CAP High School Prize Exam
April 14th, 2015
9:00 - 12:00
Competitors Information Sheet
The following information will be used to inform competitors and schools of the exam results, to determine
eligib
Bijections
Yufei Zhao
yufeiz@mit.edu
In this lecture, we will look at using bijections to solve combinatorics problems.
Given two sets A and B, a bijection (also called bijective correspondence) is a
UMA Putnam Talk
LINEAR ALGEBRA TRICKS FOR THE PUTNAM
YUFEI ZHAO
In this talk, I want give some examples to show you some linear algebra tricks for the
Putnam. Many of you probably did math contests in
Canadian Association of Physicists
2001 Prize Exam
Question 2
The diagram below shows various positions of a child in
motion on a swing. Somewhere in front of the child a stationary whistle is blowing
Canadian Association of Physicists
1994 Prize Exam
This is a three hour exam. National ranking and prizes
will be largely based on a students performance on the
three questions in part B of the exam f
MOP 2007 Blue Group
Tiling
Yufei Zhao
Tiling: Coloring and Weights
June 15, 2007
Yufei Zhao
yufeiz@mit.edu
Main discussion: Packing boxes with bricks
Probably the most basic problem about tiling is to
Trinity Training 2011
Power of a Point
Yufei Zhao
Power of a Point
Yufei Zhao
Trinity College, Cambridge
yufei.zhao@gmail.com
April 2011
Power of a point is a frequently used tool in Olympiad geometry
Canadian Association of Physicists
2000 Prize Exam
Part A: Multiple Choice
Question 1
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
Canadian Association of Physicists
1996 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, perform
MOP 2007 Black Group
Counting in Two Ways
Yufei Zhao
Counting in Two Ways
Incidence Matrices
June 26, 2007
Yufei Zhao
yufeiz@mit.edu
Problems to be discussed in lecture
Problem 1. In a certain committ
UMA Putnam Talk Lecture Notes
Determinants: Evaluation and Manipulation
Yufei Zhao
September 22, 2009
Appetizer problem
(This problem doesnt actually use determinants.)
Problem 1. Do there exist squar
AwesomeMath 2007
Track 1 Combinatorics
Week 3
Lecture 10 : A Contest of Contests
Yufei Zhao
July 31, 2007
1. (IMC 2002) Two hundred students participated in a mathematical contest. They had six
proble
Canadian Association of Physicists
1995 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, perform
Canadian Association of Physicists
1997 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, perform
Winter Camp 2009
Cyclic Quadrilaterals
Yufei Zhao
Cyclic Quadrilaterals The Big Picture
Yufei Zhao
yufeiz@mit.edu
An important skill of an olympiad geometer is being able to recognize known configurat
Winter Camp 2010
Three Lemmas in Geometry
Yufei Zhao
Three Lemmas in Geometry
Yufei Zhao
Massachusetts Institute of Technology
yufei.zhao@gmail.com
1
Diameter of incircle
A
T
B
X
C
D
Lemma 1. Let the
Canadian Association of Physicists
1998 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, perform
an 1
Trinity Training 2011
Yufei Zhao
an 1
Yufei Zhao
Trinity College, Cambridge
yufei.zhao@gmail.com
April 2011
In this lecture we look at some problems involving expressions of the form an 1. Lets
s
Canadian Association of Physicists
1999 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, perform
IMO Training 2007
Similarity
Yufei Zhao
Similarity
Yufei Zhao
July 12, 2007
yufeiz@mit.edu
1. Let ABCD be a convex quadrilateral. Show that
AC 2 BD2 = AB 2 CD2 + AD2 BC 2 2AB BC CD DA cos(A + C).
2. (
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Chapter 6
Communicating and Interpreting
Accounting Information
Chapter Overview
Role
The
of Players in the Accounting Communication Process
Disclosure Process
LO1
Players in the Accounting
Communicat
English 109
October 25, 2016
What your Critical Essay Will Look Like
An Opening paragraph
Opening paragraph should describe and briefly contextualize the
work
What kind of story/game/film is it? Nam
1
Z is a funny Z used for the set cfw_.,3, 2, 1, 0, 1, 2, 3,..
Z+ or N is the set of positive integers cfw_1, 2, 3, 4,..
COS1501 symbols
is the same as N0 which is the set cfw_0, 1, 2, 3, 4, . .
Q is
The C+ Programming
Language
Dynamic Memory Management
Techniques
Outline
Dynamic Memory Management
Interaction with Malloc and Free
Interaction with Arrays
Interaction with Constructors and Destructor
Engineering and Information Technology
C+ Memory management
Storage types
Allocation and deallocation
malloc()/free() vs. new/delete
Memory management internals
Engineering and Information Technology
Generic Programming with C+
Generic Programming
Generic programming a style of programming
supported by C+
Similar to OOP trying to make it simple to reuse code,
and abstracting general concepts
Diffe
C+ OVERLOADING OPERATORANDFUNCTION
http:/www.tutorialspoint.com/cplusplus/cpp_overloading.htm
Copyright tutorialspoint.com
C+ allows you to specify more than one definition for a function name or an o