湖北省武漢市部分重點(diǎn)中學(xué)2022-2023學(xué)年高一上學(xué)期期末聯(lián)考數(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：本題共8小題，每小題5分，共40分.在每小題給出的四個選項中，只有一項是符合題目要求的.1.下列四組函數(shù)中，同組的兩個函數(shù)是相同函數(shù)的是()A.SKIPIF1<0與SKIPIF1<0 B.SKIPIF1<0與SKIPIF1<0C.SKIPIF1<0與SKIPIF1<0 D.SKIPIF1<0與SKIPIF1<02.已知SKIPIF1<0，則SKIPIF1<0()ASKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.已知冪函數(shù)的圖象經(jīng)過點(diǎn)SKIPIF1<0，則該冪函數(shù)的大致圖象是()A. B.C. D.4.函數(shù)SKIPIF1<0的零點(diǎn)所在的大致區(qū)間是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.函數(shù)SKIPIF1<0的值域是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<06.已知函數(shù)SKIPIF1<0，若SKIPIF1<0，有SKIPIF1<0，則SKIPIF1<0的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.符號SKIPIF1<0表示不超過SKIPIF1<0的最大整數(shù)，如SKIPIF1<0，SKIPIF1<0，定義函數(shù)SKIPIF1<0，那么下列命題中正確命題的序號是()①函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，值域為SKIPIF1<0；②方程SKIPIF1<0有無數(shù)解；③函數(shù)SKIPIF1<0是周期函數(shù)；④函數(shù)SKIPIF1<0是減函數(shù)；A.①② B.②③ C.③④ D.①④8.函數(shù)SKIPIF1<0與SKIPIF1<0的圖象上存在關(guān)于SKIPIF1<0軸對稱的點(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<0二、多選題：本題共4小題，每小題5分，共20分.在每小題給出的四個選項中，有多項符合題目要求，全部選對的得5分，部分選對的得2分，有錯選的得0分.9.設(shè)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，SKIPIF1<0，則()A.SKIPIF1<0在SKIPIF1<0上單調(diào)遞減B.SKIPIF1<0C.不等式SKIPIF1<0的解集為SKIPIF1<0D.SKIPIF1<0的圖象與SKIPIF1<0軸只有2個交點(diǎn)10.已知函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增11.已知函數(shù)SKIPIF1<0，以下說法正確的有()A.若SKIPIF1<0的定義域是SKIPIF1<0，則SKIPIF1<0B.若SKIPIF1<0定義域是SKIPIF1<0，則SKIPIF1<0C.若SKIPIF1<0恒成立，則SKIPIF1<0D.若SKIPIF1<0，則SKIPIF1<0的值域不可能是SKIPIF1<012.已知定義域為SKIPIF1<0的函數(shù)SKIPIF1<0滿足：(1)對任意SKIPIF1<0，SKIPIF1<0恒成立；(2)當(dāng)SKIPIF1<0時，SKIPIF1<0，則下列選項正確的有()A.對任意SKIPIF1<0，有SKIPIF1<0B.函數(shù)SKIPIF1<0的值域為SKIPIF1<0C.存在SKIPIF1<0，使得SKIPIF1<0D.函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減的充要條件是：存在SKIPIF1<0，使得SKIPIF1<0.三、填空題：本題共4小題，每小題5分，共20分.13.函數(shù)SKIPIF1<0的定義域為______.14.已知函數(shù)SKIPIF1<0，則SKIPIF1<0______.15.已知定義在整數(shù)集合SKIPIF1<0上的函數(shù)SKIPIF1<0，對任意的SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0______.16.函數(shù)SKIPIF1<0，若關(guān)于SKIPIF1<0的方程SKIPIF1<0恰好有8個不同的實(shí)數(shù)根，則實(shí)數(shù)SKIPIF1<0的取值范圍是______.四、解答題：共70分，解答應(yīng)寫出文字說明、證明過程或演算步驟.17.化簡求值：(1)SKIPIF1<0；(2)SKIPIF1<018.已知SKIPIF1<0為第三象限角，且SKIPIF1<0.(1)化簡SKIPIF1<0；(2)若SKIPIF1<0，求SKIPIF1<0的值.19.已知函數(shù)SKIPIF1<0的部分圖像如圖所示.(1)求函數(shù)SKIPIF1<0的解析式；(2)將函數(shù)SKIPIF1<0圖像向左平移SKIPIF1<0個單位，再將圖像上各點(diǎn)的橫坐標(biāo)伸長到原來的2倍(縱坐標(biāo)不變)得到函數(shù)SKIPIF1<0的圖像，若關(guān)于SKIPIF1<0的方程SKIPIF1<0在區(qū)間SKIPIF1<0上有兩個不同的實(shí)數(shù)解，求實(shí)數(shù)SKIPIF1<0的范圍.20.國家質(zhì)量監(jiān)督檢驗檢疫局發(fā)布的《車輛駕駛?cè)藛T血液、呼氣酒精含量閥值與檢驗》標(biāo)準(zhǔn)規(guī)定：①車輛駕駛?cè)藛T血液中的酒精含量大于或等于20毫克/百毫升，小于80毫克/百毫升為酒后駕駛，酒后駕駛，暫扣駕駛證6個月，并處1000元以上2000元以下罰款。如果此前曾因酒駕被處罰，再次酒后駕駛的，處10日以下拘留，并處1000元以上2000元以下罰款，吊銷駕駛證。②血液中的酒精含量大于或等于80毫克/百毫升為醉酒駕車。醉酒駕駛，由公安機(jī)關(guān)約束至酒醒，吊銷其駕駛證，依法追究刑事責(zé)任，5年內(nèi)不得重新取得駕駛證。由檢驗標(biāo)準(zhǔn)規(guī)定可知駕駛?cè)藛T血液中的酒精含量小于20毫克/百毫升才可以正常駕車上路。經(jīng)過反復(fù)試驗，喝一瓶啤酒后酒精在人體血液中的含量變化規(guī)律的“散點(diǎn)圖”如圖，該函數(shù)近似模型如下：SKIPIF1<0，又已知酒后1小時測得酒精含量值為44.42毫克/百毫升，根據(jù)上述條件，解答以下問題：現(xiàn)行的酒駕標(biāo)準(zhǔn)類型血液中酒精含量SKIPIF1<0酒后駕車SKIPIF1<0醉酒駕車SKIPIF1<0(1)當(dāng)SKIPIF1<0時，確定SKIPIF1<0的表達(dá)式；(2)喝1瓶啤酒后多長時間后才可以駕車?(時間以整分鐘計算)(附參考數(shù)據(jù)：SKIPIF1<0，SKIPIF1<0，SKIPIF1<0)21.已知函數(shù)SKIPIF1<0(SKIPIF1<0且SKIPIF1<0).(1)當(dāng)SKIPIF1<0時，求函數(shù)SKIPIF1<0的值域；(2)已知SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0取值范圍.22.已知函數(shù)SKIPIF1<0(其中SKIPIF1<0常數(shù)).(1)如果存在SKIPIF1<0，使得不等式SKIPIF1<0能