m - Notes-math

sqrt5=2.236, tan15=2-sqrt3, (a+b)^3; sqrt3=1.732, sqrt2=1.414

bayes theorem/conditional probability

circle angle jumping technique

cut the crap-

triangle counting, similar to sum of n^2: floor of n(n+2)(2n+1)/8

sum of n: n(n+1)/2

sum of squares: n(n+1)(2n+1)/6

sum of cubes: n^2(n+1)^2/4

folder with all AOPS class material https://iu.box.com/s/sofrp55mws7n807vqxfurwfrcqw4s41n

chap 9 - triangle inequality

MATHCOUNTS State Competition Preparation (All volumes).5_books_20181116_c

Theorem 1. Of all triangles with a fixed perimeter, an equilateral triangle has the greatest area.

Theorem 2. Of all triangles with a fixed area, an equilateral triangle has the smallest perimeter.

Theorem 3. Of all triangles with the same base and same height, an isosceles triangle has the smallest perimeter.

Theorem 4. Of all triangles with the same base and same perimeter, an isosceles triangle has the greatest area.

Theorem 5. If one side of a triangle is longer than another side, then the angle opposite the longer side will have a greater degree measure than the angle opposite the shorter side. Converse is also true.

chap 10 - similar triangles - lots of examples

MATHCOUNTS State Competition Preparation (All volumes).5_books_20181116_c

In triangle ABC, if 􏰓A = 2􏰓B, then a²􏰈 b²􏰌 bc

ch13 algebra

MATHCOUNTS State Competition Preparation (All volumes).5_books_20181116_c

xⁿ􏰇 yⁿ􏰈 􏰖x 􏰇 y􏰗􏰖x^n􏰇1􏰌 x^n􏰇2y 􏰌􏰘􏰌 y^n􏰇1􏰗 for all n.

xⁿ􏰇yⁿ􏰈 (x 􏰌 y)(x^n􏰇1􏰇 x^n􏰇2y 􏰌...􏰇 y^n􏰇1) for all even n. xⁿ􏰌yⁿ􏰈 (x 􏰌 y)(x^n􏰇1􏰇 x^n􏰇2y 􏰌 ... 􏰌 y^n􏰇1) for all odd n. (1􏰇x)(1􏰌x􏰌x²􏰌x³􏰌􏰊􏰊􏰊􏰌x^n􏰇1)􏰈1􏰇xⁿ.

ch14 consecutive numbers

MATHCOUNTS State Competition Preparation (All volumes).5_books_20181116_c

(3) Consecutive integers theorems

Theorem 1: The product of k consecutive integers is divisible by k!. Theorem 2: There must be one positive integer divisible by n among n

consecutive positive integers.

Theorem 3: The number of ways to select k non-consecutive elements from n

_􏰆n 􏰇 ( k 􏰇 1) _􏰃consecutive terms is N = 􏰄_{􏰄 k}􏰁_􏰁.

n is the total number of terms. k is the number of elements selected.

ch15 venn diagram - set theory; half is just problems and solutions

MATHCOUNTS State Competition Preparation (All volumes).5_books_20181116_c

The maximum number of planes that can be formed by n points is nC3

^􏰄_􏰄3^􏰁_􏰁(1)

􏰅􏰂

MATHCOUNTS State Competition Preparation (All volumes).5_books_20181116_c

Counting Cubes

The formula for the total number of cubes, N, in a given large rectangular solid with dimension m 􏰉 n 􏰉 r is

N = m 􏰉 n 􏰉 r + (m – 1) 􏰉 (n – 1) 􏰉 (r – 1) + (m – 2) 􏰉 (n – 2) 􏰉 (r – 2) +...+ (m – I) 􏰉 ( r – J) 􏰉 1. (I and J are integers, m ≥ n ≥ r ) (5)

Counting Rectangular Prisms

95 state team 8

https://www.mathcounts.org/sites/default/files/u49/Comp%20Errata%20through%20%2700.pdf

https://math.stackexchange.com/questions/757827/1995-mathcounts-state-team-8

https://www.mathcounts.org/sites/default/files/u49/Comp%20Errata%20through%20%2700.pdf

chicken mcnugget theorem-

https://artofproblemsolving.com/wiki/index.php/Chicken_McNugget_Theorem

generating function/potatoes counting with 4-letter words:

https://math.stackexchange.com/questions/20238/6-letter-permutations-in-mississippi?rq=1

generating functions -

https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2005/readings/ln11.pdf

https://math.stackexchange.com/questions/20238/6-letter-permutations-in-mississippi?rq=1

http://users.softlab.ntua.gr/~nidal/discrete/notes/examples/gen2.pdf

https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf

https://artofproblemsolving.com/wiki/index.php/Category:LaTeX

https://artofproblemsolving.com/wiki/index.php/Category:Asymptote

shoelace theorem is in handbook 2018-2019 page 58

https://iu.box.com/s/yt717ekkurniha7xzhocwi9xz8iloasn

microsoft paint to draw circles

sum of cube odd number; sum of cube even numbers https://www.geeksforgeeks.org/sum-cubes-even-odd-natural-numbers/

Fibonacci number is sum of binomial coefficients, shown at https://proofwiki.org/wiki/Fibonacci_Number_as_Sum_of_Binomial_Coefficients and https://math.stackexchange.com/questions/2227687/binomial-coefficient-and-fibonacci-numbers. F numbers themselves https://www.mathsisfun.com/numbers/fibonacci-sequence.html.

2015 state sprint 29 no need to consider both sides since already considered as shown at https://math.stackexchange.com/questions/2671035/out-of-50-consecutive-numbers-what-is-the-probability-that-the-absolute-diffe?rq=1

https://www.houstonisd.org/cms/lib2/TX01001591/Centricity/Domain/41539/PreMathcounts Things to Know.pdf

http://mathcountsnotes.blogspot.com/2011/12/mathcounts-competition-preparation.html

mathcounts minis-

divided by year - he skipped the 2 hardest problems of 2019.

https://artofproblemsolving.com/videos/mathcounts

https://www.youtube.com/playlist?list=PLF579ECF317F5DC48

1 is not a prime not a composite

triangle area trick = b1*h1=b2*h2, can change base and use same height

keep it simple, don't over complicate it

first correct 2nd fast, deep breath, back straght, relax

principles + example; theory first, must have examples to show

there's a long distance between knowing it and using it correctly and fast

go thru target at home; let her work on sprint in school and bring back answers

self go thru number theory and explain to her; don't let her watch videos

1999 state target #8 easy https://www.youtube.com/watch?v=ptFMOMlxTss

sprint 20 https://youtu.be/pKp1c0uJMUA

target 2 https://youtu.be/SIU0UGs3F54

https://youtu.be/5tjvYMICUds

https://youtu.be/CE6lMYXSdhA

https://youtu.be/dJQiDzMWu8E 2003

https://youtu.be/2mm8DGedeQY 1990

mississippi rule of counting https://youtu.be/aFFRoDM01RY

school/chapters a lot http://mathcountsfsms.weebly.com/mathcounts.html

1999-1990 state solution book $20

https://www.mymathcounts.com/Copied-Eleven-Years-Mathcounts-National-Solutions3.php

correct and fast- deep breath, back straight, relax

target strategy, look at the 2 problems fast, work on the easier one first!! the one you know how to solve

Counting principles:

in series=multiplication=AND

in parallel=addition=OR

sequence=list of number, no adding

series = sum of numbers, has adding

only repeat past mistake problems; no need to do all

print past handbook problems, state target problems, then sprint problems

focus on middle-school math for mathcounts - past handbooks and state/chapter/school problems!

national is last thing to consider.

priority - handbooks, state, chapter, school, target, sprint, team

get knowledge points

get correct first, then improve speed! just simple, two legs.

repeat doing same problem sets after several weeks

mathguy.us has good handbooks

https://artofproblemsolving.com/wiki/index.php/Category:Theorems

https://artofproblemsolving.com/wiki/index.php/Category:Inequality

https://artofproblemsolving.com/wiki/index.php/Category:Elementary_algebra

https://artofproblemsolving.com/wiki/index.php/Category:Polynomials

https://artofproblemsolving.com/wiki/index.php/Number_theory

https://artofproblemsolving.com/wiki/index.php/Category:Definition

https://artofproblemsolving.com/wiki/index.php/Category:Mathematics

https://artofproblemsolving.com/wiki/index.php/Factoring

https://artofproblemsolving.com/wiki/index.php/Category:Set_theory

https://artofproblemsolving.com/wiki/index.php/Natural_number

Z is integers; N is natural numbers

shoelace method first seen on 1819 handbook - aops has it too for polygon area finding using vertex coordinates https://artofproblemsolving.com/wiki/index.php/Shoelace_Theorem

algebra cheat sheet - good

http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet_Reduced.pdf

https://www.youtube.com/user/ttor68/playlists Mr T/Trent math sycamore school

https://artofproblemsolving.com/community/c106725

modular arithmetic:

https://artofproblemsolving.com/wiki/index.php/Modular_arithmetic/Intermediate

https://artofproblemsolving.com/wiki/index.php/Modular_arithmetic/Introduction

totient defined https://mathoverflow.net/questions/191306/what-is-a-totient

totient = Euler's totient function

Euler's theorem = Euler's totient theorem https://artofproblemsolving.com/wiki/index.php/Euler%27s_Totient_Theorem

https://www.whitman.edu/mathematics/higher_math_online/section03.10.html

triangular number n*n+1/2