湖南省長(zhǎng)沙市xx中學(xué)2022-2023學(xué)年高一上學(xué)期期末模擬數(shù)學(xué)試題（原卷版）

高一上學(xué)期期末數(shù)學(xué)試題一?單選題(共40分)1.命題“SKIPIF1<0”的否定是()A.SKIPIF1<0 B.SKIPIF1<0CSKIPIF1<0 D.SKIPIF1<02.已知集合SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.下列說法正確是()A.若SKIPIF1<0，則SKIPIF1<0 B.若SKIPIF1<0則SKIPIF1<0C若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0 D.若SKIPIF1<0，則SKIPIF1<04.已知角SKIPIF1<0終邊上一點(diǎn)SKIPIF1<0，則SKIPIF1<0()A2 B.-2 C.0 D.SKIPIF1<05.函數(shù)SKIPIF1<0的圖象大致形狀是()A. B.C. D.6.若正數(shù)SKIPIF1<0、SKIPIF1<0滿足SKIPIF1<0，若不等式SKIPIF1<0的恒成立，則SKIPIF1<0的最大值等于()A.4 B.SKIPIF1<0 C.SKIPIF1<0 D.87.已知函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)恰有3個(gè)最值點(diǎn)和4個(gè)零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.已知定義在R上的函數(shù)SKIPIF1<0對(duì)于任意的x都滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若函數(shù)SKIPIF1<0至少有6個(gè)零點(diǎn)，則a的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0二?多選題(共20分)9.下列說法中，正確的是()A.集合SKIPIF1<0和SKIPIF1<0表示同一個(gè)集合B.函數(shù)SKIPIF1<0的單調(diào)增區(qū)間為SKIPIF1<0C.若SKIPIF1<0，SKIPIF1<0，則用SKIPIF1<0，SKIPIF1<0表示SKIPIF1<0D.已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則當(dāng)SKIPIF1<0時(shí)，SKIPIF1<010.下列說法不正確的是()A.函數(shù)SKIPIF1<0零點(diǎn)是SKIPIF1<0和SKIPIF1<0B.正實(shí)數(shù)a，b滿足SKIPIF1<0，則不等式SKIPIF1<0的最小值為SKIPIF1<0C.函數(shù)SKIPIF1<0的最小值為2D.SKIPIF1<0的一個(gè)必要不充分條件是SKIPIF1<011.已知函數(shù)SKIPIF1<0(其中SKIPIF1<0)的部分圖象如圖所示，則下列結(jié)論正確的是()A.SKIPIF1<0B.要想得到SKIPIF1<0的圖象，只需將SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位C.函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增D.函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的取值范圍是SKIPIF1<012.已知函數(shù)SKIPIF1<0若方程SKIPIF1<0有三個(gè)不同的解SKIPIF1<0，且SKIPIF1<0，則下列說法正確的是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0三?填空題(共20分)13.函數(shù)SKIPIF1<0的最小正周期SKIPIF1<0，則SKIPIF1<0__________.14.函數(shù)SKIPIF1<0的值域?yàn)開_____.15.已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值是___________.16.若函數(shù)SKIPIF1<0與SKIPIF1<0對(duì)于任意SKIPIF1<0，都有SKIPIF1<0，則稱函數(shù)SKIPIF1<0與SKIPIF1<0是區(qū)間SKIPIF1<0上的“SKIPIF1<0階依附函數(shù)”．已知函數(shù)SKIPIF1<0與SKIPIF1<0是區(qū)間SKIPIF1<0上的“2階依附函數(shù)”，則實(shí)數(shù)SKIPIF1<0的取值范圍是______．四?解答題(共70分)17.已知函數(shù)SKIPIF1<0的定義域?yàn)锳，SKIPIF1<0的值域?yàn)锽.(1)求A和B；(2)若SKIPIF1<0，求SKIPIF1<0的最大值.18.已知函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱．(1)求SKIPIF1<0，m的值；(2)將SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，再將所得圖象的橫坐標(biāo)伸長(zhǎng)到原來的3倍，縱坐標(biāo)不變，得到函數(shù)SKIPIF1<0的圖象，求SKIPIF1<0在SKIPIF1<0上的值域．19.已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)．(1)判斷函數(shù)SKIPIF1<0的單調(diào)性并用定義加以證明；(2)求使SKIPIF1<0成立的實(shí)數(shù)SKIPIF1<0的取值范圍．20.如圖，風(fēng)景區(qū)的形狀是如圖所示的扇形OAB區(qū)域，其半徑為4千米，圓心角為60°，點(diǎn)C在弧AB上．現(xiàn)在風(fēng)景區(qū)中規(guī)劃三條商業(yè)街道DE、CD、CE，要求街道DC與OA平行，交OB于點(diǎn)D，街道DE與OA垂直(垂足E在OA上)．(1)如果弧BC的長(zhǎng)為弧CA長(zhǎng)的三分之一，求三條商業(yè)街道圍成的△CDE的面積；(2)試求街道CE長(zhǎng)度的最小值．21.用打點(diǎn)滴的方式治療“新冠”病患時(shí)，血藥濃度(血藥濃度是指藥物吸收后，在血漿內(nèi)的總濃度，單位：SKIPIF1<0)隨時(shí)間(單位：小時(shí))變化的函數(shù)符合SKIPIF1<0，其函數(shù)圖象如圖所示，其中SKIPIF1<0為藥物進(jìn)入人體時(shí)的速率，k是藥物的分解或排泄速率與當(dāng)前濃度的比值.此種藥物在人體內(nèi)有效治療效果的濃度在SKIPIF1<0到SKIPIF1<0之間，當(dāng)達(dá)到上限濃度時(shí)(即濃度達(dá)到SKIPIF1<0時(shí))，必須馬上停止注射，之后血藥濃度隨時(shí)間變化的函數(shù)符合SKIPIF1<0，其中c為停藥時(shí)的人體血藥濃度.(1)求出函數(shù)SKIPIF1<0的解析式；(2)一病患開始注射后，最多隔多長(zhǎng)時(shí)間停止注射？為保證治療效果，最多再隔多長(zhǎng)時(shí)間開始進(jìn)行第二次注射？(結(jié)果保留小數(shù)點(diǎn)后一位，參考數(shù)據(jù)：SKIPIF1<0)22.設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镈，若存在SKIPIF1<0，使得SKIPIF1<0成立，則稱SKIPIF1<0為SKIPIF1<