山東省濟(jì)南市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.若全集SKIPIF1<0,則SKIPIF1<0A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.函數(shù)SKIPIF1<0定義域?yàn)?)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.若函數(shù)SKIPIF1<0是定義在R上的奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.5 D.74.已知SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則下列關(guān)系式正確的為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.已知函數(shù)SKIPIF1<0為冪函數(shù)，若函數(shù)SKIPIF1<0，則SKIPIF1<0的零點(diǎn)所在區(qū)間為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.已知函數(shù)SKIPIF1<0圖像如圖所示，則SKIPIF1<0的解析式可能是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<08.設(shè)函數(shù)SKIPIF1<0是定義在R上奇函數(shù)，滿(mǎn)足SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則實(shí)數(shù)t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.已知函數(shù)SKIPIF1<0，下列說(shuō)法正確的是()A.SKIPIF1<0為偶函數(shù) B.SKIPIF1<0C.SKIPIF1<0的最大值為1 D.SKIPIF1<0的最小正周期為SKIPIF1<010.若SKIPIF1<0，則下列不等式成立的是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<011.若函數(shù)SKIPIF1<0有且僅有3個(gè)零點(diǎn)，則實(shí)數(shù)m的值可能是()A.SKIPIF1<0 B.SKIPIF1<0 C.10 D.1112.已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，且函數(shù)圖象連續(xù)不間斷，假如存在正實(shí)數(shù)SKIPIF1<0，使得對(duì)于任意的SKIPIF1<0，SKIPIF1<0恒成立，稱(chēng)函數(shù)SKIPIF1<0滿(mǎn)足性質(zhì)SKIPIF1<0.則下列說(shuō)法正確的是()A.若SKIPIF1<0滿(mǎn)足性質(zhì)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0B.若SKIPIF1<0，則存在唯一的正數(shù)SKIPIF1<0，使得函數(shù)SKIPIF1<0滿(mǎn)足性質(zhì)SKIPIF1<0C.若SKIPIF1<0，則存在唯一的正數(shù)SKIPIF1<0，使得函數(shù)SKIPIF1<0滿(mǎn)足性質(zhì)SKIPIF1<0D.若函數(shù)SKIPIF1<0滿(mǎn)足性質(zhì)SKIPIF1<0，則函數(shù)SKIPIF1<0必存零點(diǎn)三、填空題：本題共4小題，每小題5分，共20分.13.在平面直角坐標(biāo)系中，角SKIPIF1<0的頂點(diǎn)與坐標(biāo)原點(diǎn)重合，始邊與x軸的非負(fù)半軸重合，終邊上有一點(diǎn)SKIPIF1<0，則SKIPIF1<0的值為_(kāi)_____.14.已知一個(gè)扇形的周長(zhǎng)為10，弧長(zhǎng)為6，那么該扇形的面積是______.15.已知函數(shù)SKIPIF1<0，則SKIPIF1<0的值為_(kāi)_____.16.已知函數(shù)SKIPIF1<0定義域?yàn)镾KIPIF1<0，SKIPIF1<0，對(duì)任意的SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，有SKIPIF1<0(e是自然對(duì)數(shù)的底).若SKIPIF1<0，則實(shí)數(shù)a的取值范圍是______.四、解答題：本題共6小題，共70分.解答應(yīng)寫(xiě)出文字說(shuō)明、證明過(guò)程或演算步驟.17.已知集合SKIPIF1<0或SKIPIF1<0，SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0；(2)若“SKIPIF1<0”是“SKIPIF1<0”成立的必要不充分條件，求a的取值范圍.18.設(shè)函數(shù)SKIPIF1<0，且方程SKIPIF1<0有兩個(gè)實(shí)數(shù)根為SKIPIF1<0，SKIPIF1<0.(1)求SKIPIF1<0的解析式；(2)若SKIPIF1<0，求SKIPIF1<0的最小值及取得最小值時(shí)x的值.19.已知二次函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，解不等式SKIPIF1<0；(2)若SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，求實(shí)數(shù)a的取值范圍.20.如圖，在平面直角坐標(biāo)系中，銳角SKIPIF1<0的始邊與x軸的非負(fù)半軸重合，終邊與單位圓(圓心在原點(diǎn)，半徑為1)交于點(diǎn)P.過(guò)點(diǎn)P作圓O的切線(xiàn)，分別交x軸、y軸于點(diǎn)SKIPIF1<0與SKIPIF1<0.(1)若SKIPIF1<0的面積為2，求SKIPIF1<0的值；(2)求SKIPIF1<0的最小值.21.La'eeb是2022年卡塔爾世界杯足球賽吉祥物，該吉祥物具有非常鮮明民族特征，阿拉伯語(yǔ)意為“高超的球員”，某中國(guó)企業(yè)可以生產(chǎn)世界杯吉祥物L(fēng)a'eeb，根據(jù)市場(chǎng)調(diào)查與預(yù)測(cè)，投資成本x(千萬(wàn))與利潤(rùn)y(千萬(wàn))的關(guān)系如下表x(千萬(wàn))…2…4…12…y(千萬(wàn))…0.4…0.8…12.8…當(dāng)投資成本x不高于12(千萬(wàn))時(shí)，利潤(rùn)y(千萬(wàn))與投資成本x(千萬(wàn))的關(guān)系有兩個(gè)函數(shù)模型SKIPIF1<0與SKIPIF1<0可供選擇.(1)當(dāng)投資成本x不高于12(千萬(wàn))時(shí)，選出你認(rèn)為最符合實(shí)際的函數(shù)模型，并求出相應(yīng)的函數(shù)解析式；(2)當(dāng)投資成本x高于12(千萬(wàn))時(shí)，利潤(rùn)y(千萬(wàn))與投資成本工(千萬(wàn))滿(mǎn)足關(guān)系SKIPIF1<0，結(jié)合第(1)問(wèn)的結(jié)果，要想獲得不少于一個(gè)億的利潤(rùn)，投資成本x(千萬(wàn))應(yīng)該控制在什么范圍.(結(jié)果保留到小數(shù)點(diǎn)后一位)(參考數(shù)據(jù)：SKIPIF1<0)22.已知函數(shù)SKIPIF1<0是奇函數(shù).(e是自然對(duì)數(shù)的底)(1)求實(shí)數(shù)k的值；(2)若SKIPI