江蘇省南京市2022-2023學(xué)年高一上學(xué)期期中聯(lián)考數(shù)學(xué)試題（原卷版）

高一上學(xué)期期中數(shù)學(xué)試題一?選擇題：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.已知集合SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.命題“SKIPIF1<0，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.函數(shù)SKIPIF1<0定義域為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.設(shè)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0=()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.已知SKIPIF1<0均為實數(shù)，且SKIPIF1<0，則下列結(jié)論正確的是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.已知函數(shù)SKIPIF1<0，則SKIPIF1<0的大致圖象是A. B.C. D.7.已知關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集是SKIPIF1<0，則不等式SKIPIF1<0的解集是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.已知SKIPIF1<0是奇函數(shù)，且在SKIPIF1<0上是增函數(shù)，又SKIPIF1<0，則SKIPIF1<0的解集為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0二?選擇題：本題共4小題，每小題5分，共20分.在每小題給出的選項中，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，有選錯的得0分.9.下列各組函數(shù)中是同一個函數(shù)的是()A.SKIPIF1<0與SKIPIF1<0B.SKIPIF1<0與SKIPIF1<0C.SKIPIF1<0與SKIPIF1<0D.SKIPIF1<0與SKIPIF1<010.下列命題中正確是()A.若SKIPIF1<0，則SKIPIF1<0 B.若SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<011.已知命題p：函數(shù)SKIPIF1<0有零點，命題SKIPIF1<0，SKIPIF1<0.若p，q全為真命題，則實數(shù)a的取值可以是()ASKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<012.已知函數(shù)SKIPIF1<0是偶函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0，關(guān)于SKIPIF1<0的方程SKIPIF1<0的根，下列說法正確的有()A.當(dāng)SKIPIF1<0時，方程有4個不等實根B.當(dāng)SKIPIF1<0時，方程有6個不等實根C.當(dāng)SKIPIF1<0時，方程有4個不等實根D.當(dāng)SKIPIF1<0時，方程有6個不等實根三?填空題：本題共4小題，每小題5分，共20分.13.已知函數(shù)SKIPIF1<0，則SKIPIF1<0___________.14.若“SKIPIF1<0”是“SKIPIF1<0”的充分不必要條件，則實數(shù)SKIPIF1<0的取值范圍是___________.15.已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為___________.16.函數(shù)SKIPIF1<0.(1)若SKIPIF1<0,則SKIPIF1<0___________；(2)若SKIPIF1<0是SKIPIF1<0上的減函數(shù),則實數(shù)SKIPIF1<0的取值范圍是___________.四?解答題：本大題共6小題，共70分.解答應(yīng)寫出文字說明?證明過程或演算步驟.17.已知全集SKIPIF1<0，集合SKIPIF1<0，集合SKIPIF1<0.(1)當(dāng)SKIPIF1<0時，求SKIPIF1<0；(2)若SKIPIF1<0，求實數(shù)SKIPIF1<0的取值范圍.18.化簡求值：(1)SKIPIF1<0；(2)SKIPIF1<0.19.已知二次函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0.(1)求SKIPIF1<0的解析式；(2)解關(guān)于SKIPIF1<0的不等式SKIPIF1<0.20.已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0.(1)求SKIPIF1<0的值；(2)求函數(shù)SKIPIF1<0的解析式；(3)判斷函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的單調(diào)性，并證明.21.2022年8月17日，為進一步捍衛(wèi)國家主權(quán)和領(lǐng)土完整，中國人民解放軍東部戰(zhàn)區(qū)繼續(xù)開展圍繞某島軍事演習(xí)，海陸空三軍聯(lián)手展開全域作戰(zhàn)演練，各類現(xiàn)役主力裝備悉數(shù)登場，其中解放軍長航時無人機遠海作戰(zhàn)能力再一次強力震懾住了敵對勢力.例如兩型偵察干擾無人機可以在遙控設(shè)備或自備程序控制操縱的情況下執(zhí)行任務(wù)，進行對敵方通訊設(shè)施的電磁壓制和干擾，甚至壓制敵方的防空系統(tǒng).為了檢驗實戰(zhàn)效果，某作戰(zhàn)部門對某處戰(zhàn)場實施“電磁干擾”實驗，據(jù)測定，該處的“干擾指數(shù)”與無人機干擾源的強度和距離的比值成正比，比例系數(shù)為常數(shù)SKIPIF1<0.現(xiàn)已知相距36SKIPIF1<0的SKIPIF1<0兩處配置兩架無人機干擾源，其對敵干擾的強度分別為SKIPIF1<0和SKIPIF1<0，線段SKIPIF1<0上任意一點SKIPIF1<0處的干擾指數(shù)SKIPIF1<0等于兩機對該處的干擾指數(shù)之和，設(shè)SKIPIF1<0.(1)試將SKIPIF1<0表示為SKIPIF1<0函數(shù)，并求出定義域；(2)當(dāng)SKIPIF1<0時，試確定“干擾指數(shù)”最小時SKIPIF1<0所處的位置.22.已知二次函數(shù)SKIPIF1<0.(1)若關(guān)于SKIPIF1