Titu Andreescu
Dorin Andrica
Complex
Numbers
from A toZ
Second Edition
Titu Andreescu
Dorin Andrica
Complex Numbers from
A to . Z
Second Edition
Titu Andreescu
Department of Science and Mathematics
Ed
Lecture 8 Polynomials, Part 1
Holden Lee
1/29/2011
1
What is a polynomial?
In this section, we will formally define polynomials. (As this is somewhat abstract, feel
free to skip on first reading.) In
1993 AIME SOLUTIONS
1. (Answer: 728)
We rst count those integers of the desired type with 4 or 6 as the thousands digit.
In this case, the thousands digit can be chosen in 2 ways, and then the units
Geolympiad
Summer 2015
2015 Geolympiad Summer Contest
Directions: This competition is a two day competition with 3.5 hours allotted for each day. Each day
consists of 3 geometry problems that are arra
QED Monthly Volume 2
Alexander Katz
QED Monthly Volume 2
Authored by Alexander Katz
Page 1
Contents
1 AIME Algebra Parts I and II
3
2 AIME Combinatorics Part I
25
3 AIME Combinatorics Part II
36
4 AIM
Art of Problem Solving Math League
Tryout Test
Rules:
1. There are 15 questions to be completed in 20
minutes. All answers are real numbers.
2. When you are finished, please submit your answers
to the
2
Powers of Integers
An integer n is a perfect square if n = m 2 for some integer m. Taking into account
the prime factorization, if m = p11 pkk , then n = p121 pk2k . That is, n is a
perfect square i
Math League Team Selection Test Solutions
1. Christys test scores to date are 90, 80, 70, 60, and 85. Her goal is to raise her test average at
least 3 points with her next test. What is the minimum te
Olympiad
Combinatorics
Pranav A. Sriram
August 2014
Chapter 1: Algorithms
1
Copyright notices
All USAMO and USA Team Selection Test problems in this chapter are
copyrighted by the Mathematical Associa
Math League Qualifying Test
Directions: This is a 15 question, 60 minute test. 1 point is awarded for a correct answer, and 0
points for an incorrect or blank answer. Read each problem carefully and w
BOGTRO
1
AIME Study guide
1
INTRODUCTION
Introduction
Like every year when the AIME comes around, people begin to agonize over details: what should I guess on
#15? Should I bring a granola bar or a wa
Inversion on the Fly
Gunmay Handa
[email protected]
October 3, 2015
When I tried to learn inversion, I found myself hopelessly stuck trying to
muck through difficult definitions and not finding co
1
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~c y people, breakfast cereal is an impor-
" in their diets. Cereals also contain
a1 shown to be associated with main-
33100d pressure. An analysis of the
grams) and the potassium content (in
ings of
IN THE NAME OF
ALLAH
IMO ShortList Problems
1959 2009
Collected by: Amir Hossein Parvardi (amparvardi)
Problems from:
http:/www.artofproblemsolving.com/Forum/resources.php
Published: 2010-10
Email: am
2016 RoME (MOCkSP Qualifying Test)
1. Two people, Alan and Ivan, are playing a game. Each of them will simultaneously raise either their
left hand or right hand. If they raise the same hands, Ivan win
10th Annual Harvard-MIT Mathematics Tournament
Saturday 24 February 2007
Guts Round
.
10th HARVARD-MIT MATHEMATICS TOURNAMENT, 24 FEBRUARY 2007 GUTS ROUND
Note that there are just 36 problems in the G
New Zealand Mathematical Olympiad Committee
Symmetric Polynomials
Arkadii Slinko
1
Introduction
These notes begin with two basic results about symmetric polynomials: the Fundamental Theorem of Symmetr
Math League Team Selection Test
Please write your answer to each question on the line provided. You will have 35 minutes to
complete the test. NO CALCULATORS ALLOWED. Good luck!
1. Christys test score
Harvard-MIT Mathematics Tournament
March 15, 2003
Individual Round: Combinatorics Subject Test
1. You have 2003 switches, numbered from 1 to 2003, arranged in a circle. Initially, each
switch is eithe
Thirteenth International Olympiad, 1971
1971/1.
Prove that the following assertion is true for n = 3 and n = 5, and that it is
false for every other natural number n > 2 :
If a1 , a2 , ., an are arbit
40th International Mathematical Olympiad
Bucharest
Day I
July 16, 1999
1. Determine all finite sets S of at least three points in the plane which satisfy the
following condition:
for any two distinct