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Mathematics Definitions and Formulas: A Comprehensive Guide, Exams of Science education

A.T. Still University of Health Sciences (ATSU)Science education

A concise overview of fundamental mathematical concepts and formulas, covering topics such as prime and composite numbers, decimals, fractions, percentages, basic arithmetic operations, polygons, triangles, quadratic equations, descriptive statistics, order of operations, probability, ratios, proportions, percentages, inequalities, equations, properties, and geometry. It serves as a quick reference guide for students studying mathematics, offering clear definitions and examples for each concept. Useful for quick revision and understanding of basic mathematical principles, making it a valuable resource for students and lifelong learners alike. It includes key concepts such as the pythagorean theorem, angle properties, and various geometric formulas, providing a well-rounded summary of essential mathematical knowledge. This guide is designed to aid in understanding and application of mathematical principles across various contexts.

Typology: Exams

2025/2026

Available from 10/26/2025

CarlyBlair
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CSET Multiple Subject: Mathematics
PrimeyNumbery-y
yyyyyyyyyyyy☑️yyAynaturalynumberygreaterythany1,yandythatyonlyyhasy1yandyitselfyasydivisors.yInyotherywords,
yaynaturalynumberythatyhasyexactlyytwoydifferentydivisors.yTheyfirstysevenyprimeyofythisykindyofynumb
ersyarey2,y3,y5,y7,y11,y13,y17.
CompositeyNumbery-y
yyyyyyyyyyyy☑️yyAynaturalynumberygreaterythany1ythatyisynotyayprimeynumber.yInyotherywords,yaynaturalynum
berythatyhasyatyleastythreeydifferentydivisors.yTheyfirstysevenynumbersyofythisykindypfynumbersyarey4,y6,
y8,y9,y10,y12,y14.
Changingydecimalsytoypercentsy-y
yyyyyyyyyyyy☑️yy1.yMoveytheydecimalypointytwoyplacesytoytheyright.
2.yInsertyaypercentysign.
Changingypercentsytoydecimalsy-y
yyyyyyyyyyyy☑️yy1.yEliminateytheypercentysign.
2.yMoveytheydecimalypointytwoyplacesytoytheyleft.y(Sometimesyaddingyzerosywillybeynecessary.)
Changingyfractionsytoypercentsy-y
yyyyyyyyyyyy☑️yy1.yMultiplyybyy100%.
Changingypercentsytoyfractionsy-y
yyyyyyyyyyyy☑️yy1.yDivideytheypercentybyy100.y
2.yEliminateytheypercentysign.y
3.yReduceyifynecessary.
Changingyfractionsytoydecimalsy-y
yyyyyyyyyyyy☑️yySimplyydoywhatytheyoperationysays.yInyotherywords,y13/20ymeansy13ydividedybyy20.
AddingyandySubtractingyDecimalsy-y
yyyyyyyyyyyy☑️yyLineyupytheydecimalypointsyandythenyaddyorysubtractyinytheysameymanneryyouywouldyaddyo
rysubtractyregularynumbers.yAddingyzerosycanymakeytheyproblemyeasierytoyworkywith.
MultiplyingyDecimalsy-y
yyyyyyyyyyyy☑️yyJustymultiplyyasyusual.yThenycountytheytotalynumberyofydigitsyaboveytheylineywhichyareytoyt
heyrightyofyallydecimalypoints.yPlaceyyourydecimalypointyinyyouryanswerysoythereyisytheysameynumbery
ofydigitsytoytheyrightyofyityasythereywasyaboveytheyline.
DividingyDecimalsy-y
yyyyyyyyyyyy☑️yyTheysameyasydividingyotherynumbers,yexceptythatyifytheydivisory(theynumberyyou'reydividin
gyby)yhasyaydecimal,ymoveyitytoytheyrightyasymanyyplacesyasynecessaryyuntilyityisyaywholeynumber.yThe
nymoveytheydecimalypointyinytheydividendy(theynumberybeingydividedyinto)ytheysameynumberyofyplace
s.ySometimesyyouymayyhaveytoyaddyzerosytoytheydividend.
Dividendy-y
yyyyyyyyyyyy☑️yyTheynumberybeingydividedyinto.yOrytheynumberyinsideytheydivisionysign.
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CSET Multiple Subject: Mathematics

PrimeyNumbery-y yyyyyyyyyyyy☑️ yyAynaturalynumberygreaterythany1,yandythatyonlyyhasy 1 yandyitselfyasydivisors.yInyotherywords, yaynaturalynumberythatyhasyexactlyytwoydifferentydivisors.yTheyfirstysevenyprimeyofythisykindyofynumb ersyarey2,y3,y5,y7,y11,y13,y17. CompositeyNumbery-y yyyyyyyyyyyy☑️ yyAynaturalynumberygreaterythany 1 ythatyisynotyayprimeynumber.yInyotherywords,yaynaturalynum berythatyhasyatyleastythreeydifferentydivisors.yTheyfirstysevenynumbersyofythisykindypfynumbersyarey4,y6, y8,y9,y10,y12,y14. Changingydecimalsytoypercentsy-y yyyyyyyyyyyy☑️ yy1.yMoveytheydecimalypointytwoyplacesytoytheyright. 2.yInsertyaypercentysign. Changingypercentsytoydecimalsy-y yyyyyyyyyyyy☑️ yy1.yEliminateytheypercentysign. 2.yMoveytheydecimalypointytwoyplacesytoytheyleft.y(Sometimesyaddingyzerosywillybeynecessary.) Changingyfractionsytoypercentsy-y yyyyyyyyyyyy☑️ yy1.yMultiplyybyy100%. Changingypercentsytoyfractionsy-y yyyyyyyyyyyy☑️ yy1.yDivideytheypercentybyy100.y 2.yEliminateytheypercentysign.y 3.yReduceyifynecessary. Changingyfractionsytoydecimalsy-y yyyyyyyyyyyy☑️ yySimplyydoywhatytheyoperationysays.yInyotherywords,y13/20ymeansy 13 ydividedybyy20. AddingyandySubtractingyDecimalsy-y yyyyyyyyyyyy☑️ yyLineyupytheydecimalypointsyandythenyaddyorysubtractyinytheysameymanneryyouywouldyaddyo rysubtractyregularynumbers.yAddingyzerosycanymakeytheyproblemyeasierytoyworkywith. MultiplyingyDecimalsy-y yyyyyyyyyyyy☑️ yyJustymultiplyyasyusual.yThenycountytheytotalynumberyofydigitsyaboveytheylineywhichyareytoyt heyrightyofyallydecimalypoints.yPlaceyyourydecimalypointyinyyouryanswerysoythereyisytheysameynumbery ofydigitsytoytheyrightyofyityasythereywasyaboveytheyline. DividingyDecimalsy-y yyyyyyyyyyyy☑️ yyTheysameyasydividingyotherynumbers,yexceptythatyifytheydivisory(theynumberyyou'reydividin gyby)yhasyaydecimal,ymoveyitytoytheyrightyasymanyyplacesyasynecessaryyuntilyityisyaywholeynumber.yThe nymoveytheydecimalypointyinytheydividendy(theynumberybeingydividedyinto)ytheysameynumberyofyplace s.ySometimesyyouymayyhaveytoyaddyzerosytoytheydividend. Dividendy-y yyyyyyyyyyyy☑️ yyTheynumberybeingydividedyinto.yOrytheynumberyinsideytheydivisionysign.

Divisory-y yyyyyyyyyyyy☑️ yyTheynumberyyou'reydividingyby. Polygonsy-y yyyyyyyyyyyy☑️ yyAyclosedyfigureyformedywithylineysegments,ywhichyareycalledysides.yAlsoymeansy"aymany- sidedyfigure." Triangley-y yyyyyyyyyyyy☑️ yyAythree- sidedypolygon.yItyhasythreeyanglesyinyitsyinterior.yTheysumyofytheyanglesyisyalwaysy 180 ydegrees.yItyisyn amedybyynamingyitsyverticesyorycorners,yandytheyyareyclassifiedybyyeitherytheirysideyorytheiryangles. EquilateralyTriangley-y yyyyyyyyyyyy☑️ yyHasyallythreeyofyitsysidesyofyequalylength,ywhichyinyturnymakesyeachyofytheythreeyanglesyeq ualyinymeasure.yTherefore,yeachyangleyinyanyequilateralytriangleyhasyaymeasureyofy 60 ydegreeysinceythey sumyofytheyanglesyinyanyytriangleyisy 180 ydegree. IsoscelesyTriangley-y yyyyyyyyyyyy☑️ yyAytriangleywithytwoycongruent,yoryequal,yandytheyanglesyoppositeythoseysidesyhaveyequalym easure. ScaleneyTriangley-y yyyyyyyyyyyy☑️ yyAytriangleywithynoycongruent,yoryequal,ysides.yAllythreeyofyitsysidesyareydifferentylengths.yT heyanglesyinythisytriangleywillyallyhaveydifferentymeasures,ytheylargestyangleywillybeyoppositeytheylong estyside,yandytheysmallestyangleywithybeyoppositeytheyshortestyside. IncompleteyQuadraticy-y yyyyyyyyyyyy☑️ yyAyquadraticywithyaytermymissing. Example:y Solveyforyx.yx²y-y 16 y=y 0 Factoring,y(xy+y4)(xy-y4)y=y 0 xy+y 4 y=y 0 y-->yxy=y- oryxy-y 4 y=y 0 y-->yxy=y 4 QuadraticyEquationy-y yyyyyyyyyyyy☑️ yyAnyequationythatycouldybeywrittenyasyAx²y+yBxy+yCy=y0.yToysolveythisyequation: 1.yPutyallytermsyonyoneysideyofytheyequalysign,yleavingyzeroyonytheyotheryside.y 2.yFactor. 3.ySetyeachyfactoryequalytoyzero. 4.ySolveyeachyofytheseyequation.y 5.yCheckybyyinsertingyyouryansweryinytheyoriginalyequation.term- DescriptiveyStatisticsy-y yyyyyyyyyyyy☑️ yyUsedytoyexplainyorydescribeyaysetyofynumbers.yMostyoftenyweyuseytheymean,ymedian,yorym odeytoydescribeytheseynumbers. Meany-y yyyyyyyyyyyy☑️ yyAlsoyknownyasytheyarithmeticyaverage.yOfyaysetyofydata,ytheysumyofytheydatayvaluesydivide dybyytheynumberyofydatayvalues.

yyyyyyyyyyyy☑️ yyAystatementyinywhichytheyrelationshipsyareynotyequal,yandyinywhichyitythatycomparesytwoyq uantities.yInsteadyofyusingyanyequalysigny(=)yasyinyanyequation,yweyusey>y(greaterythan)yandy<y(lessytha n),y≥y(greaterythanyoryequalyto)yandy≤y(lessythanyoryequalyto)yory≠y(notyequalyto).y Whenyworkingywithythese,ytreatythemyexactlyylikeyequations,yEXCEPT:yIfyyouymultiplyyorydivideybot hysidesybyyaynegativeynumber,yyouymustyreverseytheydirectionyofytheyinequalityysymbol. Equationy-y yyyyyyyyyyyy☑️ yyAyrelationshipybetweenynumbersyand/ orysymbolsythatysaysytwoyexpressionsyhaveytheysameyvalue. CommutativeyPropertyy-y yyyyyyyyyyyy☑️ yyTheyorderyinywhichyadditionyorymultiplicationyisydoneydoesynotyaffectytheyanswer.yNote:yS ubtractionyandydivisionydoesynotyhaveythisyproperty. CommutativeyPropertyy-y yyyyyyyyyyyy☑️ yya+by=yb+a aby=yba AssociateyPropertyy-y yyyyyyyyyyyy☑️ yyTheygrouping,ywithoutychangingytheyorder,ydoesynotyaffectytheyanswer.yNote:ySubtractiony andydivisionydoesynotyhaveythisyproperty. AssociateyPropertyy-y yyyyyyyyyyyy☑️ yyAddition:ya+(b+c)y=y(a+b)+c Multiplication:yax(bxc)y=y(axb)xc DistributiveyPropertyy-y yyyyyyyyyyyy☑️ yyMultiplicationyoutsideyparenthesesydistributingyoveryadditionyorysubtractionyinsideyparent hesesydoesynotyaffectytheyanswer.yNote:yYouycannotyuseythisypropertyywithyonlyyoneyoperation. DistributiveyPropertyy-y yyyyyyyyyyyy☑️ yya(by+yc)y=yaby+yac AdditiveyInversesy-y yyyyyyyyyyyy☑️ yyAlsoyknownyasytheyoppositeyofytheynumber.yThisyisyayvalueythat,ywhenyaddedytoyanyynumb er,yequalsy0. Perimeteryofyaysquarey-y yyyyyyyyyyyy☑️ yyPy=y4a Areayofyaysquarey-y yyyyyyyyyyyy☑️ yyAy=yS² Perimeteryofyayrectangley-y yyyyyyyyyyyy☑️ yyPy=y2by+y2h Areayofyayrectangley-y yyyyyyyyyyyy☑️ yyAy=ybh Perimeteryofyaytriangley-y yyyyyyyyyyyy☑️ yyPy=ya+b+c

Areayofyaytriangley-y yyyyyyyyyyyy☑️ yyAy=y1/2ybh Circumferenceyofyaycircley-y yyyyyyyyyyyy☑️ yyCy=yπdy or yCy=y2πr Areayofyaycircley-y yyyyyyyyyyyy☑️ yyAy=yπr² IdentityyNumbery-y yyyyyyyyyyyy☑️ yyAyvalueythat,ywhenyaddedytoyanotherynumberyorymultipliedywithyanotherynumber,ydoesynoty changeytheyvalueyofythatynumber.y 1.yForyadditionyisy0.yAnyynumberyaddedytoy 0 ygivesythatynumber.y 2.yForymultiplicationyisy1.yAnyynumberymultipliedybyy 1 ygivesythatynumber. Angley-y yyyyyyyyyyyy☑️ yyFormedybyytwoyraysythatystartyfromytheysameypointyorycommonyendpoint,ywhichyisycalledyt heyvertex.yThisyisymeasuredyinydegrees. Vertexy-y yyyyyyyyyyyy☑️ yyTheycommonyendpointyofyanyangle. Rayy-y yyyyyyyyyyyy☑️ yyAypartyofyayline,ywithyoneyendpoint,ythatycontinuesywithoutyendyinyoneydirection. AdjacentyAnglesy-y yyyyyyyyyyyy☑️ yyAnyyanglesythatyshareyaycommonysideyandyaycommonyvertex. RightyAngley-y yyyyyyyyyyyy☑️ yyAnyangleythatyhasyaymeasureyofy 90 ydegrees. AcuteyAngley-y yyyyyyyyyyyy☑️ yyAnyyangleywhoseymeasureyisylessythany 90 ydegree. ObtuseyAngley-y yyyyyyyyyyyy☑️ yyAnyyangleywhoseymeasureyisylargerythany 90 ydegreeybutysmallerythany 180 ydegree. StraightyAngley-y yyyyyyyyyyyy☑️ yyAnyangleythatyhasyaymeasureyofy 180 ydegrees. ComplementaryyAnglesy-y yyyyyyyyyyyy☑️ yyTwoyanglesywhoseysumyisy 90 ydegrees. SupplementaryyAnglesy-y yyyyyyyyyyyy☑️ yyTwoyanglesywhoseysumyisy 180 ydegrees AngleyBisectory-y