江蘇省蘇州市2022-2023學(xué)年高一上學(xué)期期中數(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()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.命題“存在一個(gè)素?cái)?shù)，它的平方是偶數(shù)”的否定是()A.任意一個(gè)素?cái)?shù)，它的平方是偶數(shù) B.任意一個(gè)素?cái)?shù)，它的平方不是偶數(shù)C.存在一個(gè)素?cái)?shù)，它的平方是素?cái)?shù) D.存在一個(gè)素?cái)?shù)，它的平方不是偶數(shù)3.若集合A的子集個(gè)數(shù)有4個(gè)，則集合A中的元素個(gè)數(shù)是()A.2 B.4 C.8 D.164.已知SKIPIF1<0是定義在SKIPIF1<0上的增函數(shù)，則()A.函數(shù)SKIPIF1<0為奇函數(shù)，且在SKIPIF1<0上單調(diào)遞增B.函數(shù)SKIPIF1<0為偶函數(shù)，且在SKIPIF1<0上單調(diào)遞減C.函數(shù)SKIPIF1<0為奇函數(shù)，且在SKIPIF1<0上單調(diào)遞增D.函數(shù)SKIPIF1<0為偶函數(shù)，且在SKIPIF1<0上單調(diào)遞減5.已知冪函數(shù)SKIPIF1<0為偶函數(shù)，則關(guān)于函數(shù)SKIPIF1<0的下列四個(gè)結(jié)論中正確的是()A.SKIPIF1<0的圖象關(guān)于原點(diǎn)對(duì)稱 B.SKIPIF1<0的值域?yàn)镾KIPIF1<0C.SKIPIF1<0在SKIPIF1<0上單調(diào)遞減 D.SKIPIF1<06.若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值是SKIPIF1<0，最小值是SKIPIF1<0，則SKIPIF1<0()A.與SKIPIF1<0有關(guān)，且與SKIPIF1<0有關(guān) B.與SKIPIF1<0有關(guān)，但與SKIPIF1<0無(wú)關(guān)C.與SKIPIF1<0無(wú)關(guān)，且與SKIPIF1<0無(wú)關(guān) D.與SKIPIF1<0無(wú)關(guān)，但與SKIPIF1<0有關(guān)7.已知函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0成中心對(duì)稱圖形的充要條件是函數(shù)SKIPIF1<0為奇函數(shù).利用該結(jié)論，則函數(shù)SKIPIF1<0圖象的對(duì)稱中心是()ASKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.若將有限集合SKIPIF1<0的元素個(gè)數(shù)記為SKIPIF1<0，對(duì)于集合SKIPIF1<0，SKIPIF1<0，下列說(shuō)法正確的是()A.若SKIPIF1<0，則SKIPIF1<0B.若SKIPIF1<0，則SKIPIF1<0或SKIPIF1<0C.若SKIPIF1<0，則SKIPIF1<0D.存在實(shí)數(shù)SKIPIF1<0，使得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.SKIPIF1<0是SKIPIF1<0的必要不充分條件B.SKIPIF1<0或SKIPIF1<0為有理數(shù)是SKIPIF1<0為有理數(shù)的既不充分又不必要條件C.SKIPIF1<0是SKIPIF1<0的充分不必要條件D.SKIPIF1<0的充要條件是SKIPIF1<010.函數(shù)SKIPIF1<0滿足條件：①對(duì)于定義域內(nèi)任意不相等的實(shí)數(shù)SKIPIF1<0恒有SKIPIF1<0；②對(duì)于定義域內(nèi)的任意兩個(gè)不相等的實(shí)數(shù)SKIPIF1<0都有SKIPIF1<0成立，則稱其為SKIPIF1<0函數(shù).下列函數(shù)為SKIPIF1<0函數(shù)的是()A.SKIPIF1<0 B.SKIPIF1<0CSKIPIF1<0 D.SKIPIF1<011.函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的函數(shù)，則()A.若SKIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0B.若SKIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0C.若函數(shù)SKIPIF1<0單調(diào)遞增，則SKIPIF1<0的取值范圍是SKIPIF1<0D.若函數(shù)SKIPIF1<0單調(diào)遞增，則SKIPIF1<0的取值范圍是SKIPIF1<012.下列說(shuō)法正確的是()A.函數(shù)SKIPIF1<0，SKIPIF1<0與函數(shù)SKIPIF1<0，SKIPIF1<0是同一個(gè)函數(shù)B.直線SKIPIF1<0與函數(shù)SKIPIF1<0的圖象至多有一個(gè)公共點(diǎn)C.滿足“值域相同，對(duì)應(yīng)關(guān)系相同，但定義域不同”的函數(shù)組不存在D.滿足“定義域相同，值域相同，但對(duì)應(yīng)關(guān)系不同”的函數(shù)有無(wú)數(shù)個(gè)三、填空題：本題共4小題，每小題5分，共20分．13.若SKIPIF1<0，則SKIPIF1<0的取值范圍是____．14.若函數(shù)SKIPIF1<0為奇函數(shù)，則SKIPIF1<0____．15.已知正數(shù)SKIPIF1<0滿足SKIPIF1<0，若不等式SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的最大值是____．16.若函數(shù)SKIPIF1<0定義域?yàn)镾KIPIF1<0，對(duì)任意的SKIPIF1<0，都有SKIPIF1<0，且SKIPIF1<0，則不等式SKIPIF1<0的解集是____．四、解答題：本大題共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.已知函數(shù)SKIPIF1<0的定義域是SKIPIF1<0，集合SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0，SKIPIF1<0；(2)若命題“SKIPIF1<0，SKIPIF1<0”是真命題，求實(shí)數(shù)SKIPIF1<0的取值范圍．18已知函數(shù)SKIPIF1<0.(1)若關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的值；(2)若關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍.19.閱讀：序數(shù)屬性是自然數(shù)基本屬性之一，它反映了記數(shù)的順序性，回答了“第幾個(gè)”的問(wèn)題.在教材中有如下順序公理：①如果SKIPIF1<0，那么SKIPIF1<0；②如果SKIPIF1<0，那么SKIPIF1<0.(1)請(qǐng)運(yùn)用上述公理①②證明：“如果SKIPIF1<0，那么SKIPIF1<0.”(2)求證：SKIPIF1<020.某地區(qū)上年度電價(jià)為0.8元/(kW·h)，年用電量為akW·h，本年度計(jì)劃將電價(jià)下降到0.55元/(kW·h)至0.75元/(kW·h)之間，而用戶期望電價(jià)為0.4元/(kW·h).經(jīng)測(cè)算，下調(diào)電價(jià)后新增用電量和實(shí)際電價(jià)與用戶的期望電價(jià)的差成反比(比例系數(shù)為SKIPIF1<0).該地區(qū)的電力成本價(jià)為0.3元/(kW·h).記本年度電價(jià)下調(diào)后電力部門的收益為SKIPIF1<0(單位：元)，實(shí)際電價(jià)為SKIPIF1<0(單位：元/(kW·h)).(收益=實(shí)際電量SKIPIF1<0(實(shí)際電價(jià)SKIPIF1<0成本價(jià)))(1)當(dāng)SKIPIF1<0時(shí)，實(shí)際電價(jià)最低定為多少時(shí)，仍可保證電力部門的收益比上年至少增長(zhǎng)20%？(2)當(dāng)SKIPIF1<0時(shí)，求收益SKIPIF1<0的最小值.21.已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，用SKIPIF1<0表示SKIPIF1<0，SKIPIF1<0中的較大者，記為SKIPIF1<0，求SKIPIF1<0的最小值；(2)若不等式SKIPIF1<0對(duì)任意SKIPIF1<0，SKIPIF1<0(SKIPIF1<0)恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.22.已知二次函數(shù)SK