2021年全国硕士研究生招生考试《数学一》真题及解析

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A 连续且取得极大值 B 连续且取得极小值 C 可导且导数为零 D 可导且导数不为零

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设函数f(x，y)可微，且f(x+1，ex)=x(x+1)2，f(x，x2)=2x2lnx，则df(1，1)=( )．

A dx+dy B dx-dy C dy D -dy

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设函数处的3次泰勒多项式为ax+bx2+cx3，则( )．

A a=1，b=0，c=-<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232738_7101.gif" /> B a=1，b=0，c=<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232738_7101.gif" /> C a=-1，b=-1，c=-<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232738_7101.gif" /> D a=-1，b=-1，c=<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232738_7101.gif" />

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设函数f(x)在区间[0，1]上连续，则( )．

A <img width="168" height="46" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232740_8350.jpg" /> B <img width="168" height="46" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232742_3830.jpg" /> C <img width="157" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232743_0705.jpg" /> D <img width="132" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232744_6319.jpg" />

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二次型f(x1，x2，x3)=(x1+x2)2+(x2+x3)2-(x3-x1)2的正惯性指数与负惯性指数依次为( )．

A 2，0 B 1，1 C 2，1 D 1，2

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β2，β3两两相交，则l1，l2依次为()．

A <img width="51" height="40" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232746_7725.jpg" /> B <img width="70" height="40" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232747_3663.jpg" /> C <img width="78" height="40" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232748_9913.jpg" /> D <img width="96" height="40" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232749_5226.jpg" />

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设A，B为n阶实矩阵，下列结论不成立的是( )．

A <img width="177" height="53" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232751_1320.jpg" /> B <img width="167" height="53" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232751_6632.jpg" /> C <img width="181" height="53" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232753_2726.jpg" /> D <img src="https://www.beizhujiaoyu.com/uploads/202208/165234134072341.jpg" alt="" />

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设A，B为随机事件，且0

A 若P(A|B)=P(A)，则P(A|<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232635_4445.gif" />)=P(A) B 若P(A|B)>P(A)，则P(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />|<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232635_4445.gif" />)>P(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />) C 若P(A|B)>P(A|<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232635_4445.gif" />)，则P(A|B)>P(A) D 若P(A|A<img width="26" height="20" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232755_4132.gif" />B)>P(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />|A<img width="26" height="20" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232755_4132.gif" />B)，则P(A)>P(B)

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设(X1，Y1)，(X2，Y2)，…，(Xn，Yn)为来自总体的简单随机样本，令=，则( )．

A <img width="322" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232759_7256.jpg" /> B <img width="342" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232800_1319.jpg" /> C <img width="411" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232801_8663.jpg" /> D <img width="432" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232802_2725.jpg" />

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设X1，X2，…，X16是来自总体N(μ，4)的简单随机样本，考虑假设检验问题：H0：μ≤10，H1：μ>10．(x)表示标准正态分布函数．若该检验问题的拒绝域

A 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(0．5) B 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(1) C 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(1．5) D 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(2)

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