湖北省部分省級(jí)示范高中2022-2023學(xué)年高一上學(xué)期期中聯(lián)考數(shù)學(xué)試題（原卷版）

高一上學(xué)期期中數(shù)學(xué)試題一、單選題(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，只有一個(gè)選項(xiàng)是符合題目要求的)1.命題“SKIPIF1<0”的否定是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.冪函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則m值為()A.2 B.3 C.4 D.2或43.已知全集為SKIPIF1<0，集合SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0元素個(gè)數(shù)為A1 B.2 C.3 D.44.函數(shù)SKIPIF1<0的最大值是()A.SKIPIF1<0 B.1 C.5 D.SKIPIF1<05.不等式SKIPIF1<0的一個(gè)必要不充分條件是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.函數(shù)SKIPIF1<0在SKIPIF1<0上是增函數(shù)，則SKIPIF1<0的取值范圍是．A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.若不等式SKIPIF1<0的解集為SKIPIF1<0，那么不等式SKIPIF1<0的解集為()A.SKIPIF1<0 B.SKIPIF1<0或SKIPIF1<0C.SKIPIF1<0或SKIPIF1<0 D.SKIPIF1<08.已知函數(shù)SKIPIF1<0，若存在SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為SKIPIF1<0SKIPIF1<0A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二、多選題(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)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.圖中陰影部分用集合符號(hào)可以表示為()A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<010.有以下判斷，其中是正確判斷的有()A.SKIPIF1<0與SKIPIF1<0表示同一函數(shù)；B.函數(shù)SKIPIF1<0的圖象與直線SKIPIF1<0的交點(diǎn)最多有1個(gè)C.函數(shù)SKIPIF1<0的最小值為2D若SKIPIF1<0，則SKIPIF1<011.《幾何原本》中的幾何代數(shù)法(用幾何方法研究代數(shù)問題)成了后世西方數(shù)學(xué)家處理問題的重要依據(jù)根據(jù)這一方法，很多代數(shù)公理、定理都能夠通過圖形實(shí)現(xiàn)證明，并稱之為“無字證明”如圖所示，AB是半圓O的直徑，點(diǎn)C是AB上一點(diǎn)(不同于A，B，SKIPIF1<0)，點(diǎn)D在半圓O上，且SKIPIF1<0，SKIPIF1<0于點(diǎn)SKIPIF1<0設(shè)SKIPIF1<0，SKIPIF1<0，則該圖形可以完成的“無字證明”為()ASKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<012.函數(shù)SKIPIF1<0圖像關(guān)于坐標(biāo)原點(diǎn)成中心對(duì)稱圖形的充要條件是函數(shù)SKIPIF1<0為奇函數(shù)，有同學(xué)據(jù)此推出以下結(jié)論，其中正確的是()A.函數(shù)SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0成中心對(duì)稱的圖形的充要條件是SKIPIF1<0為奇函數(shù)B.函數(shù)SKIPIF1<0的圖像的對(duì)稱中心為SKIPIF1<0C.函數(shù)SKIPIF1<0的圖像關(guān)于SKIPIF1<0成軸對(duì)稱的充要條件是函數(shù)SKIPIF1<0是偶函數(shù)D.函數(shù)SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對(duì)稱三、填空題(本題共4小題，每小題5分，共20分)13.已知函數(shù)SKIPIF1<0,SKIPIF1<0,則SKIPIF1<0的值為______.14.已知集合A＝{x|x＜－1或x≥1}，B＝{x|2a＜x≤a＋1，a＜1}，B?A，則實(shí)數(shù)a的取值范圍為________．15.若對(duì)任意SKIPIF1<0，SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是______.16.設(shè)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，f(x)的最小值是_____；(2)若f(0)是f(x)的最小值，則a的取值范圍是_____．四、解答題(本大題共6題，共70分.解答應(yīng)寫出文字說明，證明過程或演算步驟)17.已知集合SKIPIF1<0(1)當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0；(2)若SKIPIF1<0，求a的取值范圍18.已知點(diǎn)SKIPIF1<0在冪函數(shù)SKIPIF1<0的圖像上.(1)求SKIPIF1<0的解析式；(2)若函數(shù)SKIPIF1<0，SKIPIF1<0是否存在實(shí)數(shù)a，使得SKIPIF1<0最小值為5？若存在，求出a的值；若不存在，說明理由19.為響應(yīng)國(guó)家提出的“大眾創(chuàng)業(yè)，萬眾創(chuàng)新”的號(hào)召，小李同學(xué)大學(xué)畢業(yè)后，決定利用所學(xué)專業(yè)進(jìn)行自主創(chuàng)業(yè)．經(jīng)過調(diào)查，生產(chǎn)某小型電子產(chǎn)品需投入年固定成本5萬元，每年生產(chǎn)x萬件，需另投入流動(dòng)成本C(x)萬元，且C(x)＝SKIPIF1<0每件產(chǎn)品售價(jià)為10元，經(jīng)分析，生產(chǎn)的產(chǎn)品當(dāng)年能全部售完．(1)寫出年利潤(rùn)P(x)(萬元)關(guān)于年產(chǎn)量x(萬件)的函數(shù)解析式(年利潤(rùn)＝年銷售收入－固定成本－流動(dòng)成本)．(2)年產(chǎn)量為多少萬件時(shí)，小李在這一產(chǎn)品的生產(chǎn)中所獲利潤(rùn)最大？最大利潤(rùn)是多少？20.已知a，b均為正數(shù)，且滿足SKIPIF1<0．(1)求SKIPIF1<0最小值及取到最小值時(shí)a與b的值；(2)求SKIPIF1<0的最小值及取到最小值時(shí)a與b的值．21.設(shè)函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0，且SKIPIF1<0時(shí)，解關(guān)于x的不等式SKIPIF1<0；(2)當(dāng)SKIPIF1<0，若“SKIPIF1<0”是“SKIPIF1<0”成立的充分條件，求實(shí)數(shù)a的取值范圍.2