
http://david.balmin.com/mathinmusic.pdf

June, 2019
SD Honors Math 2018, Part I, 24
https://youtu.be/mM3FjGsmJh4

Problem 6 of 2007 IMO:

SD Honors Math  2018, Part I, 19


IMO 2017 Problem 3 (revised)
July - August, 2018
I  have posted the solutions of problems 3 and 6 of 2018 IMO in YouTube:


June 2, 2018
I  have posted the solution of USAMO 2018, Problem 3. It's an interesting fact and the solution is pretty! 
https://youtu.be/45SidE3dVTU 

December 12, 2017
I  have published an article "Solving Angles in a Parallelogram"

September 26, 2017
I  have posted the solutions of all 6 problems from 2017 International Math Olympiad (IMO) in YouTube.

August 1, 2017
I posted Math in Music video in YouTube: 

June 23, 2017
Сompleted two weeks of All-Star Academy Math Competition Camp in San Diego. The vast majority of students have graduated with flying colors! Outstanding job guys! Keep up the good work. 

February 1, 2017
I gave one lecture to the combined Gauss & Cauchy group at San Diego Math Circle. The topic was: "Preparation for AMC-10 and AMC-12 tests".

December 7, 2016
I gave two lectures at San Diego Math Circle in October and November 2016. The topic was: "Preparation for the AMC-8 test".

December 7, 2016
I was coaching two Math Club groups of students: at Oak Valley Middle School and at the 
San Diego Russian School in September and October 2016. 

May 16, 2016
Completed this school year at the Russian School on the campus of UCSD university in San Diego.

September 26, 2015
I am working as a coach of the Math Club team at Oak Valley Middle School in San Diego. This group of motivated students have ambitious goals to succeed at the various math competition tests.

December 17, 2015
I edited my paper "The Maximum Area of a Cyclic Polygon Theorem": 
http://advancinginmath.appspot.com/Papers/CyclicPolygonsTheorem1.pdf

and the solution of Problem 25 of 2011 AMC 12A (at the end of this blog).

August 3, 2015
MathLinks Math Summer camp was a success! I really enjoyed working with two groups of extremely talented students. Good luck to them in their pursuing brilliant future in math, sciences, engineering and whatever other areas of their interests might be!

May 17, 2015

I had the final math lesson of this school year at the Russian School on the campus of UCSD university in San Diego. All the students enjoyed the challenging and interesting math problems and learned a thing or two about math theory too.

January 19, 2015
I teach advanced math on Sundays at the Russian-language school on the campus of UCSD university in San Diego. I have already given three lessons there to the group of enthusiastic and talented students. These meetings are going in the creative and informal atmosphere. So far, we have discussed  mostly counting / combinatorial topics and problems. At our next meeting, we will start tackling some geometry.

November 14, 2014
I met with the students of Saint Augustine High School Math Circle who plan to participate in advanced Math Competitions later this year.

November 1, 2014
I delivered two lectures to students of San Diego Math Circle:
Euler group (7th and 8th grades) and Fermat group (5th and 6th grades).
Subject: AMC 8 test preparation. 
Students of both groups participated very actively in the process of math problem solving and in the review of math theory used in AMC 8 tests. I had a lot of positive feedback from students and their parents after the lectures.

August 3, 2014
I was teaching two groups of students at the MathLinks Summer Camp starting on July 15 and ending on August 1 (during the first and third weeks - middle-school level, during the second week - high-school level. Most students in both groups were quite advanced in school mathematics and highly motivated. All students were eager to learn more advanced math and to solve challenging math problems. They learned a lot about math and math problem-solving methods during those three weeks of camp (and had good time too!). 

June 7, 2014
I published video lesson with Introduction to Riemann's Hypothesis for school students.
http://www.youtube.com/watch?v=6qqWWshQQmA

June 7, 2014
I developed Android phone application: Riemann's Zeta-Function Calculator.
https://www.youtube.com/watch?v=dTwlUZ67PSo

October 22, 2013
Simplified the solution of Problem #4 in my Math E-Books Volume 1. 
These books are available for downloading at: http://advancinginmath.appspot.com/

October 20, 2013
My meetings with Saint Augustine High School Math Circle group in San Diego go very well!

July 28, 2013
I was teaching the group of 14 students (grades 7 - 9) at the MathLinks Summer Camp between July 8 and July 26, 2013. It was a very strong group of young people who were eager to learn advanced math and solve challenging math problems. They learned a lot about math and math problem-solving methods during those three weeks of camp (and had good time too!). 


May 23, 2013
I had the first introductory meeting with Saint Augustine High School Math Circle group in San Diego. 10 students attended this meeting. It was a great experience. All students actively participated in solving two math problems and discussions of math history and theory.

January 19, 2013
I delivered two lectures to the 10th-graders (the Gauss group) and the 12th-graders (the Cauchy group) of San Diego Math Circle at the UCSD. Subjects: "AMC 10 and 12 Test Preparation".



December 15, 2012
I gave a lecture to the 12th-graders (the Cauchy group) at the San Diego Math Circle. The topic was "Some Proofs of Math Olympiad Problems" with the emphasis on using Calculus for the strict proofs of the solutions in several Math Olympiad and AMC problems. It was a very advanced group of students. Some of them had participated in Math Olympiads and they actively participated in the discussions during my lecture.

November 8, 2012
I delivered two lectures to students of San Diego Math Circle:
Euler group (7th and 8th grades) and Fermat group (5th and 6th grades).
Subject: AMC 8 test preparation.
Both lectures had subject "AMC 8 test preparation". 

September 12 2012
Posted Youtube videos with solutions of AIME II Problems #15 and #7 :
http://www.youtube.com/watch?v=uWADhXq8n7U
http://youtu.be/WRP--6Db1qw

July 26, 2012
Yesterday was the closing day of MathLinks Summer Camp (it lasted 3 weeks). I had 11 students in my group, grades 7 - 9. It was both enjoyable and productive. The students in my group have learned the great deal about math and math problem solving during those three weeks.
Watch my videos (search for "David Balmin Math" in YouTube).

Yes, you can!
I provide step-by-step instruction for solving math problems from the annual AMC 8/10/12 (American Mathematics Competitions, grades 8, 10, 12) and AIME (American Invitational Mathematics Examination) tests.
Studying for and taking AMC and AIME tests significantly improve students' math skills. Many top universities request AMC scores as part of the enrollment application process. In order to be successful in these tests, students need solid experience in solving math problems that have level of difficulty expected in these tests.
Generally, we will focus on problem solving and will cover any topic of school math that is necessary to solve a problem. As a result, the student's knowledge and understanding of school math and problem solving skills will be improved!

Download my e-books from the "Training for Math Competition Tests" series here: 
http://advancinginmath.appspot.com/

Each book contains detailed step-by-step solutions of several math competitions problems that substitutes for 1-3 private lessons, depending on the student’s level and pace of studying.

In these books, I use the same methodology based on the principles of math problem solving that I use in private training sessions. These principles are outlined and explained in each volume of this series.

R
ead other posts below in this blog that illustrate the process of solving actual problems from the selected AMC tests.

Keep in mind that these problems were among the most complex problems in AMC 10/12 tests and may look intimidating at first glance, but, after a detailed step-by-step review, these and other AMC/AIME problems' solutions will become clear and straightforward to you.

Note: In the actual training sessions and in the YouTube video lessons, I use normal mathematical notation (not like "z^8" or "sqrt(3)")!

Click the link below to make donations via PayPal  to support this work on helping school students to perfect their skills in math problem solving:
http://advancinginmath.appspot.com/donations/index.htm

Email to dbalmin@gmail.com

Sincerely,
David Balmin