河北省xx中學(xué)2022-2023學(xué)年高一上學(xué)期綜合素質(zhì)檢測二數(shù)學(xué)試題（原卷版）

高一上學(xué)期期中數(shù)學(xué)試題第I卷(選擇題共60分)一?單項(xiàng)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(gè)選項(xiàng)中，只有一項(xiàng)是符合題目要求的.)1.下列函數(shù)中，其定義域和值域分別與函數(shù)SKIPIF1<0的定義域和值域相同的是()A.y=x B.y=lnx C.y=SKIPIF1<0 D.y=SKIPIF1<02.已知SKIPIF1<0，則A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<03.已知SKIPIF1<0，則SKIPIF1<0的值是A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<04.區(qū)塊鏈作為一種新型的技術(shù)，已經(jīng)被應(yīng)用于許多領(lǐng)域.在區(qū)塊鏈技術(shù)中，某個(gè)密碼的長度設(shè)定為512B，則密碼一共有SKIPIF1<0種可能，為了破解該密碼，最壞的情況需要進(jìn)行SKIPIF1<0次運(yùn)算.現(xiàn)在有一臺(tái)計(jì)算機(jī)，每秒能進(jìn)行SKIPIF1<0次運(yùn)算，那么在最壞的情況下，這臺(tái)計(jì)算機(jī)破譯該密碼所需時(shí)間大約為()(參考數(shù)據(jù)：SKIPIF1<0，SKIPIF1<0)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.設(shè)SKIPIF1<0，SKIPIF1<0，則下列命題正確的是()．A.若SKIPIF1<0，則SKIPIF1<0 B.若SKIPIF1<0，則SKIPIF1<0C.若SKIPIF1<0，則SKIPIF1<0 D.若SKIPIF1<0，則SKIPIF1<06.已知函數(shù)SKIPIF1<0是SKIPIF1<0上的增函數(shù)，SKIPIF1<0是其圖象上的兩點(diǎn)，那么SKIPIF1<0的解集是()A.SKIPIF1<0 B.SKIPIF1<0CSKIPIF1<0 D.SKIPIF1<07.已知SKIPIF1<0是定義域?yàn)镾KIPIF1<0的奇函數(shù)，滿足SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.0 C.2 D.508.已知函數(shù)SKIPIF1<0，SKIPIF1<0，則圖象如圖的函數(shù)可能是()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.在每小題給出的選項(xiàng)中，有多項(xiàng)是符合題目要求.全部選對的得5分，部分選對的得2分，有選錯(cuò)的得0分.)9.下面說法中，錯(cuò)誤的是()A.“SKIPIF1<0中至少有一個(gè)小于零”是“SKIPIF1<0”的充要條件；B.“SKIPIF1<0”是“SKIPIF1<0且SKIPIF1<0”的充要條件；C.“SKIPIF1<0”是“SKIPIF1<0或SKIPIF1<0”的充要條件；D.若集合SKIPIF1<0是全集SKIPIF1<0的子集，則命題“SKIPIF1<0”與“SKIPIF1<0”是等價(jià)命題.10已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則()ASKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<011.已知函數(shù)SKIPIF1<0，下列關(guān)于函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)的說法中，正確的是()A.當(dāng)SKIPIF1<0，有1個(gè)零點(diǎn) B.當(dāng)SKIPIF1<0時(shí)，有3個(gè)零點(diǎn)C.當(dāng)SKIPIF1<0，有4個(gè)零點(diǎn) D.當(dāng)SKIPIF1<0時(shí)，有7個(gè)零點(diǎn)12.定義“正對數(shù)”：SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則下列結(jié)論中正確的是.A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0第II卷(共90分)三?填空題(本題共4小題，每小題5分，共20分；)13.計(jì)算SKIPIF1<0____________14.設(shè)函數(shù)SKIPIF1<0，則使得SKIPIF1<0成立的SKIPIF1<0的取值范圍是_______________.15.已知函數(shù)SKIPIF1<0定義域?yàn)镾KIPIF1<0，且對于任意SKIPIF1<0，都有SKIPIF1<0，且SKIPIF1<0，則不等式SKIPIF1<0的解集為_________.16.對任意的SKIPIF1<0，不等式SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0_________.四?解答題：(本題共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.為了預(yù)防新型冠狀病毒，唐徠回民中學(xué)對教室進(jìn)行藥熏消毒，室內(nèi)每立方米空氣中的含藥量y(單位：毫克)隨時(shí)間x(單位：h)的變化情況如圖所示，在藥物釋放過程中，y與x成正比，藥物釋放完畢后，y與x的函數(shù)關(guān)系式為SKIPIF1<0(a為常數(shù))，根據(jù)圖中提供的信息，回答下列問題：(1)寫出從藥物釋放開始，y與x的之間的函數(shù)關(guān)系；(2)據(jù)測定，當(dāng)空氣中每立方米的含藥量降低至0.25毫克以下時(shí)，學(xué)生方可進(jìn)入教室，那么從藥物釋放開始，至少需要經(jīng)過多少小時(shí)后，學(xué)生才能回到教室．18.已知函數(shù)SKIPIF1<0，其中SKIPIF1<0為常數(shù)且滿足SKIPIF1<0．(1)求SKIPIF1<0的值；(2)證明函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是減函數(shù)，并判斷SKIPIF1<0在SKIPIF1<0上的單調(diào)性；(3)若對任意的SKIPIF1<0，總有SKIPIF1<0成立，求實(shí)數(shù)SKIPIF1<0的取值范圍．19.已知函數(shù)SKIPIF1<0是偶函數(shù)(1)求實(shí)數(shù)SKIPIF1<0的值；(2)設(shè)SKIPIF1<0，若函數(shù)SKIPIF1<0與SKIPIF1<0的圖象有公共點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍.20.已知函數(shù)SKIPIF1<0，且SKIPIF1<0.(1)若函數(shù)SKIPIF1<0的圖像與函數(shù)SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對稱，且點(diǎn)SKIPIF1<0在函數(shù)SKIPIF1<0的圖像上，求實(shí)數(shù)SKIPIF1<0的值；(2)已知SKIPIF1<0，函數(shù)SKIPIF1<0.若SKIPIF1<0的最大值為8，求實(shí)數(shù)SKIPIF1<0的值.21.已知函數(shù)SKIPIF1<0為自然對數(shù)的底數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，判斷函數(shù)SKIPIF1<0零點(diǎn)個(gè)數(shù)，并證明你的結(jié)論；(2)當(dāng)SKIPIF1<0時(shí)，關(guān)于SKIPIF1<0的不等式SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍22.設(shè)定義在實(shí)數(shù)集SKIPIF1<0上函數(shù)SKIPIF1<0,SKIPIF1<0恒不為0,若存在不等于1的正常數(shù)SKIPIF1<0,對于任意實(shí)數(shù)SKIPIF1<0,等式SKIPIF1<0恒成立,則稱函數(shù)SKIPIF1<0為SKIPIF1<0函數(shù).(1)若函數(shù)SKIPIF1<0為SKIPIF1