江蘇省蘇州市2022-2023學(xué)年高一上學(xué)期期末學(xué)業(yè)質(zhì)量陽(yáng)光指標(biāo)調(diào)研數(shù)學(xué)試題（原卷版）

高一上學(xué)期期末數(shù)學(xué)試題一、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.已知角SKIPIF1<0，那么SKIPIF1<0的終邊在()A.第一象限 B.第二象限 C.第三象限 D.第四象限2.命題“SKIPIF1<0”的否定為()A.“SKIPIF1<0” B.“SKIPIF1<0”C“SKIPIF1<0” D.“SKIPIF1<0”3.已知一個(gè)面積為SKIPIF1<0的扇形所對(duì)的弧長(zhǎng)為SKIPIF1<0，則該扇形圓心角的弧度數(shù)為()A.SKIPIF1<0 B.SKIPIF1<0 C.2 D.SKIPIF1<04.已知SKIPIF1<0，SKIPIF1<0，則“SKIPIF1<0”是“SKIPIF1<0”成立的()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5.下列四個(gè)函數(shù)中，以SKIPIF1<0為最小正周期，且在區(qū)間SKIPIF1<0上單調(diào)遞減的是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.已知SKIPIF1<0的定義域?yàn)锳，集合SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)a的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.三個(gè)數(shù)SKIPIF1<0，SKIPIF1<0之間的大小關(guān)系為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<08.已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有兩個(gè)零點(diǎn)，則實(shí)數(shù)a取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二、選擇題：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.設(shè)集合SKIPIF1<0，集合SKIPIF1<0，則下列對(duì)應(yīng)關(guān)系中是從集合A到集合B的一個(gè)函數(shù)的有()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<010.已知函數(shù)SKIPIF1<0，則下列結(jié)論中正確的有()A.SKIPIF1<0 B.SKIPIF1<0的定義域?yàn)镾KIPIF1<0C.SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增 D.若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<011.若a，b均為正數(shù)，且滿足SKIPIF1<0，則()A.SKIPIF1<0的最大值為2 B.SKIPIF1<0的最小值為4C.SKIPIF1<0的最小值是6 D.SKIPIF1<0的最小值為SKIPIF1<012.已知指數(shù)函數(shù)SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)與對(duì)數(shù)函數(shù)SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)互為反函數(shù)，它們的定義域和值域正好互換．若方程SKIPIF1<0與SKIPIF1<0的解分別為SKIPIF1<0，SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0三、填空題：本題共4小題，每小題5分，共20分．13.求值：SKIPIF1<0__________．14.已知冪函數(shù)SKIPIF1<0滿足：①是偶函數(shù)；②在區(qū)間SKIPIF1<0上單調(diào)遞減，請(qǐng)寫出一個(gè)這樣的函數(shù)SKIPIF1<0__________．15.已知SKIPIF1<0，則SKIPIF1<0__________．16.我們知道，設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镮，如果對(duì)任意SKIPIF1<0，都有SKIPIF1<0，且SKIPIF1<0，那么函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0成中心對(duì)稱圖形．若函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0成中心對(duì)稱圖形，則實(shí)數(shù)c的值為__________；若SKIPIF1<0，則實(shí)數(shù)t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.設(shè)集合SKIPIF1<0．(1)若SKIPIF1<0，SKIPIF1<0；(2)若SKIPIF1<0，SKIPIF1<0．18.已知SKIPIF1<0．(1)若角SKIPIF1<0的終邊過點(diǎn)SKIPIF1<0，求SKIPIF1<0；(2)若SKIPIF1<0，分別求SKIPIF1<0和SKIPIF1<0的值．19.某公司為了提升銷售利潤(rùn)，準(zhǔn)備制定一個(gè)激勵(lì)銷售人員的獎(jiǎng)勵(lì)方案．公司規(guī)定獎(jiǎng)勵(lì)方案中的總獎(jiǎng)金額y(單位：萬元)是銷售利潤(rùn)x(單位：萬元)的函數(shù)，并且滿足如下條件：①圖象接近圖示；②銷售利潤(rùn)x為0萬元時(shí)，總獎(jiǎng)金y為0萬元；③銷售利潤(rùn)x為30萬元時(shí)，總獎(jiǎng)金y為3萬元．現(xiàn)有以下三個(gè)函數(shù)模型供公司選擇：A．SKIPIF1<0；B．SKIPIF1<0；C．SKIPIF1<0．(1)請(qǐng)你幫助該公司從中選擇一個(gè)最合適的函數(shù)模型，并說明理由；(2)根據(jù)你在(1)中選擇的函數(shù)模型，解決如下問題：①如果總獎(jiǎng)金不少于9萬元，則至少應(yīng)完成銷售利潤(rùn)多少萬元？②總獎(jiǎng)金能否超過銷售利潤(rùn)的五分之一？20.已知函數(shù)SKIPIF1<0圖象經(jīng)過點(diǎn)SKIPIF1<0．(1)求SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值和最小值；(2)記關(guān)于x的方程SKIPIF1<0在區(qū)間SKIPIF1<0上的解從小到大依次為SKIPIF1<0，試確定正整數(shù)n的值，并求SKIPIF1<0的值．21.已知SKIPIF1<0為奇函數(shù)．(1)判斷函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)性，并證明你的判斷；(2)若關(guān)于x的方程SKIPIF1<0有8個(gè)不同的解，求實(shí)數(shù)m的取值范圍．22.已知SKIPIF1<0，SKIPIF1<0分別為定義在SKIPIF1<0上的奇函數(shù)和偶函數(shù)，且SKIPIF1<0