Chapter 0 Flashcards
Set
A collection of objects or numbers often shown with braes { } and usually named by a capital letter.
element
each object or number in a set or each entry in a matrix.
subset
when every element of Set B is contained in set A, then B is a subset of A. Symbol is C
universal set
The set of all possible elements for a situation. Symbol is U.
complement
If B is a subset of A then all of the possible elements of the set A that are not included in set B. Symbol is B’ .
union
All the elements of both set A and B, written as A U B.
intersection
All elements found in both sets A and B, written as A n B.
empty set
a set with no elements symbolized by { } or Ø.
∈
a symbol that means it is an element of.
∉
symbol that means is not an element of.
imaginary unit
i, or the principal square root of -1
complex numbers
any number that can be written in the form a+bi, where A and B are real numbers and i is the imaginary unit.
standard form
a complex number written in the form a+bi, A is the real part.
real part
in an imaginary number a+bi, A is the real part
imaginary part
in an imaginary number a+bi, B is the imaginary part
imaginary number
another name for a complex number of the form a+bi, where B cannot equal 0.
pure imaginary number
An imaginary number (a+bi) where A = 0 ( which means no real parts exist )
complex conjugates
Two complex numbers of the form a+bi and a-bi.
parabola
A “U” shaped graph.
axis of symmetry
A line about which a figure is symmetric (mirror image about a line). Found by x= -b/ 2a
vertex
A point at which a parabola intersect it axis of symmetry. X coordinate is found by -b/2a
quadratic equation
A polynomial equation of degree two, in the form of ax2+ bx2+ c= 0, where a does not equal 0
zero product property
For any real numbers A and B, if AB=0, then either a=0 or b=0 or both A and B = 0
completing the square
A process used to make a quadratic expression into a perfect square trionomial.
quadratic equations
principle Nth Root
The nonnegative root.
nth root
for any real numbers A and B, and any positive integer n, if a^n= b, then A is the nth root of B
product property of radicals
quotient property of radicals
rational to radical form B 1/n
square root of B’
systems of equations
A set of equations with the same variables.
rational to radical format B m/n
square root of B^m
substitution method
A method of solving a system of equations in which one equation is solved for one variable in terms of the other
elimination method
A method of solving a system of quit ions in which adding and subtracting the equations is used to eliminate one variable.
consistent
a system of equations that has at least one solution
independent
When a system of linear equations has exactly one solution ( lines cross once)
dependent
When a system of equations has an infinite number of solutions ( lines are parallel and are the same)
inconsistent
A system of equations that has no solutions (lines are parallel and do not touch)
system of inequalities
Set of inequalities with the same variables
matrix
Any rectangular array of variables or constants in horizontal rows and vertical columns
element
each entry in a matrix
dimensions
a description of the number of rows and columns of a matrix
row matrix
a matrix that has one row
column matrix
A matrix that has only one column
square matrix
has the same amount of columns and rows
zero matrix
a matrix in which every element is zero
equal matrix
two matrices that have the same dimensions and each element of one matrix is equal to the corresponding element of the other matrix.
