江蘇省蘇州市常熟中學(xué)2022-2023學(xué)年高二上學(xué)期一月學(xué)業(yè)質(zhì)量校內(nèi)調(diào)研數(shù)學(xué)試題（原卷版）

2022~2023學(xué)年度第一學(xué)期高二年級(jí)一月份學(xué)業(yè)質(zhì)量校內(nèi)調(diào)研高二(1)~(14)班數(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.已知各項(xiàng)均為正數(shù)的等比數(shù)列{SKIPIF1<0}，SKIPIF1<0=5，SKIPIF1<0=10，則SKIPIF1<0SKIPIF1<0=A.SKIPIF1<0 B.7 C.6 D.SKIPIF1<02.拋物線SKIPIF1<0上一點(diǎn)SKIPIF1<0到其對(duì)稱(chēng)軸的距離為()A.4 B.2 C.SKIPIF1<0 D.13.直線x+y﹣1＝0被圓(x+1)2+y2＝3截得的弦長(zhǎng)等于()A.SKIPIF1<0 B.2 C.2SKIPIF1<0 D.44.圓C為過(guò)點(diǎn)SKIPIF1<0的圓中最小的圓，則圓C上的任意一點(diǎn)M到原點(diǎn)O距離的取值范圍為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.“天問(wèn)一號(hào)”推開(kāi)了我國(guó)行星探測(cè)的大門(mén)，通過(guò)一次發(fā)射，將實(shí)現(xiàn)火星環(huán)繞?著陸?巡視，是世界首創(chuàng)，也是我國(guó)真正意義上的首次深空探測(cè)．2021年2月10日，天問(wèn)一號(hào)探測(cè)器順利進(jìn)入火星的橢圓環(huán)火軌道(將火星近似看成一個(gè)球體，球心為橢圓的一個(gè)焦點(diǎn)).2月15日17時(shí)，天問(wèn)一號(hào)探測(cè)器成功實(shí)施捕獲軌道“遠(yuǎn)火點(diǎn)(橢圓軌跡上距離火星表面最遠(yuǎn)的一點(diǎn))平面機(jī)動(dòng)”，同時(shí)將近火點(diǎn)高度調(diào)整至約265公里．若此時(shí)遠(yuǎn)火點(diǎn)距離約為11945公里，火星半徑約為3395公里，則調(diào)整后“天問(wèn)一號(hào)”的運(yùn)行軌跡(環(huán)火軌道曲線)的離心率約為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.直三棱柱SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，若點(diǎn)SKIPIF1<0在線段SKIPIF1<0上，則直線SKIPIF1<0與平面SKIPIF1<0所成角的正弦值的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.已知SKIPIF1<0是雙曲線SKIPIF1<0的左，右焦點(diǎn)，點(diǎn)SKIPIF1<0在SKIPIF1<0上，SKIPIF1<0是線段SKIPIF1<0上點(diǎn)，若SKIPIF1<0，則當(dāng)SKIPIF1<0面積最大時(shí)，雙曲線SKIPIF1<0的方程是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<08.已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且前SKIPIF1<0項(xiàng)和為SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的取值范圍為()A.SKIPIF1<0 B.SKIPIF1<0 C.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.在等差數(shù)列SKIPIF1<0中，已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是其前SKIPIF1<0項(xiàng)和，則()．A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<010.下列結(jié)論錯(cuò)誤的是()A.過(guò)點(diǎn)SKIPIF1<0，SKIPIF1<0的直線的傾斜角為30°B.若直線SKIPIF1<0與直線SKIPIF1<0垂直，則SKIPIF1<0C.直線SKIPIF1<0與直線SKIPIF1<0之間的距離是SKIPIF1<0D.已知SKIPIF1<0，SKIPIF1<0，點(diǎn)P在x軸上，則SKIPIF1<0的最小值是511.已知橢圓SKIPIF1<0的左，右焦點(diǎn)分別為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線SKIPIF1<0交橢圓于SKIPIF1<0和SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的最大值為5，則下列說(shuō)法中正確的是()A.橢圓的短軸長(zhǎng)為SKIPIF1<0B.當(dāng)SKIPIF1<0最大時(shí)，SKIPIF1<0C.橢圓的離心率為SKIPIF1<0D.SKIPIF1<0的最小值為312.如圖直角梯形SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．E為SKIPIF1<0的中點(diǎn)，以SKIPIF1<0為折痕把SKIPIF1<0折起，使點(diǎn)A到達(dá)點(diǎn)P的位置，且SKIPIF1<0，則()A.平面SKIPIF1<0平面SKIPIF1<0B.SKIPIF1<0C.二面角SKIPIF1<0的大小SKIPIF1<0D.SKIPIF1<0與平面SKIPIF1<0所成角的正切值為SKIPIF1<0三?填空題：本題共4小題，每小題5分，共20分.13.若SKIPIF1<0，則與向量SKIPIF1<0反方向的單位向量的坐標(biāo)為_(kāi)_________.14.已知拋物線SKIPIF1<0，過(guò)其焦點(diǎn)且斜率為1的直線交拋物線于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若線段SKIPIF1<0的中點(diǎn)的縱坐標(biāo)為2，則該拋物線的準(zhǔn)線方程為_(kāi)____________．15.已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的值為_(kāi)_________.16.已知直線SKIPIF1<0與橢圓SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0(SKIPIF1<0為坐標(biāo)原點(diǎn))，若橢圓的離心率SKIPIF1<0，則SKIPIF1<0的最大值為_(kāi)__________．四?解答題：本大題共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.已知圓C的方程為SKIPIF1<0.(1)直線l1過(guò)點(diǎn)P(3，1)，傾斜角為45°，且與圓C交于A，B兩點(diǎn)，求AB的長(zhǎng)；(2)求過(guò)點(diǎn)P(3，1)且與圓C相切直線l2的方程.18.已知數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且SKIPIF1<0.(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式；(2)求數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0.19.已知四棱錐SKIPIF1<0，底面ABCD為菱形，SKIPIF1<0，H為PC上的點(diǎn)，過(guò)AH的平面分別交PB，PD于點(diǎn)M，N，且SKIPIF1<0平面AMHN．(1)證明；SKIPIF1<0；(2)若H為PC的中點(diǎn)，SKIPIF1<0，PA與平面ABCD所成的角為60°，求AD與平面AMHN所成角的余弦值．20.已知橢圓SKIPIF1<0的下焦點(diǎn)為SKIPIF1<0、上焦點(diǎn)為SKIPIF1<0，其離心率SKIPIF1<0．過(guò)焦點(diǎn)SKIPIF1<0且與x軸不垂直的直線l交橢圓于A、B兩點(diǎn)．(1)求實(shí)數(shù)m的值；(2)求△ABO(O為原點(diǎn))面積的最大值．21.已知數(shù)列SKIPIF1<0滿足SKIPIF1<0(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式；(2)是否存在正實(shí)數(shù)a，使得不等式SKIPIF1<0對(duì)一切正整數(shù)n都成立？若存在，求出a的取值范圍；若不存在，請(qǐng)說(shuō)明理由.22.已知SKIPIF1<0，SKIPIF1<0分別是雙曲線SKIPIF1<0的左，右頂點(diǎn)，直線SKIPIF1<0(不與坐標(biāo)軸垂直)過(guò)點(diǎn)SKIPIF1<0，且與雙曲線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn).(1)若SKIPIF1<0，求直線SKIPIF1<0的方程；(2)若直線SKIPIF1<0與SKIPIF1<0相交于點(diǎn)SKIPIF1<0，求證：點(diǎn)SKIPIF1<0在定直線上.2023學(xué)年度第一學(xué)期高二年級(jí)一月份學(xué)業(yè)質(zhì)量校內(nèi)調(diào)研高二(15)班數(shù)學(xué)試題2023.01.11一?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.23.已知函數(shù)SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<024.已知等差數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的值為()A.－3 B.3 C.－12 D.1225.已知函數(shù)SKIPIF1<0，則“SKIPIF1<0”是“函數(shù)SKIPIF1<0在SKIPIF1<0處有極值SKIPIF1<0”的()A.充分不必要條件 B.必要不充分條件 C.充要條件 D.既不充分又不必要條件26.如圖，正方形數(shù)表中對(duì)角線一列數(shù)SKIPIF1<0構(gòu)成數(shù)列SKIPIF1<0，則SKIPIF1<0()SKIPIF1<0A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<027.設(shè)函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的可導(dǎo)函數(shù)，且SKIPIF1<0，則不等式SKIPIF1<0的解集為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<028.若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上既有極大值又有極小值，則SKIPIF1<0的取值范圍為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<029.已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若在SKIPIF1<0上，方程SKIPIF1<0有三個(gè)不同的實(shí)根，則實(shí)數(shù)k的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<030已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0 C.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.31.若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上不單調(diào)，則實(shí)數(shù)SKIPIF1<0的值可能是()A.2 B.3 C.SKIPIF1<0 D.432.已知SKIPIF1<0，則下列說(shuō)法正確的有()A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<033.已知數(shù)列SKIPIF1<0中，SKIPIF1<0成等差數(shù)列，且SKIPIF1<0.若SKIPIF1<0，則下列說(shuō)法正確是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<034.已知函數(shù)SKIPIF1<0，則下列說(shuō)法正確的是()A.當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0恰有兩個(gè)零點(diǎn)B.當(dāng)SKIPIF1<0時(shí)，不等式SKIPIF1<0對(duì)任意SKIPIF1<0恒成立C.若函數(shù)SKIPIF1<0有兩個(gè)零點(diǎn)SKIPIF1<0，則SKIPIF1<0D.當(dāng)SKIPIF1<0時(shí)，若不等式SKIPIF1<0對(duì)SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為SKIPIF1<0三?填空題：本題共4小題，每小題5分，共20分.35.已知函數(shù)SKIPIF1<0，則過(guò)(1,1)的切線方程為_(kāi)_________．36.已知函數(shù)SKIPIF1<0是SKIPIF1<0上的單調(diào)遞增函數(shù).當(dāng)實(shí)數(shù)SKIPIF1<0取最大值時(shí)，若存在點(diǎn)SKIPIF1<0，使得過(guò)點(diǎn)SKIPIF1<0的直線與曲線SKIPIF1<0圍成兩個(gè)封閉圖形，且這兩個(gè)封閉圖形的面積總相等，則點(diǎn)SKIPIF1<0的坐標(biāo)為_(kāi)_________.37.“牛頓迭代法”是牛頓在17世紀(jì)提出的一種近似求方程根的方法.如圖，設(shè)SKIPIF1<0是SKIPIF1<0的根，選取SKIPIF1<0作為SKIPIF1<0初始近似值，過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0的切線SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)橫坐標(biāo)為SKIPIF1<0，稱(chēng)SKIPIF1<0是SKIPIF1<0的一次近似值；過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0的切線，則該切線與SKIPIF1<0軸的交點(diǎn)的橫坐標(biāo)為SKIPIF1<0，稱(chēng)SKIPIF1<0是SKIPIF1<0的二次近似值；SKIPIF1<0重復(fù)以上過(guò)程，得到SKIPIF1<0的近似值序列SKIPIF1<0為“牛頓數(shù)列”，即SKIPIF1<0.已知函數(shù)SKIPIF1<0，數(shù)列SKIPIF1<0為“牛頓數(shù)列”，設(shè)SKIPIF1<0，且SKIPIF1<0.數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0__________.38.已知函數(shù)SKIPIF1<0存在三個(gè)零點(diǎn)SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，且滿足SKIPIF1<0，則SKIPIF1<0的值為_(kāi)_________.四?解答題：本大題共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.39.已知函數(shù)SKIPIF1<0的所有正數(shù)零點(diǎn)構(gòu)成遞增數(shù)列SKIPIF1<0.(1)求數(shù)列SKIPIF1<0通項(xiàng)公式；(2)設(shè)數(shù)列SKIPIF1<0滿足SKIPIF1<0，求數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0.40.甲、乙兩人進(jìn)行下象棋比賽(沒(méi)有平局)．采用“五局三勝”制．已知在每局比賽中，甲獲勝的概率為SKIPIF1<0，SKIPIF1<0．(1)設(shè)甲以3：1獲勝的概率為SKIPIF1<0，求SKIPIF1<0的最大值；(2)記(1)中，SKIPIF1<0取得最大值時(shí)SKIPIF1<0的值為SKIPIF1<0，以SKIPIF1<0作為SKIPIF1<0的值，用SKIPIF1<0表示甲、乙兩人比賽的局?jǐn)?shù)，求SKIPIF1<0的分布列和數(shù)學(xué)期望SKIPIF1<0．41.如圖，有一景區(qū)的平面圖是一半圓形，其中直徑SKIPIF1<0長(zhǎng)為SKIPIF1<