2019年高考数学真题及答案(含全国1卷,全国2卷,全国3卷共3套).pdf

1 绝密启用前全国卷2019 年普通高等学校招生全国统一考试理科数学本试卷共4 页，23 小题，满分150 分，考试用时120 分钟。注意事项：1答卷前，考生务必将自己的姓名、考生号、考场号和座位号填写在答题卡上。用2B 铅笔将试卷类型（B）填涂在答题卡的相应位置上。2作答选择题时，选出每小题答案后，用2B 铅笔在答题卡上对应题目选项的答案信息点涂黑；如需改动，用橡皮擦干净后，再选涂其它答案。答案不能答在试卷上。3非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新答案；不准使用铅笔和涂改液。不按以上要求作答无效。4考生必须保证答题卡的整洁。考试结束后，将试卷和答题卡一并交回。一、选择题：本题共12 小题，每小题5 分，共60 分。在每小题给出的四个选项中，只有一项是符合题目要求的。1已知集合24260MxxNx xx，则MN=A43xxB42 xxC22xxD23xx2设复数z满足=1iz，z 在复平面内对应的点为(x，y)，则A22+11()xyB221(1)xyC22(1)1yxD22(+1)1yx3已知0.20.32log 0.220.2abc，则AabcBacbCcabDbca第 1 页，共 42 页2 4古希腊时期，人们认为最美人体的头顶至肚脐的长度与肚脐至足底的长度之比是512（512 0.618，称为黄金分割比例)，著名的“断臂维纳斯”便是如此此外，最美人体的头顶至咽喉的长度与咽喉至肚脐的长度之比也是512若某人满足上述两个黄金分割比例，且腿长为 105 cm，头顶至脖子下端的长度为 26 cm，则其身高可能是A165 cm B175 cm C185 cm D190cm 5函数 f(x)=2sincosxxxx在,的图像大致为ABCD6我国古代典籍周易用“卦”描述万物的变化每一“重卦”由从下到上排列的6 个爻组成，爻分为阳爻“”和阴爻“”，如图就是一重卦在所有重卦中随机取一重卦，则该重卦恰有3 个阳爻的概率是A516B1132C2132D1116第 2 页，共 42 页文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W1文档编码:CR2C3S2J2Y5 HF4V6S2B7J6 ZT8L4L8W3W13 7已知非零向量a，b 满足|2|ab，且()abb，则 a 与 b的夹角为A6B3C23D568如图是求112122的程序框图，图中空白框中应填入AA=12ABA=12ACA=112ADA=112A9记nS 为等差数列na的前 n 项和已知4505Sa，则A25nanB310nanC228nSnnD2122nSnn10已知椭圆C 的焦点为121,01,0FF()，()，过 F2的直线与C 交于 A，B 两点若22|2|AFF B，1|ABBF，则 C 的方程为A2212xyB22132xyC22143xyD22154xy11关于函数()sin|sin|f xxx有下述四个结论：f(x)是偶函数f(x)在区间（2,）单调递增第 3 页，共 42 页文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E44 f(x)在,有 4 个零点f(x)的最大值为2 其中所有正确结论的编号是ABCD12已知三棱锥P-ABC 的四个顶点在球O 的球面上，P A=PB=PC，ABC 是边长为2 的正三角形，E，F分别是 PA，PB 的中点，CEF=90，则球O 的体积为A68B64C62D6二、填空题：本题共4 小题，每小题5 分，共 20 分。13曲线23()exyxx在点(0)0，处的切线方程为_14记 Sn为等比数列 an的前 n 项和若214613aaa，则 S5=_ 15甲、乙两队进行篮球决赛，采取七场四胜制（当一队赢得四场胜利时，该队获胜，决赛结束）根据前期比赛成绩，甲队的主客场安排依次为“主主客客主客主”设甲队主场取胜的概率为0.6，客场取胜的概率为 0.5，且各场比赛结果相互独立，则甲队以41 获胜的概率是 _16已知双曲线C：22221(0,0)xyabab的左、右焦点分别为F1，F2，过 F1的直线与C 的两条渐近线分别交于A，B 两点若1F AAB，120F B F B，则 C 的离心率为 _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。第1721 题为必考题，每个试题考生都必须作答。第22、23 题为选考题，考生根据要求作答。（一）必考题：共60 分。17(12 分)ABC的内角 A，B，C 的对边分别为a，b，c，设22(sinsin)sinsinsinBCABC（1）求 A；（2）若22abc，求 sinC第 4 页，共 42 页文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E45 18（12 分）如图，直四棱柱ABCDA1B1C1D1的底面是菱形，AA1=4，AB=2，BAD=60，E，M，N 分别是 BC，BB1，A1D 的中点（1）证明：MN平面 C1DE；（2）求二面角A-MA1-N 的正弦值19（12 分）已知抛物线C：y2=3x 的焦点为 F，斜率为32的直线 l 与 C 的交点为A，B，与 x 轴的交点为P（1）若|AF|+|BF|=4，求 l 的方程；（2）若3APPB，求|AB|20（12 分）已知函数()sinln(1)f xxx，()fx为()f x的导数证明：（1）()fx在区间(1,)2存在唯一极大值点；（2）()f x有且仅有2 个零点第 5 页，共 42 页文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E46 21（12 分）为了治疗某种疾病，研制了甲、乙两种新药，希望知道哪种新药更有效，为此进行动物试验试验方案如下：每一轮选取两只白鼠对药效进行对比试验对于两只白鼠，随机选一只施以甲药，另一只施以乙药一轮的治疗结果得出后，再安排下一轮试验当其中一种药治愈的白鼠比另一种药治愈的白鼠多 4 只时，就停止试验，并认为治愈只数多的药更有效为了方便描述问题，约定：对于每轮试验，若施以甲药的白鼠治愈且施以乙药的白鼠未治愈则甲药得1 分，乙药得1分；若施以乙药的白鼠治愈且施以甲药的白鼠未治愈则乙药得1 分，甲药得1分；若都治愈或都未治愈则两种药均得0 分甲、乙两种药的治愈率分别记为和 ，一轮试验中甲药的得分记为X（1）求X的分布列；（2）若甲药、乙药在试验开始时都赋予4 分，(0,1,8)ip i表示“甲药的累计得分为i时，最终认为甲药比乙药更有效”的概率，则00p，81p，11iiiipapbpcp(1,2,7)i，其中(1)aP X，(0)bP X，(1)cP X假设0.5，0.8(i)证明：1iipp(0,1,2,7)i为等比数列；(ii)求4p，并根据4p的值解释这种试验方案的合理性（二）选考题：共10 分。请考生在第22、23 题中任选一题作答。如果多做，则按所做的第一题计分。22 选修 44：坐标系与参数方程（10 分）在直角坐标系xOy 中，曲线C 的参数方程为2221141txttyt，（t 为参数）以坐标原点O 为极点，x 轴的正半轴为极轴建立极坐标系，直线l 的极坐标方程为2cos3sin110（1）求 C 和 l 的直角坐标方程；（2）求 C 上的点到l 距离的最小值第 6 页，共 42 页文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E47 23 选修 45：不等式选讲（10 分）已知 a，b，c 为正数，且满足abc=1证明：（1）222111abcabc；（2）333()()()24abbcca第 7 页，共 42 页文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E4文档编码:CG6M4L4P9X8 HT10U4Z3E6M2 ZI1H6U4Z6E48 2019 年普通高等学校招生全国统一考试理科数学?参考答案一、选择题1C2C3B4B5 D6A7B8 A9A10 B11C12D二、填空题13 y=3x141213150.18 16 2 三、解答题17解：（1）由已知得222sinsinsinsinsinBCABC，故由正弦定理得222bcabc由余弦定理得2221cos22bcaAbc因为0180A，所以60A（2）由（1）知120BC，由题设及正弦定理得2 sinsin 1202sinACC，即631cossin2sin222CCC，可得2cos602C由于0