hougin 2008-8-7 09:51
考研数学历年真题探秘之一
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[/font][/b][/align][/align][align=center][align=center][b][font=Times New Roman] [/font]——从考研数学真题中寻找哪些有价值的信息[/b][/align][/align][size=3][font=宋体]来自：万学海文[/font][size=10.5pt][font=Times New Roman]--[/font][/size][font=宋体]产品管理中心[/font][size=10.5pt][font=Times New Roman]-[/font][/size][font=宋体]教研室[/font][size=10.5pt][font=Times New Roman] [/font][/size][font=宋体]邬丽丽[/font][size=10.5pt][/size][/size]
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[font=宋体][size=12pt]通过考研数学历年真题比较我们容易发现很多规律。研究生入学考试从[/size][/font][size=12pt][font=Times New Roman]1989[/font][/size][font=宋体][size=12pt]年开始有考试，[/size][/font][size=12pt][font=Times New Roman]1998[/font][/size][font=宋体][size=12pt]年开始统考全国统考，从[/size][/font][size=12pt][font=Times New Roman]98[/font][/size][font=宋体][size=12pt]年开始考研数学试卷具有足够的代表性，它不仅充分显示了“既要有利于国家对稿层次人才的选拔，也要有利于促进高等学校各类苏雪课程教学质量的提高”的命题原则，且不少思路非常巧妙。如[/size][/font][img=173,23]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image002.gif[/img][size=3][font=宋体]已知函数[/font][img=59,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image004.gif[/img][font=宋体]在任意点[/font][img=13,15]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image006.gif[/img][font=宋体]处的增量[/font][img=100,41]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image008.gif[/img][font=宋体]，且当[/font][img=52,19]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image010.gif[/img][font=宋体]时，[/font][img=16,15]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image012.gif[/img][font=宋体]是[/font][img=23,19]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image014.gif[/img][font=宋体]的高阶无穷小，[/font][img=60,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image016.gif[/img][font=宋体]，则[/font][img=43,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image018.gif[/img][font=宋体]（[/font][font=Times New Roman] [/font][font=宋体]）[/font][/size]
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[img=27,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image024.gif[/img][img=15,15]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image026.gif[/img]
[img=27,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image028.gif[/img][img=20,32]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image030.gif[/img]
[img=28,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image032.gif[/img][img=29,32]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image034.gif[/img][/font][/size]
[font=宋体][size=3]这是一道综合题，解题的关键是建立微分方程。[/size][/font]
[size=3][font=宋体]只要掌握函数的微分的定义，去掉高阶无穷小，就能得到微分方程[/font][img=91,41]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image036.gif[/img][font=Times New Roman].[/font][font=宋体]然后求出其特解[/font][font=Times New Roman],[/font][font=宋体]再将[/font][img=35,19]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image038.gif[/img][font=宋体]代入得[/font][img=31,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image040.gif[/img][font=宋体]。[/font][/size]
[size=3][font=宋体]但是微分的定义是考生不太重视的。那么不知道微分的定义是否能求解呢[/font][font=Times New Roman]?[/font][font=宋体]其实知道导数和高阶无穷小的定义[/font][font=Times New Roman],[/font][font=宋体]亦可建立方程。其过程为[/font][/size]
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[size=3][font=宋体]即[/font][img=76,41]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image046.gif[/img][/size]
[font=宋体][size=3]此题妙在既重视基本概念，又不囿于某一特定概念；以一个选择题将微分、导数、高阶无穷小、微分方程的特解等概念及微分方程的求解方法自然集中在一起，更是独具匠心。[/size][/font]
[font=宋体][size=3]好题在试题中还不少，在此不一一列举。[/size][/font]
[size=3][font=宋体]细读历年真题，不难发现：以[/font][img=16,17]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image048.gif[/img][font=宋体]表示考察知识点相同，[/font][img=21,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image050.gif[/img][font=宋体]表示类似题型，[/font][img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img][font=宋体]表示几乎完全相同的题目，则[/font][/size]
[size=3][font=Times New Roman]2004[/font][font=宋体]年数学一第[/font][img=23,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image054.gif[/img][font=宋体]题与[/font][font=Times New Roman]2003[/font][font=宋体]年数学二第一大题第[/font][img=24,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image056.gif[/img][font=宋体]小题[/font][font=Times New Roman]([img=21,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image050.gif[/img])[/font][font=宋体]；[/font][/size]
[size=3][font=Times New Roman]2004[/font][font=宋体]年数学一第[/font][img=32,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image058.gif[/img][font=宋体]题与[/font][font=Times New Roman]2002[/font][font=宋体]年数学三第九大题[/font][font=Times New Roman]([img=21,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image050.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2004[/font][font=宋体]年数学三第[/font][img=32,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image058.gif[/img][font=宋体]题与[/font][font=Times New Roman]2000[/font][font=宋体]年数学三第九大题[/font][font=Times New Roman]([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2004[/font][font=宋体]年数学三、四第[/font][img=32,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image060.gif[/img][font=宋体]题与[/font][font=Times New Roman]1999[/font][font=宋体]年数学三第十一大题[/font][font=Times New Roman]([img=21,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image050.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2003[/font][font=宋体]年数学一第四大题与[/font][font=Times New Roman]2001[/font][font=宋体]年数学一第五大题[/font][font=Times New Roman]([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2003[/font][font=宋体]年数学二第十一大题与[/font][font=Times New Roman]1999[/font][font=宋体]年数学四第九大题[/font][font=Times New Roman]([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2003[/font][font=宋体]年数学四第十大题与[/font][font=Times New Roman]1999[/font][font=宋体]年数学三第九大题[/font][font=Times New Roman]([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2002[/font][font=宋体]年数学二第十一大题[/font][font=Times New Roman](2)[/font][font=宋体]与[/font][font=Times New Roman]1997[/font][font=宋体]年数学二第三大题[/font][font=Times New Roman](6)([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2002[/font][font=宋体]年数学三第十一大题[/font][font=Times New Roman](1)[/font][font=宋体]与[/font][font=Times New Roman]1999[/font][font=宋体]年数学三第十一大题[/font][font=Times New Roman](1)([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2001[/font][font=宋体]年数学二第一大题[/font][font=Times New Roman](5)[/font][font=宋体]与[/font][font=Times New Roman]2000[/font][font=宋体]年数学一第一大题[/font][font=Times New Roman](4) ([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2001[/font][font=宋体]年数学三、数学四第三大题与[/font][font=Times New Roman]1997[/font][font=宋体]年数学三第四大题[/font][font=Times New Roman]([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2000[/font][font=宋体]年数学二第二大题[/font][font=Times New Roman](2)[/font][font=宋体]与[/font][font=Times New Roman]1997[/font][font=宋体]年数学二第二大题[/font][font=Times New Roman](3) ([img=28,20]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image052.gif[/img]);[/font][/size]
[size=3][font=Times New Roman]2000[/font][font=宋体]年数学四第十大题与[/font][font=Times New Roman]1999[/font][font=宋体]年数学四第九大题[/font][img=27,21]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image020.gif[/img][font=宋体]；[/font][/size]
[size=3][img=33,11]file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtml1/01/clip_image063.gif[/img][/size]
[size=3][font=Times New Roman] [/font][font=宋体]从这些题目不难发现真题的价值所在，以上作者从几个方面提示学习考研数学学生在看历年考研数学的真题的时候可以从哪几个方面去考虑，根据自己的复习特点争取做到对知识体系了如指掌，对知识点不遗漏。[/font][/size]
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