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a letter that is used to represent one or more numbers
variable
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a collection of numbers, variables and operations
variable expression
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Replacing each variable in an expression by a number is called
evaluating the expression
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writing the units of each variable in a real life problem
unit analysis
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translating words into mathematics
verbal model
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the number of times the base is used as a factor
exponent
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indicate the order in which the operations should be performed
- grouping symbols
- parentheses and brackets
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mathematicians have established these to evaluate a expression involving more than one operation
order of operations
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formed when an equal sign is placed between 2 expressions
equation
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an equation that contains one or more variables
open sentence
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when variables are replace with numbers and the statement is true
solution of an equation
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finding all the solutions of an equation
solving the equation
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a type of open sentence
inequality
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number that produces a true statement when it is substituted for the variable in an inequality
solution of an inequality
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writing algebraic expressions, equations, or inequalities that represent real life situations
modeling
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expression, equation or inequality
mathematical model
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information, facts or numbers that describe something
data
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a rule that establishes a relationship between 2 quantities called the input and output
function
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a table that lists inputs and outputs
input-output table
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collection of all the input values
domain
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collection of all the output values
range
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point labeled 0 on number line
origin
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negative, 0, or positive number
integer
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the point that corresponds to a number is the
graph of the number
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drawing the point
plotting
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2 points that are the same distance from the origin but on opposite sides of the origin are
opposites
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speed and direction
velocity
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to prove that a statement is false you need to show that it is not true for only one example, called a
counterexample
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rectangular arrangement of numbers into rows and columns
matrix
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each number in a matrix is called
entry or element
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the factors are distributed to each term of the sum
distributive propertiy
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in a term that is the product of a number and a variable, the number is the what of the variable
coefficient
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terms in an expression that have the same variable raised to the same power
like terms
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allows you to combine like terms that have variables by adding coefficients
distributive property
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when all like terms have been combined and no grouping symbols are left
simplified expression
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for every real number except 0 there is a
reciprocal
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the product of a number and its reciprocal is one
inverse property of multiplication
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measure of likelihood that an event will occur
probability
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different possible results of probability
outcomes
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a collection of outcomes in probability
event
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the outcomes for an event you wish to have happen
favorable outcomes
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probability based on repetitions of an actual experiment
experimental probability
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number of favorable outcomes divided by the number of unfavorable outcomes
odds
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a different equation with the same solution as the original equation
equivalent equations
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each time you apply a transformation to an equation, you are writing a
solution step
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an equation where the variable is raised to the first power and does not occur in a denominator, inside a square root or inside absolute value symbols
linear equation
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the transformations used to isolate the variable are based on what property
properties of equality
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two triangles that have equal corresponding angles
similar triangles
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2 quantities measured in the same units
ratio of a to b
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an equation that is true for all values of the variable
identity
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an algebraic equation that relates 2 or more real life quantities
formula
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2 quantities measured in different units
rate of a per b
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a rate per one given unit
unit rate
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formed by 2 real number lines that intersect at a right angle
coordinate plane
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each point in the plane corresponds to an __________ of real numbers
ordered pair
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first number in ordered pair
x coordinate
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second number in an ordered pair
y coordinate
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graphing pairs of data on a coordinate axis
scatter plot
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an ordered pair that makes the equation true
solution of equation
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the x coordinate of a point where a graph crosses the x axis
x intercept
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the point where graph crosses y axis
y intercept
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the number of units a line rises or falls for each unit of horizontal change from left to right
slope
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compares 2 different quantities that are changing
rate of change
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2 quantities that vary directly
direct variation
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y=mx+b is written in
slope-intercept form
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any set of ordered pairs
relation
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the value of f at x or f(x)
function notation
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set of all points where x is in the domain of the function
graph of a funciton
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if there is no single line that passes through all the data points
best fitting line
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when points on a scatter plot can be approximated by a line with positive slope, x and y have a
positive correlation
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when points can be approximated by a line with negative slope, x and y
have a negative correlation
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when the points cannot be well approximated by a straight line
relatively no correlation
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y-y1 = m(x-x1)
point-slope form
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Ax+By=C
standard form of the equation of a line
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a method of estimating the coordinates of a point that lies between 2 given data points
linear interpolation
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method of estimating the coordinates of a point that lies to the right or left of all the given data points
linear extrapolation
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