variable

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