湖南省長(zhǎng)沙市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)試題時(shí)量：120分鐘；分值：150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)符合題目要求．1.命題SKIPIF1<0：SKIPIF1<0，SKIPIF1<0的否定形式SKIPIF1<0為(

)A.SKIPIF1<0，SKIPIF1<0 B.SKIPIF1<0，SKIPIF1<0CSKIPIF1<0，SKIPIF1<0 D.SKIPIF1<0，SKIPIF1<02已知集合SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.設(shè)SKIPIF1<0，則“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4.SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.設(shè)SKIPIF1<0，則SKIPIF1<0的大小關(guān)系是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<06.已知SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.流行病學(xué)基本參數(shù)：基本再生數(shù)SKIPIF1<0指一個(gè)感染者傳染的平均人數(shù)，世代間隔T指相鄰兩代間傳染所需的平均時(shí)間．在新冠肺炎疫情初始階段，可用模型：SKIPIF1<0(其中SKIPIF1<0是開始確診病例數(shù))描述累計(jì)感染病例SKIPIF1<0隨時(shí)間t(單位：天)的變化規(guī)律，指數(shù)增長(zhǎng)率r與SKIPIF1<0，T滿足SKIPIF1<0，有學(xué)者估計(jì)出SKIPIF1<0．據(jù)此，在新冠肺炎疫情初始階段，當(dāng)SKIPIF1<0時(shí)，t的值為(SKIPIF1<0)()A.1.2 B.1.7 C.2.0 D.2.58.若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)，且在SKIPIF1<0上存在最值，則SKIPIF1<0的取值范圍是()．A.SKIPIF1<0 B.SKIPIF1<0C.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.下列命題為真命題的是()A.不論SKIPIF1<0取何實(shí)數(shù)，命題SKIPIF1<0“SKIPIF1<0”為真命題B.不論SKIPIF1<0取何實(shí)數(shù)，命題SKIPIF1<0：“二次函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0軸對(duì)稱”為真命題C.“四邊形SKIPIF1<0的對(duì)角線垂直且相等”是“四邊形SKIPIF1<0是正方形”的充分不必要條件D.“SKIPIF1<0”是“SKIPIF1<0”的既不充分也不必要條件10.已知SKIPIF1<0，則下列結(jié)論正確的有()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<011.對(duì)于函數(shù)SKIPIF1<0，下列說(shuō)法正確的是()A.最小正周期為SKIPIF1<0 B.其圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱C.對(duì)稱軸方程為SKIPIF1<0 D.單調(diào)增區(qū)間SKIPIF1<012.已知函數(shù)SKIPIF1<0則以下判斷正確的是()A.若函數(shù)SKIPIF1<0有3個(gè)零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是SKIPIF1<0B.函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C.直線SKIPIF1<0與函數(shù)SKIPIF1<0的圖象有兩個(gè)公共點(diǎn)D.函數(shù)SKIPIF1<0圖象與直線SKIPIF1<0有且只有一個(gè)公共點(diǎn)三、填空題：本題共4小題，每小題5分，共20分．13.函數(shù)SKIPIF1<0的定義域?yàn)開_________．14.SKIPIF1<0___________.15.寫出不等式SKIPIF1<0成立的一個(gè)必要不充分條件__________.16.函數(shù)SKIPIF1<0的最大值為__________，當(dāng)且僅當(dāng)SKIPIF1<0__________時(shí)，等號(hào)成立．四、解答題：本題共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.已知SKIPIF1<0，且SKIPIF1<0．(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的值．18.已知函數(shù)SKIPIF1<0.(1)判斷函數(shù)SKIPIF1<0的單調(diào)性，并用單調(diào)性定義證明；(2)若SKIPIF1<0為奇函數(shù)，求滿足SKIPIF1<0的SKIPIF1<0的取值范圍.19.已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)求SKIPIF1<0的最小正周期和最大值；(2)設(shè)SKIPIF1<0，求函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間．20.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.21.某企業(yè)欲做一個(gè)介紹企業(yè)發(fā)展史的銘牌，銘牌的截面形狀是如圖所示的扇形環(huán)面(由扇形OAD挖去扇形OBC后構(gòu)成的).已知SKIPIF1<0，SKIPIF1<0，線段BA，CD與SKIPIF1<0，SKIPIF1<0的長(zhǎng)度之和為30，圓心角為SKIPIF1<0弧度.(1)求SKIPIF1<0關(guān)于x函數(shù)表達(dá)式；(2)記銘牌的截面面積為y，試問(wèn)x取何值時(shí)，y的值最大？并求出最大值.22.已知SKIPIF1<0，函數(shù)SKIPIF1<0