2020考研数学三真题完整版
一、选择题：1~8小题，第小题4分，共32分.下列每题给出的四个选项中，只有一个选项是符合题目要求的，请将选项前的字母填在答题纸指定位置上.
1.设![](https://wkrtcs.bdimg.com/rtcs/image?w=323&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"323","h":"50","c":"886aca64f2c3c49a2a15bb5555667422.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=57&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"57","h":"20","c":"47831bd949549df3a7f05d891201169a.png"})
B.![](https://wkrtcs.bdimg.com/rtcs/image?w=60&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"60","h":"20","c":"4d6e2c041ea1ce89f3225bf7146778b1.png"})
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=86&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"86","h":"21","c":"f0dcc9c0620c585db2b2790b88081744.png"})
D.![](https://wkrtcs.bdimg.com/rtcs/image?w=89&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"89","h":"21","c":"9b0d2f2b9f3ec4ad0793a39ae42770d7.png"})
2.![](https://wkrtcs.bdimg.com/rtcs/image?w=190&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"190","h":"57","c":"d19a039f4e1674174fb15e8f176bfa3f.png"})
3.设奇函数![](https://wkrtcs.bdimg.com/rtcs/image?w=42&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"42","h":"21","c":"50bbd36e1fd2333108437a2ca378be62.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=207&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"207","h":"58","c":"2e3ec9ea7734cc98dbb57f5de24ac63c.png"})
B.
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=207&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"207","h":"58","c":"f3178839859eac8e3d412c6df77650dc.png"})
D.
4.设幂级数![](https://wkrtcs.bdimg.com/rtcs/image?w=128&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"128","h":"68","c":"3ed6121c8fc1e1ed4dfb73bc4eaa3c02.png"})
A.（-2，6）
B.（-3，1）
C.（-5，3）
D.（-17，15）
5.设4阶矩阵![](https://wkrtcs.bdimg.com/rtcs/image?w=70&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"70","h":"24","c":"496756f3750a35d98d28bd96f7d9b1cb.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=181&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"181","h":"23","c":"e33b195ef02579ad38c4bf52f00720ec.png"})
B.![](https://wkrtcs.bdimg.com/rtcs/image?w=182&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"182","h":"23","c":"533e5cf38925523df79e4212425a62ba.png"})
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=182&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"182","h":"23","c":"22cc4375148b66a1defa31cf245221ae.png"})
D.![](https://wkrtcs.bdimg.com/rtcs/image?w=182&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"182","h":"23","c":"13277169f8a2851337f4bd3e743794b8.png"})
6.设![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"16","h":"20","c":"7fc56270e7a70fa81a5935b72eacbe29.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=150&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"150","h":"23","c":"37a5a3c54e698c89ae5d8e79a5b5a864.png"})
B.![](https://wkrtcs.bdimg.com/rtcs/image?w=150&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"150","h":"23","c":"c7df7daa53d5136b5d65c8552bdf93c9.png"})
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=150&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"150","h":"23","c":"4cde5006f9451ea015f4bf7b578603a3.png"})
D.![](https://wkrtcs.bdimg.com/rtcs/image?w=150&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"150","h":"23","c":"351068f9909f842f44b72ed07ab1ed42.png"})
7.设A,B,C为三个随机事件，且![](https://wkrtcs.bdimg.com/rtcs/image?w=491&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"491","h":"43","c":"eda8738015cb496ce31317bcb0b39b24.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"16","h":"43","c":"9df743fb4a026d67e85ab08111c4aedd.png"})
B.![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"16","h":"43","c":"6ca8c824c79dbb80005f071431350618.png"})
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"16","h":"43","c":"93b05c90d14a117ba52da1d743a43ab1.png"})
D.![](https://wkrtcs.bdimg.com/rtcs/image?w=27&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"27","h":"43","c":"a72b18c11198b7bf9f0fea1af1863fd2.png"})
8.设随机变量![](https://wkrtcs.bdimg.com/rtcs/image?w=55&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"55","h":"21","c":"f00acce613318349cb04ab296486fc11.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=94&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"94","h":"52","c":"50ebb3bd9f142cca0f8a2dfc57661cf9.png"})
B.![](https://wkrtcs.bdimg.com/rtcs/image?w=94&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"94","h":"52","c":"79f27baf73c397e321d3ea77e0cc2006.png"})
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=94&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"94","h":"52","c":"0ceefb064a56632ecde7fe7433c7a593.png"})
D.![](https://wkrtcs.bdimg.com/rtcs/image?w=94&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"94","h":"52","c":"9387dbdb0b7ccbe934b26dfb625ae932.png"})
9.设![](https://wkrtcs.bdimg.com/rtcs/image?w=241&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"241","h":"21","c":"7b17b0209c5019867e1a63448f99c296.png"})
10.曲线![](https://wkrtcs.bdimg.com/rtcs/image?w=116&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"116","h":"21","c":"fb53acb1c6a406be85907a54e8e85d4f.png"})
11.![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"16","h":"20","c":"f09564c9ca56850d4cd6b3319e541aee.png"})
12.设平面区域![](https://wkrtcs.bdimg.com/rtcs/image?w=289&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"289","h":"43","c":"2965a7fb3c587c57253ef870c85310df.png"})
13.行列式![](https://wkrtcs.bdimg.com/rtcs/image?w=309&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"309","h":"128","c":"a002f2782fee2ce428d425d8207c17f3.png"})
14.随机变量![](https://wkrtcs.bdimg.com/rtcs/image?w=15&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"15","h":"20","c":"02129bb861061d1a052c592e2dc6b383.png"})
三、解答题：15~23小题，共94分.请将解答写在答题纸指定位置上.解答写出文字说明、证明过程或演算步骤.
15.![](https://wkrtcs.bdimg.com/rtcs/image?w=110&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"110","h":"50","c":"fee8277dfb2a94f12f74a9f35e00af62.png"})
16.![](https://wkrtcs.bdimg.com/rtcs/image?w=106&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"106","h":"21","c":"42d9e4194e8c972d89b65436cf856b78.png"})
17.![](https://wkrtcs.bdimg.com/rtcs/image?w=307&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"307","h":"21","c":"3c2233abad2b8e82dd5b7f73b7c0b122.png"})
（1）求
![](https://wkrtcs.bdimg.com/rtcs/image?w=86.07&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"86.07","h":"68.47","dataType":"png","c":"word/media/image66.png","imgOriW":181,"imgOriH":144})
（2）
18.![](https://wkrtcs.bdimg.com/rtcs/image?w=283&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"283","h":"59","c":"e4b7e2dfe854baf3e5faa813aab92ef9.png"})
求![](https://wkrtcs.bdimg.com/rtcs/image?w=132&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"132","h":"59","c":"39ec50aa4d8ce8570406dbf6b76faf20.png"})
19.
（1）证![](https://wkrtcs.bdimg.com/rtcs/image?w=227&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"227","h":"21","c":"16a6e24c5a4d63285b688c1702acc3e1.png"})
（2）若![](https://wkrtcs.bdimg.com/rtcs/image?w=309&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"309","h":"21","c":"fd7707c7dbd747e22210c30ee93c4d6e.png"})
20.二次型![](https://wkrtcs.bdimg.com/rtcs/image?w=221&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"221","h":"27","c":"08663141842162f0083f5571d4b938bf.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=284&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"284","h":"31","c":"43f1f7f9046625fcea11c576fb683679.png"})
（1）求![](https://wkrtcs.bdimg.com/rtcs/image?w=33&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"33","h":"20","c":"b345e1dc09f20fdefdea469f09167892.png"})
（2）求
21.![](https://wkrtcs.bdimg.com/rtcs/image?w=96&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"96","h":"21","c":"e38048a3462bf035c944348b87b6bdd5.png"})
（1）证
（2）若![](https://wkrtcs.bdimg.com/rtcs/image?w=142&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"142","h":"25","c":"55b9431bd2cb9efb78b9e7fd10307b84.png"})
问![](https://wkrtcs.bdimg.com/rtcs/image?w=93&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"93","h":"25","c":"61c978b7c7f606b59b117fee8a28a01a.png"})
22.
![](https://wkrtcs.bdimg.com/rtcs/image?w=151&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"151","h":"158","c":"51441a31abb258b6269288f833bf6167.png"})
（1）求![](https://wkrtcs.bdimg.com/rtcs/image?w=56&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"56","h":"21","c":"474ba9c85a0c0fa70217c7e8b15b3436.png"})
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=33&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"33","h":"23","c":"d840d6bfb481ae77856330725cfb12e4.png"})
23.![](https://wkrtcs.bdimg.com/rtcs/image?w=212&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"212","h":"101","c":"de94c94bdf4ec879c43c565ce4fb234e.png"})
（1）求![](https://wkrtcs.bdimg.com/rtcs/image?w=225&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"225","h":"20","c":"cbee554fb0defe9a08099dcf8f30a231.png"})
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=52&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"52","h":"23","c":"fd5ef72cc6cfa6023069fa9f4c7edd21.png"})
求![](https://wkrtcs.bdimg.com/rtcs/image?w=14&md5sum=efeca580a1b24301aa792b0a7573399b&sign=8dc4471ac1&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=266&ipr={"t":"img","w":"14","h":"20","c":"7943b5fdf911af3ffcf9d8f738478e8a.png"})
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