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文科数学答案第1页共1页2020年赤峰市高三期末考试试卷文科数学参考答案2020.1说明：一、本解答给出了一种或几种解法供参考，如果考生的解法与本解答不同，可根据试题的主要考查内容比照评分标准制订相应的评分细则．二、解答右端所注分数，表示考生正确做到这一步应得的累加分数．三、只给整数分数，选择题和填空题不给中间分．一、选择题：本大题共12小题，每小题5分，共60分1.B；2.C；3.C；4.B；5.A；6.C；7.C；8.B；9.D；10.A；11.D；12.A．二、填空题：本大题共4小题，每小题5分，共20分.13.45；14.2700；15.1290，；16.(2,)e.三、解答题：共70分。解答应写出文字说明，证明过程或演算步骤。17.(12分)解：（1）PD平面ABCD，AC平面ABCDPDAC，又ABCD为菱形,BDAC，又BDPDD，AC平面PBD，DE平面PBDACDE„„„„„6分（2）由（1）知CD平面PBD，所以2111133322244342EPCDCPDECPDBPABCDVVVV„„„„„„„„„„„„„„„„„„„„„„12分18.(12分)解：（1）由12=1(2)nnaan，得12(+1)=1nnaa，即111(1)2nnaa，又11+1=02a„„„„„„„„„„„„3分文科数学答案第2页共2页+1na是以11+1=2a为首项，公比为12的等比数列1111+1=,=1222nnnnaa„„„„„„„„„„„„„„6分（2）由已知得1(1)332nnabnn112nna11(32)(32)1(31)22nnnnbnann„„„„„„„„„„„„„„„„„„„„„„8分所以数列nb的前n项和为21211125(31)222nnbbbn211125(31)222nn111222(31)1212nnn231122nnn„„„„„„„„„12分19.(12分)解：（1）22列联表如下：非“环保关注者”“环保关注者”合计女104555男153045合计2575100将22列联表中的数据代入公式计算，得2K的观测值文科数学答案第3页共3页22100(45153010)300=3.0302.7062575554599k所以在犯错误的概率不超过0.10的前提下，可以认为是否为是“环保关注者”与性别是有关的.„„„„„„„„„„„„„„„„„„„„„„„„6分（2）由题意可知，利用分层抽样的方法可得女“环保达人”3人，男“环保达人”2人.设女“环保达人”3人分别为A，B，C；男“环保达人”2人为D，E.从中抽取两人的所有情况为：(,)AB，(,)AC，(,)AD，(,)AE，(,)BC，(,)BD，(,)BE，(,)CD，(,)CE，(,)DE，共10种情况.既有女“环保达人”又有男“环保达人”的情况有(,)AD，(,)AE，(,)BD，(,)BE，(,)CD，(,)CE，共6种情况.故所求概率为63105p„„„„„„„„„„„„„„„„„„„„„„„„„12分20.(12分)解：（1）函数xf的定义域为),(，由xeaxxf)()(，得xeaxxf1'，„„„„„„„„„„„„„„„„„„„„„„„„2分由0'xf得xf在,1a上为增函数由0'xf得xf在)1,(a上为减函数„„„„„„„„„„„„„„„„„„„„„„„„4分所以，11aeafxf极小值，无极大值.„„„„„„„„„„„„„„„„„„„„„„„„6分（2）由1fxf知1minfxf，则1为xf极小值点由(1)知11a，则2axexxf2„„„„„„„„„„„„„„„„„„„„„„„„8分文科数学答案第4页共4页令2323213122131xxexxxxfxgx则xexxgx1'，xey的图象在xy图象的上方0xex10,10''xxgxxg„„„„„„„„„„„„„„„„„„„„„„„10分xg在)1,(为减函数，在),1(为增函数，egxg61)1(，即：exxxf612131)(23.„„„„„„„„„„„„„„„„„„„„„„„„„„12分21....