# algebra 2

## Terms

undefined, object
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subtracting integers
to subtract a number, add its additive inverse, for any numbers a and b,
a-b=a+(-b)
domain
the set of first numbers of the ordered pairs
function
a relationship between input and output
line plot
numerical data displayed on a number line
commutative property
for any numbers a and b,
a + b = b + a and
a x b = b x a
simplest form
an expression having no like terms and no parentheses
equation
a sentence that contains an equal sign =
comparison property
for any two numbers a and b, exactly one of the following sentences is true
a<b a=b a>b
venn diagrams
figures used to represent sets of numbers
coefficient
the numerical factor (ex. 2b, the coefficient is 2)
base
the variable x is the base
data
numerical information
verbal expression
the translation of an equation in to words (ex. three plus two)
order of operations
"please excuse my dear aunt sally", parentheses, exponents, multiply, divide, add, subtract
product
the result of the quantities being multiplied (ex. 3 x 2 = 6, 6 is the product)
algebraic expression
consists of one or more numbers and variables along with one or more arithmetic operations (ex. x-2)
variables
symbols that are used to represent unspecified numbers (ex. x and y are variables)
factors
quantities being multiplied
(ex. 3 x 2, 3 and 2 are factors)
exponent
the exponent indicates the number of times the base is used as a factor
power
an expression of the form x to the nth is power
sequence
a set of numbers in a specific order
associative property
for any numbers a, b, and c,
(a+b)+c=a+(b=) and
(ab)c=a(bc)
element
each object or number in a set
statistics
methods of collecting, organizing and interpreting data
ordered pairs
used to locate points on a graph
relation
set of ordered pairs
replacement set
a set of numbers from which replacements for a variable may be chosen
stem and leaf plot
the greatest place value is used to form the stems, the next greatest place value is used to form the leaves
negative number
the points to the left of zero on a number line
origin
the ordered pair, (0,0)
open sentences
mathematical statements with one or more variables or unknown numbers

range
the set of second numbers of the ordered pairs
evaluate
means to find the value
for every number a,
a=(-a)=0
solution
the replacement to solve an open sentence
solving the open sentence
finding a replacement for the variable that results in a true sentence
integers
a set of numbers
multiplicative property of zero
for any number a,
a x 0 = 0
set
a collection of objects or numbers
comparing numbers on the number line
if a and b represent any numbers and the graph of a is to the left of the graph of b, then a<b, if the graph of a is to the righ of the graph of b, then a>b
inequality
a sentence having the sign < or >
solution set
the set of all replacements for the variable that make the sentence true
multiplicative identity property
for any number a,
a x 1 = 1 x a
coordinate
the number that corresponds to a point on a number line
graph
to draw, or plot the points named
for any number a,
a+0=0+a
terms
the numbers in the sequence
rational number
a number that can be expressed in the form a/b, where a and b are integers and b is not eqal to 0
matrix
a rectangular arrangement of elements in rows and columns
reflexive property of equality
for any number a.
a=a
symmetric property of equality
for any numbers a and b,
if a = b, then b = a
multiplicative inverse property
for every nonzero number a/b, where a,b does not = 0, there is exactly one number b/a, such that a/b x b/a =1
discrete mathematics
deals with finite or discontinuous quantities
transitive property of equality
for any numbers a, b and c,
if a = b and b = c, then a = c
comparison property for rational numbers
for any ration numbers a/b and c/d, with b>0 and d>0,
definition of absolute value
the absolute value of a number is its distance from zero on a number line
adding integers with the same sign
add their absolute values, give the result the same sign as the integers
substitution property of equality
if a = b, then a may be replaced by b in any expression
subtract the lesser absolute value from the greater absolute value, give the result of the same sign as the integer with the greater absolute value
density property for rational numbers
between every pair of distinct rational numbers, there are infinitely many rational numbers
equivalent expressions
3x + 8x and 11x are equivalent expressions
distributive property
for any numbers a, b and c,
a(b+c)=ab+ac and (b+c)a=ba+ca
a(b-c)=ab-ac and (b-c)a=ba-ca
term
a number, a variable or a product or quotient of numbers and variables (ex. 9y+3x+2 has three terms)
like terms
terms that contain the same variables, with corresponding variables having the same power

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