湖北省武漢市重點(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)試題考試時(shí)間：2023年1月3日試卷滿(mǎn)分：150分一、單選題1.已知集合SKIPIF1<0，集合SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.命題SKIPIF1<0：SKIPIF1<0，SKIPIF1<0，則命題SKIPIF1<0的否定是()A.SKIPIF1<0，SKIPIF1<0 B.SKIPIF1<0，SKIPIF1<0C.SKIPIF1<0，SKIPIF1<0 D.SKIPIF1<0，SKIPIF1<03.已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，則函數(shù)SKIPIF1<0的定義域?yàn)?)ASKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.設(shè)函數(shù)SKIPIF1<0的最大值為SKIPIF1<0，最小值為SKIPIF1<0，則SKIPIF1<0()ASKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.已知函數(shù)SKIPIF1<0，滿(mǎn)足對(duì)任意SKIPIF1<0，都有SKIPIF1<0成立，則SKIPIF1<0的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的大小關(guān)系為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為()A.SKIPIF1<0 B.SKIPIF1<0 C.9 D.78.已知單調(diào)函數(shù)f(x)滿(mǎn)足SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)所在區(qū)間為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二、多選題9.設(shè)SKIPIF1<0，SKIPIF1<0，則下列不等式一定成立的是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<010.下列說(shuō)法正確的是()A.SKIPIF1<0是第三象限角B.若圓心角為SKIPIF1<0的扇形的弧長(zhǎng)為SKIPIF1<0，則該扇形的面積為SKIPIF1<0C.若角SKIPIF1<0的終邊過(guò)點(diǎn)SKIPIF1<0，則SKIPIF1<0D.若角SKIPIF1<0為銳角，則SKIPIF1<0為鈍角．11.已知函數(shù)SKIPIF1<0，下列說(shuō)法正確的有()A.當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0的定義域?yàn)镽B.當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0的值域?yàn)镽C.函數(shù)SKIPIF1<0有最小值的充要條件為：SKIPIF1<0D.若SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則實(shí)數(shù)SKIPIF1<0的取值范圍是SKIPIF1<012.若函數(shù)SKIPIF1<0在其定義域內(nèi)是奇函數(shù)或偶函數(shù)，則稱(chēng)SKIPIF1<0具有奇偶性.以下函數(shù)中，具有奇偶性函數(shù)是()A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0DSKIPIF1<0三、填空題13.已知函數(shù)SKIPIF1<0，則SKIPIF1<0________．14.已知SKIPIF1<0，則SKIPIF1<0______．15.已知函數(shù)SKIPIF1<0與SKIPIF1<0的圖像上存在關(guān)于SKIPIF1<0軸對(duì)稱(chēng)的點(diǎn)，則SKIPIF1<0的取值范圍是______．16.已知函數(shù)SKIPIF1<0，若SKIPIF1<0，使得不等式SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的最大值是______．四、解答題17.(1)已知SKIPIF1<0，且SKIPIF1<0為第二象限角，求SKIPIF1<0，SKIPIF1<0的值；(2)化簡(jiǎn)求值：SKIPIF1<018.已知SKIPIF1<0，SKIPIF1<0．(1)若SKIPIF1<0是SKIPIF1<0充分條件，求實(shí)數(shù)SKIPIF1<0的取值范圍；(2)若SKIPIF1<0是SKIPIF1<0的必要條件，求實(shí)數(shù)SKIPIF1<0的取值范圍．19.2022年某企業(yè)整合資金投入研發(fā)高科技產(chǎn)品，并面向全球發(fā)布了首批17項(xiàng)科技創(chuàng)新重大技術(shù)需求榜單，吸引清華大學(xué)、北京大學(xué)等60余家高校院所參與，實(shí)現(xiàn)企業(yè)創(chuàng)新需求與國(guó)內(nèi)知名科技創(chuàng)新團(tuán)隊(duì)的精準(zhǔn)對(duì)接，最終該公司產(chǎn)品研發(fā)部決定將某項(xiàng)高新技術(shù)應(yīng)用到某高科技產(chǎn)品的生產(chǎn)中，計(jì)劃該技術(shù)全年需投入固定成本6200萬(wàn)元，每生產(chǎn)SKIPIF1<0千件該產(chǎn)品，需另投入成本SKIPIF1<0萬(wàn)元，且SKIPIF1<0，假設(shè)該產(chǎn)品對(duì)外銷(xiāo)售單價(jià)定為每件0.9萬(wàn)元，且全年內(nèi)生產(chǎn)的該產(chǎn)品當(dāng)年能全部售完．(1)求出全年的利潤(rùn)SKIPIF1<0萬(wàn)元關(guān)于年產(chǎn)量SKIPIF1<0千件的函數(shù)關(guān)系式；(2)試求該企業(yè)全年產(chǎn)量為多少千件時(shí)，所獲利潤(rùn)最大，并求出最大利潤(rùn)．20.已知函數(shù)SKIPIF1<0(SKIPIF1<0，SKIPIF1<0為常數(shù)，且SKIPIF1<0)，滿(mǎn)足SKIPIF1<0，方程SKIPIF1<0有唯一解．(1)求函數(shù)SKIPIF1<0的解析式(2)如果SKIPIF1<0不是奇偶函數(shù)，證明：函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是增函數(shù)．21.我們知道，函數(shù)SKIPIF1<0的圖像關(guān)于坐標(biāo)原點(diǎn)成中心對(duì)稱(chēng)圖形的充要條件是函數(shù)SKIPIF1<0為奇函數(shù)，有同學(xué)發(fā)現(xiàn)可以將其推廣為：函數(shù)SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0成中心對(duì)稱(chēng)圖形的充要條件是函數(shù)SKIPIF1<0為奇函數(shù)，(1)求函數(shù)SKIPIF1<0的對(duì)稱(chēng)中心；(2)已知SKIPIF1<0，SKIPIF1<0，若對(duì)任意的SKIPIF1<0，總存在SKIPIF1<0，使SKI