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CSET Multiple Subjects: Subtest 2 - Math
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5/6y=y-y yyyyyyyyyyyyyy☑️ yy.83y1/3y=y 83 y1/3% 1 y=y-y yyyyyyyyyyyyyy☑️ yy1.00y=y100% 2 y=y-y yyyyyyyyyyyyyy☑️ yy2.00y=y200% 3 y1/2y=y-y yyyyyyyyyyyyyy☑️ yy3.5y=y3.50y=y350% Naturalynumbersy-y yyyyyyyyyyyyyy☑️ yy1,y2,y3,y4,...ytheynumbersyyouywouldynaturallyycountyby 0 yisynotyaynaturalynumber. Wholeynumbersy-y yyyyyyyyyyyyyy☑️ yy0,y1,y2,y3,y4,...ytheynaturalynumbersytogetherywithy 0 Integersy-y yyyyyyyyyyyyyy☑️ yy...-3,y-2,y-1,y0,y1,y2,y3...yallytheywholeynumbersytogetherywithytheiryopposites Rationalynumbersy-y yyyyyyyyyyyyyy☑️ yy-Allyvaluesythatycanybeyexpressedyinytheyformya/b,ywhereyayandybyareyintegersyandyby≠y 0 -Or,ywhenyexpressedyinydecimalyform,ytheyexpressionyeitheryterminatesyoryhasyayrepeatingypattern Examples: 4 y1/2y=y9/2;ytherefore,y 4 y1/2yisyayrationalynumber 0.3yisyayterminatingydecimal;ytherefore,y0.3yisyayrationalynumber 0.134343434...yisyayrepeatingydecimal;ytherefore,y0.134343434yisyayrationalynumber Irrationalynumbersy-y yyyyyyyyyyyyyy☑️ yyAnyyvalueythatyexistsybutyisynotyrational Examples: π:yTheydecimalynameyforypiystartsyouty3.14159265...yTheydecimalynameyforypiydoesynotyterminateynory doesyityhaveyayrepeatingypattern √2:yTheydecimalynameyforytheysquareyrootyofy 2 ystartsyouty1.414...yTheydecimalynameyforytheysquareyro otyofy 2 ydoesynotyterminateynorydoesyityhaveyayrepeatingypattern Realynumbersy-y yyyyyyyyyyyyyy☑️ yyAllytheyrationalyandyirrationalynumbers Primeynumbery-y yyyyyyyyyyyyyy☑️ yyAynaturalynumberygreaterythany 1 ythatyonlyyhasy 1 yandyitselfyasydivisorsy(anyalternateydefini tionyisyaynaturalynumberythatyhasyexactlyytwoydifferentydivisors) Theyfirstysevenyprimeynumbersyarey2,y3,y5,y7,y11,y13,yandy 17 Compositeynumbery-y
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millimetery(mm)y=y0.001ymeter 1 ymetery(inyyards)y-y yyyyyyyyyyyyyy☑️ yy1.1yyards 1 ykilogramy(inypounds)y-y yyyyyyyyyyyyyy☑️ yyabouty2.2ypounds 1 ygramy(inyounces)y-y yyyyyyyyyyyyyy☑️ yy1/30younce 1 ymetricytony(inykilograms)y-y yyyyyyyyyyyyyy☑️ yy1,000ykilograms 1 ylitery(inyquarts)y-y yyyyyyyyyyyyyy☑️ yy1.1yquarts 1 ykilometery(inymiles)y-y yyyyyyyyyyyyyy☑️ yyabouty0.6ymile Wordsythatysignalyanyoperationy-y yyyyyyyyyyyyyy☑️ yyAddition:ysum,yplus,yisyincreasedyby,ymoreythany(example:y 3 ymoreythany 7 yisywhat?) Subtraction:ydifference,yminus,yisydecreasedyby,ylessythany(example:y 3 ylessythany 7 yisywhat?) Multiplication:yproduct,ytimes,yof,yaty(examples:y2/3yofy 5 yisywhat?y 3 yaty 5 ycentsycostyhowymuch?) Division:yquotient,yratio,yisyaypartyof,ygoesyintoy(examples:y 3 yisywhatypartyofy15? y 4 ygoesyintoy 28 yhowymanyytimes?) Someyproperties/axiomsyofyadditionyandymultiplicationy-y yyyyyyyyyyyyyy☑️ yy-Communicativeyproperty -Associativeyproperty -Distributiveyproperty Communicativeypropertyy-y yyyyyyyyyyyyyy☑️ yyTheyorderyinywhichyadditionyorymultiplicationyisydoneydoesynotyaffectytheyanswer Communicativeypropertyyforyadditiony-y yyyyyyyyyyyyyy☑️ yyay+yby=yby+ya Example: 2 y+y 3 y=y 3 y+y 2 5 y=y 5 Note:ySubtractionydoesynotyhaveytheycommunicativeyproperty. 3 y-y 2 y≠y 2 y-y 3 1 y≠y- Communicativeypropertyyforymultiplicationy-y yyyyyyyyyyyyyy☑️ yyaby=yba
Note:yYouycannotyuseytheydistributiveypropertyywithyonlyyoneyoperation. 3 y(4yxy5)y≠y3(4)yxy3(5) 3 y(20)y≠y 12 yxy 15 60 y≠y 180 Identityynumbery-y yyyyyyyyyyyyyy☑️ yyAyvalueythat,ywhenyaddedytoyanotherynumberyorymultipliedywithyanotherynumber,ydoesyno tychangeytheyvalueyofythatynumber Identityynumberyforyadditiony-y yyyyyyyyyyyyyy☑️ yy0.yAnyynumberyaddedytoy 0 ygivesythatynumber 0 y+yay=yay+y 0 y=ya Exampleyofyusingytheyadditiveyidentity: 0 y+y 3 y=y 3 y+y 0 y=y 3 0 y+y 3 y=y 3 Identityynumberyforymultiplicationy-y yyyyyyyyyyyyyy☑️ yy1.yAnyynumberymultipliedybyy 1 ygivesythatynumber. 1(a)y=ya(1)y=y 1 Exampleyofyusingytheymultiplicativeyidentity: 1(3)y=y3(1)y=y 3 1(3)y=y 3 Additiveyinversey-y yyyyyyyyyyyyyy☑️ yyTheyadditiveyinverseyofyaynumbery(alsoyknownyasytheyoppositeyofytheynumber)yisyayvaluey that,ywhenyaddedytoyanyynumber,yequalsy0.yAnyynumberyaddedytoyitsyadditiveyinverseyequalsy0. Theyadditiveyinverseyofyay=y-a Foryanyynumberya,yay+y(-a)y=y 0 Example:y 7 y+y(-7)y=y 0 Multiplicativeyinversey-y yyyyyyyyyyyyyy☑️ yyTheymultiplicativeyinverseyofyaynumbery(alsoyknownyasytheyreciprocalyofytheynumber)yisy ayvalueythat,ywhenymultipliedywithyanyynon-zeroynumber,yequalsy1.yAnyynon- zeroynumberymultipliedywithyitsymultiplicativeyinverseyequalsy1. Theymultiplicativeyinverseyofyay(ay≠y0)yisy1/a Foryanyynumberyay(ay≠y0),yayxy1/ay=y 1 Example:y4/5yxy5/4y=y 1 Fractionsy-y yyyyyyyyyyyyyy☑️ yyConsistyofytwoynumbersyseparatedybyyaybarywhichyindicatesydivision:ytheynumeratoryisyab oveytheybaryandytheydenominatoryisybelowytheybar. Denominator:yTellsyyouyintoyhowymanyyequalypartsysomethingyhasybeenydivided.
Numerator:yTellsyyouyhowymanyyofythoseypartsyareybeingyconsidered. Example:y3/5y(somethingyhasybeenydividedyintoy 5 yequalyparts,yandy 3 yofythoseypartsyareybeingyused) Commonyfractiony-y yyyyyyyyyyyyyy☑️ yyAyfractionywhoseynumeratoryisysmallerythanyitsydenominator;yhasyayvalueylessythany1. Example:y3/ Improperyfractiony-y yyyyyyyyyyyyyy☑️ yyAyfractionywhoseynumeratoryisytheysameyorymoreythanytheydenominator;yhasyayvalueyequa lytoy 1 yorymoreythany1. Examples:y6/6yandy5/ Mixedynumbery-y yyyyyyyyyyyyyy☑️ yyWhenyayvalueyisyexpressedyusingyaywholeynumberytogetherywithyaycommonyfraction Example:y 2 y3/ Changingyanyimproperyfractionytoyaywholeyorymixedynumbery-y yyyyyyyyyyyyyy☑️ yyDivideytheydenominatoryintoytheynumerator Examples: 24/3y-->y 24 y÷y 3 y=y 8 19/5y-->y 19 y÷y 5 y=y 3 y4/ Changingyaymixedynumberytoyanyimproperyfractiony-y yyyyyyyyyyyyyy☑️ yyMultiplyytheywholeynumberybyytheydenominator,yaddytheynumerator,yandythenyplaceythaty valueyoverytheydenominatory Example:y 6 y2/5y-->y(5yxy6)y+y 2 y=y 32 y-->y32/ Reducingyfractionsy-y yyyyyyyyyyyyyy☑️ yyFractionymustybeyreducedytoyitsylowestyterms.yThisyisydoneybyyfindingytheygreatestycomm onyfactory(GCF)yforybothytheynumeratoryandydenominatoryandythenydividingybothytheynumeratoryandy denominatorybyythatyvalue. Example:yReducey24/ Factorsyofy24:y1,y2,y3,y4,y6,y8,y12,y 24 Factorsyofy36:y1,y2,y3,y4,y6,y9,y12,y18,y 36 GCFy=y12;ydivideynumeratoryandydenominatorybyy 12 yandyyouygety2/ Addingyfractionsy-y yyyyyyyyyyyyyy☑️ yyFirstychangeyallytheydenominatorsytoytheiryleastycommonymultipley(LCM),ywhichyinyfracti onsyisyknownyasytheyleastycommonydenominatory(LCD).yThisyvalueyisytheyleastypositiveyvalueythatyally theydenominatorsywillydivideyintoywithoutyayremainder. Example:y5/24y+y7/36y=y? Multiplesyofy24:y24,y48,y72,y96,y120,y 144 Multiplesyofy36:y36,y72,y108,y144,y180,y 216
