2021年2019年普通高等学校招生全国统一考试理科数学(北京卷)解析版.pdf

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2021年2019年普通高等学校招生全国统一考试理科数学(北京卷)解析版.pdf

2019 年普通高等学校招生全国统一考试（北京卷）理科数学本试卷共 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 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。1.已知复数z=2+i，则z zA.3B.5C.3 D.5【答案】D【解析】【分析】题先求得z，然后根据复数的乘法运算法则即得.【详解】z2i,z z(2i)(2i)5故选 D.【点睛】本容易题，注重了基础知识、基本计算能力的考查.2.执行如图所示的程序框图，输出的s值为A.1 B.2 C.3 D.4|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页，共 19 页【答案】B【解析】【分析】根据程序框图中的条件逐次运算即可.【详解】运行第一次，=1k，22 123 12s，运行第二次，2k，2222322s，运行第三次，3k，2222322s，结束循环，输出=2s，故选 B.【点睛】本题考查程序框图，属于容易题，注重基础知识、基本运算能力的考查.3.已知直线l 的参数方程为13,24xtyt（t 为参数），则点（1,0）到直线l 的距离是A.15B.25C.45D.65【答案】D【解析】【分析】首先将参数方程化为直角坐标方程，然后利用点到直线距离公式求解距离即可.【详解】直线l的普通方程为41320 xy,即 4320 xy,点1,0到直线l的距离22|402|6543d,故选 D.【点睛】本题考查直线参数方程与普通方程转化,点到直线的距离,属于容易题,注重基础知识?基本运算能力的考查.4.已知椭圆22221xyab（a b0）的离心率为12，则A.a2=2b2B.3a2=4b2C.a=2bD.3a=4b|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页，共 19 页文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9【答案】B【解析】【分析】由题意利用离心率的定义和,a b c的关系可得满足题意的等式.【详解】椭圆的离心率2221,2cecaba,化简得2234ab,故选 B.【点睛】本题考查椭圆的标准方程与几何性质,属于容易题,注重基础知识?基本运算能力的考查.5.若 x，y 满足|1|xy，且 y-1，则 3x+y 的最大值为A.-7B.1 C.5 D.7【答案】C【解析】【分析】首先画出可行域，然后结合目标函数的几何意义确定其最值即可.【详解】由题意1,11yyxy作出可行域如图阴影部分所示.设3,3zxy yzx,|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页，共 19 页文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9当直线0:3lyzx经过点2,1时,z 取最大值5.故选 C.【点睛】本题是简单线性规划问题的基本题型,根据“画?移?解”等步骤可得解.题目难度不大题,注重了基础知识?基本技能的考查.6.在天文学中，天体的明暗程度可以用星等或亮度来描述.两颗星的星等与亮度满足212152lgEmmE，其中星等为m1的星的亮度为E2（k=1,2）.已知太阳的星等是26.7，天狼星的星等是1.45，则太阳与天狼星的亮度的比值为A.1010.1B.10.1 C.lg10.1 D.1010.1【答案】D【解析】【分析】先求出12lgEE，然后将对数式换为指数式求12EE，再求12EE.【详解】两颗星的星等与亮度满足12125lg2EmmE,令21.45m，126.7m，1212221g(1.4526.7)10.155EmmE，10.110.112211010EEEE，故选 D.【点睛】考查考生的数学应用意识、信息处理能力、阅读理解能力以及指数对数运算.7.设点 A，B，C 不共线，则“AB与AC的夹角为锐角”是“|ABACBC”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【答案】C【解析】|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页，共 19 页文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9【分析】由题意结合向量的减法公式和向量的运算法则考查充分性和必要性是否成立即可.【详解】A?B?C三点不共线,|AB+AC|BC|AB+AC|AB-AC|AB+AC|2|AB-AC|2AB?AC0AB与AC的夹角为锐角.故“AB与AC的夹角为锐角”是“|AB+AC|BC|”的充分必要条件,故选 C.【点睛】本题考查充要条件的概念与判断?平面向量的模?夹角与数量积,同时考查了转化与化归数学思想.8.数学中有许多形状优美、寓意美好的曲线，曲线C：221|xyx y就是其中之一（如图）.给出下列三个结论：曲线 C 恰好经过6个整点（即横、纵坐标均为整数的点）；曲线 C 上任意一点到原点的距离都不超过2；曲线 C 所围成的“心形”区域的面积小于3.其中，所有正确结论的序号是A.B.C.D.【答案】C【解析】【分析】将所给方程进行等价变形确定x 的范围可得整点坐标和个数，结合均值不等式可得曲线上的点到坐标原点距离的最值和范围，利用图形的对称性和整点的坐标可确定图形面积的范围.|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 5 页，共 19 页文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9【详解】由221xyx y得,221yx yx,2222|3341,10,2443xxxyx厔,所以x可为的整数有0,-1,1,从而曲线22:1C xyx y恰好经过(0,1),(0,-1),(1,0),(1,1),(-1,0),(-1,1)六个整点,结论正确.由221xyx y得,222212xyxy,解得222xy,所以曲线C上任意一点到原点的距离都不超过2.结论正确.如图所示,易知0,1,1,0,1,1,0,1ABCD,四边形ABCD的面积131 1 1 122ABCDS,很明显“心形”区域的面积大于2ABCDS,即“心形”区域的面积大于3,说法错误.故选 C.【点睛】本题考查曲线与方程?曲线的几何性质，基本不等式及其应用,属于难题,注重基础知识?基本运算能力及分析问题解决问题的能力考查,渗透“美育思想”.第二部分（非选择题共 110 分）二、填空题共 6 小题，每小题 5 分，共 30 分。9.函数 f(x)=sin22x 的最小正周期是_【答案】2.|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 6 页，共 19 页文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9【解析】【分析】将所给的函数利用降幂公式进行恒等变形，然后求解其最小正周期即可.【详解】函数2sin 2fxx142cos x,周期为2【点睛】本题主要考查二倍角的三角函数公式?三角函数的最小正周期公式，属于基础题.10.设等差数列 an的前 n 项和为 Sn，若 a2=-3，S5=-10，则 a5=_，Sn的最小值为_【答案】(1).0.(2).-10.【解析】【分析】首先确定公差,然后由通项公式可得5a的值，进一步研究数列中正项?负项的变化规律,得到和的最小值.【详解】等差数列na中,53510Sa,得322,3aa,公差321daa,5320aad,由等差数列na的性质得5n时,0na,6n时,na大于 0,所以nS的最小值为4S或5S,即为10.【点睛】本题考查等差数列的通项公式?求和公式?等差数列的性质,难度不大,注重重要知识?基础知识?基本运算能力的考查.11.某几何体是由一个正方体去掉一个四棱柱所得，其三视图如图所示如果网格纸上小正方形的边长为1，那么该几何体的体积为_|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 7 页，共 19 页文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 HT7X5N9L5V7 ZE7P3V6A5B9文档编码:CF6A9B1Q3U10 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