a symbol used to represent a quantity that can change
coefficient
the number that is multiplied by the variable in an algebraic expression
algebraic expression
an expression that contains at least on variable
constant
a value that does not change
evaluate
to find the value of a numerical or algebraic expression
substitute
to replace a variable with a number or another expression in an algebraic expression
equation
a mathematical sentence that shows that two expressions are equivalent
solve
to find an answer or a solution
solution
a value or values that make an equation true
inverse operation
operations that undo each other: addition and subtraction, or multiplication and division
isolate the variable
to get a variable alone on one side of an equation or inequality in order to solve the equation or inequality
Addition Property of Equality
the property that states that if you add the same number to both sides of an equation, the new equation will have the same solution
Subtraction Property of Equality
the property that states that if you subtract the same number from both sides of an equation, the new equation will have the same solution
Multiplication Property of Equality
the property that states that if you multiply both sides of an equation by the same number, the new equation will have the same solution
Division Property of Equality
the property that states that if you divide both sides of an equation by the same nonzero number, the new equation will have the same solution
inequality
a mathematical sentence that shows the relationship between quantities that are not equivalent
algebraic inequality
an inequality that contains at least on variable
solution of an inequality
a value to values that make an inequality true
solution set
the set of values that make a statement true
term
the parts of an expression that are added or subtracted
like term
two or more terms that have the same variable raised to the same power
equivalent expression
equivalent expressions have the same value for all values of the variables
simplify
to write a fraction or expression in simplest form
ordered pair
a pair of numbers that can be used to locate a point on a coordinate plane
coordinate plane
a plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis
x-axis
the horizontal axis on a coordinate plane
y-axis
the vertical axis on a coordinate plane
x-coordinate
the first number in an ordered pair; it tells the distance to move right or left from the origin
y-coordinate
the second number in an ordered pair; it tells the distance to move up or down from the origin
origin
the point where the x-axis and y-axis intersect on the coordinate plane; (0,0)
graph of an equation
a graph of the set of ordered pairs that are solutions of the equation
integers
the set of whole numbers and their opposites
opposites
two numbers that are an equal distance from zero on a number line (additive inverse)
absolute value
the distance of a number from zero on a number line; shown by | |
power
a number produced by raising a base to an exponenet
exponential form
a number is in exponential form when it is written with a base and an exponent
exponent
the number that indicates how many times the base is used as a factor
base
when a number is raised to a power, the number that is used as a factor is the base
scientific notation
a method of writing very large or very small numbers by using power of 10
rational number
any number that can be expressed as a ratio of two integers
relatively prime
two numbers are relatively prime if their greatest common factor (GCF) is 1
reciprocal
one of two numbers whose product is 1; also called multiplicative inverse
least common denominator (LCD)
the least common multiple of two or more denominators
principal square root
the nonnegative square root of a number
perfect square
a square of a whole number
irrational number
a number that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal
real number
a rational or irrational number
Density Property
the property that states that between any two real numbers, there is always another real number
population
the entire group of objects or individuals considered for a survey
sample
a part of the population
biased sample
a sample that does not fairly represent the population
random sample
a sample in which each individual or object in the entire population has an equal chance of being selected
systematic sample
a sample of a population that has been selected using a pattern
stratified sample
a sample of a population that has been divided into subgroups
stem-and-leaf plot
a graph used to organize and display data so that the frequencies can be compared
back-to-back stem-and-leaf plot
a stem-and-leaf plot that compares two sets of data by displaying one set of data to the left of the stem and the other to the right
mean
the sum of a set of data divided by the number of items in the data set; average
median
the middle number, or the mean (average) of the two middle numbers, in an ordered set of data
mode
the number or numbers that occur most frequently in a set of data; when all numbers occur with the same frequency, we say there is no mode
outlier
a value much greater or much less than the others in a data set
variability
the spread of values in a set of data
range
the difference between the greatest and least values in a data set
quartile
three values, one of which is the median, that divide a data set into fourths
box-and-whisker plot
a graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median
bar graph
a graph that uses vertical or horizontal bars to display data
frequency table
a table that lists items together according to the number of times, or frequency, that the items occur
histogram
a bar graph that shows the frequency of data within equal intervals
line graph
a graph that uses line segments to show how data changes
scatter plot
a graph with points plotted to show a possible relationship between two sets of data
correlatoin
the description of the relationship between two data sets
line of best fit
a straight line that comes closet to the points on a scatter plot
point
an exact location in space
line
a straight path that extends without end in opposite directions
plane
a flat surface that extends forever
segment
a part of a line between two endpoints
ray
a part of a line that starts at one endpoint and extends forever
angle
a figure formed by two rays with a common endpoint called the vertex
right angle
an angle that measures 90 degrees
acute angle
an angle that measures less than 90 degrees
obtuse angle
an angle whose measure is greater than 90 degrees but less than 180 degrees
complementary angles
two angles whose measures add to 90 degrees
supplementary angles
two angle whose measures have a sum of 180 degrees
vertical angles
a pair of opposite congruent angles formed by intersecting lines
congruent
having the same size and shape
parallel lines
lines in a plane that do not intersect
perpendicular lines
lines that intersect to form right angles
transversal
a line that intersects two or more lines
Triangle Sum Theorem
the theorem that states that the measures of the angles in a triangle add up to 180 degrees
acute triangle
a triangle with all angles measuring less than 90 degrees
right triangle
a triangle containing a right angle
obtuse triangle
a triangle containing one obtuse angle
equilateral triangle
a triangle with three congruent sides
isosceles triangle
a triangle with at least two congruent sides
scalene triangle
a triangle with no congruent sides
polygon
a closed plan figure formed by three or more line segments that intersect only at their endpoints
regular polygon
a polygon with congruent sides and angles
trapezoid
a quadrilateral with exactly one pair of parallel sides
parallelogram
a quadrilateral with two pairs of parallel sides
rectangle
a parallelogram with four right angles
rhombus
a parallelogram with all sides congruent
square
a rectangle with four congruent sides
slope
a measure of the steepness of a line on a graph; the rise divided by the run
rise
the vertical change when the slope of a line is expressed as the ratio rise/run, or "rise over run"
run
the horizontal change when the slope of a line is expressed as the ratio rise/run, or "rise over run"
transformation
a change in the size or position of a figure
translation
a movement (slide) of a figure along a straight line
rotation
a transformation in which a figure is turned around a point
center of rotation
the point about which a figure is rotated
reflection
a transformation of a figure that flips the figure across a line
image
a figure resulting from a transformation
line symmetry
a figure has line symmetry if one half is a mirror-image of the other half
line of symmetry
the imaginary "mirror" in line symmetry
rotational symmetry
a figure has rotational symmetry if it can be rotated less than 360 degrees around a central point and coincide with the original figure
tessellation
a repeating pattern of plane figures that completely cover a plane with no gaps or overlaps
regular tessellation
a tessellation where a regular polygon is repeated to fill a plane
semiregular tessellation
a tessellation where two or more regular polygons are repeated to fill the plane and the vertices are all identical
perimeter
the distance around a polygon
area
the number of square units needed to cover a given surface
Pythagorean Theorem
in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
legs
in a right triangle, the sides that include the right angle
hypotenuse
in a right triangle, the side opposite the right angle
circle
the set of all points in a plane that are the same distance from a given point called the center
radius
a line segments with one endpoint at the center of the circle and the other endpoint on the circle, or the length of that segment
diameter
a line segment that passes through the center of a circle and has endpoints on the circle, or the length of that segment
circumference
the distance around a circle
face
a flat surface on a polyhedron
edge
the line segment along which two faces of a polygon intersect
vertex
on a polyhedron, the intersection of three or more faces; on a cone or pyramid, the top point
perspective
a technique used to make three-dimensional objects appear to have depth and distance on a flat surface
vanishing point
in a perspective drawing, a point on the horizon where parallel lines appear to meet
horizon line
the horizontal line in a perspective drawing that contains the vanishing point(s)
prism
a polyhedron that has two congruent, polygon-shaped bases and other faces that are all parallelograms
cylinder
a three-dimensional figure with two parallel, congruent circular bases connected by a curved lateral surface
pyramid
a polyhedron with a polygon base and triangular sides that all meet at a common vertex
cone
a three-dimensional figure with one vertex and one circular base
surface area
the sum of the areas of the faces, or surfaces, of a three-dimensional figure
lateral face
in a prism or a pyramid, a face that is not a base
lateral surface
in a cylinder, the curved surface connecting the circular bases; in a cone, the curved surface that is not a base
slant height
the distance from the base of a cone to its vertex, measured along the lateral surface
regular pyramid
a pyramid whose base is a regular polygon and whose lateral faces are all congruent
right cone
a cone in which a perpendicular line drawn from the base to the tip (vertex) passes through the center of the base
sphere
a three-dimensional figure with all points the same distance from the center
hemisphere
a half of a sphere
great circle
a circle on a sphere such that the plan containing the circle passes through the center of the sphere
ratio
a comparison of two quantities by division
equivalent ratios
ratios that name the same comparison
proportion
an equation that states that two ratios are equivalent
rate
a ratio that compares two quantities measured in different units
unit rate
a rate in which the second quantity in the comparison is one unit
unit price
a unit rate used to compare prices
conversion factor
a fraction whose numerator and denominator represent the same quantity but use different units; the fraction is equal to 1 because the numerator and denominator are equal
cross product
the product of numbers on the diagonal when comparing two ratios
dilation
a transformation that enlarges or reduces a figure
scale factor
the ratio used to enlarge or reduce similar figures
center of dilation
the point of intersection of lines through each pair of corresponding vertices in a dilation
similar
figures with the same shape but not necessarily the same size are similar
scale drawing
a drawing that uses a scale to make an object smaller than (a reduction) or larger than (an enlargement) the real object
scale
the ratio between two sets of measurements
reduction
a decrease in the size of all dimensions (in the same proportions)
enlargement
an increase in size of all dimensions in the same proportions
scale model
a proportional model of a three-dimensional object
capacity
the amount a container can hold when filled
percent
a ratio comparing a number to 100
percent change
the amount stated as a percent that a number increases or decreases
percent increase
a percent change describing an increase in a quantity
percent decrease
a percent change describing a decrease in a quantity
estimate
an answer that is close to the exact answer and is found by rounding or other methods; to find such an answer
compatible numbers
numbers that are close to the given numbers that make estimation or mental calculation easier
commission
a fee paid to a person for making a sale
commission rate
the fee paid to a person who makes a sale expressed as a percent of the selling price
sales tax
a percent of the cost of an item, which is charged by governments to raise money
withholding tax
a tax deducted from a person's earnings as an advance payment of income tax
interest
the amount of money charged for borrowing or using money
simple interest
a fixed percent of the principal
principal
the initial amount of money borrowed or saved
rate of interest
the percent charged or earned on an amount of money
experiment
in probability, any activity based on chance (such as tossing a coin)
trial
in probability, a single repetition or observation of an experiment
outcome
a possible result of a probability experiment
sample space
all possible outcomes of an experiment
event
an outcome or set of outcomes of an experiment or situation
probability
a number from 0 to 1 (or 0% to 100%) that describes how likely an event is to occur
impossible
can never happen; an event that is impossible has a probability of 0
certain
sure to happen; an event that is certain has a probability of 1
experimental probability
the ratio of the number of times an event occurs to the total number of trials, or times that the activity is performed
simulation
a model of an experiment, often one that would be too difficult or too time-consuming to actually perform
random numbers
in a set of random numbers, each number has an equal chance of appearing
theoretical probability
the ratio of the number of equally likely outcomes in an event to the total number of possible outcomes
equally likely
outcomes that have the same probability
fair
when all outcomes of an experiment are equally likely, the experiment is said to be fair
mutually exclusive
two events are mutually exclusive if they cannot occur in the same trial of an experiment
Fundamental Counting Principle
if one event has m possible outcomes and a second event has n possible outcomes after the first even has occurred, then there are m times n total possible outcomes for the two events
tree diagram
a branching diagram that shows all possible combinations or outcomes of an event
factorial
the product of all whole numbers except zero that are less than or equal to a number
permutation
an arrangement of items or events in which order is important
combination
an arrangement of items or events in which order does not matter
independent events
events for which the outcome of one event does not affect the probability of the other
dependent events
events for which the outcome of one event affects the probability of the other
odds in favor
the ratio of the number of favorable outcomes to the number of unfavorable outcomes
odds against
the ratio of the number of unfavorable outcomes to the number of favorable outcomes