Mathematics 8 Flashcards
is introduced using the concept of sets
rectangular coordinate system
is a set of all ordered pairs
cartesian product
known as xy-plane
cartesian plane
a french mathematician who is known as father of modern mathematics
rene descartes
is composed of two perpendicular number lines that meet at the point of origin (0,0) and divide the plane into four regions called quadrants
cartesian plane
four regions in the cartesian plane
quadrants
point in coordinate system
ordered pair
the first coordinate of a point is called
x-coordinate or abscissa
second coordinate of a point
y-coordinate or ordinate
horizontal lines
x-axis
vertical lines
y-axis
it is where y and x axis meets
point of origin
x>0, or x is positive
y>0, or y is positive
or (+,+)
quadrant I
x>0, or x is negative
y>0, or y is positive
or (-,+)
quadrant II
x>0, or x is negative
y>0, or y is negative
or (-,-)
quadrant III
x>0, or x is positive
y>0, or y is negative
or (+,-)
quadrant IV
is a special type of relation; a relation in which every element in the domain is mapped to exactly one element in the range
function
a horizontal line represents a
function
variable x is considered as the
independent variable
variable y is expressed as the
dependent variable
f(x) notation can also be used to define a
function
range is known as
image
domain is also known as
pre-image
is defined by f(x) = mx+b
linear function
aside from the sets of ordered pairs and the graph, linear function f defined by f(x) = mx+b can also be represented by its equation
linear equations
Ax+By=C
standard form
y=mx+b
slope-intercept form
is an equation in twl variables which can be written in two forms
linear equation
can be described by uts steepness or slope
line
can be computed by finding the quotient of the rise and the run
slope
done by identifying the slope and the y-intercept of the linear equation
slope and y-intercept
done by using x and y intercept
x-intercept and y-intercept
done by using two points in the graph
two points
done by using the slope and one point
slope and one point
done by using the slope intercept of the equation
slope-intercept form of the equation of a line
done by using the point-slope form
point-slope form of the euqation of a line
done by ysing two-point form
two-point form of the equation of a line
a ____ is any set of ordered pairs
relation
the highest exponent of x that occurs in the fuction f
degree of a function f
a notation in which a function is written in the form f(x) in terms of x
function notation
a straight line in Euclidean Geometry
line
a representation of a relation in which every element in the domain corresponds to one or more elements in the range
mapping diagram
an algebraic expression that combines numbers and/or variables using mathematical operators
mathematical phrase
the slope m of the line and is the quotient of change in y-coordinate and the change in x-coordinate
rate of change
also known as cartesian plane
rectangular coordinate system
any set of ordered pairs
relation
tells whether the line is increasing or decreasing and can be determined using the value of m
trend
if every vertical line intersects the graph no more than once, the graph represents a function
vertical line test
an algebraic method of solving systems of linear equations
elimination method
an open-source dynamic mathematics software that can be used to visualize and understand concepts in algebra, geometry, calculus and stats
GeoGebra
a method of finding the solution of a system of linear pair
graphical method
if-clause
hypothesis
then-clause
conclusion
p-q format
conditional statement
q-p format
converse statement
~p-~q format
inverse statement
~q - ~p format
contrapositive statement
a simple flow of reasoning from the if-clause tot he then-clause is called
simple implication
the statement which is accepted or known at the beginning
hypothesis
the statement drawn from the hypothesis
conclusion
reasoning that uses basic/or general statements to arrive at a conclusion; uses accepted facts
deductive reasoning
is a logical arguement in which each statement is supported/justified by given infos, definitions, axioms, postulates, theorems, and oreviously proven statements
proof
is a statement that is accepted without proof
postulate
is a statement accepted after it is prooved deductively
theorem
is one way of proof where you write a paragraph to explain why a conjecture for a given situation is true
paragraph form
is one way of writing proof where you create a table containing 2 columns (statements and reason)
two-column form
is another way of writing proof where a series of statements are organized in logical order using boxes and arrows
flow chart form
is a method of reasoning usually written in paragraph form
indirect form
