Glossary of Maths

8/22/2019 Glossary of Maths

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Glossary of Math Khalid Abouzaid


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Glossary of Math

Collected by Khalid Abouzaid


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Glossary Term Defini tion

abscissa The first number of an ordered pair. The x-coordinate of a pointgraphed in the coordinate plane.

absolute value The absolute value of a number a is its distance from zero on a

number line and is represented by a . Example: The absolute

value of -2 is 2, or 2 = 2.

absolute value function A function written as f(x) = x , where f(x) 0 for all values ofx.

accuracy The closeness of a measurement to its true value.acute angle An angle with a measure greater than 0 and less than 90.

acute triangle A triangle in which each angle measures less than 90.

Addition Property ofEquality

If you add the same number to each side of an equation, thetwo sides remain equal. For any numbers a, b, and c, ifa = b,then a + c = b + c.Example: Ifx = 3, then x + 5 = 3 + 5.

additive identity The sum of any number and 0 is the number. For any number a,a + 0 = 0 +a =a. Example: 6 + 0 = 0 + 6 = 6

additive inverse A number that when added to a given number results in a sum

of zero. Example: The additive inverse of 4 is -4 because 4 +(-4) = 0.

adjacent angles Angles that have the same vertex, share a common side, and

do not overlap. In the figure, 1 and2 are adjacent angles

adjacent arcs Arcs of a circle with one point in common. In the figure, arc PQand arc QR are adjacent arcs.

algebra A mathematical language that uses symbols, usually letters thatstand for unknowns, along with numbers.


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algebraic expression An expression consisting of one or more numbers and variablesalong with one or more arithmetic operations.

alternate exterior angles In the figure, transversal t intersects lines l and m. 1 and7,

and2 and8 are alternate exterior angles.

alternate interior angles In the figure, transversal t intersects linesl and m. 3 and5,

and4 and6 are alternate interior angles.

altitude A line segment perpendicular to the base of a figure withendpoints on the base and on the vertex opposite the base.

altitude of a trapezoid A segment perpendicular to the lines containing the bases.

altitude of a triangle A perpendicular segment in which one endpoint is a vertex ofthe triangle and the other is a point on the side opposite the

vertex.


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amplitude For functions of the formy =A sin kory = A cos k, the

amplitude is A .

analytic geometry The study of coordinate geometry from an algebraicperspective.

angle A figure formed by two rays with a common endpoint. In thefigure,RST is formed by rays SR and ST with the commonendpoint (or vertex) S.

angle bisector A ray whose endpoint is the vertex of the angle and is located inthe interior of the angle. It separates a given angle into two

angles with equal measure. In the figure, PW is the anglebisectorofP.

angle bisector of a triangle A segment that separates an angle of a triangle into twocongruent angles.

angle of depression The angle formed by a horizontal line of sight and a line of sightbelow it.


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angle of elevation The line formed by a horizontal line of sight and a line of sightabove it.

angle of rotation The degree measure of the angle through which a figure isrotated.

antilogarithm If log x = a, then x is called the antilogarithm ofa, abbreviatedantilog a.

apothem of a regularpolygon

A segment from the center of a regular polygon perpendicular toa side of the polygon.

arc A set of points along a circle.arccosine The inverse of y = cos x, written as x = arccos y.arcsine The inverse of y = sin x, written as x = arcsin y.arctangent The inverse of y = tanx, written as x = arctan y.area The number of square units needed to cover a surface enclosed

by a geometric figure.arithmetic mean The terms between any two nonconsecutive terms of an

arithmetic sequence.

arithmetic sequence A numerical pattern that increases or decreases at a constantrate or value. The difference between successive terms of thesequence is constant. Example: 2, 5, 8, 11, 14,

arithmetic series The indicated sum of the terms of an arithmetic sequence.Associative Property The way in which three numbers are grouped when they are

added or multiplied does not change their sum or product. Forany numbers a, b, and c, (a + b) + c = a + (b + c), and (ab)c =

a(bc). Example:(2 + 3) + 4 = 2 + (3 + 4) or (2 3) 5 = 2 (35).

asymptote A line that a graph approaches but never intersects.augmented matrix A coefficient matrix with an extra column containing the constant

terms.

average The sum of data divided by the number of items in the data set,also called the mean.

axes The two perpendicular number lines in a coordinate system.axis of a cylinder The segment whose endpoints are the centers of the circular

bases of a cylinder.back-to-back bar graph A graph plotted on a two-quadrant coordinate system with the

horizontal scale repeated on each direction from the centralaxis, used to show comparisons.


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back-to-back stem-and-leaf plot

Used to compare two sets of data. The leaves for one set ofdata are on one side of the stem, and the leaves for the otherset of data are on the other side.

bar graph A graph that compares different categories of data by showingeach category as a bar whose length is related to the frequency.

bar notation In repeating decimals, the line or bar placed over the digits that

repeat. Example: 2.63636363 = 2.63 .

base angles of anisosceles triangle

The equal angles formed by the base and the congruent sidesof an isosceles triangle.

base angles of a trapezoid The pairs of angles of a trapezoid with their vertices at the

endpoints of the same base.

base in a percent

proportion

The number to which the percentage is compared.

base of a three-dimensional figure

The faces on the top and bottom of the figure.

base of an expression In an expression of the formxn, the base is x.base of an isoscelestriangle

The side opposite the vertex angle.


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bases of a trapezoid The parallel sides of a trapezoid.

best-fit line The line that most closely approximates the data in a scatterplot.

betweenness PointR is between points P andQ if and onlyifR, P, andQ arecollinear and PR +RQ =PQ.

biased sample A sample in which one or more parts of the population arefavored over others.

biconditional The conjunction of a conditional statement and its converse.bimodal data Data with two modes.binomial An algebraic expression that has two terms. Examples: x + 1, x2

+y, a 2bbinomial experiment An experiment in which there are exactly two possible outcomes

for each trial, a fixed number of independent trials, and theprobabilities for each trial are the same.

bisect To separate something into two congruent parts.

boundary A line or curve that separates the coordinate plane into regions.box-and-whisker plot A diagram that divides a set of data into four parts using the

median and quartiles.Cartesian coordinateplane

A plane divided into four quadrants by the intersection of the x-axis and the y-axis at the origin.


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center of a circle The given point from which all points on a circle are the samedistance. In the figure, P is the centerof the circle.

center of an ellipse The point at which the major axis and minor axis of an ellipseintersect.

center of a hyperbola The midpoint of the segment whose endpoints are the foci.center of rotation The fixed point about which a figure rotates or spins.centimeter A metric unit of length. 1 centimeter = 0.01 metercentral angle An angle whose vertex is the center of a circle and whose sides

intersect the circle. In the figure, MTD is a central angle ofcircle T.

centroid of a triangle The point of intersection of the three medians of a triangle. Inthe figure, X is the centroid of triangle JKM.

characteristic The part of the logarithm of a number which is the exponent of10 used to write the number in scientific notation.

chord A segment whose endpoints are on a circle. In the figure, JR isa chord.

circle The set of all points in a plane that are the same distance from agiven point called the center.

circle graph A graph that compares parts of a set of data as a percent of thewhole set.

circular functions Functions defined using a unit circle.


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circumcenter The point of concurrency of the perpendicular bisectors of atriangle.

circumference The distance around a circle.circumscribed polygon A polygon with each side tangent to a circle.

Closure Property A set of numbers is closed for addition or multiplication if thesum or product of two numbers is still included in the samenumber system.

cluster Data that are grouped closely together.clustering An estimation method in which a group of numbers close in

value are rounded to the same number.coefficient The numerical factor of a term.coinciding lines The graphs of two equations that represent the same line.

collinear points Three or more points that lie on the same line. In the figure, P,Q, and L are collinear points.

combination An arrangement or listing in which order is not important.common denominator A common multiple of the denominators of two or more

fractions. Example: 24 is the common denominatorof1

3,5

8,

and3

4because 24 is the LCM of 3, 8, and 4.

common difference The difference between any two consecutive terms in anarithmetic sequence.

common factor A whole number that is a factor of each number in a set ofnumbers. Example: 5 is a common factorof 10, 15, 25, and 100.

common logarithm A logarithm that uses 10 as the base.common multiples Multiples that are shared by two or more numbers. Example:

Some common multiples of 2 and 3 are 6, 12, and 18.common ratio The quotient between any two consecutive terms in a geometric

sequence.Commutative Property

The order in which two numbers are added or multiplied doesnot change their sum or product. For any numbers a and b, a +

b = b + a and ab = ba. Example: 2 + 3 = 3 + 2 or 2

3 = 3

2


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compass An instrument used to draw circles and arcs of circles.

compatible numbers Two numbers that are easy to add, subtract, multiply, or dividementally.

complementary angles Two angles are complementary if the sum of their measures is

90. In the figure, 1 and2 are complementary angles.

complementary events The events of one outcome happening and that same outcomenot happening. The sum of the probabilities of complementaryevents is 1.

complements Two events are complements if the sum of their probabilities is1.

complex fraction A fraction that has one or more fractions in the numerator ordenominator.

complex number Any number that can be written in the form a +bi, where a andb are real numbers and i is the imaginary unit.

complex plane The complex number a +bi is graphed as the ordered pair (a, b)in the complex plane. The real axis is horizontal, and theimaginary axis is vertical.

components of a vector Two or more vectors whose sum is the given vector.composite number A whole number greater than 1 that has more than two factors.composition of functions A function is performed, and then a second function is

performed on the result of the first function. The composition off

and g is denoted by f g, and [f g][x] =f[g(x)].compound event An event which consists of two or more simple events.compound inequality Two or more inequalities that are connected by the words and

oror.compound statement Two or more statements that are connected by the words and oror.


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concave polygon A polygon for which a point on at least one of its diagonals lies

outside the polygon. In the figure, diagonal JL lies outsidepolygon JKLMN.

concentric circles Circles that lie in the same plane, have the same center, andhave radii of different lengths. In the figure, circle R with radius

RS and circle R with radiusRT are concentric circles.

conclusion The part of a conditional statement immediately following theword then.

concurrent Three or more lines or segments that meet at a common point.

In the figure, JR , KP , and MQ are concurrent.

conditional probability The probability of an event under the condition that somepreceding event has occurred.

conditional statement A statement that something is true or will be true provided thatsomething else is also true. The statement can be written in theform If A, then B.

cone A three-dimensional figure with one circular base and onevertex. A curved surface connects the base and the vertex.

congruencetransformation

A mapping for which a geometric figure and its image arecongruent.

congruent Having the same measure.congruent figures Figures that have the same shape and size.


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congruent solids Two solids are congruent if all of the following conditions aremet. 1. The corresponding angles are congruent. 2.Corresponding edges are congruent. 3. Corresponding facesare congruent. 4. The volumes are congruent.

conic section Any figure that can be obtained by the intersection of a plane

with a right cone.conjecture A conclusion reached that is based on inductive reasoning.conjugate of a complexnumber

The conjugate of the complex numbera + biis a bi.

conjugate of a binomial The conjugate of the binomial a b c d + is a b c d .

conjunction A compound statement formed by joining two statements withthe word and.

consecutive integers Integers in counting order.consecutive interiorangles

In the figure, transversal t intersects lines land m. 3 and6,

and4 and5 are consecutive interior angles.

consecutive sides Sides of a polygon that share a vertex. In the figure, PS and

PQ are consecutive sides.

consistent system A system of equations that has at least one ordered pair thatsatisfies both equations.

constant A term that does not contain a variable.constant function A linear function of the form f(x) = b.constant of variation The number k in an equation of the form y =kx.construction The process of drawing a figure using only a compass and a

straightedge.continuous function A function is said to be continuous at point (x1, y1,) if it is defined

at that point and passes through that point without a break.contrapositive The statement formed by negating both the hypothesis and

conclusion of the converse of a conditional statement.convenience sample A sample which includes members of the population that are

easily accessed.convergent series An infinite series that has a sum or limit.converse The statement formed by exchanging the hypothesis and

conclusion of a conditional statement.


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convex polygon A polygon for which all diagonals are located in the interior ofthe polygon.

coordinate The number that corresponds to a point on a number line.coordinate grid (see coordinate plane)coordinate plane A plane, also called a coordinate grid or coordinate system, in

which a horizontal number line and a vertical number lineintersect at their zero points.

coordinate proof A geometric proof that uses figures on a coordinate plane.coordinate system (see coordinate plane)coplanar Points or lines that lie in the same plane. In the planeM, points

A, B, and C are coplanar, and AB and BCare coplanar.

corollary A statement that can be easily proved using a theorem.corresponding angles Angles that have the same position on two different parallel

lines cut by a transversal. In the figure, 1 and5, 2 and6,

3 and7, and4 and8 are corresponding angles.

corresponding parts Parts of congruent or similar figures that match.cosecant In a right triangle with acute angleA, the cosecant ofA =

the measure of the hypotenusethe measure of the leg opposite A

.


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cosine In a right triangle with acute angleA, the cosine ofA =the measure of the leg adjacent to

the measure of the hypotenuseA .

cotangent In a right triangle with acute angleA, the cotangent ofA =the measure of the leg adjacent tothe measure of the leg opposite

A

A .

coterminal angles Two angles in standard position that have the same terminalside.

counterexample A specific case which proves a statement false.Cramers Rule A method that uses determinants to solve a system of linear

equations.critical points Points at which the nature of a graph changes.cross products The product of the terms on the diagonals when two ratios are

compared. Example: In the proportion2 8

3 12= , the cross

products are 2 12 and 3 8.

cube of a number The product in which a number is a factor three times. Example:The cube of 2, or 2 cubed, is 8 because 2 2 2 = 8.

cube (geometric figure) A solid figure with six square faces.

cubic function A function that can be described by an equation of the formy

=ax3 +bx2+cx +d, where a 0.

cubic units Used to measure volume and tells the number of cubes of agiven size needed to fill a three-dimensional figure.cumulative frequencyhistogram

A histogram organized using a cumulative frequency table.

cumulative frequencytable

A table in which the frequencies are accumulated for each item.

cup A customary unit of capacity equal to 8 fluid ounces.cylinder A solid figure whose bases are formed by congruent circles in

parallel planes and whose lateral surface is curved. Thesegment whose endpoints are the centers of the circular basesis called the axis of the cylinder. The altitude is a segmentperpendicular to the bases with an endpoint in each base.

data Numerical information gathered for statistical purposes.decagon A polygon having ten sides.


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deductive reasoning The process of using facts, rules, definitions, or properties toreach a valid conclusion.

degree The most common unit of measure for angles. If a circle weredivided into 360 equal-sized parts, each part would have an

angle measure of 1 degree, denoted as 1.

degree of a monomial The sum of the exponents of all its variables.degree of a polynomial The greatest degree of any term in the polynomial.denominator The bottom number in a fraction.dependent events Two or more events in which the outcome of one event affects

the outcome of the other events.dependent system A consistent system of equations that has an infinite number of

solutions.dependent variable The variable in a relation whose value depends on the value of

the independent variable.depressed polynomial The quotient when a polynomial is divided by one of its binomial

factors.

determinant A square array of numbers having a numerical value. Thenumerical value of the square array of numbers.diagonal A segment joining two nonconsecutive vertices of a polygon. In

the figure, SQ is a diagonal.

diameter The distance across a circle through its center. In the figure,

TG is a diameterof circle K.

dilation A transformation in which a figure is enlarged or reduced.dimensional analysis The process of carrying units throughout a computation.direct variation An equation of the formy =kx, where k = 0.discontinuous function A function is said to be discontinuous at point (x1, y1) if there is a

break in the graph of the function at that point.discrete Data that can be described by whole numbers or fractional

values.discriminant In the Quadratic Formula, the expression under the radical sign,

b2 - 4ac.disjunction A compound statement formed by joining two segments with the

word or.Distance Formula The distance between two points, with coordinates (x1, y1) and

(x2, y2), is given by ( ) ( )2 2

2 1 2 1d x x y y= + .


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Distributive Property To multiply a sum by a number, multiply each addend of thesum by the number outside the parentheses. For any numbersa, b, and c, a(b +c) =ab +ac and a(b c) =ab ac. Example:

2(5 + 3) = (2 5) + (2 3) and 2(5 3) = (2 5) (2 3)divisible A number is divisible by another if, upon division, the remainder

is zero.Division Property ofEquality

If you divide each side of an equation by the same nonzeronumber, the two sides remain equal.

Division Property forInequalities

For all numbers a, b and c, the following are true: 1. Ifc is

positive and a b,

thena

c

b

c> . 2. Ifc is negative and a , and ifc is

negative and a >b, thena

c

b

c< .

domain The set of the first numbers or abscissas of the ordered pairs ina relation.double bar graph A graphical display that uses paired horizontal or vertical bars to

compare data.e The irrational number 2.71828. e is the base of natural

logarithms.edge The intersection of faces of a three-dimensional figure.element of a matrix Each number in a matrix.elimination method The use of addition or subtraction in combination with

multiplication or division to eliminate one variable and solve asystem of equations.

ellipse The set of all points in a plane such that the sum of the

distances from two given points in the plane, called foci, isconstant.

empirical study Performing an experiment, collecting and combining data, andanalyzing the results.

empty set A set with no elements shown by the symbol {}or . Asolution set with no members. Also called a null set.

equal sign A symbol of equality, =.equally likely outcomes Outcomes for which the probability of each occurring is equal.equation A mathematical sentence stating that two expressions are

equal. Example: 3 (7 + 8) = 9 5


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equiangular triangle A triangle with three congruent angles.

equilateral triangle A triangle having all three sides congruent and all three anglescongruent.

equivalent equations Equations that have the same solution.equivalent expressions Expressions that have the same value or that have the same

mathematical meaning for all replacement values of theirvariables. Examples: 3 + 2 = 10 5, 2x + 3x = 5xequivalent fractions

Fractions that have the same value. Example:2

3and

4

6

equivalent ratios Two ratios that have the same value. Example: 5:4 = 10:8evaluate Find the value of an expression.even number A whole number that is divisible by 2.even function A function whose graph is a symmetric with respect to the y-

axis.event A specific outcome or type of outcome.excluded values Any values of a variable that result in a denominator of 0 must

be excluded from the domain of that variable.expanded form (orexpanded notation)

The sum of the products of each digit and its place value of anumber. Example: 867 = 800 + 60 + 7

experimental probability The ratio of the number of positive outcomes to the total numberof events or trials in a probability experiment.

exponent A number that indicates how many times a number orexpression is to be multiplied by itself. Example: In theexpression 53, the exponent is 3.

exponential decay Exponential decay occurs when a quantity decreasesexponentially over time.

exponential function A function that can be described by an equation of the formy =ax, where a > 0 and a 1.

exponential growth Exponential growth occurs when a quantity increasesexponentially over time.expression A mathematical combination of numbers, variables, and

operations. Examples: 5 + 23, 4x, 6x +y2


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exterior of an angle All points outside the sides of the angle. A is in the exterior of

XYZ.

exterior angle of a triangle An angle that forms a linear pair with an angle of the triangle. In

the figure, 1 is an exterior angle.

exterior angles In the figure, tranversal t intersects lines l and m. 1, 2, 7,

and8 are exterior angles.

extraneous solutions Results that are not solutions to the original equation.extrapolation Predicting for an x-value greater than any in the data set.extremes

In the proportiona c

b d= , a and d are the extremes.

face of a three-dimensional figure

The flat surface of a three-dimensional figure.

factor In an algebraic or numerical expression, the quantities beingmultiplied are called factors. Example: 3 and 11 are factors of33.

factor a polynomial Express a polynomial as the product of monomials andpolynomials.

factor tree A diagram showing the prime factorization of a number. Thefactors branch out from the previous factors until all of thefactors are prime numbers.

factored form A monomial expressed as a product of prime numbers and

variables with no variable having an exponent greater than 1.factorial The expression ofn!, read n factorial, where n is greater thanzero, is the product of all positive integers beginning with n and

counting backward to 1. Example: 5! = 5 4 3 2 1 = 120failure Any outcome other than the desired outcome of an event.fair game A game in which players of equal skill have an equal chance of

winning.family of graphs Graphs and equations of graphs that have at least one

characteristic in common.


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Fibonacci sequence A sequence in which the first two terms are 1 and each of theadditional terms is the sum of the two previous terms.

flow proof A proof that organizes statements in logical order, starting withthe given statements. Each statement is written in a box with thereason verifying the statement written below the box. Arrows are

used to indicate the order of the statements.fluid ounce A customary unit of capacity.foot A customary unit of length. 1 foot = 12 inchesformula An equation that states a rule for the relationship between

certain quantities. Example:A =r2 is the formula for finding thearea of a circle.

45-45-90 triangle A right triangle with two 45 angles.fractal A complex two- or three-dimensional figure that can be

endlessly magnified and is generated by using iteration.fraction A number representing some part of a whole or part of a set. A

quotient in the form ab

.

frequency The number of cycles per unit of time in a periodic function.frequency How often a piece of data occurs.frequency distribution A system of organizing data by determining classes and the

frequency of values in each class.frequency table A table of tally marks used to record and display how often

events occur.front-end estimation An estimation method in which the front digits are added or

subtracted first, and then the digits in the next place valueposition are added or subtracted.

function A relation in which exactly one element of the range is pairedwith each element of the domain .

function notation A way to name a function that is defined by an equation.Example: In function notation, the equation y = 3x 8 is writtenas f(x) = 3x 8.

function rule An expression which describes the relationship between eachinput and output.

function table A table used to organize the input numbers, output numbers,and the function rule.

functional value The element in the range that corresponds to a specific elementin the domain.

Fundamental CountingPrinciple

If an event M can occur in m ways and is followed by an event Nthat can occur in n ways, then event M followed by event N canoccur in m n ways.

gallon A customary unit of capacity equal to four quarts.geometric mean Missing terms between two nonconsecutive terms in ageometric sequence.

geometric probability Using the principles of length and area to find the probability ofan event.

geometric sequence A sequence in which each term after the nonzero first term isfound by multiplying the previous term by a constant called the

common ratio r, where r 0 or 1. Example: 1, 4, 16, 64, 256, geometric series The indicated sum of the terms of a geometric sequence.


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gram A unit of mass in the metric system. 1000 grams = 1 kilogramgraph To draw, or plot, the points named by certain numbers or

ordered pairs on a number line or coordinate plane.great circle For a given sphere, the intersection of the sphere and a plane

that contains the center of the sphere.

greatest common factor(GCF)

The greatest number that is a factor of two or more numbers.Example: The greatest common factorof 30, 60, and 15 is 15.

greatest integer function A step function, written as f(x) = [[x]], where f(x) is the greatestinteger less than or equal to x.

half-plane The two regions of the coordinate plane separated by the graphof a linear equation.

height of a parallelogram The shortest distance from the base of a parallelogram to itsopposite side.

height of a triangle The measure of the segment from a vertex of a triangle to theline containing the opposite side (base) and perpendicular tothat side.

hemisphere One of the two congruent parts into which a great circleseparates a sphere.

heptagon A polygon having seven sides.hexagon A polygon having six sides.histogram A bar graph in which the data are organized into equal intervals.

The height of the bar represents the frequency in that interval.hour A commonly used unit of time. There are 60 minutes in one hour

and 24 hours in one day.hyperbola The set of all points in the plane such that the absolute value of

the difference of the distances from two given points in theplane, called foci, is constant.

hypotenuse The side opposite the right angle in a right triangle.


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hypothesis The part of a conditional statement immediately following theword if.

identity An equation that is true for every value of the variable.Identity Property The sum of an addend and zero is the addend. The product of a

factor and one is the factor. Example: 5 + 0 = 5 and 5 1 = 5if-then statement Conditional statement in the form If A, then B.image The position of a figure after a transformation.imaginary part of acomplex number

b in the complex number a +bi.

imaginary unit i, or the principal square root of 1.improper fraction A fraction that has a numerator that is greater than or equal to

the denominator. Examples: 21 2,4 1

incenter The point of concurrency of the angle bisectors of a triangle.inch A customary unit of length. 12 inches = 1 footincluded angle An angle formed by two given sides of a triangle. In the figure,

A is the included angle of

ABand

AC.

included side A side common to two given angles of a triangle. In the figure,

AB is the included side ofA andB.

inclusive events Two events that can occur at the same time and whoseoutcomes may be the same.

inconsistent system A system of equations with no ordered pair that satisfies bothequations.

independent events Two or more events in which the outcome of one event does notaffect the outcome of the other events.

independent system A system of equations with exactly one solution.independent variable The variable in a function whose value is subject to choice.indirect measurement A technique using proportions to find a measurement.indirect proof (or indirectreasoning)

In an indirect proof, one assumes that the statement to beproved is false. One then uses logical reasoning to deduce thata statement contradicts a postulate, theorem, or one of the

assumptions. Once a contradiction is obtained, one concludesthat the statement assumed false must be true.

inductive reasoning A conclusion based on a pattern of examples.inequality An open sentence that uses the symbol , or to compare

two quantities.infinite sequence A sequence which has infinitely many terms.infinite series The indicated sum of the terms of an infinite sequence.infinity Lines and sets that never end are said to continue to infinity.


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inscribed angle An angle whose vertex lies on a circle and whose sides contain

chords of the circle. In the figure, RST is inscribed in circle P.

inscribed polygon A polygon in which every vertex of the polygon lies on the circle.

integers The set of whole numbers and their opposites {, -2, -1, 0, 1, 2,}.

intercept The point at which a line or curve cuts across another line,curve, or surface.interior angles In the figure, transversal t intersects lines l and m. 3, 4, 5,

and6 are interior angles.

interior of an angle All points between the two sides of an angle.

interpolation Predicting an x-value between the least and greatest values ofthe set.

interquartile range The difference between the upper and lower quartilesrepresenting the middle half of the data in the set.

intersecting lines Lines that are coplanar and have exactly one point in common.intersection The set of elements common to two or more sets as in

compound inequalities and Venn diagrams.interval On a scale, the difference between the greatest and least

values in each category.inverse The statement formed by negating both the hypothesis and

conclusion of a conditional statement.inverse of a relation The inverse of any relation is obtained by switching the

coordinates in each ordered pair.inverse functions Two functions fand g are inverse functions if and only if both of

their compositions are the identity function.

[ ] [ ]( ) ( )f g x g f x=o o for all values ofx.inverse operations Pairs of operations that undo each other. Examples: Addition

and subtraction are inverse operations. Multiplication anddivision are inverse operations.

inverse variation An equation of the formxy =k, where k 0.


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inversely proportional y varies inversely as xn if there is some nonzero constant k such

that xny =k orn

ky

x= , n > 0.

irrational numbers Numbers that cannot be expressed as fractions, terminating

decimals, or repeating decimals.irregular figure A figure that cannot be classified as a single polygon.isometry A mapping for which the original figure and its image are

congruent.isosceles trapezoid A trapezoid with two congruent legs.

isosceles triangle A triangle with at least two congruent sides.

joint variation y varies jointly as xn and znif there is some nonzero constant k

such that y =kxnzn, where x 0, z 0, and n> 0.key A sample data point used to explain the stems and leaves.kilogram The basic unit of mass in the metric system. 1 kilogram = 1000

gramskilometer A metric unit of length. 1 kilometer = 1000 meters.

kite A quadrilateral with exactly two distinct pairs of adjacentcongruent sides.

lateral area The surface area of a cone, a cylinder, a prism, or a pyramid,not including the bases.

lateral edge of a prism The intersection of the two adjacent lateral faces.lateral edge of a pyramid The edge of the lateral face that joins the vertex to a vertex of

the base of the pyramid.lateral face of a prism A face that is not a base.lateral face of a pyramid Faces that intersect at the vertex.latus rectum The line segment through the focus of a parabola and

perpendicular to the axis of symmetry.leading coefficient The coefficient of the term in a polynomial with the highest

degree.leaf A digit written to the right of the vertical line in a stem-and-leaf-

plot.


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least commondenominator (LCD)

The least common multiple of the denominators of two or morefractions. Example: 12 is the least common denominatorof1 3 5, , and

3 4 6.

least common multiple

(LCM)

The least nonzero number that is a common multiple of two or

more numbers. Example: 36 is the least common multiple of 3,9, and 12.

legs The sides of a right triangle that form the right angle.

legs of an isosceles

triangle

The congruent sides of an isosceles triangle.

legs of a trapezoid The nonparallel sides of a trapezoid.

like fractions Fractions that have the same denominator.like terms Terms that contain the same variables raised to the same

power. Example: 5x2 and 6x2 are like terms.limit The value that the terms of a sequence approach.line A never-ending straight path.line graph Numerical data displayed to show trends or changes over time.line of best fit A line that describes the trend of the data in a scatter plot.line of reflection The line a figure is flipped over in a reflection.


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line of symmetry A line that divides a figure into two halves that are reflections ofeach other.

line plot A number line labeled with a scale to include all the data with amark placed above a data point each time it occurs.

line segment Part of a line containing two endpoints and all the pointsbetween them.

line symmetry Figures that match exactly when folded in half have line

symmetry.linear equation An equation in the formAx +By =C, whereA 0 and B 0,

whose graph is a straight line.linear function A function in which the graph of the solutions forms a line

defined by y =mx +b where m and b are real numbers.linear inequality A relation whose boundary is a straight line.linear programming The process of finding the maximum or minimum values of a

function for a region defined by inequalities.linear term In the equation f(x) =ax2 +bx +c, bx is the linear term.liter The basic unit of capacity in the metric system.locus The set of points that satisfy a given condition.logarithm In the function x =by, y is called the logarithm, base b, ofx.

Usually written as y = logbx and read y equals log base b ofx.logarithmic equation An equation that contains one or more logarithms.logarithmic function The function y = log b x, where b > 0 and b 1, which is the

inverse of the exponential function y =bx.lower bound The integer less than or equal to the least real zero of the

polynomial function P(x).lower extreme The least number of a set of data.lower quartile Divides the lower half of a set of data into two equal parts.magnitude The length of a vector.major arc An arc with a measure greater than 180. In the figure, arcACB

is a major arc.

major axis The longer of the two line segments that form the axes ofsymmetry of an ellipse.

mantissa The common logarithm of a number between 1 and 10.


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mapping A diagram that illustrates how each element of the domain ispaired with an element in the range.

mathematical induction A method of proof that depends on a recursive process and isused to prove statements about positive integers.

matrix A rectangular arrangement of numbers or elements in rows andcolumns.

matrix logic A method of deductive reasoning that uses a table to solveproblems.

maximum The highest point or the critical point on the graph of a curvewhere the curve changes from an increasing curve to adecreasing curve.

mean The sum of the numbers in a set of data divided by the numberof pieces of data in the set.

mean deviation The arithmetic mean of the absolute value of the deviations fromthe mean of a set of data.

means In the proportion a cb d= , b and c are the means.

measure of centraltendency

A number or piece of data that represents the whole set of data.

measure of variation A measure that describes the spread of the values in a set ofdata.

median The middle number in a set of data when the data are arrangedin numerical order. If the data has an even number, the medianis the mean of the two middle numbers.

median-fit line A line drawn by using the medians of the x- and y-coordinates ofgroups of points in a scatter plot.

median of a trapezoid A segment joining the midpoints of the legs of a trapezoid.


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median of a triangle A segment in which one endpoint is the vertex of a triangle andthe other endpoint is the midpoint of the side opposite thatvertex.

meter The basic unit of length in the metric system.metric system A base-ten system of measurement using the basic units: meter

for length, kilogram for mass, and liter for capacity.midpoint On a line segment, the point that is halfway between the

endpoints.midsegment A segment with endpoints that are the midpoints of two sides of

a triangle.

mile A customary unit of length. 1 mile = 5280 feet or 1760 yardsmilligram A metric unit of mass. 1 milligram = 0.001 grammilliliter A metric unit of capacity. 1 milliliter =0.001 literminimum The lowest point on the graph of a curve.minor of an element The determinant formed when the row and column of the

determinant containing a certain element are deleted.minor arc An arc with a measure less than 180. In the figure, arcAB is a

minor arc.

minor axis The shorter of the two line segments that form the axes ofsymmetry and which does not contain the foci of an ellipse.

minute (angles)A unit of angle measure that is

1

60of a degree.

minute (time) A commonly used unit of time. There are 60 seconds in oneminute and there are 60 minutes in one hour.

mixed number The indicated sum of a whole number and a fraction. Examples:

112

,3

24

,5

48

mode The number(s) or item(s) that appear most often in a set of data.monomial A number, a variable, or a product of a number and one or more

variables. Examples: 3, y, 2x, 5xy2

multiple The product of a number and any whole number. Example: 8 isa multiple of 4.


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Multiplication Property forInequalities

For all numbers a, b, and c, the following are true. 1. Ifc is

positive and a bc, c 0. 2. Ifc is negative and a

bc, c 0, and ifc is negative and a >b, then ac


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nonconsecutive sides Sides of a polygon that do not share a vertex. In the figure, PS

and QR are nonconsecutive sides.

noncoplanar Points or lines that do not lie in the same plane.non-Euclidean geometry The study of geometrical systems that are not in accordance

with the Parallel Postulate of Euclidean geometry.nonterminating decimal An infinite number of digits following either a repeating or a not-

repeating pattern.normal curve A symmetric bell-shaped graph of a normal distribution.normal distribution A frequency distribution that often occurs when there is a large

number of values in a set of data: about 68% of the values arewithin one standard deviation of the mean, 95% of the values

are within two standard deviations of the mean, and 99% of thevalues are within three standard deviations.

normal form The equation of a line that is written in terms of the length of thenormal from the line to the origin.normal line A line that is perpendicular to another line, curve, or surface.nth order matrix A square matrix withn rows and n columns.nth root For any real numbers a and b, and any positive integer n, ifan =

b, then a is an nth root ofb. Example: 2 is the fifth root of 32since 25 = 32.

null set A set with no elements shown by the symbol {}or . Asolution set with no members. Also called an empty set.

number line A line with equal distances marked off to represent numbers.number theory The study of numbers and the relationships between them.numerator The top number in a fraction.

numerical expression A mathematical expression that has a combination of numbersand at least one operation. 4 + 2 3 is a numerical expression.

obtuse angle An angle that measures more than 90 but less than 180.


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obtuse triangle A triangle having one obtuse angle.

octagon A polygon having eight sides.octants The eight regions of three-dimensional space.odd function A function whose graph is symmetric with respect to the origin.odd number A whole number that is not divisible by 2.odds The ratio that compares the number of ways an event can occur

(successes) to the number of ways the event cannot occur(failures).

one-to-one function 1. A function where each element of the range is paired withexactly one element of the domain2. A function whose inverse is a function.

open sentence A mathematical statement with one or more variables.opposite rays Two rays that are part of the same line and have only their

endpoints in common. In the figure, ray XY and ray YZ areopposite rays.

opposite vectors Two vectors that have the same magnitude and oppositedirections.

opposites Every positive rational number and its negative pair.order of operations 1. Evaluate expressions inside grouping symbols. 2. Evaluate all

powers. 3. Do all multiplications and/or divisions from left toright. 4. Do all additions and/or subtractions from left to right.ordered pair A pair of numbers used to locate a point in the coordinate plane

or the solution of an equation in two variables. An ordered pairis written in the form (x-coordinate, y-coordinate).

ordered triple Three numbers used to locate a point in space or the solution ofa system of equations in three variables.

ordinate The second number of an ordered pair. The y-coordinate of apoint graphed in the coordinate plane.

origin The point (0, 0) in a coordinate plane where the x-axis and they-axis intersect.

orthocenter The point of concurrency of the altitudes of a triangle.

orthogonal drawing The two-dimensional top view, left view, front view, and rightview of a three-dimensional object.

ounce A customary unit of weight. 16 ounces = 1 poundoutcome One possible result of a probability event. Example: 4 is an

outcome when a number cube is rolled.outlier Any element of a set of data that is at least 1.5 interquartile

ranges less than the lower quartile or greater than the upperquartile.


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parabola The graph of a quadratic function.

paragraph proof A logical argument used to validate a conjecture in paragraphform.

parallel lines Lines in the same plane that never intersect and have the sameslope.

parallel planes Planes that do not intersect. In the figure, plane PQR || planeJKL.

parallel vectors Vectors that have the same or opposite directions.parallelogram A quadrilateral with both pairs of opposite sides parallel and

congruent.

parent graph The simplest of the graphs or the anchor graph in a family ofgraphs.

partial fraction One of the fractions that were added or subtracted to result in agiven rational expression.

Pascals triangle A triangular array of numbers such that the (n +1)th row is thecoefficient of the terms of the expansion (x +y)nforn = 0, 1, 2, .

pentagon A polygon having five sides.percent A ratio that compares a number to 100. Example: 76 out of 100

is 76 percent or 76%.percent of change A ratio that compares the change in a quantity to the original

amount.


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percent of decrease The ratio of an amount of decrease to the original amount,expressed as a percent.

percent of increase The ratio of an amount of increase to the original amount,expressed as a percent.

percentile The point below which a given percent of the data lies.

perfect square A number whose square root is a rational number. Example: 25is a perfect square since 25 = 52

perfect square trinomial Trinomials that are the square of a binomial. Example: x2 + 2x +1 is a perfect square trinomial since x2 + 2x + 1 = (x + 1)2.

perimeter The distance around a closed geometric figure.period In a repeating decimal, the digit or digits that repeat. Example:

The period of0.54 is 4.

period of a function The least possible value of for which f(x) =f(x +).

periodic function A function is called periodic if there is a number such that f(x)

=f(x +) for all x in the domain of the function.

permutation An arrangement or listing of a group of objects in which order is

important.perpendicular bisector A segment that is perpendicular to another segment and passes

through that segments midpoint.

perpendicular lines Lines which meet to form right angles and whose slopes have aproduct of 1.

perspective view The view of a three-dimensional figure from the corner.phase shift The least value ofk+c, for which the trigonometric function

f(k+c) = 0. A horizontal translation of a trigonometric function.pi The ratio of the circumference of a circle to its diameter. The

Greek letter represents this number. The value of pi is

3.1415926 . Approximations for pi are 3.14 and22

7.

piecewise function A function in which different equations are used for differentintervals of the domain.

pint A customary unit of capacity. 1 pint =2 cups


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plane A two-dimensional flat surface that extends in all directions.

plane Euclidean geometry Geometry based on Euclids axioms dealing with a system ofpoints, lines, and planes.

Platonic Solids The five regular polyhedra: tetrahedron, hexahedron,octahedron, dodecahedron, or icosahedron.

point A specific location in space with no size or shape.point of inflection A critical point of a graph where the graph changes its curvature

from concave down to concave up or vice versa.point of symmetry The common point of reflection for all points of a figure. In the

figure, Ris apoint of symmetry.

point-slope form An equation of the formy y1 =m(xx1), where m is the slopeand (x1, y1) is a given point on a nonvertical line.

point symmetry Two distinct points Pand Pare symmetric with respect to a

point, M, if and only ifMis the midpoint ofPP. Point Missymmetric with respect to itself.

polar coordinate system A grid of concentric circles and their center, which is called thepole, whose radii are integral multiples of 1.

polar equation An equation that uses polar coordinates.polar form The complex numberx+yiwritten as r(cos +isin ) where r =

2 2x y+ and = Arctan

y

xwhenx> 0 and = Arctan

y

x+

whenx< 0.polar graph The representation of the solution set which is the set of points

whose coordinates (r, ) satisfy a given polar equation.polygon A simple closed figure in a plane formed by three or more line

segments.polygonal convex set The solution of a system of linear inequalities.polygonal region Any polygon and its interior form a polygonal region.polyhedron A solid with four or more flat surfaces that are polygonal

regions.polynomial A monomial or sum of monomials. Examples: 5x, 3x2 + 2polynomial equation A polynomial that is set equal to zero.polynomial function A function y=P(x) where P(x) is a polynomial in one variable.polynomial in one variable An expression of the formanx

n+an - 1x

n - 1+. . . +a1x+ao wherethe coefficents ao, a1, . . ., an represent complex numbers, an isnot zero, and n represents a nonnegative integer.


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population A large group of data from which a sample of statistical data isselected.

positive correlation In a scatter plot, as x increases, y increases.positive integer Any integer that is greater than zero.positive number Any number that is greater than zero.postulate A rule of geometry that is accepted as being true without proofpound A customary unit of weight. 1pound = 16 ouncespower An expression of the formxn, read x to the nth power. Example:

74 is 7 raised to the fourth power, or 7 7 7 7.power function An equation in the form f(x) =axb, where a and b are real

numbers.precision The preciseness of a measurement depends on the unit of

measure. The smaller the unit, the more precise themeasurement.

precision unit The smallest unit on a measuring tool.prediction equation An equation suggested by the points of a scatter plot that is

used to predict other points.preimage The position of a figure before a transformation.prime factorization Expressing a composite number as a product of its prime

factors. Example: The prime factorization of 63 is 3 3 7.prime number A whole number, greater than 1, whose only factors are 1 and

itself.prime polynomial A polynomial that cannot be written as a product of two

polynomials with integral coefficients.principal square root The nonnegative square root of a number.principal values The unique solutions of a trigonometric equation if the values of

the function are restricted to two adjacent quadrants.prism A polyhedron with two parallel, congruent faces called bases. A

solid with the following characteristics: 1. Two faces, called thebases, are formed by congruent polygons that lie in parallelplanes. 2. The faces that are not bases, called lateral faces, areformed by parallelograms. 3.The intersection of two adjacentlateral faces are called lateral edges and are parallel segments.

probability The ratio of the number of favorable outcomes for an event tothe number of possible outcomes of the event. P(a) =

number of favorable outcomestotal number of possible outcomes

.

product The result obtained by multiplying two or more numbers orvariables.

proof A logical argument used to validate a conjecture.


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property A statement that is true for any numbers or variables.proportion

An equation of the forma c

b d= stating that two ratios are

equivalent.

protractor An instrument used to measure angles.pure imaginary number The complex numbera +bi when a = 0 and b 0.pyramid A solid figure that has a polygon for a base and triangles for

sides. A pyramid is named for the shape of its base. A solid withthe following characteristics: 1. All the faces, except one,intersect at a common point called the vertex. 2. The face thatdoes not intersect at the vertex is called the base. The base isformed by a polygon. 3. The faces meeting at the vertex arecalled lateral faces. They are formed by triangles.

Pythagorean Theorem Ifa and b are the measures of the legs of a right triangle and cis the measure of the hypotenuse, then c2 =a2 +b2.

Pythagorean triple Whole numbers that satisfy the Pythagorean Theorem.quadrant One of four regions into which the x- and y-axes separate the

coordinate plane. [Alg2-R2]quadrantal angle An angle in standard position whose terminal side coincides

with one of the axes.quadratic equation An equation of the formax2 +bx +c = 0, where a 0.

Quadratic Formula The solutions of a quadratic equation in the formax2

+bx +c =

0, where a 0, are given by the formula x =2

4

2

b b ac

a

.

quadratic function A function described by an equation of the form f(x) =ax2 +bx +c, where a 0.

quadratic inequality An inequality of the form y >ax2+bx +c, y


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radical sign The symbol , used to indicate a root.

radicand The expression under the radical sign.radius The distance from the center of a circle to any point on the

circle.

random Outcomes occur at random if each outcome is equally likely tooccur.

random sample A sample that is chosen without any preference, representativeof the entire population.

range of a data set The difference between the greatest number and the leastnumber in a set of data.

range of a relation The set of second numbers in the ordered pairs of a relation.

rate The ratio of two measurements having different units ofmeasure. Example: 60 miles per hour

rate of change The change in a quantity over time.ratio A comparison of two number by division.rational equation An equation that contains rational expressions.rational expression An algebraic fraction whose numerator and denominator are

polynomials.rational function A function that contains rational expressions represented as the

quotient of two polynomials in the form f(x) =( )( )

g xh x

, where h(x)

0.

rational inequality Any inequality that contains one or more rational expressions.rational numbersThe set of numbers that can be written in the form

a

b, where a

and b are integers and b 0. Examples: 1 2 31 , , 2.3 21 9 10

= =

ray A part of a line that extends indefinitely in one direction from afixed point.

real numbers The set of rational numbers and irrational numbers together.reciprocal The multiplicative inverse of a number.rectangle A parallelogram with four right angles.

rectangular form A complex number written as x +yi where x is the real part andyi is the imaginary part.


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rectangular prism A solid figure that has two pairs of parallel opposite faces andcongruent bases that are all rectangles.

recursive formula A formula used for determining the next term of a sequenceusing one or more of the previous terms.

reduced sample space The subset of a sample space that contains only thoseoutcomes that satisfy a given condition.

reference angle The acute angle formed by the terminal side of an angle instandard position and the x-axis.

reflection A transformation in which a figure is flipped over a line ofsymmetry.

regression line A line of best fit.regular polygon A polygon that has all sides congruent and all angles congruent.

regular polyhedron A polyhedron in which the faces are regular congruentpolygons.

regular prism A right prism with bases that are regular polygons.

regular pyramid A pyramid whose base is a regular polygon and in which thesegment from the vertex to the center of the base is the altitude.


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regular tessellation A tessellation in which only one shape is used to form thepattern and that shape is a regular polygon.

relation A set of ordered pairs.relative error The ratio of the half-unit difference in precision to the entire

measure, expressed as a percent.relatively prime Two or more numbers having 1 as their only common factor.

remote interior angles The angles in a triangle that are not adjacent to a given exteriorangle of the triangle. In the figure, 2 and3 are remoteinterior angles for exterior angle 4.

repeating decimal A decimal whose digits repeat in groups of one or more.Example: 0.181818

replacement set A set of numbers from which replacements for a variable maybe chosen.

resultant The sum of two or more vectors.rhombus A parallelogram with four congruent sides.

right angle An angle that measures exactly 90.

right cone A cone with an axis that is also an altitude.right cylinder A cylinder with an axis that is also an altitude.right prism A prism with lateral edges that are also altitudes.


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right triangle A triangle having one right angle.

rise The vertical change between any two points on a line on thecoordinate plane.

root The solution of a quadratic equation.rotation A transformation in which a figure is turned around a fixed point.

rotational symmetry A figure that can be turned or rotated less than 360 about afixed point so that the figure looks exactly as it did before beingturned is said to have rotational symmetry.

run The horizontal change between any two points on a line on thecoordinate plane.

sample Some portion of a larger group selected to represent that group.sample space The list of all possible outcomes for an event.scalar A constant multiplied by a vector.scalar multiplication Each element of a matrix is multiplied by the scalar, or constant,

and a new matrix is formed.scale A ratio or rate between the actual size of an object and the size

of its model.scale of a data set The set of all possible values of a set of data, including the least

and greatest numbers in the set, separated by equal intervals.scale drawing A drawing that is similar to an actual object, but is eitherenlarged or reduced.

scale factor A scale written as a ratio in simplest form.scale model A replica of an original object that is too large or too small to be

built at actual size.


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scalene triangle A triangle with no congruent sides.

scatter plot A graph that shows the general relationship between two sets ofdata.

scientific notation A system of writing numbers using multiplication and powers often. A number of the form a 10n, where 1


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semi-regular tessellation A tessellation formed using combinations of two or threedifferent regular polygons with the same pattern of polygons ateach vertex.

sequence A set of numbers in a specific order.series The sum of the terms in a sequence.set A collection of objects or numbers, often shown using braces {}

and usually named by a capital letter.set-builder notation A concise way of writing a solution set. Example: {tt < 17}represents the set of all numbers t such that t is less than 17.

sides of an angle The two rays that form an angle. In the figure, rays SR and ST

are sides ofRST.

sides of a polygon The segments that form a closed figure.

sigma notation For any sequence a1, a2, a3, , the sum of the first k terms may

be written k =1

k

n

n

a

= which is read the summation fromn = 1 to k

ofan. Thus,1

k

n

n

a

= =a1 +a2 +a3+ +ak, where k is an integer

value.significant digits All of the digits of a measurement that are known to be accurate

plus one estimated digit.similar figures Figures that have the same shape but not necessarily the same

size.

similar solids Solids that have the same shape but not necessarily the samesize.simplest form of anexpression

An expression is in simplest form when it is replaced by anequivalent expression having no like terms or parentheses.

simplest form of a fraction A fraction is in simplest form when the greatest common factorof the numerator and the denominator is 1.

simplify Write an expression in simplest form.simulation A mathematical experiment that approximates a real-world

process.


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sine In a right triangle with acute angleA, the sine ofA

=the measure of the leg oppositethe measure of the hypotenuse

A .

skew lines Two nonparallel lines that do not intersect. In the figure, AX and

BC are skew segments.

skewed distribution A curve or histogram that is not symmetric representing datathat are not balanced around the mean.

slant height The altitude or height of each lateral face of a pyramid.slope The ratio of the change in the y-coordinates (rise) to the

corresponding change in the x-coordinates (run) as you move

from one point to another along a line.

slope formula The slope m of a line passing through two points is the ratio ofthe difference in the y-coordinates to the corresponding

difference in the x-coordinates.2 1

2 1

y y

m x x

=

slope of a curve The slope of a line tangent to a particular point on the graph of acurve.

slope-intercept form An equation of the formy =mx +b, where m is the slope and bis the y-intercept.

solid A three-dimensional figure formed by intersecting planes.solution A replacement value for the variable in an open sentence. A

value for the variable that makes an equation true. Example:The solution of 12 =x + 7 is 5.

solution of a system ofequations

The ordered pair representing the solution common to bothequations in a system of equations.

solution set The set of elements from the replacement set that make anopen sentence true.

solve an equation The process of finding all values of the variable that make anequation a true statement.

solve a triangle The process of finding the measures of all sides and all anglesin a triangle.

space A boundless three-dimensional set of all points.


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sphere The set of all points in space that are a given distance from agiven point, called the center. It has the followingcharacteristics: 1. A radius is a segment whose endpoints arethe center and a point on the sphere. 2. A chord is a segmentwhose endpoints are points on the sphere. 3. A diameteris a

chord of the sphere that contains the center.

spherical geometry The branch of geometry that deals with a system of points, greatcircles (lines), and spheres (planes).

square a number To multiply a number by itself.square of a number The product of a number and itself. Example: The square of 6,

or 6 squared, is 36 because 6 6 = 36.square (geometric figure) A parallelogram with four congruent sides and four right angles.

square matrix A matrix with the same number of rows and columns.square root One of the two equal factors of a number. Ifa2 = b, then a is the

square root ofb. Example: 12 is a square root of 144 since 122=144.

square units Used to measure area and tells the number of squares of agiven size needed to cover a two-dimensional figure.

standard deviation A measure of the average amount by which individual items ofdata deviate from the arithmetic mean of all the data.

standard error of themean

The standard deviation of the distribution of a sample mean.

standard form Numbers written without exponents.standard form of a linearequation

A linear equation of the formAx +By =C, whereA 0, andAand B are real numbers and not both zero.

statistics The study of collecting, organizing, and interpreting data.statement A sentence that is either true or false, but not both.

stem A digit written to the left of the vertical line in a stem-and-leafplot.stem-and-leaf plot A display of data in which each piece of the data is separated

into two numbers that are used to form a stem and a leaf.step function A function whose graph is a series of disjointed steps or line

segments.straight angle An angle that measures 180.straightedge Any object that can be used as a guide to draw a straight line.


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stratified random sample A sample in which the population is first divided into similar,nonoverlapping groups; a simple random sample is thenselected from each group.

Subtraction Property ofEquality

If you subtract the same number from each side of an equation,the two sides remain equal. For any numbers a, b, and c, ifa =

b, then a c =b c. Example: ifx = 3, then x 2 = 3 2.success The desired outcome of an event.supplementary angles Two angles are supplementary if the sum of their measures is

180.

surface area The sum of the areas of all the faces of a three-dimensionalfigure.

survey A question or set of questions designed to collect data about a

specific group of people.symmetry A geometric property of a figure in which it can be folded so that

each half matches the other exactly or rotated about a point less

than 360 so that the final image matches the original figure.synthetic division A method used to divide a polynomial by a binomial.system of equations A set of two or more equations with the same variables.system of inequalities A set of two or more inequalities with the same variables.systematic randomsample

A sample in which the items in the sample are selectedaccording to a specified time or item interval.

tangent In a right triangle with acute angleA, the tangent ofA =the measure of the leg opposite

the measure of the leg adjacent toA

A.

tangent line A line that intersects a circle or curve in exactly one point.term in an expression A number, a variable, or a product or quotient of numbers and

variables.term in a sequence Each number in a sequence.terminal side of an angle A ray of an angle that rotates about the center.terminating decimals A decimal whose digits end. Example: 0.2, -1.345tessellation A repetitive pattern of polygons that fit together with no holes or

gaps.tetrahedron A triangular pyramid.

theorem A statement that can be justified by logical reasoning and mustbe proven before it is accepted as true.


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theoretical probability The ratio of the number of favorable outcomes to the totalnumber of possible outcomes.

third-order determinant Determinants of a 3 3 matrix.

30-60-90 triangle A right triangle with a 30 angle and a 60 angle.three-dimensional figure A figure that encloses a part of space.transformation A mapping or movement of a geometric figure that changes its

shape or position.translation A transformation in which a figure is slid in any direction.

transversal A line that intersects two or more other lines to form eight ormore angles.

trapezoid A quadrilateral with exactly one pair of parallel opposite sides.

tree diagram A diagram used to show the total number of possible outcomesof an event.

triangle A polygon having three sides.trigonometric functions Functions of the angles of a right triangle that are certain ratios

of the sides of the triangle.trigonometric identity An equation involving trigonometric ratios that is true for all

values of the angle.

trigonometric ratios The ratios of the measures of two sides of a right triangle.trigonometry The study of the properties of triangles. Trigonometry means

angle measurement.

trinomial An algebraic expression that has three terms. Examples: x2 +2x+ 1, a +b - c

ton A customary unit of weight. 1 ton = 2000 poundstruth table A convenient way to organize truth values.truth values The true or false nature of a statement.


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two-column proof A deductive argument that contains statements and reasonsorganized in two columns.

unbiased sample A sample that is selected so that it is representative of the entirepopulation.

uniform tessellations Tessellations containing the same arrangement of shapes and

angles at each vertex.union The graph of a compound inequality containing the word or; the

solution is a solution of either inequality, not necessarily both.unit circle A circle of radius 1 unit whose center is at the origin of a

coordinate system.unit rate A rate with a denominator of 1.unit vector A vector of length 1 that is parallel to the x-, y-, orz-axis.unlike fractions Fractions whose denominators are different.upper bound The integer greater than or equal to the greatest real zero of the

polynomial function P(x).upper extreme The greatest number of a set of data.upper quartile The median of the upper half of a set.variable A letter or other symbol used to represent an unspecified

number or value.variance The mean of the squares of the deviations from the arithmetic

mean.vector A directed segment representing a quantity that has both

magnitude, or length, and direction.Venn diagram A diagram that uses circles to show relationships among sets of

numbers or objects.vertex form A quadratic function in the formy =a(x h)2 +k, where (h, k) is

the vertex of the parabola and x =h is its axis of symmetry.vertex of an angle The common endpoint of the rays forming the angle.

vertex of a conic section A point at which a conic section intersects its axis of symmetry.vertex of a parabola The maximum or minimum point of a parabola.vertex of a prism The point where three or more planes intersect.vertical angles Opposite angles formed by the intersection of two lines. In the

figure, the vertical angles are1 and3, and2 and4.

vertical line test A test used to determine if a relation is a function.volume The number of cubic units needed to fill the space occupied by

a solid.


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voluntary responsesample

A sample that involves only those who want to participate.

weighted average The sum of the product of the number of units and the value perunit divided by the sum of the number of units.

whisker The segments extending from the ends of the box in a box-and-

whisker plot.whole numbers The set {0, 1, 2, 3, }.x-axis The horizontal number line on a coordinate plane.

x-coordinate The first number in an ordered pair.x-intercept The x-coordinate at which a graph intersects the x-axis.yard A customary unit of length. 1 yard = 3 feet = 36 inchesy-axis The vertical number line on a coordinate plane.

y-coordinate The second number in an ordered pair.y-intercept The y-coordinate at which a graph intersects the y-axis.zero exponent For any nonzero number a, a0 = 1.zero matrix A matrix in which every element is zero.zero pair The result of a positive counter paired with a negative counter.Zero Product Property

For all numbers a and b, ifab = 0, then a = 0, b = 0, or both aand b equal zero.

zero vector A vector with initial and terminal points at the origin.zeros The roots, or x-intercepts, of a function.


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Midpoint on aCoordinate Plane

M = (2

21 xx +,

2

21 yy +)

Midpoint on a

Number LineM=

a + b

2

Midpoint in Space M= (x1 +x2

2

,y1 +y1

2

,z1 +z2

2

)

Distance on a

Coordinate Planed= (x2 -x1)

2+ (y2 -y1)

2

Distance on a

Number Lined= a - b

Distance in Space

d= (x2 -x1)2

+ (y2 -y1)2

+ (z2 -z1)2

Arc Lengthl =

N

360 2r

Slope m =y2 -y1x2 -x1

Slope-Intercept Form

of a line

y = mx + b

Point-Slope Form of

a line

y -y1 = m(x -x1)

Coordinate

Geometry

Equation for a Circle

on a CoordinatePlane

(x - h)2

+ (y - k)2

= r2

Matrices Matrix Multiplication

22

11

ba

ba =

22

11

yx

yx 1 1 1 2 1 1 1 2

2 1 2 2 2 1 2 2

a x b x a y b y

a x b x a y b y

+ + + +

Quadratic Formula x =2 4

2b b ac

a

Difference of TwoSquares

a2 - b2 = (a + b)(a - b)

Polynomials

Perfect squaretrinomials

a2 + 2ab + b2 = (a + b)2

a2 - 2ab + b2 = (a - b)2

Logarithms Change of BaseFormula

logan =logb n

logb a

Permutations ( )( )

!

!,

n

n rP n r

=

Combinations

( ) ( )!

! !,

n

n r rC n r =

Probability

and Statistics

Standard Deviation( ) ( ) ( )

2 2

1 2- + - + + -=

nx x x x x x

n

L2

Pythagorean

Theorem

a2 + b2 = c2Trigonometry

Law of Sines sin sin sinA B Ca b c

= =


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Law of Cosines a2=b2+c2 2bc cosATrigonometric

Functionssin =

opp

hypcos =

adj

hyptan =

opp

adj

csc =hyp

oppsec =

hyp

adjcot =

adj

opp

Quotient Identities tan = sin cos

cot = cos sin

Reciprocal Identitiescsc =

1

sin sec =

1

cos cot =

1

tan

Pythagorean

Identities

cos2+ sin2= 1

tan2+ 1 = sec2

cot2+ 1 = csc2

Additive Identity For any numbera, a + 0 = 0 + a = a.

Multiplicative

IdentityFor any numbera, a 1 = 1 a = a.

Substitution (=) Ifa = b, then a may be replaced by b.

Reflexive (=) a = aSymmetric (=) Ifa = b, then b = a.

Transitive (=) Ifa = b andb = c, then a = c .

Commutative (+) For any numbers a andb, a + b = b + a

Commutative () For any numbers a andb, ab = ba.Associative (+) For any numbers a, b, andc, (a + b) + c = a + (b + c).

Associative () For any numbers a, b, andc, (ab) c = a (b c).Distributive For any numbers a, b, andc,

a(b + c) = ab + ac anda(b c) = ab ac.

Additive Inverse For any numbera, there is exactly one number a such that

a + (a) = 0.MultiplicativeInverse

For any numbera

b, where a, b 0, there is exactly one number

such thata

b b

a= 1.

Multiplicative (0) For any numbera, a 0 = 0 a = 0.Addition (=) For any numbers a, b, andc, ifa = b, then a + c = b + c.

Subtraction (=) For any numbers a, b, andc, ifa = b, then a c = b c.

Division and

Multiplication (=)For any numbers a, b, andc, with c 0, ifa = b, then ac = bc ana

c

b

c= .

Addition (>) For any numbers a, b, andc, ifa > b, then a + c > b + c.Subtraction (>) For any numbers a, b, andc, ifa > b, then a c > b c.

Division and

Multiplication (>)

For any numbers a, b, andc,

1. ifa > b andc > 0, then ac > bc and ac

b

c> .

2. ifa > b andc < 0, then ac < bc and ac

b

c< .

Algebraic

Properties

Zero Product For any real numbers a andb, ifab = 0, then a = 0, b = 0, or bot


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a andb equal zero.

square P = 4s

rectangle P = 2l + 2w

Perimeter and

Circumference

circumference of a

circleC= 2rorC= d

square A = s2rectangle A = lw orA = bh

parallelogram A = bh

trapezoid A =1

2h(b1 + b2)

rhombus A =1

2d1d2 orA = bh

triangle A =1

2bh

regular polygon A =1

2Pa

circle A = r2

Area

sector of a circle A =N

360 r2

prism L = Ph

cylinder L = 2rhpyramid L =

1

2Pl

Lateral

Surface Area

cone L = rlprism T= Ph + 2B

cylinder T= 2rh + 2r2

cube T= 6s2

pyramidT=

1

2Pl

+Bcone T= rl + r2

Total Surface

Area

sphere T= 4 r2

cube V= s3

rectangular prism V= lwh

prism V=Bh

cylinder V= r2hpyramid V=

1

3Bh

cone V=1

3r2h

Volume

sphere V= 43r

3

Length 1 kilometer = 1,000 meters

1 meter = 100 centimeters

1 centimeter = 10 millimeters

1 foot = 12 inches

1 yard = 3 feet or 36 inche

1 mile = 1,760 yards or 5,2feet

Measurement

Conversions

Volume and Capacity 1 liter = 1,000 milliliters

1 kiloliter = 1,000 liters

1 cup = 8 fluid ounces

1 pint = 2 cups


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1 quart = 2 pints1 gallon = 4 quarts

Weight and Mass 1 kilogram = 1,000 grams1 gram = 1,000 milligrams

1 metric ton = 1,000 kilograms

1 pound = 16 ounces1 ton = 2,000 pounds

Time 1 minute = 60 seconds1 hour = 60 minutes

1 day = 24 hours

1 week = 7 days1 year = 12 months or 52

weeks or 365 days

1 leap year = 366 days

Metric to Customary 1 meter39.37 inches1 kilometer 0.62 mile1 centimeter 0.39 inch

1 kilogram 2.2 pounds1 gram = 0.035 ounce

1 liter 1.057 quartsFahrenheit to Celsius C=

95 (F 32)Temperature

Celsius to Fahrenheit F=59 C+ 32

Documents

Glossary of Maths