ろ′1 □whiehorthe恥oTYhgbestdescribesdedueti、,e reasoning? 田 theargumentsbelov上 監禁善書 誓書嵩嵩謀 議謹書晋n A uslngloglCtOdraW′COnCiusionsbasedon acceptedstatements B acceptlngthemeanlngOfatem1両thout de魚nition I C de師ngmathematicaltemstocorTeSPOnd Withphysicalo申ects CllOne(S),ifan〕′,uSe。eductivereasoning? DinferTingageneraltnlthbyexamiTmga Ionly numbeI’Ofspecificexamples Honl)′ lSClの)跡 bothIandIJ neitherInorlI 田Inthediagrambe・ow,,∠1≡∠4. C湘j父 田 土。「。m:Atriangl。hasatm。= anh E。」。。isp.。mgtheth。。remab。V。。, co五adiction.Hebeganbyassumingthatin △Abc,∠Aand∠Bareb。th。btuse∴Whi。h theoremlViIIEduardousctoreacha i 。。五adi。ti。,1? A IfLWOanglesofatriangleareequal,thesides OPPOSitetheanglesareequal B r IftwosupplementaIyanglesareequal,the angleseachmeasure900. C lVhichofthefbllo、VlngCOnCIusionsdoesnot Thelargestangleinatriangleisoppositeme Jongestside. havetobetrue? D A ∠3and∠4aTeSupPlemenar)angles. Thesumofthemeasuresofdleanglesofa 高angleis1800. B LineTisparalleltolineI71. (Sl基調)i! C ∠1≡∠3 D‘∠2≡∠3 CSGi働 ー 6 − CALIFORNIA STANDARDSTBST 田UsethepI・00ftoansiYerthequestionbeloW,・ 窪 Prol,e:△ABD≡△CBD Statement l ︵∠ tJ 4 l. AB≡BC;DisthemidpointofAC 2. AD三三CD 3. BD三三BD 4. △ABD…≡△CBD 。土連理旦 DeJ融。。。fh.Ii。p。int ReHexil,e Propcrty WThatreasor,LCanbeusedtoprovethattlletrianglesare B C D AAS ASA SAS SSS A ー 7 − misisasampleofCaJifomiaStandardsTbstqucsLionsThisisNOTail 時StbrmTcsはCOrCSCa…0Lbep珂e億ed basedonpeTlbmanceonreIeaset圧est【iueStiomcopyngh一@20090alit仰iaDepartmentorEducatioil. Cl\LlFORNIlt STANDIRDSTdsT 擦誓−うー人毛ゝ臨 認諾露頭題詞圃題穎園 田Inthe恥I・el,。1。、恒B>BC A Ifweassumethatm∠4・=m∠C,itfollovt・stllat AB=BC・ThiscontradictstlleglVenStatement thatAB>BC.WhatconclusioneanbedraWn fromthiseontradiction? A m∠A二m∠B B∴∴m∠4≠m∠B C m∠A二m∠C D m∠A≠m∠c c5くす〇万24 Tii誌asam函orCallfomねS一狐dards′圏qucs(rons.ThisisN ba駁1°噂巾manceonrc嵐edtc叫uc洲)噂.Copy 1心i新調・塙はC。rCSCa…0Lbcprかcled i’読Dcpa”’mcntOr−Ed面 CALIFORNIASTANDARDSTIST 田町setheprooftoanswerthequestionbeloW′・ Gil′en:∠2≡∠3 Prove:∠1≡∠4 t Statement l. ∠2≡∠3 2. ∠1≡∠2;∠3竺∠4 3. ∠1≡∠4 Whatreasoncanbeusedtojus憤fystatement2? A Complementsofcongruentanglesarecongruent. B、VerticaIanglesarecongmenL C SupplementsofcongruentanglesareCOngment. D Correspondinganglesarecongruent. ba鍵donpc命manceonre庖ゞ鎚le点q嶋高く,時.Copy厘hl④2009C小暗−rnねDcparmenl0「助uc涌on. C′ヽLrFORトはltSTANDARDSTEST 田‘荊oll71eSinapla,7e。l岬i,,t。樹tl,Z。X。。砂 OnepOl証’’ WllichofthefoIIoWlngbestdescribesa ifaquadrikiteraihasperpendicuIar COuTZte7”e:rampletotheassertionabove? diagonais,thenitisarhombus. A coplanarlines B parallellines WI tllfi 土。血。ftll。踊ngisa。。unt。脚。!。t。 istatenlental〕0ヽre? C perpendicu】arlines Dintersectlnglines (=Stmlm 田、唖h聖recanseⅣeaSaCOunterexanlpl。t。 theconJeCturebeloW? ifonepairofoppositesidesofa quadriiateralisparal胤,thenthe quadrilateraIisapara旧ogram. A rectangle B rhombus C square D 仕apezoid 回 Given:TRAPisanisoscelestrapezoidwith diagonaIsRPandTA・Wmichofthefbllowfmg mI∬tbetrue? A RP⊥コA B RPliTA C T D 、 ヽ , RP三TA RPbisectsTA O Jゴ六 ー10 − T博isasampIeofCallfomaS−andardsns団UCSしion ThisisNOTail 風向m・罵SISCOrCSCa…Oibcprqec−cd b枇donp諭m州CConreieがC壷申し一面0時C。Py垂h∼@2009C用心maDc函mentor削りぐ証0∩. 回studentsinaeIassre、YrOtetIleOremSint早 0WTllVOrds.OnestudentWrOtethefbl10Wlng 回 triangJesmustbesimilar? 小′00btusetriandes Statement. 時′oscalenetriangles、涌hcongruentbases TheareaofaparaILeiogramisthe t、、′Orighttriangles PrOductofanybase(b)andanyheight(h). tW′OisoscelestdanglesWithcongmenL VeneXangles 叢亜董園田 C E A CEandBEarecongruent. B ∠ACEisahghtangle. C ACandDEareparallel. D ∠Aand∠Bareeongnent. baぶed()nPerfommCeOnTelease近喧しque諒ons Copyr−gh!㊧2009 ai組)rnaDep独tmcn(0rEdueaIioil. lralIe10gramFGHI)diagonaIsIGandFH 回para・・elogramABCDissho、Tnb.I。W. LraWnandintersectatpointM・Whiehof OIJoIYlngStatementslnlLSEbetrue? A AFGImstbeanobtuse血ngle. △HIGmlStbeanacutetriangle・ △相4cmuStbecongmentto△HMG. △GMIImustbecollglmenttO△初F. 03 恥te 回 WhichpairoftriangLescanbeestablishedto Ofthefollo高ngbeStdescribesthe ;SShollmbelolV? I〕eCOngmenttOpI’0Vethat∠DAB≡/BCD? A AADCand△BCD B △AED and△BEC C △DABand△BCD D ADECand△BEA CSG川ilb 回 If△ABCand△XYZaretwotriangIessuch thatE=若W,hichorthefbuowhgwould besu餓cienttoprovethetriangIesaresimilar? A ∠A=∠X A LOthsimilarandcongrluent B ∠B≡∠Y Biimila.。u。n。,。。ngm。nt C ∠C≡∠Z c Lngm。n。butn。.Sim血 D ∠X≡∠Y ithersimilarnorcongruent CSCi能)も basedonpedbmanceonre血潮teslq嶋高0踏・Copynghl@料09⊂高車miaDeparim如。「註壷。n. 回whichofth諭lo、Yingstatementsmustbetme ifAGHII〉△JKL? 回 i)eloW,AC≡DFand∠A≡∠D. G△:<L A ThetWOthnglesmustbescalene. additionalinformationwouIdbeenough B ThetwotriangiesmusthaveexactlyOneaCute tobrOVethat△ABC≡△DEF? angle・ C AtleastolleOfthesidesofthetwotriangles A AB≡DE B AB=BC C BC≡EF D BC≡DE mustbeparallel. D ThecoITeSPOndingsidesofthetwotIiangles mustbeproponionaL CSC;頭rIJ 回ⅥichmethodIistedbelo、VCOuldI20tbeusedto provethattTYOtrianglesaI’eCOngruent? A Proveallthreesetsofcorrespondingsides COngment. B Proveallthreesetsofcorrespondingangles COngru nn・ C Provedla白WOSidesandanincludedangleof Onetrianglearecongruenttotwosidesandan includedangleoftheohertriangle. D Provemattwoanglesandanincludedsideof OnetIianglearecongmenttOtWOanglesand anincludedsideoftheothertriangle. CSCIOiji basedonpe五m肌CeOnrele地溝dt的岬C諒。恥・Copyngh{@2009〇品かmiaD型丁血n国手軸ue壷on. 回 A B C D basedonpe爪}rmanCeOnでeIe谷eJ誌lqlしe高踏・C・,Pynghi@2009C痛心r胴Dep孤menIor蘭uc証(川. 回、Vhichofthe制owingsetsofnumberscou・d representthelengthsofthesidesofatriangIe? 回 A 2,2,5 ノ く J 5 n も 1 1 D ︵′⊃ 4. 5 C 3 4 5 B 国禁祭器慧諾parallellinesl Whichstatementaboutanglesland2mI‘St betrue? A ∠1三∠2. B ∠listhecomplementof∠2. 回。lriIa.。ralA。。。isapa.。1°。gram.m a飾acentanglesarecongruent∵Whichstatement C ∠listhesupplementof∠2. mhstbetrue? D ∠land∠2areIightangles. A QuadrilateralABCDisasquare B QuadIilateralABCDisarl10mbus. C QuadrilateralABCDisarectangle. D QuadrilateralABCDisanisosceles (:S6−1ぼか trapezoid. basedonpc重〕manCC(mrCbがed記SLqLIeStions.Copynghl@2009C証romiaDepartmen10rEdue証on. CALIFORトロ人STANDARDS 日詰豊㌢ateralshoWTnl)el0両atis ediameter Ofacircleis12meters,If po車pisinthesameplaneasth。。i.。。, andis6metersfl・Omthecenteroftheeire⊥C, C i Whieh bestdescribestheloeationofpoiIltP? A PointPlllu買beonthecircle. B Po証PilluStbeinsidethecircle. C PointPmaybeeitherou扇(尭thecircleor Onthecircle. A D PointPmavbeeimerinsidethecircleor On thecircle. A 53。 (雷のil! B 1370 C 1800 回 D 233o 回IfABCDisaparalIel。g.am,Whatisth。!.ngth OfsegmentBD? A校7C WhかisIn∠2? B C B ll D 15。相好 105 A A 10 C 12 D 14 CSc‥mim ー16 − 叩icofC描0品aS舶用d油snS叫的ions・Thi諒NOTanopc蘭Cr basedonpe両町聞CeOnrCi孤Cdie31畔Sli‘撮Copy函i@2009Ca 諭「高Depar面釧Ior助ue油0∩ CllLIFORMA STAND,lRDSTEkT 回ArightcircuIar.。n。llaS.adius5in。h.san。 heightSinehes. WhatisthelateraIareaofthecone?(Latcrai areaofeone二でrl,Whereにslantheight) W′hLtisthea.。a。哩唖r。 l A 40汀Sqin・ B 445打Sqin. C 5汀、厨sq証 D S升、暦sqin. CSGl筋} “yllndricalbarrelmeasures22inchesin eterlhowmanyincheswillitrollin OlutionsaIongasmoothsurface? 121升ln. 1687rin. 1767rin. ー17 − mpIeofCalifomiaSIandardSTcstques高ons・ThisisNOTanopcraiion baSedon時論ma博cOnreI眺ed似que諦0博.Copy函1③2009C。l br…DcpaT山肌0rEdu幽ion. 回 回AsewlngClubismakingaquiItconsisdng Of25squareswiでheachsideofthesquare Ofthisfigure、、rillbefbldedup me謎,uring30ccntimeters・Ifthequnthas fiveroWSandfivecolumns,iihatisthe 」 5ccntimeters一一一十 perimeteroftllequilt? A 150cm B 300cm C 600clm D 900clll CSG〕用ii 回Theminutehandof・aclockis5in.hcsl。ng. Whatistheareaofthecircle)insquareinches, i CreatedasthehandsWeePSanhouI・? ∴∴∴ lVh atwT i A lO汀 D 狐‰10肪 C llbetheと91聖堂.)rthebo 18 − ・? CALIFORNIA STANDARDS TEST i rectaTlgIeshownbelowhaslength 回Ac・assroomglobehasadiameteroflSinches・ leterSandwidthlOmeters, 4m lz_ 4m I l乙 IflbuI’trianglesareremoITedfromthe ngleassho、Vn,Whatwillbetheareaofthe Whichofthefbllovnngistheapproximate Lining庫gure? Surfaeearea,lnSquZげeinches,Oftheglobe? A 136mコ B 144m: A 113.O C 168m2 B 226.l D 184mつ (SurfaeeArea=祐r2) C 254.3 C細i; D lO17.4 GcごくC的 回 IfRSTlVisarhombus,Whatistheareaof Al XT? 回豊慧諾詩話善書霊警h radiusof24inches・Sinceroughly75%of Earth,ssurfaceiscoveredbyW,ateI−hewanted topaint75%ofhismodelbluetoillustrate thisfact.ApproximateIyhowmanysquare inchesonhismodelWillbepaintedblue? (SumceArea=4詰) C D 54 72 鈍 57 B 26 33.40 87 A A 18誘 B 36、万 C 36 D 48 b妹edonper短m肌Ce。nre厄にed隊団しぼ痛心博ClIPyr回し④2009C同部日日aD叩anm3両()「Edu的くね∩. 回 A 37.5 8 42.5 C 50 D 100 田中atistheam,ins。。ar。in。h。S(in.),。fthe 回航恥r。b。1。、高as。uar。W,ithmr COngmentparaIlelogramsinside. C O O D 冶∴∴誘 5 C J B 2 2 5 .⊃ A Vhatisthearea,mSquareunits,Oftheshaded portion? A 60 B∴84 C l14 D I29 CScこ映ニ†  ̄  ̄r ̄− ̄−”)‥ ̄”一、一、i、ノ▲ii↓・⊥し○○aLU(CSじail0°l Dc b融on函manCeOnr比粗目eStqt面0耶・Copy重点㊧2009C品miaDe叫m帥(Ur軸油川. CALIFORi LASTANDAJtDST 回whatisthearca,insquar。.entimeters, OfrhombusRSTVifRT=16cmand 回madet、YOCandlesintheshapeofrigllt angularprisms・The丘rstcandleisI5cm Sl′=12cm? l)8cmIong,andScmlVide.Thesecond dleis5cmhigherbuthastlleSamelength Width・HoWimuchadditionaIlVaXWaS ne ユedtomakethetailercandle? A 320cm〕 B 640cJlll C 960cm1 D 1280cm〕 R rSc!Oiie 回申ang}。S。fatria元。ha、,。m。aS。r。S。r55。 A 40 OfthefblloWmgcouldI70tbe B 48 extehorangleofthetriangIe? B 0 0 0 0 −ヽJ O −ヽ. 〇 ・−・i 2 2 つ﹂ A C 96 D 192 C D 回Theperimete.S。ftwr。S。uareSa.。inm。ti。。f 4to9・WmatistheratiobetlVeentheareasof thetW0Squares? 回 A 2to3 置禁謙語謹書蕊詰 1 B 4to9 Ofpolygonisit? C I6to27 D 16し08l CSq:脚il A quadri撮eral B hexagon C L)etagOn D deeagon ー 21− mpleofC細bmiaSiand祉d了rtstqucslions・ThisisNOTanopcration basedonpe同町聞CeO旧C厄融tcslquc諦onsCopy直(@2000C【ti 短miaDC型ttment0IEdumtion. CJILIFORNI^STANDARDST 回、耽tis′n∠ェ? ABiiの. D 何十40)○∴∴∴Z(ズー40)o 八・一 C A∴3 0 B 60o O C O D O .4 5 00 0ノ B D 950 ハ U A C 85o 回Ifthcmeasureofan。Xteri。rangl。。fm。guIa. polygonis1200,hoil7manysidesdoesthe polygonhave? A 3 B 4 回 lhemeasuresoftheinteriorangLesofa 摺諾恕藍嵩宝器h。 i D 5 /O C A B 努tangle?lシ∴∴ j砂∴∴8 28 _四一も㊨TTも新砂 クの,一定0ニケ10 C 十ZO 十Zu D 一三竺__i吏__ L・O L(シ メータZriCl的 b独融onpe諭rmancmnreleZLm=estqt・e高踏・Copy垂直④2009C聞miaD申しmenIorEdu諦0∩. 回 団Aregularpolygonha叩S鵬・Whafisthe measureofeachextenorangle? B C D 15 30 45 00 A 回、耽tk,n∠1? A B C D A 340 B 56o 回wLatisth。meaSur。。fa。鴎.hra。gl。。ra regularhexagon? C 64o B C D 30 00 12 的 A D 920 ー 23 − かmpIcofCalifomiaStandmdsT錐[qucStions.miSisNOTanopcra b的9donpc五manceonreie独鵜d略しqucsLionゞCopy垂hi@2009 Cai高誼aDeparmnnn orEduc諦on C′ゝLIFORNIA STANDARDSTEsT 回Adiagra平OmaprOOfofthe担gorean triangle’S巾′potenusehasIengm5.If theoremlSPicturedbelo、V. On早eghasJength2,W′hatisthelengthofthe 醇 回A止血Iineisbeingcon里edtore−rOute i畠iIHo、冊。undthe。Xt。..。r。famti。nal W品Iifeprescr、,e・Theplansho涌gtheold i andtheneWrouteisshoWnbeloW. WhichstatementWOuldnotbellSedintheproof OfthePythagoreantheorem? A TheZueaOfathangleequals÷ab・ B Thefourrighttrimglesarecongruent・ C TheareaoftheinnersquarelSequal【oh描of theaI・eaOfthelargeI・Square・ D Theareaofthelargersquareisequa圧Otlle SumOftheareasofthesmallersquareandthe 氏urcongmentl証ngles・ CSc川iり= newrouteisestablished? A 24 B 68 C 92 D 160 ー 24 − 1mPieofCali如ninS伽dardsTb5時C涌onsm諒NOT細Opera血 based伽P諭manceonreie独融te諏qし雌高ons・Copynghl⑫2000& 荊miaDcpar回られtorEduc油Cn. 団 i 1・Putmeipof庇caSOnpitA・ 2・Openthecompasssothatthepencj川p Iisonp0両 3.DraW′inarCaboveAB 4・WIithoutchanglngtheopenlng,putthe metaltiponpointBanddl・aWallarC intersectlngtheかstarcatpointC.i 5.DraW′ACandBC. I C b謎Cdonp約m細CeOnreiea頃日自 quu点onゞ・Copyn如⑫2000C山肌miaDcpartmc。〔。rEd言霊三 〇,l CALIFORNIA STANDARDSTEST i 回紫紫嵩COnStruC血ssho、、’ninthe 回 A ananglebisector B alineparalleltoagl、,enline C ananglecon rmenttOaglVenangle D aperpendicularbisectorofasegment  ̄27 ̄I mis短snmpIeofCal加midS(mdard沌5時e諒DnS・ThisisNOTan°pC甲OnalIeStfom・鴫stSCOrCSCannOLbcprかC融 basedon草証)manCeOnrelcasc両esLqL−eSlionS・Copy垂hi@2m C描面Ⅷ証De匹直menlorEducL高0∩. C.lLIFORNIAST.lND,、IDSTEさ;T 回 回FigureABCOisaparallelogram. LttyPeOftriangJeisfomedbythepoints ,2),B(6,−1),andC(−1,3)? y hght equilateral isosceles SCalene CSC川115 回 polnt(−3,2)liesonacirelewhose tionis五十3)2+(y+l)ユニγ2言Irhi。h。f Ol10Wmgmustbetheradiusofthecircle? B C D 3 而 9 m A ー 28 − mpiCOfCa璃bmiaS一抑d油ns叫∞五〇nS・Th証sNOTampcraiion bascdonpc血mance。nrel眺ed鵬−qL−e諒,眠・C。Pynghl㊨2009C.i) 請T…De酋tmem0「Educ諒oil. CALlPORト:IA STANDARDSTEST i 回、馳istheⅧue串ininches? 回申ecircIebel0、、,,示andあarecho.ds intersectingatE. A 7、万 B 14 C14J言 B D 0 つ﹂ C 回Asquareiscircum・・ibedaboutacircle・What istheratiooftheareaofthecircletothearea 7 ハブ 1 1− A D Zl Ofthesquare? C 1 一 4 1 一 2 2 一 打 A ∴ ∴ ∴ ∴ B ー 35 − Thssss sampicofCallfomiaStanねrdSmStqUCStionsm演sNOTanopera basedonpem〕rm抑Ceonre庖sed鳳qLiC高ons C時yrighl@2009 tcs(form.¶ぉtSCOrCSCamOibeprqectcd )T高aDe匹mentorEduc痛0∩ b綬don申ねmanceonr捉胱d胤qucsll眺・Copynght@200C聞け開高D℃p加n帥0「Edこ高n.
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