山東省濟(jì)寧市2022-2023學(xué)年高二上學(xué)期期末數(shù)學(xué)試題（原卷版）

2022-2023學(xué)年度第一學(xué)期質(zhì)量檢測(cè)高二數(shù)學(xué)試題本試卷共4頁(yè).滿分150分，考試時(shí)間120分鐘.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若直線SKIPIF1<0與直線SKIPIF1<0平行，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.已知圓SKIPIF1<0：SKIPIF1<0，圓SKIPIF1<0：SKIPIF1<0，則兩圓的位置關(guān)系為()A.內(nèi)切 B.相交 C.外切 D.外離3.假設(shè)SKIPIF1<0，且SKIPIF1<0與SKIPIF1<0相互獨(dú)立，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.已知雙曲線SKIPIF1<0，拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，拋物線SKIPIF1<0的準(zhǔn)線與雙曲線SKIPIF1<0的兩條漸近線分別交于點(diǎn)SKIPIF1<0，若SKIPIF1<0為正三角形，則雙曲線SKIPIF1<0的漸近線方程為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<05.已知數(shù)列SKIPIF1<0為等比數(shù)列，且SKIPIF1<0是SKIPIF1<0與SKIPIF1<0的等差中項(xiàng)，若SKIPIF1<0，則該數(shù)列的前5項(xiàng)和為()A.2 B.10 C.31 D.626.已知平面SKIPIF1<0的一個(gè)法向量為SKIPIF1<0，直線SKIPIF1<0的一個(gè)方向向量為SKIPIF1<0，則直線SKIPIF1<0與平面SKIPIF1<0所成角的正弦值為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.已知拋物線SKIPIF1<0，過(guò)SKIPIF1<0的焦點(diǎn)且斜率為2的直線SKIPIF1<0交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，以SKIPIF1<0為直徑的圓與拋物線SKIPIF1<0的準(zhǔn)線相切于點(diǎn)SKIPIF1<0，若點(diǎn)SKIPIF1<0的縱坐標(biāo)為4，則拋物線SKIPIF1<0的標(biāo)準(zhǔn)方程為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<08.已知數(shù)列SKIPIF1<0為等差數(shù)列且SKIPIF1<0，數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，則SKIPIF1<0()ASKIPIF1<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.下列說(shuō)法中正確的是()A.直線SKIPIF1<0在SKIPIF1<0軸上的截距是SKIPIF1<0B.直線SKIPIF1<0的傾斜角是SKIPIF1<0C.直線SKIPIF1<0恒過(guò)定點(diǎn)SKIPIF1<0D.過(guò)點(diǎn)SKIPIF1<0且在SKIPIF1<0.軸?SKIPIF1<0軸上的截距相等的直線方程為SKIPIF1<010.拋擲兩枚質(zhì)地均勻的正四面體骰子，每個(gè)骰子四個(gè)面的點(diǎn)數(shù)分別為SKIPIF1<0，分別觀察底面上的數(shù)字，記事件SKIPIF1<0“第一枚骰子底面數(shù)字為奇數(shù)”，事件SKIPIF1<0“第二枚骰子底面數(shù)字為奇數(shù)”，事件SKIPIF1<0“兩枚骰子底面數(shù)字之和為偶數(shù)”，事件SKIPIF1<0“兩枚骰子底面數(shù)字之和為奇數(shù)”，下列判斷中正確的是()A.事件SKIPIF1<0與事件SKIPIF1<0互斥B.事件SKIPIF1<0與事件SKIPIF1<0互為對(duì)立事件C.事件SKIPIF1<0與事件SKIPIF1<0相互獨(dú)立D.SKIPIF1<011.已知等比數(shù)列SKIPIF1<0前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)積為SKIPIF1<0，則下列結(jié)論中正確的是()A.數(shù)列SKIPIF1<0是遞增數(shù)列 B.SKIPIF1<0C.SKIPIF1<0的最大值為SKIPIF1<0 D.SKIPIF1<0的最大值為SKIPIF1<012.已知SKIPIF1<0為雙曲線SKIPIF1<0的右焦點(diǎn)，直線SKIPIF1<0與該雙曲線相交于SKIPIF1<0兩點(diǎn)(其中SKIPIF1<0在第一象限)，連接SKIPIF1<0，下列說(shuō)法中正確的是()A.SKIPIF1<0的取值范圍是SKIPIF1<0B.若SKIPIF1<0，則SKIPIF1<0C.若SKIPIF1<0，則點(diǎn)SKIPIF1<0的縱坐標(biāo)為SKIPIF1<0D.若雙曲線的右支上存在點(diǎn)SKIPIF1<0，滿足SKIPIF1<0三點(diǎn)共線，則SKIPIF1<0的取值范圍是SKIPIF1<0三?填空題：本題共4小題，每小題5分，共20分.13.已知等差數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0_______.14.如圖所示，在空間四邊形SKIPIF1<0中，SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0上，且SKIPIF1<0為SKIPIF1<0中點(diǎn)，若SKIPIF1<0.則SKIPIF1<0__________.15.如圖所示?點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0頂點(diǎn)，SKIPIF1<0為SKIPIF1<0的右焦點(diǎn)，若SKIPIF1<0，則橢圓SKIPIF1<0的離心率為__________.16.已知圓心在SKIPIF1<0軸上移動(dòng)的圓經(jīng)過(guò)點(diǎn)SKIPIF1<0，且與SKIPIF1<0軸，SKIPIF1<0軸分別相交于SKIPIF1<0兩個(gè)動(dòng)點(diǎn)，則點(diǎn)SKIPIF1<0的軌跡方程為__________.四?解答題：本題共6小題，共70分.解答應(yīng)寫出必要的文字說(shuō)明?證明過(guò)程或演算步驟.17.在空間直角坐標(biāo)系中，已知向量SKIPIF1<0，其中SKIPIF1<0分別是平面SKIPIF1<0與平面SKIPIF1<0的法向量.(1)若SKIPIF1<0，求SKIPIF1<0.的值；(2)若SKIPIF1<0且SKIPIF1<0，求SKIPIF1<0的值.18.已知圓SKIPIF1<0的圓心在直線SKIPIF1<0上，且與直線SKIPIF1<0相切于點(diǎn)SKIPIF1<0.(1)求圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)求直線SKIPIF1<0被圓SKIPIF1<0截得的弦SKIPIF1<0的長(zhǎng).19.某班級(jí)從3名男生和2名女生中隨機(jī)抽取2名同學(xué)參加學(xué)校組織的校史知識(shí)競(jìng)賽.(1)求恰好抽到1名男生和1名女生的概率；(2)若抽到的2名同學(xué)恰好是男生甲和女生乙，已知男生甲答對(duì)每道題的概率均為SKIPIF1<0，女生乙答對(duì)每道題的概率均為SKIPIF1<0，甲和乙各自回答兩道題，且甲?乙答對(duì)與否互不影響，各題的結(jié)果也互不影響.求甲答對(duì)2道題且乙只答對(duì)1道題的概率.20.已知數(shù)列SKIPIF1<0滿足：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<0.21.如圖，在直三棱柱SKIPIF1<0中，SKIPIF1<0，點(diǎn)SKIPIF1<0滿足SKIPIF1<0.(1)當(dāng)SKI