湖南省株洲市2020届高三一模考试
理科数学试题卷
第Ⅰ卷（选择题 共60分）
一、单项选择题：每题均有四个选项，其中只有一个正确的，本大题共12小题，每小题5分，共60分。
【1】若复数![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"35.00","h":"41.00","dataType":"png","c":"word/media/image1_1.png","imgOriW":917,"imgOriH":1093})
为纯虚数，则实数等于（ ）
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=12.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"12.00","h":"19.00","dataType":"png","c":"word/media/image3_1.png","imgOriW":317,"imgOriH":493})
（B） （C） （D）
【2】已知全集![](https://wkrtcs.bdimg.com/rtcs/image?w=45.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"45.00","h":"19.00","dataType":"png","c":"word/media/image7_1.png","imgOriW":1199,"imgOriH":493})
，，，则（ ）
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=43.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"43.00","h":"21.00","dataType":"png","c":"word/media/image11_1.png","imgOriW":1128,"imgOriH":564})
（B） （C） （D）
【3】南宋数学家秦九韶在《数书九章》中提出的秦九韶算法至今仍是多项式求值比较先进的算法，已知![](https://wkrtcs.bdimg.com/rtcs/image?w=267.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"267.00","h":"24.00","dataType":"png","c":"word/media/image15_1.png","imgOriW":4518,"imgOriH":407})
，程序框图设计的是求的值，在处应填的执行语句是（ ）
![](https://wkrtcs.bdimg.com/rtcs/image?w=204.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_30","w":"204.00","h":"216.00","dataType":"png","c":"word/media/image18.png","imgOriW":204,"imgOriH":216})
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=80.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"80.00","h":"19.00","dataType":"png","c":"word/media/image19_1.png","imgOriW":2116,"imgOriH":493})
（B） （C） （D）
【4】在如图所示的正方形中随机投掷![](https://wkrtcs.bdimg.com/rtcs/image?w=43.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"43.00","h":"19.00","dataType":"png","c":"word/media/image23_1.png","imgOriW":1128,"imgOriH":493})
个点，则落入阴影部分（曲线为正态分布的密度曲线）的点的个数的估计值为（ ）
（附：![](https://wkrtcs.bdimg.com/rtcs/image?w=19.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_39","w":"19.00","h":"17.00","dataType":"png","c":"word/media/image26_1.png","imgOriW":493,"imgOriH":458})
⁓，则，。）
![](https://wkrtcs.bdimg.com/rtcs/image?w=200.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_45","w":"200.00","h":"139.00","dataType":"png","c":"word/media/image30.png","imgOriW":200,"imgOriH":139})
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=28.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"28.00","h":"19.00","dataType":"png","c":"word/media/image31_1.png","imgOriW":740,"imgOriH":493})
（B） （C） （D）
【5】将函数![](https://wkrtcs.bdimg.com/rtcs/image?w=91.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"91.00","h":"21.00","dataType":"png","c":"word/media/image35_1.png","imgOriW":2398,"imgOriH":564})
的图象向左平移个单位，然后纵坐标不变，横坐标变为原来的倍，得到的图象，下面四个结论正确的是（ ）
（A）函数![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"35.00","h":"21.00","dataType":"png","c":"word/media/image38_1.png","imgOriW":917,"imgOriH":564})
在上的最大值为
（B）将函数的图象向右平移个单位后得到的图象关于原点对称
（C）点![](https://wkrtcs.bdimg.com/rtcs/image?w=43.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_59","w":"43.00","h":"41.00","dataType":"png","c":"word/media/image41_1.png","imgOriW":1128,"imgOriH":1093})
是函数图象的一个对称中心
（D）函数在区间上为增函数
【6】设变量![](https://wkrtcs.bdimg.com/rtcs/image?w=28.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"28.00","h":"17.00","dataType":"png","c":"word/media/image43_1.png","imgOriW":740,"imgOriH":458})
满足约束条件，则目标函数的最大值为（ ）
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"35.00","h":"41.00","dataType":"png","c":"word/media/image46_1.png","imgOriW":917,"imgOriH":1093})
（B） （C） （D）
【7】在![](https://wkrtcs.bdimg.com/rtcs/image?w=61.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"61.00","h":"19.00","dataType":"png","c":"word/media/image50_1.png","imgOriW":1622,"imgOriH":493})
中，，，，在边的中线上，则的最小值为（ ）
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=27.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_13","w":"27.00","h":"41.00","dataType":"png","c":"word/media/image58_1.png","imgOriW":705,"imgOriH":1093})
（B） （C） （D）
【8】如图，网格纸上小正方形的边长为![](https://wkrtcs.bdimg.com/rtcs/image?w=9.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"9.00","h":"17.00","dataType":"png","c":"word/media/image62_1.png","imgOriW":246,"imgOriH":458})
，粗线画出的是某几何体的三视图，则此几何体的外接球的体积为（ ）
![](https://wkrtcs.bdimg.com/rtcs/image?w=200.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_4","w":"200.00","h":"186.00","dataType":"png","c":"word/media/image63.png","imgOriW":200,"imgOriH":186})
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=52.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"52.00","h":"45.00","dataType":"png","c":"word/media/image64_1.png","imgOriW":1375,"imgOriH":1199})
（B） （C） （D）
【9】高斯是德国著名的数学家，近代数学奠基者之一，享有“数学王子”的称号，用其名字命名的“高斯函数”为：设![](https://wkrtcs.bdimg.com/rtcs/image?w=41.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"41.00","h":"19.00","dataType":"png","c":"word/media/image68_1.png","imgOriW":1093,"imgOriH":493})
，用表示不超过的最大整数，则称为高斯函数。例如：，，已知函数，则函数的值域为（ ）
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=40.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"40.00","h":"41.00","dataType":"png","c":"word/media/image76_1.png","imgOriW":1058,"imgOriH":1093})
（B） （C） （D）
【10】已知双曲线![](https://wkrtcs.bdimg.com/rtcs/image?w=157.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"157.00","h":"44.00","dataType":"png","c":"word/media/image80_1.png","imgOriW":2569,"imgOriH":719})
的左、右焦点分别为，若双曲线上存在点使，则该双曲线的离心率的取值范围是（ ）
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=144.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"144.00","h":"45.00","dataType":"png","c":"word/media/image84_1.png","imgOriW":2418,"imgOriH":761})
（B）
（C）![](https://wkrtcs.bdimg.com/rtcs/image?w=99.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"99.00","h":"45.00","dataType":"png","c":"word/media/image86_1.png","imgOriW":1975,"imgOriH":907})
（D）
【11】在![](https://wkrtcs.bdimg.com/rtcs/image?w=45.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"45.00","h":"19.00","dataType":"png","c":"word/media/image88_1.png","imgOriW":1199,"imgOriH":493})
中，已知，，，是边上的一点，将沿折叠，得到三棱锥，若该三棱锥的顶点在底面的射影在线段上，设，则的取值范围是（ ）
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=55.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"55.00","h":"25.00","dataType":"png","c":"word/media/image102_1.png","imgOriW":1446,"imgOriH":670})
（B） （C） （D）
【12】已知抛物线![](https://wkrtcs.bdimg.com/rtcs/image?w=16.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"16.00","h":"19.00","dataType":"png","c":"word/media/image106_1.png","imgOriW":423,"imgOriH":493})
：的焦点为，直线过焦点与抛物线分别交于两点，且直线不与轴垂直，线段的垂直平分线与轴交于点，则（ ）
（A）![](https://wkrtcs.bdimg.com/rtcs/image?w=33.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"33.00","h":"23.00","dataType":"png","c":"word/media/image118_1.png","imgOriW":881,"imgOriH":599})
（B） （C） （D）
第Ⅱ卷（非选择题 共90分）
二、填空题：本大题共4小题，每小题5分，共20分。
【13】已知等比数列![](https://wkrtcs.bdimg.com/rtcs/image?w=31.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"31.00","h":"24.00","dataType":"png","c":"word/media/image122_1.png","imgOriW":811,"imgOriH":635})
为单调递增数列，设其前项和为，若，，则的值为 。
【14】已知![](https://wkrtcs.bdimg.com/rtcs/image?w=169.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"169.00","h":"45.00","dataType":"png","c":"word/media/image128_1.png","imgOriW":2635,"imgOriH":705})
，则 。
【15】二项式![](https://wkrtcs.bdimg.com/rtcs/image?w=73.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"73.00","h":"45.00","dataType":"png","c":"word/media/image130_1.png","imgOriW":1682,"imgOriH":1040})
的展开式中的系数为，则 。
【16已知函数![](https://wkrtcs.bdimg.com/rtcs/image?w=199.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"199.00","h":"41.00","dataType":"png","c":"word/media/image134_1.png","imgOriW":2995,"imgOriH":623})
，若函数有两个极值点，且，则实数的取值范围是 。
三、解答题：本大题共70分，请写出解答的详细过程。
【17】（本小题满分12分）已知数列![](https://wkrtcs.bdimg.com/rtcs/image?w=31.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"31.00","h":"24.00","dataType":"png","c":"word/media/image139_1.png","imgOriW":811,"imgOriH":635})
中，，，前项和为，若
![](https://wkrtcs.bdimg.com/rtcs/image?w=56.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"56.00","h":"24.00","dataType":"png","c":"word/media/image145_1.png","imgOriW":1481,"imgOriH":635})
且。
（Ⅰ）求数列![](https://wkrtcs.bdimg.com/rtcs/image?w=31.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"31.00","h":"24.00","dataType":"png","c":"word/media/image147_1.png","imgOriW":811,"imgOriH":635})
的通项公式；
（Ⅱ）记![](https://wkrtcs.bdimg.com/rtcs/image?w=76.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"76.00","h":"25.00","dataType":"png","c":"word/media/image148_1.png","imgOriW":2010,"imgOriH":670})
，求数列的前项和。
【18】（本小题满分12分）如图，等腰直角![](https://wkrtcs.bdimg.com/rtcs/image?w=45.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"45.00","h":"19.00","dataType":"png","c":"word/media/image152_1.png","imgOriW":1199,"imgOriH":493})
中，，平面平面，，，。
（Ⅰ）求证：![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"67.00","h":"19.00","dataType":"png","c":"word/media/image159_1.png","imgOriW":1763,"imgOriH":493})
；
（Ⅱ）求二面角![](https://wkrtcs.bdimg.com/rtcs/image?w=77.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"77.00","h":"19.00","dataType":"png","c":"word/media/image160_1.png","imgOriW":2046,"imgOriH":493})
的正弦值。
![](https://wkrtcs.bdimg.com/rtcs/image?w=200.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_26","w":"200.00","h":"138.00","dataType":"png","c":"word/media/image161.png","imgOriW":200,"imgOriH":138})
【19】（本小题满分12分）目前，浙江和上海已经成为新高考综合试点的“排头兵”，有关其它省份新高考改革的实施安排，教育部部长在十九大上做出明确表态：到2020年，我国将全面建立起新的高考制度。新高考规定：语文、数学和英语是考生的必考科目，考生还需从物理、化学、生物、历史、地理和政治六个科目中选取三个科目作为选考科目。若一个学生从六个科目中选出了三个科目作为选考科目，则称该学生的选考方案确定；否则，称该学生选考方案待确定。例如，学生甲选择“物理、化学和生物”三个选考科目，则学生甲的选考方案确定，“物理、化学和生物”为其选考方案。
某校为了解高一年级![](https://wkrtcs.bdimg.com/rtcs/image?w=28.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"28.00","h":"19.00","dataType":"png","c":"word/media/image162_1.png","imgOriW":740,"imgOriH":493})
名学生选考科目的意向，随机选取名学生进行了一次调查，统计选考科目人数如下表：
![](https://wkrtcs.bdimg.com/rtcs/image?w=642.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_26","w":"642.00","h":"191.00","dataType":"png","c":"word/media/image164.png","imgOriW":1154,"imgOriH":343})
（Ⅰ）估计该学校高一年级选考方案确定的学生中选考生物的学生有多少人？
（Ⅱ）将列联表填写完整，并通过计算判定能否有![](https://wkrtcs.bdimg.com/rtcs/image?w=32.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"32.00","h":"19.00","dataType":"png","c":"word/media/image165_1.png","imgOriW":846,"imgOriH":493})
％把握认为选历史是否与性别有关？
![](https://wkrtcs.bdimg.com/rtcs/image?w=642.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_26","w":"642.00","h":"162.00","dataType":"png","c":"word/media/image166.png","imgOriW":1115,"imgOriH":282})
（Ⅲ）从选考方案确定的![](https://wkrtcs.bdimg.com/rtcs/image?w=19.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"19.00","h":"19.00","dataType":"png","c":"word/media/image167_1.png","imgOriW":493,"imgOriH":493})
名男生中随机选出名，设随机变量，求的分布列及数学期望。
![](https://wkrtcs.bdimg.com/rtcs/image?w=641.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_26","w":"641.00","h":"133.00","dataType":"png","c":"word/media/image172.png","imgOriW":1147,"imgOriH":237})
【20】（本小题满分12分）在直角坐标系![](https://wkrtcs.bdimg.com/rtcs/image?w=32.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"32.00","h":"21.00","dataType":"png","c":"word/media/image173_1.png","imgOriW":846,"imgOriH":564})
中，已知圆：与直线：相切，点为圆上一动点，轴于点，且动点满足，设动点的轨迹为曲线。
（Ⅰ）求曲线![](https://wkrtcs.bdimg.com/rtcs/image?w=16.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"16.00","h":"19.00","dataType":"png","c":"word/media/image184_1.png","imgOriW":423,"imgOriH":493})
的方程；
（Ⅱ）设![](https://wkrtcs.bdimg.com/rtcs/image?w=33.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"33.00","h":"21.00","dataType":"png","c":"word/media/image185_1.png","imgOriW":881,"imgOriH":564})
是曲线上两动点，线段的中点为，的斜率分别为，且，求的取值范围。
【21】（本小题满分12分）已知函数![](https://wkrtcs.bdimg.com/rtcs/image?w=157.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"157.00","h":"41.00","dataType":"png","c":"word/media/image193_1.png","imgOriW":2646,"imgOriH":695})
，，。
（Ⅰ）求函数![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"35.00","h":"21.00","dataType":"png","c":"word/media/image196_1.png","imgOriW":917,"imgOriH":564})
的单调区间；
（Ⅱ）若![](https://wkrtcs.bdimg.com/rtcs/image?w=81.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_3","w":"81.00","h":"21.00","dataType":"png","c":"word/media/image197_1.png","imgOriW":2151,"imgOriH":564})
恒成立，求的最小值。
![](https://wkrtcs.bdimg.com/rtcs/image?w=641.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_26","w":"641.00","h":"62.00","dataType":"png","c":"word/media/image199.png","imgOriW":1159,"imgOriH":112})
【22】（本小题满分10分）选修4—4：坐标系与参数方程
在平面直角坐标系![](https://wkrtcs.bdimg.com/rtcs/image?w=32.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_66","w":"32.00","h":"21.00","dataType":"png","c":"word/media/image200_1.png","imgOriW":846,"imgOriH":564})
中，以为极点，轴的非负半轴为极轴，建立极坐标系，曲线的极坐标方程为，直线的参数方程为为参数。直线与曲线分别交于两点。
（Ⅰ）若点![](https://wkrtcs.bdimg.com/rtcs/image?w=16.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_68","w":"16.00","h":"17.00","dataType":"png","c":"word/media/image211_1.png","imgOriW":423,"imgOriH":458})
的极坐标为，求的值；
（Ⅱ）求曲线![](https://wkrtcs.bdimg.com/rtcs/image?w=16.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_66","w":"16.00","h":"19.00","dataType":"png","c":"word/media/image214_1.png","imgOriW":423,"imgOriH":493})
的内接矩形周长的最大值。
【23】（本小题满分10分）选修4—5：不等式选讲
设函数![](https://wkrtcs.bdimg.com/rtcs/image?w=184.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_7","w":"184.00","h":"27.00","dataType":"png","c":"word/media/image215_1.png","imgOriW":3529,"imgOriH":511})
，。
（Ⅰ）当![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_7","w":"35.00","h":"19.00","dataType":"png","c":"word/media/image217_1.png","imgOriW":917,"imgOriH":493})
时，求不等式的解集；
（Ⅱ）已知![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_7","w":"60.00","h":"21.00","dataType":"png","c":"word/media/image219_1.png","imgOriW":1587,"imgOriH":564})
恒成立，求的取值范围。
理科数学参考答案
一、单项选择题
![](https://wkrtcs.bdimg.com/rtcs/image?w=609.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_15","w":"609.00","h":"43.00","dataType":"png","c":"word/media/image221.png","imgOriW":913,"imgOriH":64})
二、填空题
![](https://wkrtcs.bdimg.com/rtcs/image?w=642.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_15","w":"642.00","h":"72.00","dataType":"png","c":"word/media/image222.png","imgOriW":1059,"imgOriH":119})
![](https://wkrtcs.bdimg.com/rtcs/image?w=641.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_15","w":"641.00","h":"326.00","dataType":"png","c":"word/media/image223.png","imgOriW":1376,"imgOriH":701})
![](https://wkrtcs.bdimg.com/rtcs/image?w=642.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_15","w":"642.00","h":"341.00","dataType":"png","c":"word/media/image225.png","imgOriW":1139,"imgOriH":607})
![](https://wkrtcs.bdimg.com/rtcs/image?w=642.00&md5sum=0f883bbb6e49f443dcf39307adc0a7e3&sign=2f53efee79&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=428&ipr={"t":"img","r":"r_15","w":"642.00","h":"360.00","dataType":"png","c":"word/media/image231.png","imgOriW":1238,"imgOriH":694})
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