2013 Math Talent Quest Online Training Program
2013 Math Talent Quest Online Training Program
Introduction
Welcome to the 2013 Math Talent Quest Online Training Program!
Please read this document carefully. It includes all the basic information regarding the training
program.
Introduction to the Program:
You are given a username and a password to log in to this website. This will be our primary source
for the training program.
Username: OTP2013
Password: geometry
By joining this program, you are expected to spend about 1 hour or more every night to complete
our lessons and problems. Remember that this program may be much more rigorous than many of
the other classes you’ve taken. It is important that you keep in mind that the material may not be
easy. Spend some time every day studying some math, and you will improve. It is important not to
give up when facing a difficult problem, as one learns most from challenging problems.
Since the students taking part in this training program come from states from all across the nation,
there is no way for us to meet in person and actually talk to you. Hence, the class structure will be
very different from what you are used to in school. Instead, this program heavily relies on your
own self-studying. It is important that you are motivated to train yourself; while no one is going to
be sitting behind you and watching you closely, it is easy to fall behind if you slack off. More
details will be explained below.
This training program will last for one month, from Sunday, June 15th, to Monday, July 15th. A
detailed schedule may be found on the online portal.
Online Forum:
2013 Math Talent Quest Online Training Program
An online forum will be exclusive to the members of the training program. You may discuss any
problems or ask any questions on the forum. However, you may not discuss any problems or
exams we give out to you until they are due.
This forum will also include important announcements for the program, and thus everyone is
required to register an Art of Problem Solving account (found at http://www.aops.com) and
complete the AoPS username form found on the online portal.
Here is how you access the Math Talent Quest forum:
1. Go to http://www.aops.com. You must be signed in in order to see the forum!
2. Click on “Community” on the top green bar of the website.
3. Scroll down, and you should see a section called “High School Contests & Programs.”
Under that, there should be a link called “Other Contests & Programs.” The last link listed
under “Other Contests & Programs” is “Math Talent Quest.” Click on that. (Alternatively,
you can use the Find Function on “Math Talent Quest.”)
4. At the very top, there is a link called “Math Talent Quest Training.” Click on that.
You may discuss anything you’d like on the Training-Program-exclusive forum, but please limit
the number of frivolous posts. We highly encourage you to ask questions whenever you are unsure
about something.
Lessons:
Each weekday night, starting June 15th, a document will be posted on the online portal. There are a
total of 21 lessons, covering all four areas of algebra, geometry, combinatorics, and number theory.
You are expected to read and understand them thoroughly. Tests are given out on Sundays and are
due on the following Saturday. Scores will be posted and top 5 individuals will be announced on
the following Tuesday.
Practice Problems:
Practice sets will are found at the ends of each daily handout. You are expected and required to do
these problems. When problems have numerical answers, submit your answers through our online
form, the link of which may also found on the online portal.
You may not discuss these problems with anyone until they are due, after which these problems
will appear on our forum on AoPS and you may discuss them with each other.
Practice Exams:
A total of 3 practice exams will be given out during this program. These exams range in difficulty
and differ in format. Detailed instruction for each of these will be included in these exams. These
exams will include both short answers questions and free response questions. You must submit
your full solutions for the free response questions. That includes all of the steps that you did, with
words to explain what you did.
After the completion of each exam, you need to scan your solutions to the exams and send them to
us by email to [email protected].
2013 Math Talent Quest Online Training Program
You must send your solutions by the deadline of each of these exams (included in the schedule).
No late work will be accepted unless extreme circumstances are provided.
You may not collaborate on any practice problems or exams before they are due. Any violation of
this rule will result in automatic dismissal from the training program.
Proofs and Solution Writing:
You may be accustomed to math problems asking for a specific number or a specific length. A
proof is a math problem that does not necessarily ask you for a number, but specifically, a series
of logically connected arguments to prove that a certain statement is true. Generally, a proof has
the key words “Show that…” or “Prove that…” in the question sentence. For example, an example
of an easy proof would be:
Problem: In a square of side length 2, five points are chosen inside. Show that there exists two
such points such that the distance between the two points is less than
2.
BAD Solution: The optimal way to put the 5 points as far from each other is to put 4 of them
on the corners. However, the point in the square farthest from all four corners is the center of
the square, which is
apart.
2 units away, so there must be two points that are a distance of
2
The previous solution is bad in that some parts of the solution are not justified. For
example, we don’t know that putting the 4 points on the corners will necessarily optimize
the distances. For example, this solution does not justify why there can’t be, say, 5 points
in a circle that satisfies the conditions. While intuition may tell you that the above solution
seems right, the solution is very handwavy. All steps in a proof must be logically
consistent!
GOOD Solution: Let’s break the square up into 4 smaller squares, each with side length of 1.
Since there are 4 squares and 5 points, there must be two points in the same square. However,
the maximum distance between two points in a square of side length 1 is the diagonal, so the
distance between those two points must be less than 2 .
This solution is much cleaner. Every step of the proof follows something logically, and
there are few assumptions made. The difference between this and the last proof is that we
tried generalizing the “most favorable outcome” with 4 different points at a time. On the
other hand, this proof uses much more obvious version, only needing to maximize the
distance between 2 points.
Unless otherwise specified, we expect full solutions or proofs for your tests. In general, you should
keep in mind that the solution to a math problem is significantly more important than the answer to
a problem. Thus, you shouldn’t guess on your problems just because you want to get a problem
right, but rather to spend time and find a proper solution to each problem.