湖北省武漢市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（一）（原卷版）

高一上學(xué)期期末數(shù)學(xué)試題一、單選題(本大題共8小題，共40.0分.在每小題列出的選項(xiàng)中，選出符合題目的一項(xiàng))1.設(shè)集合SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.設(shè)命題p：所有的等邊三角形都是等腰三角形，則p的否定為()A.所有的等邊三角形都不是等腰三角形 B.有的等邊三角形不是等腰三角形C.有的等腰三角形不是等邊三角形 D.不是等邊三角形的三角形不是等腰三角形3.著名的物理學(xué)家牛頓在17世紀(jì)提出了牛頓冷卻定律，描述溫度高于周圍環(huán)境的物體向周圍媒質(zhì)傳遞熱量逐漸冷卻時(shí)所遵循的規(guī)律.新聞學(xué)家發(fā)現(xiàn)新聞熱度也遵循這樣的規(guī)律，即隨著時(shí)間的推移，新聞熱度會(huì)逐漸降低，假設(shè)一篇新聞的初始熱度為SKIPIF1<0，經(jīng)過時(shí)間SKIPIF1<0天SKIPIF1<0之后的新聞熱度變?yōu)镾KIPIF1<0，其中SKIPIF1<0為冷卻系數(shù).假設(shè)某篇新聞的冷卻系數(shù)SKIPIF1<0，要使該新聞的熱度降到初始熱度的SKIPIF1<0以下，需要經(jīng)過天(參考數(shù)據(jù)：SKIPIF1<0)()A.6 B.7 C.8 D.94.函數(shù)SKIPIF1<0圖象大致為()A. B.C. D.5.設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.已知函數(shù)SKIPIF1<0定義域?yàn)镾KIPIF1<0，則函數(shù)SKIPIF1<0的定義域?yàn)?)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為SKIPIF1<0，則a的取值范圍為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<08.已知函數(shù)SKIPIF1<0，SKIPIF1<0，函數(shù)SKIPIF1<0有4個(gè)不同的零點(diǎn)SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0的取值范圍為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二、多選題(本大題共4小題，共20.0分.在每小題有多項(xiàng)符合題目要求)9.已知SKIPIF1<0為第二象限角，則下列說法正確的是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<010.已知函數(shù)SKIPIF1<0，SKIPIF1<0，若存在實(shí)數(shù)m，使得對(duì)于任意SKIPIF1<0，都有SKIPIF1<0，則稱函數(shù)SKIPIF1<0，SKIPIF1<0有下界，m為其一個(gè)下界；類似的，若存在實(shí)數(shù)M，使得對(duì)于任意的SKIPIF1<0，都有SKIPIF1<0，則稱函數(shù)SKIPIF1<0，SKIPIF1<0有上界，M為其一個(gè)上界.若函數(shù)SKIPIF1<0，SKIPIF1<0既有上界，又有下界，則稱該函數(shù)為有界函數(shù).下列說法正確的是()A.若函數(shù)SKIPIF1<0在定義域上有下界，則函數(shù)SKIPIF1<0有最小值B.若定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0有上界，則該函數(shù)一定有下界C.若函數(shù)SKIPIF1<0為有界函數(shù)，則函數(shù)SKIPIF1<0是有界函數(shù)D.若函數(shù)SKIPIF1<0定義域?yàn)殚]區(qū)間SKIPIF1<0，則該函數(shù)是有界函數(shù)11.已知a為實(shí)數(shù)，SKIPIF1<0且SKIPIF1<0，函數(shù)SKIPIF1<0，則下列說法正確的是()A.當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0的圖像關(guān)于SKIPIF1<0中心對(duì)稱 B.當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0為減函數(shù)C.函數(shù)SKIPIF1<0圖像關(guān)于直線SKIPIF1<0成軸對(duì)稱圖形 D.函數(shù)SKIPIF1<0圖像上任意不同兩點(diǎn)的連線與x軸有交點(diǎn)12.已知SKIPIF1<0奇函數(shù)，SKIPIF1<0恒成立，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，設(shè)SKIPIF1<0，則()A.SKIPIF1<0B.函數(shù)SKIPIF1<0為周期函數(shù)C.函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減D.函數(shù)SKIPIF1<0的圖像既有對(duì)稱軸又有對(duì)稱中心三、填空題(本大題共4小題，共20.0分)13.冪函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則SKIPIF1<0______.14.已知集合SKIPIF1<0沒有非空真子集，則實(shí)數(shù)a構(gòu)成的集合為______.15.已知SKIPIF1<0均為實(shí)數(shù)且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為______.16.已知偶函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，已知當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的解集為______.四、解答題(本大題共6小題，共70.0分.解答應(yīng)寫出文字說明，證明過程或演算步驟)17.已知函數(shù)SKIPIF1<0(1)求函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間；(2)設(shè)SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的值.18.在①SKIPIF1<0，②SKIPIF1<0，③SKIPIF1<0這三個(gè)條件中任選一個(gè)，補(bǔ)充在下面的橫線上，并回答下列問題.設(shè)全集SKIPIF1<0，______，SKIPIF1<0(1)若SKIPIF1<0，求SKIPIF1<0；(2)若“SKIPIF1<0”是“SKIPIF1<0”的充分不必要條件，求實(shí)數(shù)a的取值范圍.19.2022年冬天新冠疫情卷土重來，我國大量城市和地區(qū)遭受了奧密克戎新冠病毒的襲擊，為了控制疫情，某單位購入了一種新型的空氣消毒劑用于環(huán)境消毒，已知在一定范圍內(nèi)，每噴灑1個(gè)單位的消毒劑，空氣中釋放的濃度SKIPIF1<0單位：毫克/立方米SKIPIF1<0隨著時(shí)間SKIPIF1<0單位：小時(shí)SKIPIF1<0變化的關(guān)系如下：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0若多次噴灑，則某一時(shí)刻空氣中的消毒劑濃度為每次投放的消毒劑在相應(yīng)時(shí)刻所釋放的濃度之和.由實(shí)驗(yàn)知，當(dāng)空氣中消毒劑的濃度不低于SKIPIF1<0毫克/立方米SKIPIF1<0時(shí)，它才能起到殺滅空氣中的病毒的作用.(1)若一次噴灑4個(gè)單位的消毒劑，則有效殺滅時(shí)間可達(dá)幾小時(shí)？(2)若第一次噴灑2個(gè)單位的消毒劑，6小時(shí)后再噴灑SKIPIF1<0個(gè)單位的消毒劑，要使接下來的4小時(shí)中能夠持續(xù)有效消毒，試求a的最小值.SKIPIF1<0精確到SKIPIF1<0，參考數(shù)據(jù)：SKIPIF1<0取SKIPIF1<020.已知函數(shù)SKIPIF1<0，將函數(shù)SKIPIF1<0向右平移SKIPIF1<0個(gè)單位得到的圖像關(guān)于y軸對(duì)稱且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最大值.(1)求函數(shù)SKIPIF1<0的解析式：(2)方程SKIPIF1<0在SKIPIF1<0上有4個(gè)不相等的實(shí)數(shù)根，求實(shí)數(shù)SKIPIF1<0的取值范圍.21.已知函數(shù)SKIPIF1<0SKIPIF1<0.(1)試判斷函數(shù)SKIPIF1<0的奇偶性；(2)當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的值域；(3)已知SKIPIF1<0，若SKIPIF1<0，使得SKIPIF1<0，求實(shí)數(shù)a的取值范圍.22.已知函數(shù)SKIPIF1<0(1)若關(guān)于x的不