江苏省1993年普通高校单独招生统一考试试卷
数 学
一、选择题（本大题共10小题，每小题3分，共30分，每小题列出的四个选项中，只有1项是符合题目要求的，把所选项前的字母填在题后括号内。）
1、设集合C={复数}，R={实数}，M={纯虚数}，其中C是全集，则（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=77&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"77","h":"20","dataType":"gif","c":"word/media/image1.png"})
B． C． D．
2、已知函数![](https://wkrtcs.bdimg.com/rtcs/image?w=36&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"36","h":"21","dataType":"gif","c":"word/media/image5.png"})
是R上的奇函数，而且在上是增函数，则在上是（ ）
A．减函数 B．增函数 C．先增后减的函数 D．先减后增的函数
3、设![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"13","h":"15","dataType":"gif","c":"word/media/image8.png"})
、为非零实数，，且，下列各式中能成立的是（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=119&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"119","h":"25","dataType":"gif","c":"word/media/image12.png"})
B．
C．![](https://wkrtcs.bdimg.com/rtcs/image?w=132&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"132","h":"25","dataType":"gif","c":"word/media/image14.png"})
D．
4、函数![](https://wkrtcs.bdimg.com/rtcs/image?w=101&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"101","h":"41","dataType":"gif","c":"word/media/image16.png"})
（其中常数）的最小正周期为（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=24&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"24","h":"41","dataType":"gif","c":"word/media/image18.png"})
B． C． D．
5、不等式![](https://wkrtcs.bdimg.com/rtcs/image?w=97&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"97","h":"49","dataType":"gif","c":"word/media/image22.png"})
的解集是（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=71&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"71","h":"41","dataType":"gif","c":"word/media/image23.png"})
B． C． D．
6、若A、B、C是三角形的三个内角，则（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=125&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"125","h":"21","dataType":"gif","c":"word/media/image27.png"})
B．
C．![](https://wkrtcs.bdimg.com/rtcs/image?w=140&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"140","h":"21","dataType":"gif","c":"word/media/image29.png"})
D．
7、复数![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"13","h":"13","dataType":"gif","c":"word/media/image31.png"})
是纯虚数的一个充分必要条件是（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=60&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"60","h":"23","dataType":"gif","c":"word/media/image32.png"})
B． C． D．
8、在长方体![](https://wkrtcs.bdimg.com/rtcs/image?w=124&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"124","h":"23","dataType":"gif","c":"word/media/image36.png"})
中，与对角线异面的棱共有（ ）
A．6条 B．8条 C．4条 D．2条
9、若直线![](https://wkrtcs.bdimg.com/rtcs/image?w=9&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"9","h":"19","dataType":"gif","c":"word/media/image38.png"})
过点，且倾斜角为，则直线的方程为（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=80&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"80","h":"25","dataType":"gif","c":"word/media/image41.png"})
B． C． D．
10、已知椭圆的对称轴是坐标轴，离心率![](https://wkrtcs.bdimg.com/rtcs/image?w=40&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"40","h":"41","dataType":"gif","c":"word/media/image45.png"})
，长轴的长等于6，那么椭圆方程是（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=81&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"81","h":"44","dataType":"gif","c":"word/media/image46.png"})
B．
C．![](https://wkrtcs.bdimg.com/rtcs/image?w=81&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"81","h":"44","dataType":"gif","c":"word/media/image47.png"})
或 D．或
二、填空题（本大题共10题，每小题3分，共30分，把答案填在题中的横线上。）
11、函数![](https://wkrtcs.bdimg.com/rtcs/image?w=123&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"123","h":"41","dataType":"gif","c":"word/media/image50.png"})
的定义域是____________。
12、圆心是![](https://wkrtcs.bdimg.com/rtcs/image?w=48&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"48","h":"21","dataType":"gif","c":"word/media/image51.png"})
，半径是的圆的极坐标方程为____________。
13、![](https://wkrtcs.bdimg.com/rtcs/image?w=93&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"93","h":"41","dataType":"gif","c":"word/media/image53.png"})
=____________。
14、复数![](https://wkrtcs.bdimg.com/rtcs/image?w=52&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"52","h":"45","dataType":"gif","c":"word/media/image54.png"})
的实部是____________，虚部是____________。
15、若![](https://wkrtcs.bdimg.com/rtcs/image?w=84&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"84","h":"41","dataType":"gif","c":"word/media/image55.png"})
，且，则=____________。
16、已知两球的表面积之比为4：1，那么这两个球的体积之比为
____________。
17、双曲线![](https://wkrtcs.bdimg.com/rtcs/image?w=93&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"93","h":"44","dataType":"gif","c":"word/media/image58.png"})
的焦点坐标为____________。
18、函数![](https://wkrtcs.bdimg.com/rtcs/image?w=157&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"157","h":"28","dataType":"gif","c":"word/media/image59.png"})
的反函数是____________。
19、就函数的奇偶性而言，函数![](https://wkrtcs.bdimg.com/rtcs/image?w=73&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"73","h":"41","dataType":"gif","c":"word/media/image60.png"})
是____________函数。
20、有![](https://wkrtcs.bdimg.com/rtcs/image?w=17&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"17","h":"15","dataType":"gif","c":"word/media/image61.png"})
个男同学和个女同学站成一排，如果女同学必须排在一想，则共有排法____________种。
三、解答题（本大题共6题，共40分。）
21、化简：![](https://wkrtcs.bdimg.com/rtcs/image?w=200&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"200","h":"21","dataType":"gif","c":"word/media/image63.png"})
22、已知![](https://wkrtcs.bdimg.com/rtcs/image?w=71&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"71","h":"21","dataType":"gif","c":"word/media/image64.png"})
，化简：
23、方程![](https://wkrtcs.bdimg.com/rtcs/image?w=184&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"184","h":"24","dataType":"gif","c":"word/media/image66.png"})
和方程
有一个根互为倒数，求![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"13","h":"19","dataType":"gif","c":"word/media/image68.png"})
角。
24、正方体的棱长为，已知、分别在、上，且。求
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=60&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"60","h":"23","dataType":"gif","c":"word/media/image76.png"})
的余弦值； （2）的面积；
（3）画出过A、![](https://wkrtcs.bdimg.com/rtcs/image?w=20&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"20","h":"23","dataType":"gif","c":"word/media/image72.png"})
、三点的截面。
![](https://wkrtcs.bdimg.com/rtcs/image?w=221&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"221","h":"211","dataType":"wmf","c":"word/media/image78.png","imgOriW":442,"imgOriH":422})
25、在55和555之间插入几个等差中项时，其中最末一个等差中项等于![](https://wkrtcs.bdimg.com/rtcs/image?w=76&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"76","h":"49","dataType":"gif","c":"word/media/image79.png"})
展开式中含项的系数。
26、设F是椭圆![](https://wkrtcs.bdimg.com/rtcs/image?w=81&md5sum=7b9b2b3625f755c4cc9021f892924dc5&sign=2554d0cd93&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=1&ipr={"t":"img","w":"81","h":"44","dataType":"gif","c":"word/media/image81.png"})
的一个坐标为非负数的焦点，P为椭圆上的动点，连FP且延长到M点，使，求M点的轨迹方程。
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