Deriving Taylor Series using Non-Calculus Methods
Tristan Shin
14 October 2015
Note: In this paper, taking limits is not considered calculus. Also, for purposes of
simplicity, we are assuming that the Taylor series exist (for certain values of x, that is)

The Perpendicularity Lemma
droid347 and yojan sushi
September 2, 2015
Abstract
In this note, we introduce the Perpendicularity Lemma, a simple result that, when applied, can reduce
quite a few complex olympiad geometry problems to mere computations. Credi

Two New Proofs of Leibnizs .
The 2015 WOOTer
Page 1
Two New Proofs of Leibnizs Inequality
Author
The 2015 WOOTer
1
First Proof: Sums of Squares of Distances
1.1
A Quick Theorem
The first proof utilizes the following fact:
Theorem 1.1. In the Cartesian pla

100 Geometry Problems: Bridging the Gap from AIME to USAMO
David Altizio
August 3, 2014
Abstract
This is a collection of one-hundred geometry problems from all around the globe designed for bridging the
gap between computational geometry and proof geometr

2015 AoPS Mathematical Olympiad
AoPSMC
May 23, 2015
Welcome to the 2015 AoPSMO! Before you start the test, here are a few things you need to know:
1. You have 3 hours total to take the test in.
2. Please submit your solutions through PM.
3. Solutions will

AIME Counting Problems
1.
[85-5] A sequence of integers a1, a2, a3, is chosen so that an = an-1 an-2 for each n 3.
What is the sum of the first 2001 terms of this sequence if the sum of the first 1492 terms
is 1985, and the sum of the first 1985 terms is

Secondary School Admission Test Score Report
About You
Name
Jason Jiang
Grade
8
Gender
Male
Date of Birth
22 Jul 2004
Jason Jiang
47735 Pavillon Rd
Canton, MI 48188
The Test You Took
Registration ID
170829764
Test Date
15 Oct 2016
Test Level
Upper
Test Ce

Educational materials developed through the Howard County History Labs Program, a partnership between the Howard County Public School
System and the UMBC Center for History Education.
Shays Rebellion
Historical Thinking Skills Assessed: Close Reading, Cor