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Math Midterm
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Gravity
Terms in this set (92)
Rene Descartes
mathematician who developed a system that connects the fields of algebra and geometry
origin
the point on a number line paired with the number zero
x-axis
horizontal number line
y-axis
vertical number line
quadrants
the four sections that a plane is divided into by the axes
ordered pair
a method of naming or locating any point on the coordinate plane
graph
the point paired with the ordered pair
coordinate
the ordered pair paired with the point
abscissa
the first number in the ordered pair
ordinate
the second number in the ordered pair
Midpoint Formula
M( x₁+x₂/2, y₁+y₂/2 )
transformation
movement of geometric figures in the plane
pre-image
position of the figure before the transformation
image
position of the figure after the transformation
four types of transformations
reflection
translation
rotation
dilation
reflection
a figure flipped over a line
reflection over x-axis
P'(x,-y)
reflection over y-axis
P'( -x,y)
translation
figure is slid in any direction
vector
directed line segment
<a,b>
component rotation for a vector
P(x,y) : <a,b>
P'(x+a, y+b)
rotation
a figure is turned about a point
90° clockwise rotation
P'(y,-x)
90° counterclockwise rotation
P'(-y,x)
180° rotation
P'(-x,-y)
dilation
a figure is enlarged or reduced
scale factor
a multiple
"κ"
reduction
if |κ|<1
enlargement
if |κ|>1
dilation rule
κ P(x,y) →P'(κx,κy)
relation
a set of ordered pairs
5 ways to illustrate a relation
set notation
mapping
table
equation
graph
domain
the set of all first coordinates in ordered pairs of a relation
range
the set of all second coordinates in ordered pairs of a relation
inverse of a relation
a relation formed by switching the abscissa and ordinate of every ordered pair
independent variable
variable graphing on horizontal axis
dependent variable
variable graphed on verticle axis
Linear Equation
an equation in the form of Ax+By=C, where A,B,C
intercepts
The points where the graph crosses (intersects) the axes
x-intercepts
The points where the graph crosses the x -axis
y-intercepts
The points where the graph crosses (intersects) the y-axis
function
A relation between two sets(domain and range) such that each member of the domain is paired with exactly one member of the range
vertical line test (for a function)
If there exists a vertical line that intersects the graph in more than one point, then the relation is not a function
sequence
A set of numbers written in a specific order
arithmetic sequence
a sequence in which the pattern of numbers either increases or decreases at a constant rate
term
A number in the sequence
Common difference
Constant rate at which the sequence increases or decreases
Slope
Steepness
Slope
m
origin
the point on a number line paired with the number zero
unit distance
the distance chosen to represent 1
positive integers
the numbers paired with points that are unit distances to the right of the origin
negative integers
the numbers paired with points that are unit distances to the left of the origin
graph
the point paired with the number
coordinate
the number paired with the point
absolute value
the distance from the origin to the point
range
the difference between the greatest number and the least number
mean
average
median
"middle number"
mode
the number(s) that occur the most
numerical expression
an expression containing a number or numbers and an operation or operations
value of the expression
the number that the expression is equivalent to
simplify an expression
to give its value
variable
a letter or symbol that represents a number or numbers
variable or algebraic expression
an expression containing a number or numbers, a variable or variables, and an operation or operations
exponent
a number that tells how many times the base is used as a factor
exponential form
written with an exponent
evaluate
find its value
When multiplying a number and a variable or variables and a number the number always comes first
Multiplication rule for translation
Less than More than Fewer than Subtracted from
Phrases done in reverse order
Parentheses Brackets Fraction bar Braces
Four types of grouping symbols
Do inside grouping symbols Do exponents Do multiplication or division whichever comes first Do addition or subtraction whichever comes first
Order of operations
(x-y)
"the difference of"
(x+y)
"the sum of"
mathematical sentence
expressions joined by one of the inequality symbols
open sentence
a mathematical sentence with a variable
equation
a mathematical sentence with an = sign
set
a collection of items
mathematical sentence symbols
equal to greater than less than greater than or equal to less than or equal to not equal to not greater than not less than not greater than or equal to not less than or equal to
element or member of a set
an item in the set
domain or replacement set
a set of numbers that the variable is allowed to stand for
root(s) or solution(s)
the values in the domain that make the sentence true
solution set
the set which contains the root(s) of the sentence
natural numbers
counting numbers
whole numbers
natural numbers and zero
integers
whole numbers and their opposites
rational numbers
a number or numbers that can be written as a fraction whose numerator and denominator are integers
irrational numbers
a number whose decimal form neither terminates nor repeats
three types of irrational numbers
pi square roots that aren't perfect crazy decimals
real numbers
all of the above
imaginary numbers
i=square root of -1
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