湖北省黃岡市2022-2023學(xué)年高一上學(xué)期元月期末數(shù)學(xué)試題（原卷版）

高一上學(xué)期期末數(shù)學(xué)試題一?選擇題：共8小題，每小題5分，共40分.在每小題給出的四個(gè)選項(xiàng)中，只有一項(xiàng)是符合題目要求的.1.命題“SKIPIF1<0”的否定為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.已知集合SKIPIF1<0則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.下列函數(shù)中最小正周期為SKIPIF1<0且是奇函數(shù)的為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<04.衡量病毒傳播能力的一個(gè)指標(biāo)叫做傳播指數(shù)SKIPIF1<0，它指的是在自然情況下(沒(méi)有外力介人，同時(shí)所有人都沒(méi)有免疫)一個(gè)感染者傳染的平均人數(shù).它的計(jì)算公式是：SKIPIF1<0確診病例增長(zhǎng)率SKIPIF1<0系列間隔，其中系列間隔是指在一個(gè)傳播鏈中兩例連續(xù)病例的間隔時(shí)間(單位：天).根據(jù)統(tǒng)計(jì)，某種傳染病例的平均增長(zhǎng)率為SKIPIF1<0，兩例連續(xù)病例間隔時(shí)間平均為4天.根據(jù)以上數(shù)據(jù)計(jì)算，若甲感染這種傳染病，則經(jīng)過(guò)4輪傳播后由甲引起的得病總?cè)藬?shù)(不含甲)為()A.81人 B.120人 C.243人 D.36人5.已知SKIPIF1<0，則有()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<06.已知角SKIPIF1<0終邊過(guò)點(diǎn)SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.已知SKIPIF1<0是定義在R上的奇函數(shù)，SKIPIF1<0，對(duì)SKIPIF1<0，且SKIPIF1<0有SKIPIF1<0，則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.已知函數(shù)SKIPIF1<0若關(guān)于SKIPIF1<0的方程SKIPIF1<0有SKIPIF1<0個(gè)不同的實(shí)數(shù)根，則實(shí)數(shù)SKIPIF1<0的取值范圍為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二?多項(xiàng)選擇題：本題共4小題，每小題5分，共20分.在每小題給出的四個(gè)選項(xiàng)中，有多項(xiàng)符合題目要求.全部選對(duì)的得5分，部分選對(duì)的得2分，有選錯(cuò)的得0分.9.下列計(jì)算結(jié)果為有理數(shù)的是()ASKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<010.若SKIPIF1<0，則使“SKIPIF1<0”成立的一個(gè)必要不充分條件是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<011.函數(shù)SKIPIF1<0，以下正確的是()A.若SKIPIF1<0的最小正周期為SKIPIF1<0，則SKIPIF1<0B.若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0C.當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0單調(diào)且在SKIPIF1<0不單調(diào)，則SKIPIF1<0.D.當(dāng)SKIPIF1<0時(shí)，若對(duì)任意SKIPIF1<0有SKIPIF1<0成立，則SKIPIF1<0的最小值為SKIPIF1<012.空曠的田野上兩根電線桿之間的電線有相似的曲線形態(tài).這些曲線在數(shù)學(xué)上稱為懸鏈線.懸鏈線在工程上有廣泛的應(yīng)用.在恰當(dāng)?shù)淖鴺?biāo)系中，這類函數(shù)的表達(dá)式可以為SKIPIF1<0(其中SKIPIF1<0為非零常數(shù))，則對(duì)于函數(shù)SKIPIF1<0以下結(jié)論正確的是()A.若SKIPIF1<0，則SKIPIF1<0為偶函數(shù)B.若SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)為0和SKIPIF1<0C.若SKIPIF1<0，則函數(shù)SKIPIF1<0的最小值為2D.若SKIPIF1<0為奇函數(shù)，且SKIPIF1<0使SKIPIF1<0成立，則SKIPIF1<0的最小值為SKIPIF1<0三?填空題：本大題共4小題，每小題5分，共20分13.函數(shù)SKIPIF1<0定義域?yàn)開_________.14.已知函數(shù)SKIPIF1<0的圖象過(guò)定點(diǎn)SKIPIF1<0，且點(diǎn)SKIPIF1<0在指數(shù)函數(shù)SKIPIF1<0圖象上，則SKIPIF1<0__________.15.已知SKIPIF1<0，則SKIPIF1<0的最小值為__________.16.已知SKIPIF1<0，SKIPIF1<0，若對(duì)SKIPIF1<0，總存在SKIPIF1<0，使得SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為__________.四?解答題：本大題共6小題，共70分.解答應(yīng)寫出文字說(shuō)明?證明過(guò)程或演算步驟.17.(1)已知SKIPIF1<0，求SKIPIF1<0的值.(2)已知SKIPIF1<0，求SKIPIF1<0的值.18.設(shè)函數(shù)SKIPIF1<0.(1)若不等式SKIPIF1<0的解集為SKIPIF1<0，求SKIPIF1<0的值；(2)若SKIPIF1<0，且SKIPIF1<0都有SKIPIF1<0，求SKIPIF1<0的最大值.19.已知函數(shù)SKIPIF1<0為奇函數(shù).(1)求函數(shù)SKIPIF1<0的最大值與最小值，并分別寫出取最大值與最小值時(shí)相應(yīng)SKIPIF1<0的取值集合.(2)求函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間.20.某兒童玩具廠生產(chǎn)的某一款益智玩具去年年銷量為2百萬(wàn)件，每件銷售價(jià)格為20元，成本16元.今年計(jì)劃投入適當(dāng)廣告費(fèi)進(jìn)行促銷.預(yù)計(jì)該款玩具的年銷售量SKIPIF1<0百萬(wàn)件與年廣告費(fèi)用SKIPIF1<0百萬(wàn)元滿足SKIPIF1<0，現(xiàn)已知每件玩具的銷售價(jià)為年平均每件玩具所占廣告費(fèi)的SKIPIF1<0與原銷售價(jià)之和.(1)當(dāng)投入廣告費(fèi)為2百萬(wàn)元時(shí)，要使該玩具的年利潤(rùn)不少于12百萬(wàn)元，求SKIPIF1<0的取值范圍；(2)若SKIPIF1<0時(shí)，則當(dāng)投入多少百萬(wàn)元浩費(fèi)該玩具生產(chǎn)廠獲得最大利潤(rùn).21.已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0圖象與SKIPIF1<0的圖象關(guān)于SKIPIF1<0對(duì)稱.(1)若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，求實(shí)數(shù)SKIPIF1<0的取值范圍；(2)不等式SKIPIF1<0在SKIPIF1<0上恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.22.已知SKIPIF1<0為SKIPIF1<0上的偶函數(shù)，當(dāng)SKIPIF1<0