山東省青島市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.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.已知集合SKIPIF1<0，則SKIPIF1<0的元素個(gè)數(shù)為()A.0 B.1 C.2 D.32.下述正確的是()A.若SKIPIF1<0為第四象限角，則SKIPIF1<0B.若SKIPIF1<0，則SKIPIF1<0C.若SKIPIF1<0的終邊為第三象限平分線，則SKIPIF1<0D.“SKIPIF1<0”是“SKIPIF1<0”的充要條件3.函數(shù)SKIPIF1<0的定義域是A.(0,1] B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<04.若函數(shù)SKIPIF1<0為奇函數(shù)，則SKIPIF1<0()A.0 B.1 C.2 D.35.若SKIPIF1<0，則下列不等式中正確的是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<06已知函數(shù)SKIPIF1<0，則()A.SKIPIF1<0的最小正周期為SKIPIF1<0B.點(diǎn)SKIPIF1<0是SKIPIF1<0圖象的一個(gè)對(duì)稱中心C.直線SKIPIF1<0是SKIPIF1<0圖象的一條對(duì)稱軸D.SKIPIF1<0在SKIPIF1<0上單調(diào)遞增7.若定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.已知函數(shù)SKIPIF1<0，對(duì)任意SKIPIF1<0且SKIPIF1<0恒成立，且SKIPIF1<0是偶函數(shù)，設(shè)SKIPIF1<0，則SKIPIF1<0的大小關(guān)系為()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.已知SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<010.已知函數(shù)SKIPIF1<0，則()A.若SKIPIF1<0，則函數(shù)SKIPIF1<0為偶函數(shù)B.若SKIPIF1<0，則函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減C.若SKIPIF1<0，則函數(shù)SKIPIF1<0的定義域SKIPIF1<0D.若SKIPIF1<0，則函數(shù)SKIPIF1<0只有一個(gè)零點(diǎn)11.下述正確的是()A.若SKIPIF1<0，則SKIPIF1<0的最大值是25B.若SKIPIF1<0，則SKIPIF1<0的最大值是SKIPIF1<0C.若SKIPIF1<0，則SKIPIF1<0的最小值是4D.若SKIPIF1<0，則SKIPIF1<0的最小值是1212.已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0是增函數(shù) D.當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0三?填空題：本題共4個(gè)小題，每小題5分，共20分.13.計(jì)算：SKIPIF1<0___________.14.已知SKIPIF1<0為坐標(biāo)原點(diǎn)，點(diǎn)SKIPIF1<0的初始位置坐標(biāo)為SKIPIF1<0，線段SKIPIF1<0繞點(diǎn)SKIPIF1<0順時(shí)針轉(zhuǎn)動(dòng)SKIPIF1<0后，點(diǎn)SKIPIF1<0所在位置的坐標(biāo)為___________.15.若SKIPIF1<0，則SKIPIF1<0___________.16.已知函數(shù)SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0時(shí)恒成立，則SKIPIF1<0的取值范圍是___________.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.已知全集為SKIPIF1<0.(1)求SKIPIF1<0；(2)若SKIPIF1<0，且SKIPIF1<0，求SKIPIF1<0的取值范圍.18.已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0的取值范圍；(2)若SKIPIF1<0，解關(guān)于SKIPIF1<0不等式SKIPIF1<0.19.已知函數(shù)SKIPIF1<0是SKIPIF1<0的一個(gè)零點(diǎn).(1)求SKIPIF1<0；(2)若SKIPIF1<0時(shí)，方程SKIPIF1<0有解，求實(shí)數(shù)SKIPIF1<0的范圍.20.已知函數(shù)SKIPIF1<0且SKIPIF1<0圖象過點(diǎn)SKIPIF1<0.(1)求SKIPIF1<0的值及SKIPIF1<0的定義域；(2)求SKIPIF1<0在SKIPIF1<0上最大值；(3)若SKIPIF1<0，比較SKIPIF1<0與SKIPIF1<0的大小.21.2022年卡塔爾世界杯剛結(jié)束不久，留下深刻印象的除了精彩的足球賽事，還有靈巧可愛、活力四射的吉祥物，中文名叫拉伊卜，在全球范圍內(nèi)收獲了大量的粉絲，開發(fā)商設(shè)計(jì)了不同類型含有拉伊卜元素的擺件、水杯、鑰匙鏈、體恤衫等.某調(diào)查小組通過對(duì)該吉祥物某擺件官網(wǎng)銷售情況調(diào)查發(fā)現(xiàn)：該擺件在過去的一個(gè)月內(nèi)(以30天記)每件的銷售價(jià)格SKIPIF1<0(單位：百元)與時(shí)間SKIPIF1<0(單位：天)的函數(shù)關(guān)系式近似滿足SKIPIF1<0(SKIPIF1<0為正常數(shù))，日銷售量SKIPIF1<0(件)與時(shí)間SKIPIF1<0的部分?jǐn)?shù)據(jù)如下表所示：SKIPIF1<0(天)510152530SKIPIF1<0(件)115120125115110已知第10天的日銷售收入為132百元.(1)求SKIPIF1<0的值；(2)給出以下四種函數(shù)模型：①SKIPIF1<0，②SKIPIF1<0，③SKIPIF1<0，④SKIPIF1<0.請(qǐng)根據(jù)上表中的數(shù)據(jù)，選擇你認(rèn)為最合適的一種函數(shù)來(lái)描述日銷售量SKIPIF1<0(單位：件)與時(shí)間SKIPIF1<0(天)的變化關(guān)系，并求出該函數(shù)解析式；(3)求該吉祥物擺件的日銷售收入SKIPIF1<0