Glossary of mathematics terms meaning and definition
Glossary of mathematics terms meaning and definition
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Glossary of mathematics terms meaning and definition
Mathematics Glossary of Terms |
absolute value: number's distance from zero on a number line (e.g., the absolute value of 2 and the absolute value of -2 are both 2, i.e., |2| = 2 and |-2| = 2) |
additive inverse: two numbers are additive inverses of each other if their sum is 0 (e.g., since -4 + 4 = 0, then -4 and 4 are additive inverses of each other) |
algebraic expression: numeral and/or variable joined by any combination of the four basic operations (+, -, x, /) and involving any power(s) of numeral and/or variable (e.g., 3-8, 7x4, 4+x, y/2, n-2, 3(4+8)-7, y ^{2} -2) |
angle measure: the measure in degrees or radians of the radial distance between two rays that meet at a point |
area: the size of a region measured in number of square units |
arithmetic sequence: a sequence with a constant difference between consecutive terms (e.g., 2, 5, 8, 11,... is an arithmetic sequence with a constant difference of 3) |
associative property: a property of addition or multiplication in which the regrouping of the addends or factors does not change the outcome of the operations [i.e., (a + b) + c = a + (b + c) and (ab)c = a(bc)] |
attribute: a characteristic of an object, such as color, shape, or size |
bar graph: a graphical display representing data in different categories or groups. The length of a |
rectangle or bar is used to represent the numerical amount |
bionomial: a polynomial which is the sum of two terms |
box and whisker plot: a graphical display that shows the median, quartiles, and extremes of a set of data, |
the spread of the data and the concentration of the data. the display does not show any other specific data values |
capacity: the maximum amount that can be contained by an object. Often refers to measurement of liquid |
cardinal numbers: the counting numbers (1, 2, 3...) |
centroid: the point of intersection of the medians of a triangle |
circle graph: a graphical display that shows data as parts of a whole circle |
circumcenter: the point of intersection of the perpendicular bisectors of a triangle |
circumference: the distance around a circle; the formula for circumference of a circle is pi times the diameter (c = ðd) |
closed figure: the boundary of a simple 2-dimensional region, including shapes with straight and curved sides |
collinear points: a set of points lying on the same line combinations: a set of items selected, without regard to order, from a given set of items commutative: property a property of addition or multiplication in which the sum or product stays the |
same when the order of the addends or factors is changed (i.e., a + b = b + a and ab = ba) |
concrete: physical objects used to represent mathematical situations |
congruency: geometric figures having the same size and shape; all corresponding parts of congruent |
figures have the same measure |
concurrent lines: lines that have a common point |
coordinate plane: a 2-dimensional system in which the coordinates of a point are its distances from two |
intersecting perpendicular lines called axes. The formal name for this system is cartesian coordinate system |
counting technique: methods to determine the number of possible outcomes of an event. Some of the methods are tree diagram, list, rules for multiplication, combinations, and permutations |
curve fitting: the sketching of a line or curve to best describe a relationship between two variables on a scatter plot |
deductive reasoning: a series of logical steps in which a conclusion is drawn directly from a set of statements that are known or assumed to be true. (e.g., if 5 + 4 = 9 and 6 + 3 = 9 , then 5 + 4 = 6 + 3) |
diagonal: for a polygon in the plane, any line segment joining non-adjacent vertices. For a polyhedron in space, a line segment joining two vertices not in the same face |
dilation: a transformation which produces a figure similar to the original by proportionally shrinking or stretching the figure |
dimensional analysis: a method of converting units within a measurement system |
direct variation: a relationship in which the ratio of two variables is constant |
discrete mathematics: the study of mathematical properties of sets and systems that have only a finite number of elements. |
distributive property: a property which establishes a relationship between multiplication and addition such that multiplication distributes across the addition [i.e., a(b+c) = ab + ac] |
divisibility (rules of): special tests to determine if a particular integer is a factor of a given number, (e.g., a |
number is divisible by 10 if it ends in a 0) |
domain: the set of input values for a function |
elapsed time: the amount of time between a beginning time and an ending time |
equally likely outcomes: events in a sample space that have the same probability of occurring |
equation: a mathematical sentence of equality between two expressions (e.g., n + 50 = 75 or 75 = n + 50 means that n + 50 must have the same value as 75) |
equivalent: numbers or expressions that have the same value |
estimation: the process of finding a number close to an exact amount |
euclidean geometry: the geometry (plane and solid) based on Euclid’s postulates |
event: one of the many occurrences that can take place during a probability activity |
expanded notation: the sum of terms representing a quantity |
explicit relationship: a sequence rule using the number of the term to define the function [e.g., in the sequence 3, 6, 9,..., the explicit rule is f(n) = 3n where n is the number of the term and f(n) is the value of the term] |
experimental probability: a probability calculated from the results of an experiment |
exponent: a number which is placed to the right of and above another number (base). the value of the exponent determines how many times the base is used as a factor (e.g., 3 ^{4} = 3 x 3 x 3 x3; {3 is the base and is used as a factor 4 times} the exponent is 4) |
exponential function: a function whose general equation is a y=ab ^{x} or y=ab ^{kx} , where a, b, and k |
stand for constants. |
expression: a mathematical phrase with no equal sign such as 6, 3n, or + 4 |
face: a plane surface of a three-dimensional figure |
factors: the numbers or terms multiplied in an expression |
formula: an equation that states a fact or rule (e.g., a=l w) |
frequency table: a display to show how often items, numbers, or a range of numbers occur |
function: a relationship in which every value of x has a unique value of y (e.g., the relation y = 2x + 1 is a |
function because for every different x, there is one and only one y) |
function notation: a notation that describes a function. for a function ƒ, when x is a member of the domain, the symbol ƒ(x) denotes the corresponding member of the range [e.g., an equation of a function might be ƒ(x) = x+3] |
geometric sequence: a sequence with a constant ratio between two consecutive terms. Each successive term is found by multiplying the preceding term by the preceding term by the ratio. (e.g., 1, 2, 4, |
8, 16, …is a geometric sequence with a ratio of 2.) |
graph: a pictorial representation of information or relationships between numbers |
histogram: a graphical display representing continuous data in different categories or groups |
incenter: the point of intersection of the angle bisectors of a triangle |
indirect measurement: a measurement which is found by using a formula or other strategy and not actually measuring something (e.g., finding the height of a tree without actually holding a ruler next to it) |
inductive reasoning: a type of type of mathematical reasoning which involves observing patterns and using those observations to make generalizations |
inequality: a mathematical sentence in which the value of the expressions on either side of the relation symbol are unequal. relation symbols include > (greater than), < (less than), ≥greater than or |
equal to), < (less than or equal to), (e.g., x < y, 7 > 3, n =4). |
inference: a conclusion drawn from data |
integer: a set of whole numbers and its opposites (i.e. …..-3, -2, -1, 0, 1, 2, 3, ….) |
inverse operations: two operations that “undo” each other (e.g., addition and subtraction) |
inverse variation: a relationship in which the product of two variables is constant |
irrational numbers: numbers which cannot be represented by an exact ratio of two integers. (e.g., the |
square root of 2) line graph: a graphical representation using points connected by line segments to show how something |
changes over time |
line of best fit: a line drawn on a scatter plot to estimate the relationship between two sets of data |
line plot: a graph using marks (e.g., x, ) above a number on a number line to show the frequency of data |
linear function: a function with no exponents other than one and with no products of the variables (e.g., |
y=x+4, y= -4, and 3x-4y = 1/2 are linear functions); in a rectangular coordinate system, the graph of a linear function is a line |
manipulatives: tools, models, blocks, tiles, and other objects which are used to explore mathematical ideas and solve mathematical problems |
matrices: rectangular arrays of numbers arranged in rows and columns |
maxima: the greatest value in a data set or the greatest value of a function |
mean: in a collection of data, the sum of all the data divided by the number of data |
measures of central tendency: numbers which tend to cluster around the “middle” of a set of values. three such numbers are mean, median, and mode |
median: the middle number (or the mean of the two middle numbers when necessary) in a collection of numbers that is arranged in order from least to greatest |
minima: the least value in a data set or the least value of a function mode: the number(s) that occur(s) most often in a collection of data model: to represent or show mathematical ideas and relationships and real-world situations using objects, |
pictures, graphs, tables, functions, and other methods |
monomial: a polynomial with only one term |
multiple: the product of a whole number and any other whole number |
multiplicative inverse: two numbers are multiplicative inverses of each other if their product is 1 (e.g., |
since 4 x 1/4 = 1, 1/4 and 4 are multiplicative inverses) |
one-dimensional: a figure that has length but no width or height |
ordinal numbers: numbers used to express order (e.g., 1st, 2nd, 3rd) |
orthocenter: the point of intersection of the altitudes of a triangle |
outcome of an event: one of the possible occurrances in a probability situation |
parallel(ism): lines that lie in the same plane and never meet. also, planes lying in space that never meet |
patterns: regularities in situations such as those in nature, events, shapes, designs, and sets of numbers |
(e.g., spirals on pineapples, geometric designs in quilts, the number sequence 3, 6, 9, 12, . . . ) percent: a special ratio that compares a number to 100 and uses the % sign (e.g., 1/2 = 50% and 2/3 = 66 |
2/3%) |
perimeter: the distance around a geometric shape |
perpendicular(ity): lines in the same plane which intersect to form a right angle |
pictograph: a graphical representation that shows numerical information by using picture symbols |
place value: the value of a digit as determined by its position in a number (e.g., in the number "11" the |
one is worth either 10 or 1, depending on the position) polynomial: a mathematical expression consisting of a sum of terms each of which is a product of a |
constant and one or more variables |
polynomial degree: the highest power or sum of powers in any term of a given polynomial |
polynomial term: an algebraic expression that is an addend in a polynomial expression |
population: a group of people, objects, or events that fit a particular description |
power: a number expressed using an exponent (e.g., the number 5 ^{3} is read five to the third power or five |
cubed) |
precision: the smallest place value to which an approximate number or measurement is expressed (e.g., if pi is represented as 3.14, then its precision is .01) |
prism: a three-dimensional figure with parallelogram faces and two parallel, congruent bases |
probability of an event: a number that represents the likelihood that the event will occur |
properties of operations: mathematical principals that are always true (e.g., commutative, associative, distributive, inverses) |
proportion: an equation of the form a/b=c/d which states that the two ratios are equivalent |
pythagorean theorem: the sum of the squares of the lengths of the two legs (a, b) of a right triangle is equal to the square of the length of the hypotenuse (c). The formula is a ^{2} + b ^{2} = c ^{2 } |
quadratic function: a function of the second degree [i.e., a function of the form f(x) = ax ^{2} + bx + c]; in a rectangular coordinate system, the graph of a quadratic function is a parabola |
radical: another name for the roots of numbers, such as the square root of 5 or √5 |
range: the set of output values for a function |
range (of data set): the difference between the greatest and the smallest numbers in a set of data (e.g., the range of 2, 7, 13, and 17 is 15) |
rate: a ratio comparing two different units (e.g., miles per hour) |
ratio: a comparison of two whole numbers by division |
rational number: a real number that can be written as a quotient/ratio of two integers a/b, where b does not equal 0; a repeating or terminating decimal, integer, fraction, or whole number |
real number: any number that is either rational or irrational |
recursive relationship: a function rule which uses the value of the preceding term in the definition |
reflection (flip): a transformation which produces the mirror image of a figure (i.e., flipping a figure across a line) |
rotation (turn): a transformation obtained by rotating a figure around a fixed point (i.e., turning a figure about a point) |
sample space: the set or collection of all possible outcomes of a probability experiment |
scale: choice of increments and range of numbers on an axis |
scale drawing: a scaled representation of physical objects or drawings |
scatter plot: a graphical representation consisting of ordered pairs possibly showing a relationship between two variable quantities |
scientific notation: representation of a number as the product of a number between 1 and 10 and a power of 10; used especially for very small or very large numbers (e.g., 6,900,000 = 6.9 x 10 ^{6} or .00069 = 6.9 x10 ^{-4} ) |
similarity: two or more figures having the same shape but not necessarily the same size |
simulation: a representation of a situation or problem with a similar but simpler model or a more easily |
manipulated model in order to determine experimental results |
slides: a transformation in which the figures moves in a linear direction |
slope: the ratio of the rise to the run of any two distinct points on a line |
solutions: the values of a variable that make an equation or inequality a true statement |
statistical investigation: a procedure for obtaining data and drawing conclusions or making decisions on |
the basis of available data stem and leaf plot: a method of organizing data for the purpose of comparison where the "leaf" is the |
number in the smallest place value and the "stem" includes the numbers in the larger place values |
surface area: the sum of the areas of the faces of a solid figure |
symmetry: a figure has symmetry if there exists some line or point through which all points of the figure |
can be reflected to generate another point on the figure theoretical probability: a probability of a given event calculated from mathematical counting techniques. |
(e.g., the chance of getting heads when flipping a coin is 1 out of 2.) |
three-dimensional: an object that has length, width, and height |
transformation: a rule for moving every point in a plane figure to a new location. |
translation (slide): a transformation that slides a figure a given distance in a given direction |
trend: the general drift, tendency, or direction of a set of data |
trigonometric ratio: a comparison of the measures of the lengths of two sides of a right triangle expressed |
in fractional or decimal form; there are six trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) associated with any angle |
trigonometry: the study of right triangle measurements and ratios, useful for calculating indirect measurements |
two-dimensional: a figure that has length and width but not height (i.e., a plane figure such as a rectangle or circle) |
valid argument: an explicit demonstration or proof that has been shown to be true |
validate: to give evidence that a solution or process is correct |
variable: a letter or symbol which represents one or more numbers variability: numbers that describe how spread out a set of data is. (e.g., range and quartile) vertex (vertices): the points where two line segments come together (corners) volume: the amount of space enclosed in a three-dimensional figure, measured in cubic units whole numbers: the numbers in the set {0, 1, 2, 3, …} |
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