江蘇省南京市2022-2023學(xué)年高一上學(xué)期期末數(shù)學(xué)試題（原卷版）

高一上學(xué)期期末數(shù)學(xué)試題一、單項(xiàng)選擇題(本題共8小題，每小題5分，共40分.)1.函數(shù)SKIPIF1<0的定義域?yàn)?)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.“SKIPIF1<0”是“SKIPIF1<0”的()A充分不必要條件 B.必要不充分條件C.充要條件 D.既不充分也不必要條件3.在某個(gè)物理實(shí)驗(yàn)中，測(cè)得變量x和變量y的幾組數(shù)據(jù)，如下表：xSKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0ySKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0則下列選項(xiàng)中對(duì)x，y最適合的擬合函數(shù)是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.《九章算術(shù)》是一部中國(guó)古代的數(shù)學(xué)專(zhuān)著.全書(shū)分為九章，共收有246個(gè)問(wèn)題，內(nèi)容豐富，而且大多與生活實(shí)際密切聯(lián)系.第一章《方田》收錄了38個(gè)問(wèn)題，主要講各種形狀的田畝的面積計(jì)算方法，其中將圓環(huán)或不足一匝的圓環(huán)形天地稱(chēng)為“環(huán)田”.書(shū)中提到這樣一塊“環(huán)田”：中周九十二步，外周一百二十二步，徑五步，如圖所示，則其所在扇形的圓心角大小為()(單位：弧度)(注：匝，意為周，環(huán)繞一周叫一匝.)A.4 B.5 C.6 D.75.已知函數(shù)SKIPIF1<0，則SKIPIF1<0的值為()A.SKIPIF1<0 B.SKIPIF1<0 C.4 D.SKIPIF1<06.函數(shù)SKIPIF1<0的圖像大致為()A. B.C. D.7.在科學(xué)技術(shù)中，常常使用以SKIPIF1<0為底的對(duì)數(shù)，這種對(duì)數(shù)稱(chēng)為自然對(duì)數(shù).若取SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.4 D.68.函數(shù)SKIPIF1<0的零點(diǎn)為SKIPIF1<0，函數(shù)SKIPIF1<0的零點(diǎn)為SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是()ASKIPIF1<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.)9.已知角SKIPIF1<0的終邊經(jīng)過(guò)點(diǎn)SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<010若SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<011.已知函數(shù)SKIPIF1<0，則()A.SKIPIF1<0的最小正周期為SKIPIF1<0 B.SKIPIF1<0的圖象關(guān)于SKIPIF1<0軸對(duì)稱(chēng)C.SKIPIF1<0的最小值為2 D.SKIPIF1<0在SKIPIF1<0上為增函數(shù)12.已知函數(shù)SKIPIF1<0，對(duì)于任意SKIPIF1<0，SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0三、填空題(本題共4小題，每小題5分，共20分.)13.函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)_________中心對(duì)稱(chēng).(寫(xiě)出一個(gè)正確的點(diǎn)坐標(biāo)即可)14.已知關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為SKIPIF1<0，則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為_(kāi)________.15.已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿(mǎn)足SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0___________.16.對(duì)于非空集合SKIPIF1<0，定義SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0是兩個(gè)非空集合，且SKIPIF1<0，則SKIPIF1<0___________；若SKIPIF1<0，SKIPIF1<0，且存在SKIPIF1<0，SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是_______________.四、解答題(本題共6小題，共70分.)17.求下列各式的值：(1)SKIPIF1<0；(2)SKIPIF1<0.18.若SKIPIF1<0.(1)求SKIPIF1<0的值；(2)若SKIPIF1<0，求SKIPIF1<0的值.19.已知集合SKIPIF1<0，SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0；(2)在①SKIPIF1<0，②SKIPIF1<0這兩個(gè)條件中任選一個(gè)，補(bǔ)充在下面問(wèn)題中，并解答該問(wèn)題.若_________，求實(shí)數(shù)SKIPIF1<0的取值范圍.注：如果選擇多個(gè)條件分別解答，按第一個(gè)解答計(jì)分.20.函數(shù)SKIPIF1<0(SKIPIF1<0，SKIPIF1<0)在一個(gè)周期內(nèi)的圖象如圖所示.(1)求SKIPIF1<0的解析式；(2)將SKIPIF1<0圖象向右平移SKIPIF1<0個(gè)單位長(zhǎng)度后得到函數(shù)SKIPIF1<0的圖象，設(shè)SKIPIF1<0，證明：SKIPIF1<0為偶函數(shù).21.某企業(yè)為響應(yīng)國(guó)家節(jié)水號(hào)召，決定對(duì)污水進(jìn)行凈化再利用，以降低自來(lái)水的使用量.經(jīng)測(cè)算，企業(yè)擬安裝一種使用壽命為4年的污水凈化設(shè)備.這種凈水設(shè)備的購(gòu)置費(fèi)(單位：萬(wàn)元)與設(shè)備的占地面積SKIPIF1<0(單位：平方米)成正比，比例系數(shù)為0.2.預(yù)計(jì)安裝后該企業(yè)每年需繳納的水費(fèi)SKIPIF1<0(單位：萬(wàn)元)與設(shè)備占地面積SKIPIF1<0之間的函數(shù)關(guān)系為SKIPIF1<0.將該企業(yè)的凈水設(shè)備購(gòu)置費(fèi)與安裝后4年需繳水費(fèi)之和合計(jì)為SKIPIF1<0(單位：萬(wàn)元).(1)要使SKIPIF1<0不超過(guò)7.2萬(wàn)元，求設(shè)備占地面積SKIPIF1<0的取值范圍；(2)設(shè)備占地面積SKIPIF1<0為多少時(shí)，SKIPIF1<0值最小？22.已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)利用函數(shù)單調(diào)性的定義，證明：SKIPIF1<0在區(qū)間SKIPIF1<0上是增函數(shù)；(2