2015年北京高考数学文科试题及答案.pdf
绝密启封并使用完毕前2015 年普通高等学校招生全国统一考试数学文北京卷本试卷共5 页，150 分。考试时长120 分钟。考生务必将答案答在答题卡上，在试卷上作答无效。考试结束后，将本试卷和答题卡一并交回。第一部分选择题共 40 分一、选择题：共8 个小题，每题5 分，共 40 分。在每题的四个选项中，选出符合题目要求的一项。1假设集合52,Axx33,Bxx则AB(A)32xx (B)52xx (C)33xx (D)53xx2圆心为 1，1且过原点的圆的方程是A22111xyB 22111xyC22112xyD22112xy3以下函数中为偶函数的是A2sinyxxB2cosyxxClnyxD2xy 4某校老年、中年和青年教师的人数见下表，采用分层抽样的方法调查教师的身体状况，在抽取的样本中，青年教师有320 人，则该样本的老年人数为A90 B100 C180 D300类别人数老年教师900 中年教师1800 青年教师1600 合计4300（5）执行如下图的程序框图，输出的k 值为A3 B 4 (C)5 (D)6 6设,a b是非零向量，“a ba b”是“a/b”的（A）充分而不必要条件（B）必要而不充分条件C充分必要条件D既不充分也不必要条件7某四棱锥的三视图如下图，该四棱锥最长棱的棱长为(A)1 B B (D)2 8某辆汽车每次加油都把油箱加满，下表记录了该车相邻两次加油时的情况。在这段时间内，该车每100 千米平均耗油量为加油时间加油量升加油时的累计里程千米2015 年 5 月 1 日12 35000 2015 年 5 月 15 日48 35600 注：“累计里程”指汽车从出厂开始累计行驶的路程A6 升B8 升C10 升D12 升第二部分非选择题共110 分二、填空题共6 小题，每题5 分，共 30 分9复数1ii的实部为1013222,3,log 5三个数中最大数的是11在ABC中，23,6,3abA则B12已知2,0是双曲线22210yxbb的一个焦点，则b13如图，ABC及其内部的点组成的集合记为D，,P x y为 D中任意一点，则23zxy的最大值为14 高三年级 267 位学生参加期末考试，某班 37 位学生的语文成绩，数学成绩与总成绩在全年级中的排名情况如以下图所示，甲、乙、丙为该班三位学生。从这次考试成绩看，在甲、乙两人中，其语文成绩名次比其总成绩名次靠前的学生是在语文和数学两个科目中，两同学的成绩名次更靠前的科目是文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8三、解答题共6 题，共 80 分，解答应写出文字说明，演算步骤或证明过程15 本小题 13 分已知函数2sin2 3 sin2xfxx.求fx的最小正周期；求fx在区间20,3上的最小值。16 本小题 13 分已知等差数列na满足124310,2.aaaa求na的通项公式；设等比数列nb满足2337,ba ba；问：6b与数列na的第几项相等？文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 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HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J817 本小题13 分某超市随机选取1000 位顾客，记录了他们购买甲、乙、丙、丁四种商品的情况，整理成如下统计表，其中“”表示购买，“”表示未购买。商品顾客人数甲乙丙丁100 217 200 300 85 98 估计顾客同时购买乙和丙的概率；估计顾客在甲、乙、丙、丁中同时购买3 种商品的概率；如果顾客购买了甲，则该顾客同时购买乙、丙、丁中那种商品的可能性最大？18 本小题14 分如图，在三棱锥VABC中，平面VAB平面ABC，VAB为等边三角形，ACBC,且2ACBC,O M分别为,AB VA的中点。求证:VB/平面MOC;求证：平面MOC平面VAB;求三棱锥VABC的体积。文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J819 本小题 13 分设函数2ln,02xfxkx k。I 求fx的单调区间和极值；II 证明：假设fx存在零点，则fx在区间1,e上仅有一个零点。(20)(本小题 14 分)已知椭圆C：2233xy,过点0,1D且不过点2,1E的直线与椭圆C交于,A B 两点，直线AE与直线3x交于点M。1求椭圆C的离心率；II 假设AB垂直于 x 轴，求直线BM的斜率；III试判断直线BM与直线DE的位置关系，并说明理由。文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8绝密考试结束前2015 年普通高等学校招生全国统一考试数学文北京卷参考答案一、选择题共8 小题，每题5 分，共 40 分1A 2D 3B 4 C 5B 6A 7C 8 B 二、填空题共6 小题，每题5 分，共 30 分91102log 511412313714乙数学三、解答题共6 小题，共80 分15 13 分解：sin3cos3fxxx2sin33xfx的最小正周期为2.20,3x.33x当3x时，即23x时，fx取得最小值.所以fx在20,3上的最小值为23.3f(16)(共 13 分)解：设等差数列na的公差为d.432,2.aad又121110,210,4.aaada421221,2,.nannn设等比数列nb的公比为q.23328,16,baba12,4.qb6 1642128.b由12822,63.nn6b与数列na的第 63 项相等.文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J817 共 13 分解：从统计表可以看出，在这1000 位顾客中有200 位顾客同时购买了乙和丙，所以顾客同时购买乙和丙的概率可以估计为2000.21000从统计表可以看出，在这1000 位顾客中，有100 位顾客同时购买了甲、丙、丁，另有 200 位顾客同时购买了甲、乙、丙，其他顾客最多购买了2 种商品。所以顾客在甲、乙、丙、丁中同时购买3 种商品的概率可以估计为1002000.31000与同理，可得：顾客同时购买甲和乙的概率可以估计为2000.21000，顾客同时购买甲和丙的概率可以估计为1002003000.61000，顾客同时购买甲和丁的概率可以估计为1000.11000，所以，如果顾客购买了甲，则该顾客同时购买丙的可能性最大。18 共 14 分解：因为,O M分别为,AB VA的中点，所以OM VB又因为VB平面MOC,OM平面MOC所以VB平面MOC因为ACBC，O为AB的中点，所以OCAB.又因为平面VAB平面ABC，且OC平面ABC，平面VAB平面ABCAB所以OC平面VAB，又因为OC平面MOC所以平面MOC平面VAB在等腰直角ABC中，2,ACBC所以2,1.ABOC所以正VAB的面积3.VABS又因为OC平面VAB，所以1333C VABVABVOC S,文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8文档编码:CO10V4T6S2M9 HM4A6D8I3A6 ZV10A5Y2F2J8又因为VABCC VABVV,所以33VABCV.(19)(共 13 分)解：由2ln02xfxkx k所以fx的定义域为0,2.kxkfxxxx令0,fx解得xkfx与fx在区间0,上的情况如下：x0,kk,kfx0fx减1ln2kk增所以，fx的单调减区间为0,k，单调增区间为,k；fx在xk处取得极小值fk1ln2kk.由知，fx在区间0,上的最小值为fk1ln2kk.因为fx存在零点，所以1ln2kk0，所以ke.当ke时，fx在区间1,e上单调递减，且0fe.所以xe是fx在区间1,e上的唯一的零点.当ke时，fx在区间0,e
