NYSED.gov
CommonCoreStateStandards:A
StatewideDialogue
WhatistheCommonCoreState
StandardsInitiativeandhowisNew
YorkStateinvolved?
1
What is the Common Core State
What
Standards Initiative (CCSSI)?
Standards
New York is one of 51 states and territories tha
MATH 110 - Exam 2 - Fall 2010 - All Sections
No books, notes, or calculators allowed.
Do NOT write on this exam.
There is no time limit.
1. Which of the following functions could have the graph shown below?
(a) f (x) = (x + 3)4 + 4
(b) f (x) = (x + 3)4 +
CHAPTER 3
LINESAND
ANGLES
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28
PARALLEL LINES
Def: line that do not intersect.
B
Illustration:
A
l
m
Notation:
D
C
l | m
A B | C D
p. 129
Examples of Parallel Lines
Hardwood Floor
Opposite sides of windows,
Prime Numbers
Some Simple Tips and Reminders
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Definitions
Even Numbers Any number that
can be divided by 2
Odd Numbers Any number that
cannot be divided by 2
Composite Number An integer that
can be divided
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SolvingEquations
SolvingEquations
Overview
BodduSRao
AlinearorFirstdegreeEquation
AlinearorFirstdegreeEquation
Eg.2y+1=13
1.Solving linear equations by
using inverse operations
using
x 7 = -3
+ 7 = +7 (ad
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1-2 Simplifying Expressions.
Expressions
A group of symbols used to represent a
number
3x + 3 y
Value
The number represented by the expression
Equation
A combination of an expression and a value
3 x + 3 y =
DONOW(notlater):
Comparethenumberofboystogirlsintheclass.
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The number of boys =
The number of girls =
If we compare boys to girls we get
_ boys to _ girls.
Whatdowecallacomparisonbetween
twoormorequantities?
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MATHEMATICS
SQUARES
SQUARE ROOTS
TODAYS MATH PREVIEW
q AREA
OF SQUARES
q AREA OF RECTANGLES
q AREA OF TRIANGLES
q CONNECTIONS
Exponents
Pythagorean Theorem
MATH RELATIONS
q Sq
uare Ro ts
o
q Sc ntific
ie
C
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Classifying Triangles
1
Geometry
11/17/11
Two Ways to Classify Triangles
By
Their Sides
By Their Angles
Geometry
2
11/17/11
Classifying Triangles
Classifying
By Their Sides
By
Scalene
Isosceles
Geometry
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Linear Equations
Linear equations are functions which
have two variables. They have an
independent and dependent variable.
Independent and Dependent
Variables
Independent Variables
Independent variables
are
LessonObjectives
Bytheendofthislessonyoushouldbeableto:
Multiplypowerswiththesamebase.
Dividepowerswiththesamebase.
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Multiplyingpowersofthesamenumber
Copythetextbelowintoyourbooksandthenanswerthequestions
a)
Warm up Nov. 1
List all pairs of angles that fit the description.
5
4
a.
b.
c.
d.
Corresponding
Alternate Interior
Alternate Exterior
Consecutive Interior
6
3
7
2
1
8
t
HIDDEN MESSAGE
MAN .
BOARD
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Correspond
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MATRIX: A rectangular
MATRIX:
arrangement of
numbers in rows and
columns.
columns.
The ORDER of a matrix
The ORDER
is the number of the
rows and columns.
rows
The ENTRIES are the
The ENTRIES
Numbers
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Perfect Square
Squares of whole
numbers
Square root
One of two equal factors of a
number. If a squared equals b
then a is the square root of b.
The square root of 144 is 12
because 12 squared is 14
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Laws of Exponents
Whenever we have variables which
contain exponents and have equal bases,
we can do certain mathematical
operations to them. Those operations
are called the Laws of Exponents
x
b
b = base
x
Exponential Growth and Decay
Exponential Growth and Decay
are functions which have been
widely used to model the
behavior of a variety of topics
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Growth and Decay are largely used in:
Growth can
be modeled b
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Algebra I
By Monica Yuskaitis
Definitions
Variable A variable is a letter
or symbol that represents a
number (unknown quantity).
8 + n = 12
Definitions
A variable can use any letter of
the alphabet.
n+5
x
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Exponential
Functions are
functions which
can be
represented by
graphs similar
to the graph on
the right
All base exponential functions are similar because
they all go through the point (0,1), regardless of
GE OM E T R Y
Circle Terminology
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Radius (or Radii for plural)
A
O
The segment joining
the center of a circle to
a point on the circle.
Example: OA
Diameter
A chord that passes
through the center of a
circ
Graphing Linear Equations
Graphing
Linear Equations can be graphed on
Linear
a Cartesian Coordinate system
Cartesian
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y-axis
x-axis
Cartesian Coordinate system
y-axis
Quadrant II
Quadrant I
Origin
Quadrant I
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Integers
Integers
The set of whole numbers and
their opposites
Operations with
Integers
Addition
Subtraction
Multiplication
Division
Addition of Integers
When the signs of the numbers being added
are t
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MATRIX: A rectangular
MATRIX:
arrangement of
numbers in rows and
columns.
columns.
The ORDER of a matrix
The ORDER
is the number of the
rows and columns.
rows
The ENTRIES are the
The ENTRIES
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ProvingTrianglesCongruent
The Idea of a Congruence
Twogeometricfigureswithexactlythe
samesizeandshape.
F
B
A
C
E
D
Howmuchdoyou
Howmuchdoyou
needtoknow.
.abouttwotriangles
toprovethatthey
arecongruent?
Correspondi
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.com library
55
Grade
Hoops
Add
Subtract
Multiply
Divide
Facts
Q 1 pt.
Q 1 pt.
Q 1 pt.
Q 1 pt.
Q 1 pt.
Q 2 pt.
Q 2 pt.
Q 2 pt.
Q 2 pt.
Q 2 pt.
Q 3 pt.
Q 3 pt.
Q 3 pt.
Q 3 pt.
Q 3 pt.
Q 4 pt.
Q 4 pt.
Q 4 pt.
Q 4 pt.
Q 4
Multiplying
With
Fractions
Lesson 5-1
Just Follow These Easy
Steps!
s
s
s
Multiply the numerators and write
down the answer as your new
numerator.
Multiply the denominators and
write down the answer as your new
denominator.
Simplify.
Example 1
5
8
3
x
4
1