2018年北京海淀区高考一模试题:数学(理

2018年北京海淀区高考一模试题:数学(理

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拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net海淀区高三年级第二学期期中练习数学(理科)第Ⅰ卷(选择题共40分)一、选择题:本大题共8小题,每小题5分,共40分.在每小题列出的四个选项中,选出符合题目要求的一项.(海淀·理科·题1)1.在复平面内,复数(是虚数单位)对应的点位于()A.第一象限B.第二象限C.第三象限D.第四象限【解析】C;,该复数对应的点位于第三象限.(海淀·理科·题2)2.在同一坐标系中画出函数,,的图象,可能正确的是()【解析】D;在B、C、D三个选项中对应的,只有选项D的图象正确.(海淀·理科·题3)3.在四边形中,,且,则四边形()A.矩形B.菱形C.直角梯形D.等腰梯形【解析】B;∵即一组对边平行且相等,即对角线互相垂直;∴该四边形为菱形.(海淀·理科·题4)4.在平面直角坐标系中,点的直角坐标为.若以原点为极点,轴正半轴为极轴建立极坐标系,则点的极坐标可以是()A.B.C.D.【解析】C;经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net易知,.(海淀·理科·题5)5.一个体积为的正三棱柱的三视图如图所示,则这个三棱柱的左视图的面积为()A.B.C.D.【解析】A;设该三棱柱底面边长为,高为,则左视图面积为.由三视图可得:,解得.于是为所求.(海淀·理科·题6)6.已知等差数列,等比数列,则该等差数列的公差为()A.或B.或C.D.【解析】C;经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net,解得.因此该等差数列的公差为.(海淀·理科·题7)7.已知某程序框图如图所示,则执行该程序后输出的结果是()A.B.C.D.【解析】A;∵,∴对应的.(海淀·理科·题8)8.已知数列具有性质:对任意,与两数中至少有一个是该数列中的一项.经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net现给出以下四个命题:①数列具有性质;②数列具有性质;③若数列具有性质,则;④若数列具有性质,则.其中真命题有()A.个B.个C.个D.个【解析】B;①∵,都不在数列中,∴数列不具有性质;②容易验证数列具有性质;③取,则在数列中,而数列中最小的数,因此;④由对②的分析可知,.由于,不在数列中,因此必然在数列中.又,故,于是,等式成立.第Ⅱ卷(非选择题共110分)二、填空题:本大题共6小题,每小题5分,共30分.(海淀·理科·题9)9.某校为了解高三同学寒假期间学习情况,抽查了名同学,统计他们每天平均学习时间,绘成频率分布直方图(如图).则这名同学中学习时间在到小时内的人数为.【解析】30;由,解得.于是在这名同学中学习时间在到小时内的人数为.(海淀·理科·题10)10.如图,为的直径,且,为的中点,过作的弦,且,则弦的长度为.经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net【解析】7;由得.由已知和相交弦定理得,解得.于是.(海淀·理科·题11)11.给定下列四个命题:①“”是“”的充分不必要条件;②若“”为真,则“”为真;③若,则;④若集合,则.其中为真命题的是(填上所有正确命题的序号).【解析】①,④;(海淀·理科·题12)12.在二项式的展开式中,的系数是,则实数的值为.【解析】1;由二项式定理,.当时,,于是的系数为,从而.(海淀·理科·题13)13.已知有公共焦点的椭圆与双曲线中心为原点,焦点在轴上,左右焦点分别为经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net,且它们在第一象限的交点为,是以为底边的等腰三角形.若,双曲线的离心率的取值范围为.则该椭圆的离心率的取值范围是.【解析】;如图,设椭圆的半长轴长,半焦距分别为,双曲线的半实轴长,半焦距分别为,,则,问题转化为已知,求的取值范围.设,则,.∵,∴,即.(海淀·理科·题14)14.在平面直角坐标系中,点集,,则(1)点集所表示的区域的面积为_____;(2)点集所表示的区域的面积为.【解析】;.;经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net(1)如左图所示,点集是以为圆心为半径的圆,其表示区域的面积为;(2)如右图所示,点集是由三段圆弧以及连结它们的三条切线段围成的区域,其面积为.三、解答题:本大题共6小题,共80分.解答应写出文字说明,演算步骤或证明过程.(海淀·理科·题15)15.(本小题满分13分)已知函数的图象如图所示.(Ⅰ)求的值;(Ⅱ)设,求函数的单调递增区间.经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net【解析】(Ⅰ)由图可知,,又由得,又,得∵,∴,(Ⅱ)由(Ⅰ)知:因为所以,,即.故函数的单调增区间为.(海淀·理科·题16)16.(本小题满分13分)某商场为吸引顾客消费推出一项优惠活动.活动规则如下:消费额每满元可转动如图所示的转盘一次,并获得相应金额的返券,假定指针等可能地停在任一位置.若指针停在区域返券元;停在区域返券元;停在区域不返券.例如:消费元,可转动转盘次,所获得的返券金额是两次金额之和.(Ⅰ)若某位顾客消费元,求返券金额不低于元的概率;(Ⅱ)若某位顾客恰好消费元,并按规则参与了活动,他获得返券的金额记为(元).求随机变量的分布列和数学期望.【解析】设指针落在、、区域分别记为事件、、.则,,.(Ⅰ)若返券金额不低于元,则指针落在或区域.∵即消费元的顾客,返券金额不低于元的概率是.(Ⅱ)由题意得,该顾客可转动转盘次.随机变量的可能值为,,,,.经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net;;;;;所以,随机变量的分布列为:0306090120其数学期望.(海淀·理科·题17)17.(本小题满分14分)如图,三棱柱中,侧面底面,,,且,为中点.(Ⅰ)证明:平面;(Ⅱ)求直线与平面所成角的正弦值;(Ⅲ)在上是否存在一点,使得平面,若不存在,说明理由;若存在,确定点的位置.经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net【解析】(Ⅰ)证明:因为,且为的中点,所以.又由题意可知,平面平面,交线为,且平面,所以平面.(Ⅱ)如图,以为原点,所在直线分别为轴建立空间直角坐标系.由题意可知,,又∴.所以得:,,,,,,则有:,,.设平面的一个法向量为,则有,令,得,所以..因为直线与平面所成角和向量与所成锐角互余,所以.(Ⅲ)设,即,得.所以,得经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net令平面,得,即,得,即存在这样的点,为的中点.(海淀·理科·题18)18.(本小题满分13分)已知函数,其中为常数,且.(Ⅰ)当时,求在()上的值域;(Ⅱ)若对任意恒成立,求实数的取值范围.【解析】(Ⅰ)当时,,得令,即,解得,所以函数在上为增函数,据此,函数在上为增函数,而,,所以函数在上的值域为.(Ⅱ)由,令,得,即,当时,,函数在上单调递减;当时,,函数在上单调递增;若,即,易得函数在上为增函数,此时,,要使对恒成立,只需即可,所以有,即.而,即,所以此时无解.若,即,易知函数在上为减函数,在上为增函数,要使对恒成立,只需,即经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net,由和得.若,即,易得函数在上为减函数,此时,,要使对恒成立,只需即可,所以有,即,又因为,所以.综合上述,实数的取值范围是.(海淀·理科·题19)19.(本小题满分13分)已知椭圆的中心在原点,焦点在轴上,左右焦点分别为,,且,点在椭圆上.(Ⅰ)求椭圆的方程;(Ⅱ)过的直线与椭圆相交于、两点,且的面积为,求以为圆心且与直线相切的圆的方程.【解析】(Ⅰ)设椭圆的方程为,由题意可得:椭圆两焦点坐标分别为,.∴.∴,又,,故椭圆的方程为.(Ⅱ)当直线轴,计算得到:,,,不符合题意.当直线与轴不垂直时,设直线的方程为:,由,消去y得.经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net显然成立,设,,则,.又即,又圆的半径.所以,化简,得,即,解得.所以,.故圆的方程为:.(Ⅱ)另解:设直线的方程为,由,消去得,恒成立,设,,则,.所以.又圆的半径为.所以,解得,所以.故圆的方程为:.经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net(海淀·理科·题20)20.(本小题满分14分)已知数列满足:,,.(Ⅰ)求的值;(Ⅱ)设,试求数列的通项公式;(Ⅲ)对于任意的正整数,试讨论与的大小关系.【解析】(Ⅰ)∵,,,,∴;;.(Ⅱ)由题设,对于任意的正整数,都有:,∴.∴数列是以为首项,为公差的等差数列.∴.(Ⅲ)对于任意的正整数,当或时,;当时,;当时,.证明如下:首先,由,,,可知时,;其次,对于任意的正整数,时,;时,所以.时,事实上,我们可以证明:对于任意正整数,…(*)(证明见后),所以此时.经济增长:在优化结构、提高效益和降低消耗的基础上,“十一五”期市GDP年均增长12%以上(现14%以上),2010年达到650亿元以上,人均GDP力争1000美元;财政收入达到80亿元;规模以上工业销售达到550亿以上;全社会固定资产投资年均长20%,五年累计1000亿元;社会消费品销售额260亿元,年均增长20%,外贸进口总额2.5亿美元,年均增长15%;五年累计招商引资突破500亿元,力争达到600亿元湖西苏州青旅:园区星海街200号(星海体育休闲中心北部6楼)联系电话:0512-传真:0512-湖东苏州青旅:园区湖东邻里中心Z107-1(好利来蛋糕店斜对面)联系电话:0512-传真:0512-新区趣普仕:苏州市新区狮山路35号金河国际大厦1号1910A区联系电话:0512-传真:0512-畅途旅游网:http://www.917trip.comhttp://www.chujingtong.comhttp://www.weiweitingting.orgwww.szcytsxh.comwww.zijiala.comwww..comwww.fulongfloor.comwww.canary-mirror.comhttp://www.917trip.cn/jingdian/专注品质,苏州市民首选出游助手! 拟建中的阜阳市中国XXXX国际服装城依托中国XX国际服装城,拟建成为皖西北地区规格最高、规模最大、商务及功能最优的现代化、国际化服装专业市场,建设规模占地约128亩,建筑面积约25万平方米,项目总投资约5亿元人民币。经过1--2年的开发建设,能达到正常运营期的中国XX.XX国际服装城将吸纳全国和世界各地的经销商、代理商企业物流总部等500—1000家,预计年交易额实现68亿元人民币,每年实现税收8000—10000万元人民币,每年实现利润1.68亿元人民币,实现就业和创业人员约2万以上。苏州青旅园区星海部(十佳营业部)、园区湖东营业部、趣普仕旅行社新区分公司华东地区首家通过ISO9001认证的AAA级旅行社省诚信旅行社许可证号L-JS-GJ00026http://www.917trip.cnhttp://www.sz100.net综上可知:结论得证.对于任意正整数,(*)的证明如下:1)当()时,,满足(*)式.2)当时,,满足(*)式.3)当时,于是只须证明,如此递推,可归结为1)或2)的情形,于是(*)得证.内部资料仅供参考9JWKffwvG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z8vG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^G89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z8vG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$U*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$U*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz84!z89Amv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$U*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$U*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum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