CHAPTER 1 STUDY GUIDE
Cultural diffusion the process by which one idea or technique of a society is spread to another
Paleolithic Old Stone Age (2.5 million -10000 BCE), marked by the first emergence of human species,
the use of simple tools and spread of
CHAPTER 13/14 STUDY GUIDE
Lady Murasaki woman who wrote the Tale of Genji, the 1st novel in any language; novel relates
life history of prominent and amorous son of the Japanese emperor and shows evidence of
mannered style of Japanese society
Bushi region
CCOT Essay Japan
Date: 1853 1914
Thesis: From Matthew Perrys arrival in 1853 until 1914, Japan had gone under a change of
westernization because they were forced to open up trade with America and in political structure,
but Japans lack of a source of natu
Some may refer to me as a nerd, but I know a particular who would call me by a higher
status, such as his savior. It may sound strange to be called a savior, but from the incident that
happened last year, I would rather say that I deserve it. Through my f
Week12Problem1
Points and areontheparabola
lengthof
?
(A)
(B)
(C)
,andtheoriginisthemidpointof
.Whatisthe
(D)7(E)
Solution
Let
so
and
.Thenthemidpointof
and
.
Fromthefirstequation,
so
is
.Substitutingintothesecondequation,weget
,
.Wehavethat
Theansweris(E
Week7Problem1
Let
beadiameterofacircleand beapointon
with
.Let and bepointsonthe
circlesuchthat
and
isaseconddiameter.Whatistheratiooftheareaoftriangle
tothe
areaoftriangle
?
(A) (B) (C) (D) (E)
Solution
Let
bethecenterofthecircle.
Since
isthemidpointof
,
Week6Problem1
Triangle
hassidelengths
triangle
parallelto
intersects
(A)27(B)30(C)33(D)36(E)42
,
at
and
,and
at
.Thelinethroughtheincenterof
.Whatistheperimeteroftriangle
?
Solution
Let betheincenteroftriangle
.
Since liesontheanglebisectorof
,
.But
Hence
Week4Problem1
If
(A)
(B)
and
(C)0(D)1(E)2
with and real,whatisthevalueof
?
Solution
Bydefinitionof
,
get
forall ,so
forall .Expanding,we
.Forthisequationtoholdforall ,wemusthave
Then
Hence,
.Substitutingintotheequation
.Theansweris(A).
,weget
,so
and
.
,a
1
Math Zoom Academy MC-III - [email protected]
Math Zoom Academy - MC-III
AIME Review
1. An ordered pair (m, n) of non-negative integers is called simple if the addition m + n in base 10
requires no carrying. Find the number of simple ordered pairs of non
1
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Math Zoom Academy MC-III
Solving Inequalities
Important Inequalities
It is required that you are familiar with trivial inequalities (squares, square roots, and absolute values are
all non-negative), AM-GM-HM,
1
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Math Zoom Academy MC-III
Geometry - Special Angles
Facts to Remember
Special angles are the angles 30 , 60 , 90 and 45 .
An equilateral triangle has three 60 angles.
In ABC , if C = 90 , A = 60 , and B =
1
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Math Zoom Academy MC-III
AIME Algebra Practice
These AIME problems are related to algebra; however, as with many AIME level problems, other subject
areas are involved as well.
1. (1983 AIME #1) Let x, y , and
1
Math Zoom Academy MC-III - [email protected]
Math Zoom Academy - MC-III
Algebra - Solving Equations
Useful Theorems
Fundamental Theorem of Algebra (also know as the Gauss-dAlembert Theorem).
Every nonconstant polynomial with complex coecients has at le
1
Math Zoom Academy MC-III - [email protected]
Math Zoom Academy MC-III
Algebra - More Equations
Techniques for Solving Equations
We introduce some common or uncommon techniques to solve equations.
Observation
It is easy to observe and identify solutions
Week10Problem1
Twopedestriansstanding10feetawayand40feetawayfromthebaseofabillboardstructurehaveequivalentviews
ofthebillboard,meaningthattheanglesmarkedinthediagramarecongruent.Ifthebillboardis9feettall,whatisits
height offtheground?
Week10Problem2
Let
a