中国科学技术大学2020年自主招生综合评价测试数学卷
发布时间：2020-07-31 08:33:56
中国科学技术大学
2020年自主招生综合评价测试数学卷
1.方程![](https://wkrtcs.bdimg.com/rtcs/image?w=99&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"99","h":"43","c":"72fb25d5ecb2be7a3854cbf5de476a3d.png"})
2.函数![](https://wkrtcs.bdimg.com/rtcs/image?w=290&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"290","h":"30","c":"a988b0703c6c700b065e5ea05cb96fb7.png"})
3.已知集合![](https://wkrtcs.bdimg.com/rtcs/image?w=136&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"136","h":"20","c":"a7ea2977162ce262978c1222dc5efca7.png"})
4.已知复数![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"13","h":"20","c":"fbade9e36a3f36d3d676c1b808451dd7.png"})
5.正方体的十二条棱中，取四条两两不相交的棱，有________种取法.
6.整数![](https://wkrtcs.bdimg.com/rtcs/image?w=32&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"32","h":"20","c":"f10bc3c94b77e1d6b9f98106daf335c1.png"})
9.椭圆![](https://wkrtcs.bdimg.com/rtcs/image?w=105&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"105","h":"44","c":"7d50507d421bd95ec706415c52cd1ff0.png"})
(1)求C上一点![](https://wkrtcs.bdimg.com/rtcs/image?w=91&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"91","h":"54","c":"ab6b1eda0e9bc4ce3a5e3c855aa839b9.png"})
(2)P在C上，Q在T上，求证![](https://wkrtcs.bdimg.com/rtcs/image?w=73&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"73","h":"43","c":"0ec536cfde64e5b4e39f713f92ed0006.png"})
10.已知![](https://wkrtcs.bdimg.com/rtcs/image?w=105&md5sum=f236b28fee75f6e57e964d246b82509f&sign=808f92cd61&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=553&ipr={"t":"img","w":"105","h":"23","c":"e4292d572410b7011d2bee37f67dd35a.png"})
（注：填空题有8小题，解答题有3小题，还少2个填空题，1个解答题）
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