glossary - starting a mathcounts programalternate exterior angles given the diagram below, ......

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Glossary absolute value If x ~ 0 then Ixl = x else Ixl = -x. acute angle 1. An angle with measure between 00 and 900. 2. An angle with measure between 0 radians and ~ radians. additive inverse If x is a real number then -x is the additive inverse so that their sum is O. i.e. x+(-x) = O. adjacent angles Two angles sharing a common ray. i.e. LABe and LeBD are adjacent as they share ac. algorithm Any special method or set of instructions that solve certain types of problems. alternate exterior angles Given the diagram below, LABG and LHEF are said to be alternate exterior angles of the two lines intersected by a third line. alternate interior angles Given the diagram above, LABE and LBEF are said to be alternate interior angles of the two lines intersected by a third line. altitude (height) Any line segment connecting a vertex of a polygon to a point on a line containing a side of the polygon and this segment is the longest such segment. annulus The ring like region bounded by two concentric circles. apothem The perpendicular segment connecting the c~nter of a regular polygon to any of its sides. approximation A continual approach or coming nearer and nearer to a definite value. area A number associated with a geometric region on a plane. The number has square units. 107

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Glossary

absolute value If x ~ 0 then Ixl = x else Ixl = -x.

acute angle 1. An angle with measure between 00 and 900.

2. An angle with measure between 0 radians and ~ radians.additive inverse If x is a real number then -x is theadditive inverse so that their sum is O. i.e. x+(-x) = O.

adjacent angles Two angles sharing a common ray.

i.e. LABe and LeBD are adjacent as they share ac.

algorithm Any special method or set of instructions thatsolve certain types of problems.

alternate exterior angles Given the diagram below, LABGand LHEF are said to be alternate exterior angles of thetwo lines intersected by a third line.

alternate interior angles Given the diagram above, LABE

and LBEF are said to be alternate interior angles of thetwo lines intersected by a third line.

altitude (height) Any line segment connecting a vertex of apolygon to a point on a line containing a side of thepolygon and this segment is the longest such segment.

annulus The ring like region bounded by two concentriccircles.

apothem The perpendicular segment connecting the c~nter ofa regular polygon to any of its sides.

approximation A continual approach or coming nearer andnearer to a definite value.

area A number associated with a geometric region on aplane. The number has square units.

107

Glossary

arithmeticmean Given a set of numbers, this is thequotient of the sum of the numbers and the total quantityof those numbers. i.e. Given {2, 5, 8, 9}, the mean is2+5+8+9

4 = 6.

arithmetic sequence A progression of numbers, eachdifferent by a constant amount (the common difference) fromits predecessor. i.e. 3, 6, 9, 12, 15, ....

base 10 The counting system with ten distinct digits toform numbers. i.e. 0,1,2,3,4,5,6,7,8,9,10,11,....

binary The counting system with two distinct digits toform numbers. i.e. 0,1,10,11,100,101,110,111,1000, ....

bisect To divide (a geometrical figure).into two equalparts.

center (centre) 1. The point from which all the points of acircle are equidistant. 2. The invariant point of variousperspectives of regular polygons.

chord A line segment whose endpoints are the points of aparticular circle.

circle In a plane, the set of points equidistant from agiven point of the plane.

circumference 1. The boundary of a specific geometricobject such as a circle. 2. The length of such boundary.

circumscribe To draw a geometric figure such as circle or apolygon such that it contains the endpoints of anotherpolygon.

coefficient A numerical or constant multiplier of variablesin an algebraic expression. i.e. 5x2 + 2x + 1 hascoefficients of 5 and 2.

collinear A set of points which have the property ofexisting on the same line.

combination A selection of objects from a set withoutregard to order. Also called the unordered arrangement.

commission A percentage of the money taken in on sales,given as pay to salesclerk or agent, in addition to wages.

108

Glossary

common divisor (common factor) An integer that exactlydivides all numbers in a particular set.

common denominator An integer that is a multiple of alldenominators of a set of fractions.

common factor (common divisor) An integer that exactlydivides all numbers in a particular set.

common fraction (simple fraction, proper fraction) Afraction whose numerator is of lesser value than its

d. . 1 2 5

enomlnator. l.e. 4'3'10'....

common multiple .An integer that is a multiple of a set ofother integers.

complementary angles Two angles whose measure in degrees

sum to 900. (in radians: ~)

composite number A natural number that is the product oftwo other natural numbers other than itself and 1.

compound interest Interest paid on both the principal andthe accumulated unpaid interest.

concentric A family of geometrical figures, usuallycircles, having the same center.

cone A solid with a plane base bounded by a closed curvedsuch as a circle every point of which is joined to a fixedpoint (the vertex) outside the plane of the base.

congruent Geometrical figures having identical size andshape so that they may be exactly superimposed. Forexample, triangles with corresponding sides of the samelength and corresponding angles of the same measure.

convex A polygon having no interior angle greater than 1800or 1t radians.

coordinate system Any system for locating points by theircoordinates with respect to some set of reference points,lines, directions, etc.

109

Glossary

coordinates of a point A set of numbers that uniquelyidentifies the position of a point relative to a set offixed reference points, lines, directions, etc.

counting numbers (natural numbers) {I, 2, 3, ...}.

cross section A cutting through a three dimensionalgeometrical solid, usually at right angles with some axis.

cube A solid with six identical square sides that aremutually perpendicular.

cuboid Shaped in some respect like a cube, especiallyhaving rectangular but not necessarily square faces.

cylinder A solid bounded by two parallel planes and by thelocus of a line that moves round a curve, typically acircle.

data Numbers, things, facts, that are known or assumed fora problem.

decagon A ten sided polygon.

deci~ Relating to or using powers of 10 or the base 10.

degree measure

center point.

3~0 of one revolution of a ray about a given

It is used to measure angles.

denominator The divisor in a simple (cornmon)fractionindicating the size of each of the parts whose number isgiven by the numerator.

dependent events An event which is determined by anotherevent.

110

Glossary

diagonal of a polygon A line segment whose endpoints arevertices of a polygon that are not joined by any of itsedges.

diametercircle.

1. A chord containing the center of a given2. The length of the chord given above.

die (plural: dice) A cube with digits 1 to 6 on its faces.

difference The result of the subtraction of one number fromanother.

digit Any single symbol used to represent the numbers fromo to b-l in counting in base b. i.e. base 10 uses thedigits, 0,1,2,3,4,5,6,7,8,9; base 16 uses the digits,0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F; and base 2 uses 0,1.

direct variation (direct proportion) The relation betweentwo variable quantities the corresponding values of whichare a constant multiple of the one another. i.e. y = 3x.

discount to deduct from, reduce the quantity, cost, orvalue of.

disjoint sets Sets having no common members. i.e. The setof even numbers is disjoint from the set of odd numbers.

dividend A number or quantity that is to be divided byanother number or quantity.

divisible Capable of being exactly divided by another.

divisor (factor) The number or quantity that is to bedivided into another number or quantity.

dodecagon A polygon with twelve sides.

dodecahedron A polyhedron with twelve faces.

domain (essential domain) 1. The set of values of theindependent variables of a given function, partialfunction, or multi-valued function. 2. The set of all thefirst members of the ordered pairs that constitute afunction. .

edge A line segment which two faces of a solid or a linealong where two surfaces meet.

III

Glossary

empty set (null set) A set having no members.

endpoint A minimal, maximal, or terminating point ofsegment.

equation Two expressions separated by the equal sign (==)that have the same value.

equidistant Being the same distance from one or morepoints.

equilateral A polygon having all sides of equal length or asolid with all edges of equal length.

equilateral triangle A triangle with all sides congruent.

equivalent Expressions of numbers that represent the samevalue. i.e. Fractions are equivalent if they are

. 12 3

reduc1ble to the same va ue, such as 4 == 6.

estimate To calculate an approximate value for anexpression.

evaluate To determine the unique member of the range of afunction corresponding to a given member of its domain.

even number {O, -2, 2, -4, 4, -6, 6, ...}

event In probability, a possible outcome of a trial. i.e.The events that constitute the possible outcomes of a trialinvolving throwing a pair of dice three times are triplesof pairs each member of which is one of the numbers 1 to 6;thus there are (62)3 such events in the sample space.

expanded notation A method in which the place value ofdecimal (and other bases) can be represented.i.e. 3406.76 == 3xl03 + 4xl02 + 6xlOO + 7xIO-1 + 6xIO-2.

exponent A number or expression written superscript toanother and indicating the power to which the latter is tobe raised. i.e. 43 ==4x4x4 ==64, the three indicates howmany times the 4 will be used as a factor.

expression Any symbol or well-formed string of symbols of aparticular theory. i.e. In algebra, 4x2 + ax + 4.

112

Glossary

exterior angle of a polygon An angle contained between oneside of a polygon and the extension of the adjacent side.

A B

LADE isexterior

Cfactor (divisor) The number or quantity that is to beexactly divided into anoth~r number or quantity.

factorial The function that computes the product of thefirst n natural numbers. i.e. n! = 1.2.3 n.

formula A formal expression of some rule or other result.

i.e. Converting from Fahrenheit to Celsius: C-;(F-320).

fraction Any division of two integers. Placed in the form:2 . 13 (two-thlrds) or 4 (one fourth). See numerator anddenominator.

frequency distribution The set of relative frequencies ofsample points falling within given intervals of the rangeof the random variable.

function A relation between two sets that associates aunique element of the second with each element of thefirst.

geometric mean Given a set of numbers, this is thenth root of the product of the numbers where n is.the totalquantity of those numbers. i.e. Given {2, 5, 8, 9}, the

geometric mean is ~2(5) (8)(9) ~ 5.18004012822...

geometric sequence A progression of numbers whosesuccessive members differ by a constant multiplier.i.e. 1,2,4,8,16,....

greatest COJrmOn

integer d thatsuch that if cis the highest

divisor (GCD) (highest common factor) Anexactly divides integers a and b, and isdivides a and b, then c must divide d, as dsuch value. i.e. The GCD of 24,60,84 is 12.

113

Glossary

greatest common factor (GCF) Same as greatest commondivisor.

half-life The period required for the disintegration ofhalf the organisms in a sample. i.e. Plutonium will losehalf of its radioactivity in 50 years.

harmonic sequence A sequence whose reciprocals form an.

thm t . 1 1 1arl e lC sequence. i.e.1'2'3'4'....

harmonic mean A number that can be inserted between two

given numbers to form a three term harmonic sequence.1 1

i.e. Given set {2'3}'the reciprocalsof the arithmetic5 2

sequence of 2, 2' 3, yields 5 as harmonic mean for the set.

height (altitude) Any line segment connecting a vertex of apolygon to a point on a line containing a side of thepolygon and this segment is the longest such segment.

hemisphere Half of a sphere, bounded by a plane containingits center.

heptagon A seven sided polygon.

hexagon A six sided polygon.

hypotenuse Side opposite the right angle in right triangle.

icosahedron A polyhedron with twenty faces.

image(s) of a point(s) (under a transformation) The set ofpoint(s) resulting from moving a given set of points duringa transformation.

improper fraction A fraction with a numerator greater thanor equal to the denominator.

independent events Of two or more random variablesdistributed so that the value of one variable will have noeffect on that taken by the others.

inequality The relationship between two numbers, quantities,etc., that holds they are comparable but not equal.

i.e. a < b (a is less than b) a S b (a is less than or equal to b)

a > b (a is greater than b) a ~ b (a is greater than or equal to b)

114

Glossary

infinite series

l..e.

The sum of an infinite sequence of terms.

00 1 1 1~ 2n = 1 + :2 + 4 + ~ + ... = 2i=o

inscribe To construct (a geometric figure) inside anotherfigure so that the first only intersects the second at itsvertices.

integer {O, -1, 1, -2,.2, -3, 3, ...}

integral divisors Factors of an integer which are integers.

interior angle of a polygon Any angle formed by twoadjacent sides of a polygon.

A

E

11

LABC,LBCD,and

LCDE are

C interior

intersection (n) A point or set of points cornman to two ormore sets or figures.

inverse variation The relationship that hold between twovariable quantities that an increase by a multiple in onebrings about a decrease by the same factor in the other.

irrational number Numbers that cannot be represented as aratio of two integers.

isosceles trapezoid A trapezoid with the non-parallel sidescongruent.

isosceles triangle A triangle with two sides congruent.

lateral edge A segment connecting a vertex of abase of aprism to its corresponding vertex on its opposite base or asegment connecting the apex of a pyramid to a vertex of thepyramid's base.

lattice point(s) On the Cartesian plane, any set of integerordered pairs. On a grid like, . . . . . the points thatmake up the grid.

115

Glossary

lateral surface area The sum of the areas of all faces of apolyhedron that are not bases.

least common denominator (LCD) The smallest integer orpolynomial of lowest degree that is exactly divisible byall the denominators of a given set of fractions. i.e.

. ff ' 111 h d .

G~ven the set 0 ract~ons: 2'3'5 ave a common eno~nator

of 30; therefore each fraction can be expressed as:15 10 6 .

13'30'30' respect~vely.

least common multiple (LCM)' The smallest integer orquantity that is exactly divisible by all of a given set ofnumbers or quantities. i.e. The LCM of 3,5, and 10 is 30.

length of a segment A measure of the extent of a linesegment that is zero only when its endpoints coincide andis otherwise positive and unaffected by changing theorientation of the line. i.e. On the Cartesian plane,

segment AB has length V(dl-bl)£+(d2-b2)£ where A is thepoint (dl,d2) and B is (bl,b2).

linear equation A polynomial equation of the first degree,of the form y = mx + b.

linear function Any function that has an equationassociated with it making it appear as a linear equation ofthe first degree. i.e. f(x) = mx + b.

line segment The set of points of a line resulting from twopoints and all points between them.

maximum The largest element of a set s. i.e. The set ofnon positive numbers have a maximum of O.

median of a set of data If a set has an odd number ofelements, then the data element in the exact middle afterthe set has been ordered. If the set has an even number ofelements, then the mean of the two data elements in theexact middle after the set has been ordered. i.e. Themedian of {2,3,5,5,4} is 4 and the median of {2,3,5,5,4,6}is 4.5.

median of a triangle A line segment with one endpoint atthe vertex of an angle of the triangle and the otherendpoint at the midpoint of the opposite side from thevertex.

116

Glossary

midpoint B is the midpoint of segment AC, if A, B, and Care collinear and length of AB equals the length of BC.

minimum The smallest element of a set s.i.e. The set of non negative numbers have a minimum of o.

mixed number A number form consisting of an integer with a

fractional part. Le. 4~ or If.

mode of a set of data The data item in a set which has thehighest frequency. Le. {l,2,5,5,4}has mode 5 and{3,3,4,5,6,6,7} has mode 3 and 6.

multiple Any number or polynomial that is the product of agiven number or polynomial and an integral multiplier.

multiplicative inverse (reciprocal) A value that multipliedby a given number yields a product of 1.

1 1i.e. The inverse of 5 is 5' since 5x5 = 1.

natural number (counting number) A number from the set{1,2,3,4, ...}.

negative number A number less than O.

numerator The dividend in a vulgar (improper or common)7

fraction. Le. In 8' 7 is thenumerator.obtuse angle An angle whose measure is between 900

(~ radians) and 1800 (x radians) .

octagon A polygon with eight sides.

octahedron A polyhedron with 8 faces.

odd number A number from the set {1,-1,3,-3,5,-5,...}.

opposite of a number (additive inverse) A value when addedto a given number gives a sum of O. Le. -4 is theopposite of 4, 6 is the opposite of -6, and -a is theopposite of a.

ordered pair An ordered set of two elements. i.e. (0,0)

designates the origin on the Cartesian plane and (1,2) a point in thefirst quadrant.

origin The point on a graph which has all coordinates as O.i.e. (0,0)is the origin on the Cartesianplane.

117

Glossary

outcome That coming out of or results from something else.i.e. The roll of a die results in a 4.

palindrome A number reading the same forward or backward.i.e. 1234321 or 1221. Also, words can do thesame, such as A MAN, A PLAN, A CANAL, PANAMA or A TOYOTA.

parallel (II symbol) Sets that never intersect even whenthose sets are extended.i.e. A B These two segmentsare

C D parallel,even if extended.

parallelogram A quadrilateral with opposite sides parallel.

Pascal's triangle A triangular array of integers, with 1 atthe apex, in which each number is the sum of the twonumbers above it in the preceding row.i.e. 1

1 11 2 1

1 3 3 11 4 6 4 1

pentagon A polygon with five sides.

percent (per cent) In everyproportion as a fraction of. 51.e. 5% = 100.

hundred, expressing awhich the denominator is 100.

percent increase/decrease An amount representing, inpercent form, of an increase or decrease from the originalvalue. i.e. The original cost of a $1.00 hamburger israised to $1.15. This is a 15% increase in cost from theoriginal value of the hamburger.

perfect squareinteger. i.e.

An integer that is the square of another1,4,9,16,25,... .

perimeter 1. The boundary of a curve enclosing a region ofa plane, such as a circle or a polygon. . 2. The length ofsuch boundary.

permutation (ordered arrangement) An orqered arrangement ofspecified number of objects selected from a set.i.e. Given the set {O,1,2}, taking permutations of 2 out of thethree results in sets of {l,2}, {l,0}, {2,1}, {2,0}, {0,1}, and {0,2}.

118

Glossary

perpendicular (i) A pair of lines, rays, and/or segmentsthat intersect to form a right angle.

perpendicular bisector Any line, segment, plane, that is

perpendicular to a given segment at i~s midpoint.

pi (x) The ratio of the circumference of any circle to itsdiameter. x ~ 3.14159265358979... which is irrational.

polygon A simple closed figure in a plane made up of linesegments, any two of which intersect only at one endpoint.

polyhedron A solid figure, or its surface, that is boundedby four or more polygonal faces in such a way that pairs offaces meet along edges, and three of more edges meet ineach vertex.

positive number A number greater than O.

prime factorization The factoring of a natural number intofactors of prime numbers.i.e. 12 = 22x3 and 504 = 23x32x7.

prime number A natural number with no divisors besidesitself and 1. Le.2,3,5,7,11,13,17,19, An infiniteset, the largest known as of August, 1989 is391582x2216193_1.

prism A polyhedron with two parallel and congruentpolygonal bases, so that all parallel cross sections arealso congruent with the bases and all lateral faces areparallelograms.

probability A measure or estimate of the degreeconfidence one may have in the occurrence of anmeasured on a scale from 0 (impossibility) to 1(certainty) .

ofevent,

product The result of the multiplication of two or morenumbers or expressions.

119

Glossary

proper divisor (proper factor) A divisor (factor) of agiven number other than the number itself.

proper fraction A fraction with a numerator less than itsdenominator.

proportion A linear relationship between two variablequantities or one variable quantity and the inverse of thesecond. With numbers, two equal ratios.

1 3i.e. 2 is proportionalto 6.

pyramid A polyhedron with one polygonal base and lateralfaces that are triangles with a common vertex.

Pythagorean triple Any set of three integers satisfying thePythagorean Theorem, a2 + b2 = c2.

quadrant 1. A quarter of the circumference of a circle.2. The area within a circle enclosed between twoperpendicular radii and the circumference. 3. Any of thefour sections of the Cartesian plane that is by thecoordinate axes.

y-ax~sII

TI

quadrant quadrant

x-ax~s

IIIquadrant

IVquadrant

quadrilateral A polygon with four sides.

quotient The result of the division of one number orexpression by another. i.e. 8+2 = 4.

radicand A number or quantity from which a root is to beextracted, usually preceded by the radical sign.i.e. 7 is the radicandof V7.

radius 1. A line segment with one endpoint the center of acircle and the other a point of the circle. 2. The lengthof such a segment.

120

Glossary

random Chosen without regard to any characteristics of theindividual members of the population so the each has anequal chance of being selected.

range of a data set The difference of the highest andlowest elements of the data set.

rate The amount, degree, etc. of anything in relation tounits of something else. i.e. Forty miles per hour.

ratio A quotient of two numbers, magnitudes, quantities, orexpressions, such as a measure of the relative size of twoclasses. i.e. The ratio of a side of a square to its diagonal: 1:V2.

rational number . A number that can be expressed as a ratioof two integers, excluding 0 as a denominator.

1 3 1 4 26i.e. 2,4,75 since these can be written2'1,!r.

ray The set of points of a line consisting of twoparticular points and the set that contains all pointsbetween the given two and all points that make exactly oneof the given points between these points and the othergiven point. i.e. A point and all points in one direction.

real number Any rational or irrational number.

reciprocal (multiplicative inverse)by a given number yields a product

i.e. The inverse of 5 is i, since 5~ = 1.

A value that multipliedof 1.

rectangle A quadrilateral with three right angles.

rectangular prism A prism with all faces as rectangles.

reflection A planar transformation in which the coordinatesof an object are changed to those of a point on aperpendicular line of the object's point equidistant from agiven line.

vI\]regular polygon A polygon with all angles congruent and allsides congruent.

121

Glossary

relatively prime (coprime) Numbers not having any commondivisors other than 1. Le. 8 and 9 and relativelyprime.

remainder The amount left over when one quantity cannot beexactlydividedby another.Le. 29+8 = 3 with a remainder of 5.

repeating decimal (recurring decimal) A rational numberwhose representation as a decimal contains a pattern ofdigits that repeats after the decimal point.

1 5i.e. 3 = 0.333333... and 7 = 0.714285714285714285....

repetend The digit or digits that repeat in a repeating

decimal. i.e.~ = 0.333333...,3 is the repetendand in

t = 0.714285714285714285..., 714285 is the repetend.

replacement set A set of values from which a value can beused for a variable in an expression.

revolution A turning or spinning motion of an object arounda center of axis.

revolutions per minute (RPM) A rate measuring the number ofcomplete revolutions made by an object in one minute.

rhombus A quadrilateral with four sides congruent.

right angle An angle with measure of 900 (~ radians).

right circular cone A cone with the line containing thevertex and the center of the base being perpendicular tothe base plane...

right circular cylinder A cylinder with the line containingthe centers of both bases being perpendicular to each baseplane.

right polyhedron A polyhedron with its edges perpendicular.

right prism A prism with all lateral edges perpendicular tothe base planes.

right pyramid A pyramid with a regular polygonal base andthe line containing the vertex and the center of the basepolygon being perpendicular to the base plane.

122

Glossary

right triangle A triangle containing a right angle.

sale price The cost of an item sold in a store.

sales tax A tax levied on sales or on receipts from sales,usually added to the price by the seller.

scalene triangle A triangle with no two sides congruent.

scientific notation The expressionpoint notation as multiples of thebase less than the given number.i.e. 123.45 is written 1.2345x102.

of numbers in floatinglargest power of the

semicircle An arc of a circle that is half of itscircumference.

semiperimeter Half of a perimeter of a polygon.

sequence An ordered set of objects, especially numbers,either finite or denumerable, and so capable of beingindexed by the natural numbers. i.e. 2,4,6,8,....

series The sum of a finite or infinite sequence of terms.

"i. e. Lk2 = t +22 + 32 +...+n2 = n(n+ 1)(2n+ I)

t~1 6

set A collection, possibly infinite, of distinct numbers,objects, etc. that is treated as an entity in itself.i.e. The set of integers {O,-1,1,-2,2,-3,3,...}.

significant digits The digits of a number that express aquantity to some specific degree of accuracy, rounding thelast figure up if the next digit is 5 or greater.i.e. 3.14159 to four significant digits is 3.142.

similar figures Having the same shape but not the samesize. i.e. Two polygons are similar if their correspondingangles are congruent and their corresponding sides areproportional.

simple interest Interest paid only on the principle lent.

slope 1. The ratio of the rise to the run of any twodistinct points of a line on the Cartesian plane. 2. Thetangent of the angle between the direction of the line andthe x-axis on the Cartesian plane.

123

Glossary

slope-intercept form The equation of the line written inthe form: y = mx + b where m is the slope and b is the y-intercept on the Cartesian plane.

solution set The set of all solutions of a system ofalgebraic equations. i.e. The solution set of x2+2x+l=0 is {-I}.

space diagonal A diagonal of a polyhedron that connectsvertices not on the same face.

sphere The set of points equidistant from a given point.

square A rectangular rhombus or a rhombic rectangle.

square root A n~mber or quantity that when multiplied byitself gives a product equal to a given number or quantity.

standard notation The usual form that a number is written.i.e. 1234 or 1234.567.

stem-and-leaf plot A way to graphically represent a setnumbers as a way to show frequency distribution. Givenset {14,23,24,30,34}, the stem could represent the tenscolumn and the leaf the units in the following chart:

stem Leaf1 42 3,43 0,4

ofthe

sum The result of adding two or more numbers orexpressions.i.e. 1+2+3+4= 10, 10 is the sum.

supplementary angles Two angles with the sum of theirmeasures being 1800 (x radians) .

system of equations (inequalities) A set of equations (orinequalities that are to be solved simultaneously ortreated together.

tangent of

In a triangle AABC with LC being right, the. . . BC

(

the leg opposite LA)

LA 1S the rat10, AC th I d . LA.

e eg a Jacent

tangent

tangent figures Two geometric figures with exactly onepoint in common.

tangent line A line that intersects a curve at one point.

124

Glossary

tens digit In a decimal number, the digit to the left ofthe units digit. Le. 1234.56,3 is the tensdigit.

ter.m Any expression that forms a separable part of someother expression. i.e. 3x2+2x-4, has three terms, 3x2, 2x, and -4.

ter.minatingdecimal A decimal that has a finite number ofdigits to the left of the decimal point. Le. 3.45or 7.875.

tessellate The act of covering or paving a plane withidentical shapes.

tetrahedron A triangular pyramid or four faced polyhedron.

time-and-a-half A rate of payment one and a half times theusual rate, as for working overtime.

total surface area The sum of the areas of all faces of apolyhedron.

trapezoid A quadrilateral with one pair of parallel sides.

triangle A three sided polygon.

trisect To divide into three equal parts.

union (u) The set of elements that belong to either of agiven pair of sets.

unit fraction A fraction with a numerator of 1 and a

denominator of some other integer. Le. ~ or 110

units digit In any particular base numeral, the digit tothe immediate left.of the decimal point.i.e. 123.456, 3 is the units digit.

variable A symbol, such as x, y, or z, representing anunspecified member of a class of objects, numbers, etc.

125

Glossary

vertical angles A pair of angles with sides that areopposite rays.

LJAR and LEATare ve rtical.

vertex 1. The intersection of two sides of a polygon.2. The intersection point of the two rays of an angle.3. The designated non-coplanar point mentioned in thedefinition of a cone or pyramid.

volume A quantity associated with the extent of a threedimensional space enclosed by a solid.

whole number Any number from the set {O,1,2,3,4,...}

x-axis The horizontal line axis on the Cartesian plane.y-axis

x-axis

x-coordinate (abscissa) In an ordered pair the first term.i.e. Given (3,2), 3 is the x-coordinate.

x-interceptthe x-axis.

A point of a set such as a line that intersectsi.e. The intercept of 2x+y=12 is 6.

y-axis The vertical line axis on the Cartesian plane.

y-coordinate (ordinate) In an ordered pair the second term.i.e. Given (3,2), 2 is the y-coordinate.

y-interceptthe y-axis.

A point of a set such as a line that intersectsi.e. The intercept of y=2x+12 is 12.

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