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Mathematics Quick Reference: Key Concepts and Formulas, Exams of Science education

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

A concise overview of fundamental mathematical concepts and formulas, including prime and composite numbers, decimal and fraction conversions, basic arithmetic operations, geometry, algebra, and statistics. It serves as a quick reference guide for students reviewing key topics in mathematics. A range of topics from number theory and basic arithmetic to geometry, algebra, and descriptive statistics, making it a useful tool for students needing a quick review of essential mathematical concepts. It includes definitions and formulas for various mathematical concepts, such as prime numbers, composite numbers, decimal and fraction conversions, polygons, triangles, quadratic equations, descriptive statistics, order of operations, probability, ratio, proportion, percent, inequality, equation, commutative property, associative property, distributive property, additive inverses, perimeter and area formulas, identity number, angles, pythagorean theorem.

Typology: Exams

2025/2026

Available from 10/25/2025

DrShirley
DrShirley 🇺🇸

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CSET Multiple Subject: Mathematics
PrimeiNumberi-i
iiiiiiiiiiii☑️iiAinaturalinumberigreaterithani1,iandithationlyihasi1iandiitselfiasidivisors.iIniotheriwords,iainatura
linumberithatihasiexactlyitwoidifferentidivisors.iTheifirstiseveniprimeiofithisikindiofinumbersiarei2,i3,i5,i
7,i11,i13,i17.
CompositeiNumberi-i
iiiiiiiiiiii☑️iiAinaturalinumberigreaterithani1ithatiisinotiaiprimeinumber.iIniotheriwords,iainaturalinumberithati
hasiatileastithreeidifferentidivisors.iTheifirstiseveninumbersiofithisikindipfinumbersiarei4,i6,i8,i9,i10,i12,i1
4.
Changingidecimalsitoipercentsi-i
iiiiiiiiiiii☑️ii1.iMoveitheidecimalipointitwoiplacesitoitheiright.
2.iInsertiaipercentisign.
Changingipercentsitoidecimalsi-i
iiiiiiiiiiii☑️ii1.iEliminateitheipercentisign.
2.iMoveitheidecimalipointitwoiplacesitoitheileft.i(Sometimesiaddingizerosiwillibeinecessary.)
Changingifractionsitoipercentsi-i
iiiiiiiiiiii☑️ii1.iMultiplyibyi100%.
Changingipercentsitoifractionsi-i
iiiiiiiiiiii☑️ii1.iDivideitheipercentibyi100.i
2.iEliminateitheipercentisign.i
3.iReduceiifinecessary.
Changingifractionsitoidecimalsi-i
iiiiiiiiiiii☑️iiSimplyidoiwhatitheioperationisays.iIniotheriwords,i13/20imeansi13idividedibyi20.
AddingiandiSubtractingiDecimalsi-i
iiiiiiiiiiii☑️iiLineiupitheidecimalipointsianditheniaddiorisubtractiinitheisameimanneriyouiwouldiaddiorisubtract
iregularinumbers.iAddingizerosicanimakeitheiproblemieasieritoiworkiwith.
MultiplyingiDecimalsi-i
iiiiiiiiiiii☑️iiJustimultiplyiasiusual.iThenicountitheitotalinumberiofidigitsiaboveitheilineiwhichiareitoitheirightio
fiallidecimalipoints.iPlaceiyouridecimalipointiiniyourianswerisoithereiisitheisameinumberiofidigitsitoitheir
ightiofiitiasithereiwasiaboveitheiline.
DividingiDecimalsi-i
iiiiiiiiiiii☑️iiTheisameiasidividingiotherinumbers,iexceptithatiifitheidivisori(theinumberiyou'reidividingiby)iha
siaidecimal,imoveiititoitheirightiasimanyiplacesiasinecessaryiuntiliitiisiaiwholeinumber.iThenimoveitheide
cimalipointiinitheidividendi(theinumberibeingidividediinto)itheisameinumberiofiplaces.iSometimesiyoui
mayihaveitoiaddizerositoitheidividend.
Dividendi-i
iiiiiiiiiiii☑️iiTheinumberibeingidividediinto.iOritheinumberiinsideitheidivisionisign.
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CSET Multiple Subject: Mathematics

PrimeiNumberi-i iiiiiiiiiiii☑️  iiAinaturalinumberigreaterithani1,iandithationlyihasi 1 iandiitselfiasidivisors.iIniotheriwords,iainatura linumberithatihasiexactlyitwoidifferentidivisors.iTheifirstiseveniprimeiofithisikindiofinumbersiarei2,i3,i5,i 7,i11,i13,i17. CompositeiNumberi-i iiiiiiiiiiii☑️  iiAinaturalinumberigreaterithani 1 ithatiisinotiaiprimeinumber.iIniotheriwords,iainaturalinumberithati hasiatileastithreeidifferentidivisors.iTheifirstiseveninumbersiofithisikindipfinumbersiarei4,i6,i8,i9,i10,i12,i 1

Changingidecimalsitoipercentsi-i iiiiiiiiiiii☑️  ii1.iMoveitheidecimalipointitwoiplacesitoitheiright. 2.iInsertiaipercentisign. Changingipercentsitoidecimalsi-i iiiiiiiiiiii☑️  ii1.iEliminateitheipercentisign. 2.iMoveitheidecimalipointitwoiplacesitoitheileft.i(Sometimesiaddingizerosiwillibeinecessary.) Changingifractionsitoipercentsi-i iiiiiiiiiiii☑️  ii1.iMultiplyibyi100%. Changingipercentsitoifractionsi-i iiiiiiiiiiii☑️  ii1.iDivideitheipercentibyi100.i 2.iEliminateitheipercentisign.i 3.iReduceiifinecessary. Changingifractionsitoidecimalsi-i iiiiiiiiiiii☑️  iiSimplyidoiwhatitheioperationisays.iIniotheriwords,i13/20imeansi 13 idividedibyi20. AddingiandiSubtractingiDecimalsi-i iiiiiiiiiiii☑️  iiLineiupitheidecimalipointsianditheniaddiorisubtractiinitheisameimanneriyouiwouldiaddiorisubtract iregularinumbers.iAddingizerosicanimakeitheiproblemieasieritoiworkiwith. MultiplyingiDecimalsi-i iiiiiiiiiiii☑️  iiJustimultiplyiasiusual.iThenicountitheitotalinumberiofidigitsiaboveitheilineiwhichiareitoitheirightio fiallidecimalipoints.iPlaceiyouridecimalipointiiniyourianswerisoithereiisitheisameinumberiofidigitsitoitheir ightiofiitiasithereiwasiaboveitheiline. DividingiDecimalsi-i iiiiiiiiiiii☑️  iiTheisameiasidividingiotherinumbers,iexceptithatiifitheidivisori(theinumberiyou'reidividingiby)iha siaidecimal,imoveiititoitheirightiasimanyiplacesiasinecessaryiuntiliitiisiaiwholeinumber.iThenimoveitheide cimalipointiinitheidividendi(theinumberibeingidividediinto)itheisameinumberiofiplaces.iSometimesiyoui mayihaveitoiaddizerositoitheidividend. Dividendi-i iiiiiiiiiiii☑️  iiTheinumberibeingidividediinto.iOritheinumberiinsideitheidivisionisign.

Divisori-i iiiiiiiiiiii☑️  iiTheinumberiyou'reidividingiby. Polygonsi-i iiiiiiiiiiii☑️  iiAiclosedifigureiformediwithilineisegments,iwhichiareicalledisides.iAlsoimeansi"aimany- sidedifigure." Trianglei-i iiiiiiiiiiii☑️  iiAithree- sidedipolygon.iItihasithreeianglesiiniitsiinterior.iTheisumiofitheianglesiisialwaysi 180 idegrees.iItiisinamedi byinamingiitsiverticesioricorners,ianditheyiareiclassifiedibyieitheritheirisideioritheiriangles. EquilateraliTrianglei-i iiiiiiiiiiii☑️  iiHasiallithreeiofiitsisidesiofiequalilength,iwhichiiniturnimakesieachiofitheithreeianglesiequaliinimea sure.iTherefore,ieachiangleiinianiequilateralitriangleihasiaimeasureiofi 60 idegreeisinceitheisumiofitheiangl esiinianyitriangleiisi 180 idegree. IsoscelesiTrianglei-i iiiiiiiiiiii☑️  iiAitriangleiwithitwoicongruent,ioriequal,ianditheianglesioppositeithoseisidesihaveiequalimeasure. ScaleneiTrianglei-i iiiiiiiiiiii☑️  iiAitriangleiwithinoicongruent,ioriequal,isides.iAllithreeiofiitsisidesiareidifferentilengths.iTheiangle siinithisitriangleiwilliallihaveidifferentimeasures,itheilargestiangleiwillibeioppositeitheilongestiside,iandit heismallestiangleiwithibeioppositeitheishortestiside. IncompleteiQuadratici-i iiiiiiiiiiii☑️  iiAiquadraticiwithiaitermimissing. Example:i Solveiforix.ix²i-i 16 i=i 0 Factoring,i(xi+i4)(xi-i4)i=i 0 xi+i 4 i=i 0 i-->ixi=i- orixi-i 4 i=i 0 i-->ixi=i 4 QuadraticiEquationi-i iiiiiiiiiiii☑️  iiAniequationithaticouldibeiwritteniasiAx²i+iBxi+iCi=i0.iToisolveithisiequation: 1.iPutiallitermsionioneisideiofitheiequalisign,ileavingizeroionitheiotheriside.i 2.iFactor. 3.iSetieachifactoriequalitoizero. 4.iSolveieachiofitheseiequation.i 5.iCheckibyiinsertingiyouriansweriinitheioriginaliequation.term- DescriptiveiStatisticsi-i iiiiiiiiiiii☑️  iiUseditoiexplainioridescribeiaisetiofinumbers.iMostiofteniweiuseitheimean,imedian,iorimodeitoides cribeitheseinumbers. Meani-i iiiiiiiiiiii☑️  iiAlsoiknowniasitheiarithmeticiaverage.iOfiaisetiofidata,itheisumiofitheidataivaluesidividedibyithein umberiofidataivalues.

Wheniworkingiwithithese,itreatithemiexactlyilikeiequations,iEXCEPT:iIfiyouimultiplyioridivideibothisid esibyiainegativeinumber,iyouimustireverseitheidirectioniofitheiinequalityisymbol. Equationi-i iiiiiiiiiiii☑️  iiAirelationshipibetweeninumbersiand/orisymbolsithatisaysitwoiexpressionsihaveitheisameivalue. CommutativeiPropertyi-i iiiiiiiiiiii☑️  iiTheiorderiiniwhichiadditioniorimultiplicationiisidoneidoesinotiaffectitheianswer.iNote:iSubtractio niandidivisionidoesinotihaveithisiproperty. CommutativeiPropertyi-i iiiiiiiiiiii☑️  iia+bi=ib+a abi=iba AssociateiPropertyi-i iiiiiiiiiiii☑️  iiTheigrouping,iwithoutichangingitheiorder,idoesinotiaffectitheianswer.iNote:iSubtractioniandidivi sionidoesinotihaveithisiproperty. AssociateiPropertyi-i iiiiiiiiiiii☑️  iiAddition:ia+(b+c)i=i(a+b)+c Multiplication:iax(bxc)i=i(axb)xc DistributiveiPropertyi-i iiiiiiiiiiii☑️  iiMultiplicationioutsideiparenthesesidistributingioveriadditioniorisubtractioniinsideiparenthesesid oesinotiaffectitheianswer.iNote:iYouicannotiuseithisipropertyiwithionlyioneioperation. DistributiveiPropertyi-i iiiiiiiiiiii☑️  iia(bi+ic)i=iabi+iac AdditiveiInversesi-i iiiiiiiiiiii☑️  iiAlsoiknowniasitheioppositeiofitheinumber.iThisiisiaivalueithat,iwheniaddeditoianyinumber,iequals i0. Perimeteriofiaisquarei-i iiiiiiiiiiii☑️  iiPi=i4a Areaiofiaisquarei-i iiiiiiiiiiii☑️  iiAi=iS² Perimeteriofiairectanglei-i iiiiiiiiiiii☑️  iiPi=i2bi+i2h Areaiofiairectanglei-i iiiiiiiiiiii☑️  iiAi=ibh Perimeteriofiaitrianglei-i iiiiiiiiiiii☑️  iiPi=ia+b+c Areaiofiaitrianglei-i iiiiiiiiiiii☑️  iiAi=i1/2ibh

Circumferenceiofiaicirclei-i iiiiiiiiiiii☑️  iiCi=iπdi or iCi=i2πr Areaiofiaicirclei-i iiiiiiiiiiii☑️  iiAi=iπr² IdentityiNumberi-i iiiiiiiiiiii☑️  iiAivalueithat,iwheniaddeditoianotherinumberiorimultipliediwithianotherinumber,idoesinotichangei theivalueiofithatinumber.i 1.iForiadditioniisi0.iAnyinumberiaddeditoi 0 igivesithatinumber.i 2.iForimultiplicationiisi1.iAnyinumberimultipliedibyi 1 igivesithatinumber. Anglei-i iiiiiiiiiiii☑️  iiFormedibyitwoiraysithatistartifromitheisameipointioricommoniendpoint,iwhichiisicalleditheiverte x.iThisiisimeasurediinidegrees. Vertexi-i iiiiiiiiiiii☑️  iiTheicommoniendpointiofianiangle. Rayi-i iiiiiiiiiiii☑️  iiAipartiofiailine,iwithioneiendpoint,ithaticontinuesiwithoutiendiinioneidirection. AdjacentiAnglesi-i iiiiiiiiiiii☑️  iiAnyianglesithatishareiaicommonisideiandiaicommonivertex. RightiAnglei-i iiiiiiiiiiii☑️  iiAniangleithatihasiaimeasureiofi 90 idegrees. AcuteiAnglei-i iiiiiiiiiiii☑️  iiAnyiangleiwhoseimeasureiisilessithani 90 idegree. ObtuseiAnglei-i iiiiiiiiiiii☑️  iiAnyiangleiwhoseimeasureiisilargerithani 90 idegreeibutismallerithani 180 idegree. StraightiAnglei-i iiiiiiiiiiii☑️  iiAniangleithatihasiaimeasureiofi 180 idegrees. ComplementaryiAnglesi-i iiiiiiiiiiii☑️  iiTwoianglesiwhoseisumiisi 90 idegrees. SupplementaryiAnglesi-i iiiiiiiiiiii☑️  iiTwoianglesiwhoseisumiisi 180 idegrees AngleiBisectori-i iiiiiiiiiiii☑️  iiAirayifromitheivertexiofianiangleithatidividesitheiangleiintoitwoicongruent,ioriequal,ipieces. VerticaliAnglesi-i iiiiiiiiiiii☑️  iiIfitwoistraightilinesiintersect,itheyidoisoiatiaipoint.iFourianglesiareiformed.iThoseianglesiareioppo siteieachiother.