湖南省長沙市四校2022-2023學(xué)年高二上學(xué)期期中聯(lián)考數(shù)學(xué)試題(B卷)（原卷版）

長沙市四校聯(lián)考2022-2023學(xué)年度第一學(xué)期期中考試(B)高二數(shù)學(xué)一?單項選擇題：本題共8小題，每小題5分，共40分.在每小題給出的四個選項中，只有一項是符合題目要求的.1.若數(shù)列SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是等比數(shù)列，則SKIPIF1<0值是()A.12 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.已知方程SKIPIF1<0表示橢圓，則SKIPIF1<0的取值范圍為()A.SKIPIF1<0且SKIPIF1<0 B.SKIPIF1<0且SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<03.等差數(shù)列SKIPIF1<0的前SKIPIF1<0項和為SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.已知數(shù)列SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，其中SKIPIF1<0是等差數(shù)列，且SKIPIF1<0，則SKIPIF1<0()A2022 B.－2022 C.SKIPIF1<0 D.10115.橢圓SKIPIF1<0的左、右焦點分別為SKIPIF1<0、SKIPIF1<0，動點A在橢圓上，B為橢圓的上頂點，則SKIPIF1<0周長的最大值為()A.8 B.10 C.12 D.166.已知圓SKIPIF1<0，直線SKIPIF1<0，若SKIPIF1<0上存在點SKIPIF1<0，過SKIPIF1<0作圓SKIPIF1<0的兩條切線，切點分別為SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的取值范圍為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.已知SKIPIF1<0是棱長為8的正方體外接球的一條直徑，點M在正方體表面上運動，則SKIPIF1<0的最小值為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.08.設(shè)SKIPIF1<0是數(shù)列SKIPIF1<0的前SKIPIF1<0項和，SKIPIF1<0，若不等式SKIPIF1<0對任意SKIPIF1<0恒成立，則SKIPIF1<0的最小值為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二?多項選擇題：本題共4小題，每小題5分，共20分.在每小題給出的選項中，有多項符合題目要求.全部選對的得5分，部分選對的得2分，有選錯的得0分.9.若SKIPIF1<0是等差數(shù)列，則下列數(shù)列中仍為等差數(shù)列的是()A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0(SKIPIF1<0為常數(shù))D.SKIPIF1<010.已知橢圓SKIPIF1<0分別為它的左?右焦點，SKIPIF1<0為橢圓的左?右頂點，點SKIPIF1<0是橢圓上異于SKIPIF1<0的一個動點，則下列結(jié)論中正確的有()A.SKIPIF1<0的周長為15 B.若SKIPIF1<0，則SKIPIF1<0的面積為9C.SKIPIF1<0為定值 D.直線SKIPIF1<0與直線SKIPIF1<0斜率的乘積為定值11.已知直線SKIPIF1<0與圓SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點，則()A.SKIPIF1<0的面積為定值 B.SKIPIF1<0C.圓SKIPIF1<0上總存在3個點到直線SKIPIF1<0的距離為2 D.線段SKIPIF1<0中點的軌跡方程是SKIPIF1<012.古希臘畢達哥拉斯學(xué)派數(shù)學(xué)家用沙粒和小石子來研究數(shù)，他們根據(jù)沙?；蛐∈铀帕械男螤睿褦?shù)分成許多類，如圖中第一行圖形中黑色小點個數(shù)：1，3，6，10，…稱為三角形數(shù)，第二行圖形中黑色小點個數(shù)：1，4，9，16，…稱為正方形數(shù)，記三角形數(shù)構(gòu)成數(shù)列SKIPIF1<0，正方形數(shù)構(gòu)成數(shù)列SKIPIF1<0，則下列說法正確的是()A.SKIPIF1<0B.1225既是三角形數(shù)，又是正方形數(shù)C.SKIPIF1<0D.SKIPIF1<0，總存在SKIPIF1<0，使得SKIPIF1<0成立三?填空題：本題共4小題，每小題5分，滿分20分.13.設(shè)等差數(shù)列{an}的前n項之和為Sn滿足S10﹣S5＝20，那么a8＝14.已知數(shù)列SKIPIF1<0的前SKIPIF1<0項和為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則數(shù)列SKIPIF1<0_____________．15.已知圓SKIPIF1<0關(guān)于直線SKIPIF1<0對稱，SKIPIF1<0為圓C上一點，則SKIPIF1<0的最大值為__________．16.已知橢圓SKIPIF1<0的右焦點SKIPIF1<0和上頂點B，若斜率為SKIPIF1<0的直線l交橢圓C于P，Q兩點，且滿足SKIPIF1<0，則橢圓的離心率為___________.四?解答題：本題共6小題，共70分.解答應(yīng)寫出必要的文字說明?證明過程或演算步驟.17已知直線SKIPIF1<0(1)求證：直線l過定點，并求出此定點;(2)求點SKIPIF1<0到直線l的距離的最大值.18.設(shè)等差數(shù)列{an}的前n項和為Sn，a8=4，a13=14.(1)求數(shù)列{an}的通項公式；(2)求Sn的最小值及相應(yīng)的n的值；(3)在公比為q的等比數(shù)列{bn}中，b2=a8，b1+b2+b3=a13，求SKIPIF1<0.19.已知正項數(shù)列SKIPIF1<0滿足SKIPIF1<0且SKIPIF1<0．(1)求數(shù)列SKIPIF1<0的通項公式；(2)令SKIPIF1<0，求數(shù)列SKIPIF1<0的前SKIPIF1<0項的和SKIPIF1<0．20.如圖，在四棱錐SKIPIF1<0中，四邊形SKIPIF1<0是矩形，SKIPIF1<0平面SKIPIF1<0，E為SKIPIF1<0的中點．.(1)若點M在線段SKIPIF1<0上，試確定點M的位置使得直線SKIPIF1<0平面SKIPIF1<0．并證明；(2)若SKIPIF1<0，求平面SKIPIF1<0與平面SKIPIF1<0所成角的余弦值．21.記數(shù)列{an}前n項和為Sn，bn＝an＋1－Sn，且{bn}是以－1為公差的等差數(shù)列，a1＝2，a2＝3．(1)求{an}的通項公式；(2)求數(shù)列{anSKIPIF1<0}的前n項和．22.如圖，橢圓SKIPIF1<