algebra 2
Terms
undefined, object
copy deck
- 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
- additive inverse property
-
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
- additive identity property
-
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,
1. if a/b<c/d, then ad<bc
2. if ad<bc, then a/b<c/d - 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
- adding integers with different signs
- 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