遼寧省六校2022-2023學(xué)年高二上學(xué)期12月月考數(shù)學(xué)試題（原卷版）

2022—2023學(xué)年度(上)六校高二月考數(shù)學(xué)試題考試時(shí)間：120分鐘滿分150分一、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，SKIPIF1<0，則SKIPIF1<0()ASKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.若直線l的傾斜角SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則其斜率k滿足()．A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0，或SKIPIF1<0 D.SKIPIF1<0，或SKIPIF1<03.若向量SKIPIF1<0(x，4，5)，SKIPIF1<0(1，﹣2，2)，且SKIPIF1<0與SKIPIF1<0的夾角的余弦值為SKIPIF1<0，則x＝()A.3 B.﹣3 C.﹣11 D.3或﹣114.若直線SKIPIF1<0被圓SKIPIF1<0所截得的弦長為SKIPIF1<0,則實(shí)數(shù)SKIPIF1<0的值為()ASKIPIF1<0或SKIPIF1<0 B.SKIPIF1<0或SKIPIF1<0 C.SKIPIF1<0或SKIPIF1<0 D.SKIPIF1<0或SKIPIF1<05.SKIPIF1<0的展開式中常數(shù)項(xiàng)為A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.1056.已知直線SKIPIF1<0與雙曲線SKIPIF1<0交于A，B兩點(diǎn)，點(diǎn)SKIPIF1<0是弦AB中點(diǎn)，則雙曲線C的漸近線方程是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.某校高一開設(shè)4門選修課，有4名同學(xué)選修，每人只選1門，恰有2門課程沒有同學(xué)選修，則不同的選課方案有()A.96種 B.84種 C.78種 D.16種8.已知橢圓C：SKIPIF1<0SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過點(diǎn)SKIPIF1<0作傾斜角為SKIPIF1<0的直線與橢圓相交于A，B兩點(diǎn)，若SKIPIF1<0，則橢圓C的離心率e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，計(jì)20分．在每小題給出的選項(xiàng)中，有多個(gè)選項(xiàng)是符合題目要求的，全部選對得5分，有選錯(cuò)的得零分，部分選對得2分.9.已知直線l在x軸，y軸上的截距分別為1，SKIPIF1<0，O是坐標(biāo)原點(diǎn)，則下列結(jié)論中正確的是()A.直線l的方程為SKIPIF1<0B.過點(diǎn)O且與直線l平行的直線方程為SKIPIF1<0C.若點(diǎn)SKIPIF1<0到直線l的距離為SKIPIF1<0，則SKIPIF1<0D.點(diǎn)O關(guān)于直線l對稱的點(diǎn)為SKIPIF1<010.已知正方體SKIPIF1<0的棱長為SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0分別是SKIPIF1<0，SKIPIF1<0的中點(diǎn)，SKIPIF1<0在正方體內(nèi)部且滿足SKIPIF1<0，則下列說法正確的是()A.直線SKIPIF1<0平面SKIPIF1<0 B.直線SKIPIF1<0與平面SKIPIF1<0所成的角為SKIPIF1<0C.直線SKIPIF1<0與平面SKIPIF1<0的距離為SKIPIF1<0 D.點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<011.過雙曲線SKIPIF1<0的右焦點(diǎn)SKIPIF1<0作直線SKIPIF1<0與雙曲線交于A，B兩點(diǎn)，使得SKIPIF1<0，若這樣的直線有且只有兩條，則實(shí)數(shù)SKIPIF1<0的取值范圍可以是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<012.直線l與拋物線SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，則()A.直線l斜率為定值 B.直線l經(jīng)過定點(diǎn)C.SKIPIF1<0面積最小值為4 D.SKIPIF1<0三、填空題：本題共4小題，每小題5分，計(jì)20分.13.若SKIPIF1<0，則SKIPIF1<0的值為___________14.設(shè)函數(shù)SKIPIF1<0若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則實(shí)數(shù)a的取值范圍是______．15.已知三棱錐P－ABC，PA⊥面ABC，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．則三棱錐P－ABC外接球表面積為______．16.過x軸上點(diǎn)SKIPIF1<0的直線與拋物線SKIPIF1<0交于A，B兩點(diǎn)，若SKIPIF1<0為定值，則實(shí)數(shù)a的值為______．四、解答題：本題共6小題，計(jì)70分.解答應(yīng)寫出文字說明、證明過程或演算步驟.17.在SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0邊的中點(diǎn)M在SKIPIF1<0軸上，BC邊的中點(diǎn)N在SKIPIF1<0軸上.(1)求AB邊上的高CH所在直線方程；(2)設(shè)過點(diǎn)C的直線為SKIPIF1<0，且點(diǎn)A與點(diǎn)B到直線SKIPIF1<0距離相等，求SKIPIF1<0的方程.18.設(shè)SKIPIF1<0內(nèi)角SKIPIF1<0所對邊分別為SKIPIF1<0，已知SKIPIF1<0，SKIPIF1<0．(1)若SKIPIF1<0，求SKIPIF1<0周長；(2)若SKIPIF1<0邊的中點(diǎn)為SKIPIF1<0，且SKIPIF1<0，求SKIPIF1<0的面積．19.如圖，在四棱錐S﹣ABCD中，ABCD為直角梯形，SKIPIF1<0，BC⊥CD，平面SCD⊥平面ABCD．△SCD是以CD為斜邊的等腰直角三角形，BC＝2AD＝2CD＝4，E為BS上一點(diǎn)，且BE＝2ES．(1)證明：直線SKIPIF1<0平面ACE；(2)求直線AS與平面ACE所成角的余弦值．20.在平面直角坐標(biāo)系SKIPIF1<0中,動(dòng)點(diǎn)SKIPIF1<0與兩點(diǎn)SKIPIF1<0連線斜率分別為SKIPIF1<0,且滿足SKIPIF1<0,記動(dòng)點(diǎn)SKIPIF1<0的軌跡為曲線SKIPIF1<0.(1)求曲線SKIPIF1<0的標(biāo)準(zhǔn)方程;(2)已知點(diǎn)SKIPIF1<0為曲線SKIPIF1<0在第一象限內(nèi)的點(diǎn),且SKIPIF1<0,若SKIPIF1<0交SKIPIF1<0軸于點(diǎn)SKIPIF1<0交SKIPIF1<0軸于點(diǎn)SKIPIF1<0,試問:四邊形SKIPIF1<0的面積是否為定值?若是,求出該定值;若不是,請說明理由.21.如圖，在四邊形SKIPIF1<0中，SKIPIF1<0于交SKIPIF1<0點(diǎn)SKIPIF1<0SKIPIF1<0，SKIPIF1<0.沿SKIPIF1<0將SKIPIF1<0翻折到SKIPIF1<0的位置，使得二面角SKIPIF1<0的大小為SKIPIF1<0.(1)證明：平面SKIPIF1<0平面SKIPIF1<0；(2)在線段SKIPIF1<0上(不含端點(diǎn))是否存在點(diǎn)SKIPIF1<0，使得二面角SKIPIF1<0的余弦值為SKIPIF1<0，若存在，確定點(diǎn)SKIPIF1<0的位置，若不存在，請說明理由.22.已知雙曲線SKIPIF1<0右焦點(diǎn)為SKIPIF1<0，漸近線方程為SKIPIF1<0．(1)求雙曲線SKIPIF1<0