大理州2024届高中毕业班第一次复习统一检测数学.考卷答案

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大理州2024届高中毕业班第一次复习统一检测数学.考卷答案试卷答案

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选项中有两项为多余六、语法填空(共10小题;每小题1分,满分10分)选项

阅读下面短文,在空白处填入1个适当的单词或括号内单词的正确形式

Certainly,therearemanynon-verbalcuesthathavecompletelydifferentmeaningsindifferentGulangyuIsland,offthecoastofXiamen,Fujian,waslistedasaworldheritagesite.EveryOcultures.Oneofthemostimportantmeansofnon-verbalcommunicationinanycultureiseyecontact.year,1(million)ofChinesepeoplevisittheisland2(enjoy)itsnaturaldelightsandtheEyeContactinWesternEurope3(combine)offoreignandChinesearchitecture.蝶Ontheonehand,theEuropeancustomsofeyecontact-especiallyinsuchcountriesasSpain,Therecognitionofthisbeautifuland4(cultural)remarkableislandis5honor.ButFranceandGermany-aresimilartothoseintheUnitedStates.Itisconsideredproperandpolitetothefactthatitisaheritagesitemeansmuchmorethanthat.Theword"heritage"referstothe6keepalmostcontinuouseyecontactwithanotherperson.1(value)thingsweinheritfromthepast.Andthereareover1,000worldheritagesites,7Ontheotherhand,Europeansoftenavoideyecontactincrowdedpublicsituations-suchas(make)arichtapestry(ofmemories,bothnaturalandman-made.Just8atimema-whilewalkingthroughabusydowntownorridingpublictransportation.2Thismayhappenwhenchine,theytakeusbacktoourancestorsandevenearlier,enablingustowanderatboththenaturalheisinterestedinthemandtriestoexpresshisinterestbymakingeyecontact.Therefore,itisimpor-worldandhumanhistory.tantforvisitorstounderstandthefullmeaningsofwhattheymaybesuggestingbyreturningtheeyeGulangyuIslandandeveryworldheritageitemareworthyofcareandprotection.Sincetheycontactgivenbysomeoneelse.cameintoexistence,they9(remind)usofourrichandvariousculturalsignificance,andthethingsthatmadeus10weare.扣英语(人教版)第3页(共4页)衡水金卷·先享题·高一同步周测卷八英语(人教版)第4页(共4页)新教材

分析(I)由已知可得$\overrightarrow{OC}$=(1+cosx,1+sinx),进而由f(x)=|$\overrightarrow{OC}$|2结合和差角公式,可将f(x)的解析式化为正弦型函数的形式,进而得到函数图象的对称中心及单调递减区间;
(Ⅱ)若f(x0)=3+$\sqrt{2}$,则sin(x0+$\frac{π}{4}$)=$\frac{1}{2}$,结合x0∈[$\frac{π}{2}$,$\frac{3π}{4}$],可得x0,进而得到答案.

解答解:∵A(cosx,sinx),B(1,1),$\overrightarrow{OA}$+$\overrightarrow{OB}$=$\overrightarrow{OC}$,
∴$\overrightarrow{OC}$=(1+cosx,1+sinx)-------2分
∴f(x)=|$\overrightarrow{OC}$|2=(1+cosx)2+(1+sinx)2=3+2(sinx+cosx)=3+2$\sqrt{2}$sin(x+$\frac{π}{4}$)…4分
(Ⅰ)由x+$\frac{π}{4}$=kπ,k∈Z得:x=kπ-$\frac{π}{4}$,k∈Z,
∴f(x)的对称中心是(kπ-$\frac{π}{4}$,3)k∈Z,…6分
由x+$\frac{π}{4}$∈[$\frac{π}{2}$+2kπ,$\frac{3π}{2}$+2kπ],k∈Z得:x∈[$\frac{π}{4}$+2kπ,$\frac{5π}{4}$+2kπ],k∈Z,
∴f(x)的单调递减是[$\frac{π}{4}$+2kπ,$\frac{5π}{4}$+2kπ],k∈Z…8分
(Ⅱ)∵f(x0)=3+2$\sqrt{2}$sin(x0+$\frac{π}{4}$)=3+$\sqrt{2}$,
∴sin(x0+$\frac{π}{4}$)=$\frac{1}{2}$,
∵x0∈[$\frac{π}{2}$,$\frac{3π}{4}$],即x0+$\frac{π}{4}$∈[$\frac{3π}{4}$,π],
∴x0+$\frac{π}{4}$=$\frac{5π}{6}$,
∴x0=$\frac{7π}{12}$.
∴tanx0=tan($\frac{π}{4}$+$\frac{π}{3}$)=$\frac{1+\sqrt{3}}{1-\sqrt{3}}$=-2-$\sqrt{3}$-----12分

点评本题考查的知识点是向量的模,正弦型函数的图象和性质,三角函数的求值,难度中档.