planet/高考数学/2021年全国高考甲卷数学文科试题.tm

<TeXmacs|2.1.2>

<style|<tuple|generic|chinese>>

<\body>
  <doc-data|<doc-title|2021\<#5E74\>\<#5168\>\<#56FD\>\<#9AD8\>\<#8003\>\<#7532\>\<#5377\>\<#6570\>\<#5B66\>\<#FF08\>\<#6587\>\<#FF09\>\<#8BD5\>\<#9898\>>>

  <subsubsection*|\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>>

  <\enumerate>
    <item>\<#8BBE\>\<#96C6\>\<#5408\><math|M=<around*|{|1,3,5,7,9|}>,N=<around*|{|x\|2*x\<gtr\>7|}>>\<#FF0C\>\<#5219\><math|M\<cap\>N<long-arrow|\<rubber-equal\>|>><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<around*|{|7,9|}>>
      </cell>|<\cell>
        B. {5, 7, 9}
      </cell>|<\cell>
        C. {3, 5, 7, 9}
      </cell>|<\cell>
        D. {1, 3, 5, 7, 9}
      </cell>>>>
    </wide-tabular>

    <item>\<#4E3A\>\<#4E86\>\<#89E3\>\<#67D0\>\<#5730\>\<#519C\>\<#6751\>\<#7ECF\>\<#6D4E\>\<#60C5\>\<#51B5\>\<#FF0C\>\<#5BF9\>\<#8BE5\>\<#5730\>\<#519C\>\<#6237\>\<#5BB6\>\<#5EAD\>\<#5E74\>\<#6536\>\<#5165\>\<#8FDB\>\<#884C\>\<#62BD\>\<#6837\>\<#8C03\>\<#67E5\>\<#FF0C\>\<#5C06\>\<#519C\>\<#6237\>\<#5BB6\>\<#5EAD\>\<#5E74\>\<#6536\>\<#5165\>\<#7684\>\<#8C03\>\<#67E5\>\<#6570\>\<#636E\>\<#6574\>\<#7406\>\<#5F97\>\<#5230\>\<#5982\>\<#4E0B\>\<#9891\>\<#7387\>\<#5206\>\<#5E03\>\<#76F4\>\<#65B9\>\<#56FE\>\<#FF1A\>

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    \<#6839\>\<#636E\>\<#6B64\>\<#9891\>\<#7387\>\<#5206\>\<#5E03\>\<#76F4\>\<#65B9\>\<#56FE\>\<#FF0C\>\<#4E0B\>\<#9762\>\<#7ED3\>\<#8BBA\>\<#4E2D\>\<#4E0D\>\<#6B63\>\<#786E\>\<#7684\>\<#662F\><underline|<space|3em>>

    A\<#FF0E\>\<#8BE5\>\<#5730\>\<#519C\>\<#6237\>\<#5BB6\>\<#5EAD\>\<#5E74\>\<#6536\>\<#5165\>\<#4F4E\>\<#4E8E\>4.5\<#4E07\>\<#5143\>\<#7684\>\<#519C\>\<#6237\>\<#6BD4\>\<#7387\>\<#4F30\>\<#8BA1\>\<#4E3A\>6%

    B\<#FF0E\>\<#8BE5\>\<#5730\>\<#519C\>\<#6237\>\<#5BB6\>\<#5EAD\>\<#5E74\>\<#6536\>\<#5165\>\<#4E0D\>\<#4F4E\>\<#4E8E\>10.5\<#4E07\>\<#5143\>\<#7684\>\<#519C\>\<#6237\>\<#6BD4\>\<#7387\>\<#4F30\>\<#8BA1\>\<#4E3A\>10%

    C\<#FF0E\>\<#4F30\>\<#8BA1\>\<#8BE5\>\<#5730\>\<#519C\>\<#6237\>\<#5BB6\>\<#5EAD\>\<#5E74\>\<#6536\>\<#5165\>\<#7684\>\<#5E73\>\<#5747\>\<#503C\>\<#4E0D\>\<#8D85\>\<#8FC7\>6.5\<#4E07\>\<#5143\>

    D\<#FF0E\>\<#4F30\>\<#8BA1\>\<#8BE5\>\<#5730\>\<#6709\>\<#4E00\>\<#534A\>\<#4EE5\>\<#4E0A\>\<#7684\>\<#519C\>\<#6237\>\<#FF0C\>\<#5176\>\<#5BB6\>\<#5EAD\>\<#5E74\>\<#6536\>\<#5165\>\<#4ECB\>\<#4E8E\>4.5\<#4E07\>\<#5143\>\<#81F3\>8.5\<#4E07\>\<#5143\>\<#4E4B\>\<#95F4\>

    <item>\<#5DF2\>\<#77E5\><math|<around*|(|1-i|)><rsup|2>*z=3+2*i>\<#FF0C\>\<#5219\><math|z=><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|-1-<frac|3|2>i>
      </cell>|<\cell>
        B. <math|-1+<frac|3|2>i>
      </cell>|<\cell>
        C. <math|-<frac|3|2>+i>
      </cell>|<\cell>
        D. <math|-<frac|3|2>-i>
      </cell>>>>
    </wide-tabular>

    <item>\<#4E0B\>\<#5217\>\<#51FD\>\<#6570\>\<#4E2D\>\<#662F\>\<#589E\>\<#51FD\>\<#6570\>\<#7684\>\<#4E3A\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<cwith|1|1|1|1|cell-halign|l>|<table|<row|<\cell>
        A. <math|f<around*|(|x|)>=-x>
      </cell>|<\cell>
        B. <math|f<around*|(|x|)>=<around*|(|<frac|2|3>|)><rsup|x>>
      </cell>|<\cell>
        C. <math|f<around*|(|x|)>=x<rsup|2>>
      </cell>|<\cell>
        D. <math|f<around*|(|x|)>=<sqrt|x|3>>
      </cell>>>>
    </wide-tabular>

    <item>\<#70B9\><math|<around*|(|3,0|)>>\<#5230\>\<#53CC\>\<#66F2\>\<#7EBF\><math|<frac|x<rsup|2>|16>-<frac|y<rsup|2>|9>=1>\<#7684\>\<#4E00\>\<#6761\>\<#6E10\>\<#8FD1\>\<#7EBF\>\<#7684\>\<#8DDD\>\<#79BB\>\<#4E3A\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<frac|9|5>>
      </cell>|<\cell>
        B. <math|<frac|8|5>>
      </cell>|<\cell>
        C. <math|<frac|6|5>>
      </cell>|<\cell>
        D. <math|<frac|4|5>>
      </cell>>>>
    </wide-tabular>

    <item>\<#9752\>\<#5C11\>\<#5E74\>\<#89C6\>\<#529B\>\<#662F\>\<#793E\>\<#4F1A\>\<#666E\>\<#904D\>\<#5173\>\<#6CE8\>\<#7684\>\<#95EE\>\<#9898\>\<#FF0C\>\<#89C6\>\<#529B\>\<#60C5\>\<#51B5\>\<#53EF\>\<#501F\>\<#52A9\>\<#89C6\>\<#529B\>\<#8868\>\<#6D4B\>\<#91CF\>\<#FF0E\>\<#901A\>\<#5E38\>\<#7528\>\<#4E94\>\<#5206\>\<#8BB0\>\<#5F55\>\<#6CD5\>\<#548C\>\<#5C0F\>\<#6570\>\<#8BB0\>\<#5F55\>\<#6CD5\>\<#8BB0\>\<#5F55\>\<#89C6\>\<#529B\>\<#6570\>\<#636E\>\<#FF0C\>\<#4E94\>\<#5206\>\<#8BB0\>\<#5F55\>\<#6CD5\>\<#7684\>\<#6570\>\<#636E\>L\<#548C\>\<#5C0F\>\<#6570\>\<#8BB0\>\<#5F55\>\<#8868\>\<#7684\>\<#6570\>\<#636E\>V\<#7684\>\<#6EE1\>\<#8DB3\><math|L=5+lg
    V>. \<#5DF2\>\<#77E5\>\<#67D0\>\<#540C\>\<#5B66\>\<#89C6\>\<#529B\>\<#7684\>\<#4E94\>\<#5206\>\<#8BB0\>\<#5F55\>\<#6CD5\>\<#7684\>\<#6570\>\<#636E\>\<#4E3A\>4.9\<#FF0C\>\<#5219\>\<#5176\>\<#89C6\>\<#529B\>\<#7684\>\<#5C0F\>\<#6570\>\<#8BB0\>\<#5F55\>\<#6CD5\>\<#7684\>\<#6570\>\<#636E\>\<#4E3A\><underline|<space|3em>>(<math|<sqrt|10|10>\<approx\>1.259>)

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. 1.5
      </cell>|<\cell>
        B. 1.2
      </cell>|<\cell>
        C. 0.8
      </cell>|<\cell>
        D. 0.6
      </cell>>>>
    </wide-tabular>

    <item>\<#5728\>\<#4E00\>\<#4E2A\>\<#6B63\>\<#65B9\>\<#4F53\>\<#4E2D\>\<#FF0C\>\<#8FC7\>\<#9876\>\<#70B9\><math|A>\<#7684\>\<#4E09\>\<#6761\>\<#68F1\>\<#7684\>\<#4E2D\>\<#70B9\>\<#5206\>\<#522B\>\<#4E3A\><math|E>\<#FF0C\><math|F>\<#FF0C\><math|G>.
    \<#8BE5\>\<#6B63\>\<#65B9\>\<#5F62\>\<#622A\>\<#53BB\>\<#4E09\>\<#68F1\>\<#9525\>A-EFG\<#540E\>\<#FF0C\>\<#6240\>\<#5F97\>\<#591A\>\<#9762\>\<#4F53\>\<#7684\>\<#4E09\>\<#89C6\>\<#56FE\>\<#4E2D\>\<#FF0C\>\<#6B63\>\<#89C6\>\<#56FE\>\<#5982\>\<#56FE\>\<#6240\>\<#793A\>\<#FF0C\>\<#5219\>\<#76F8\>\<#5E94\>\<#7684\>\<#4FA7\>\<#89C6\>\<#56FE\>\<#662F\><underline|<space|3em>>

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        C. <image|<tuple|<#89504E470D0A1A0A0000000D49484452000000B4000000B20806000000EB94E52F000000097048597300000B1300000B1301009A9C1800000A0449444154789CEDDD5B48D36F1CC7F1CF63EEA0D6BF82AC74744E41E964592195999A8748C288144BBAA89B2EC28B08BAEBAA9BE8AAEE232A82C4D2D2A861F3D02A2C143ACB2A94083B4D92C698BA74BFFF857F97F99F6EDAB6677BFCBCAEA6FE7C7E5FE9DDD3CF9D129AA66900006800047E1BFFF1E8E7C61AFFF540F85A37D0F3FFEDF118738CAF9F45F373DBD7F1E38F9D6CD6F1C7FB3BEF44B3FB5A7FA2B526FB590239B7AFF38F5F63A299FCAD33D1D7FCFDBC63D7FF3D8B103142689A479BDA37067A3B901F62ECFABE8EF5174220EB4FC6D7B9C7AFE5EF2F8AAF757CCD16C83A819C23986BAA450821C4EF1D9A28BA0921448CEC2188822976A22F747474E0D5AB57484E4E86C16008E74C44FF238480DD6E87D3E9C49E3D7B909898E8FB385F971C3F7FFE444A4A0AEC763B8C4623743A5DC807269A8C10020E87030070E4C8115CBE7CD9D731C2E70EFDFCF973D8ED7600C0C0C000060606423729D1147DFEFC79C2AFF90CDA6432796FAF58B102E9E9E91082BF4D933C0E87034F9F3EC5E0E0E0A4C7F90CDAE3F1786F1F387000E7CE9D0BEE744453F4EEDD3BE4E4E4E0CB972F931EE7F75E8EA1A1210C0F0F076D30A2E9E8EFEF4720F730F36E3B520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A8326A53068520A83A6A8E0F178A0699ADFE31834450587C30197CBE5F738064D51E19F7FFE417C7CBCDFE3183445B48282025CBD7A157ABD1E3131FE738D0DC34C4453A6691A2A2B2BD1D8D888C6C6461C3F7E1CB1B1FE7365D01451344D831002FBF6ED437D7D3D8410D0340DCB962DE32F85147D8410D8BF7F3FEAEBEB018C04DED2D2827DFBF6616868C8EFF733688A18BF7EFDC2E1C387515B5B0B00301A8DB877EF1E76EEDC89C1C1C180D6E02507458CF2F272DCBA75CBFBF18D1B3750545434A53518344584BEBEBE3F627EF0E001F2F2F2A6BC0E2F392822CC9F3F1F6FDEBC81C96482D96C9E56CC0077688A20E9E9E9E8ECECC49C3973A6BD0677688A287F1333C0A0490287C381E7CF9F87646D064D6177F4E851646464E0FCF9F3415F9B415358656767A3A6A6060070EAD429F4F4F404757D064D61B377EF5E58AD5600238F085AAD56984CA6A09E83415358545454E0EEDDBB0080B973E7C26C3663FBF6ED413F0FEFB6A390197DA2514141011A1B1BBD9FBF7CF93276EFDE1D927332680A1921040A0B0BFF88B9B5B515D9D9D9213B272F3928A44E9E3C89458B16213E3E1E8D8D8D218D19E00E4D2156505080E6E666D8EDF690C70C30680A83B4B434A4A5A585E55CBCE4A0A0F2783C52CFCFA02968CACACA70E9D225A933F092838262F3E6CD686F6F47757535E2E2E270E8D02129737087A6BF32303080E2E262B4B7B70300121212909898286D1EEED0342DA30F9A949797E3FEFDFB00469EFA59575787DCDC5C697331689A1621044A4A4AD0D0D0E0FD5C43434358EE9A9B0C83A629FBF5EB17F2F2F2BC4F3432180CB87DFBB6F498015E43D334D86C367474740018792DE0FDFBF75158582879AA110C9AA66CCD9A35DE5F02EBEAEA9093932377A03178C941D392969616D05B73851B7768520A83A6098DEEC02D2D2D72079902064D131242A0B4B414B9B9B9B879F3A6EC7102C2A0C92797CB85B2B232D4D5D541D3349C3D7B164EA753F6587EF19742FAC3E82380478E1CF1BE3A3B212101172F5EC4ECD9B3254FE71F83A63F8CBED9F89D3B77BC9FB3582CD8BA75ABC4A902C74B0EF2723A9D282B2BF3C63C6FDE3C343434444DCC007768FA8FDBEDC6B163C7505D5D0D6024E6DADADA887AD02410DCA10900A0D7EBB17FFF7ECC9A350B0070FDFAF5A88B19E00E4D631C3C78105D5D5DC8CDCDC5962D5B648F332D0C9AFE70FAF469D923FC155E72905218F40CE476BB919F9F1FB2F768968941CF302E970B252525B0582CC8C8C880D96C963D5250F11A7A86292A2AF2BED244AFD74B7D416B2830E819242B2B0B6D6D6DDE8F9F3C79828D1B374A9C28F878C93103381C0EECDAB5CB1BF3A2458B60B158B069D326C993051F7768C50D0F0F63CF9E3D78FCF8318091B71AA8ADAD45565696E4C942833BB4E2AC56AB376600A8AFAF57366680412B2F27270757AE5CC1D2A54BF1E8D123ECDCB953F64821C54B8E19E0D0A143D8BD7B37162F5E2C7B9490E30E3D03C4C4C4CC88980106AD94EFDFBFE3FDFBF7B2C7908A412B42D33494979763DBB66DDE374F9C89780DAD888C8C0CBC78F102C0C8D340BF7EFD8AF8F878C953851F77E82837383888B56BD77A639E3D7B361E3E7C38236306187454EBEFEF474949095EBF7E0D0058B060019A9B9BB161C306C993C9C34B8E2834FA560339393978F6EC1900C06834A2A1A10199999992A7938B4147212104323333BD6F696B3018D0D6D686F5EBD74B9E4C3E5E7244A9CACA4A00405252129E3E7DCA98FF
      </cell>|<\cell>
        D. <image|<tuple|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
      </cell>>>>
    </wide-tabular>

    <item>\<#5728\><math|\<vartriangle\>ABC>\<#4E2D\>\<#FF0C\>\<#5DF2\>\<#77E5\><math|B=120<rsup|\<circ\>>>\<#FF0C\><math|AC=<sqrt|19>>\<#FF0C\><math|AB=2>\<#FF0C\>\<#5219\><math|BC=><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. 1
      </cell>|<\cell>
        B. <math|<sqrt|2>>
      </cell>|<\cell>
        C. <math|<sqrt|5>>
      </cell>|<\cell>
        D. 3
      </cell>>>>
    </wide-tabular>

    <item>\<#8BB0\><math|S<rsub|n>>\<#4E3A\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#524D\><math|n>\<#9879\>\<#548C\>.
    \<#82E5\><math|S<rsub|2>=4>\<#FF0C\><math|S<rsub|4>=6>\<#FF0C\>\<#5219\><math|S<rsub|6>=><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. 7
      </cell>|<\cell>
        B. 8
      </cell>|<\cell>
        C. 9
      </cell>|<\cell>
        D. 10
      </cell>>>>
    </wide-tabular>

    <item>\<#5C06\>3\<#4E2A\>1\<#548C\>2\<#4E2A\>0\<#968F\>\<#673A\>\<#6392\>\<#6210\>\<#4E00\>\<#884C\>\<#FF0C\>\<#5219\>2\<#4E2A\>0\<#4E0D\>\<#76F8\>\<#90BB\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. 0.3
      </cell>|<\cell>
        B. 0.5
      </cell>|<\cell>
        C. 0.6
      </cell>|<\cell>
        D. 0.8
      </cell>>>>
    </wide-tabular>

    <item>\<#82E5\><math|\<alpha\>\<in\><around*|(|0,<frac|\<pi\>|2>|)>>,
    <math|tan 2*\<alpha\>=<frac|cos \<alpha\>|2-sin
    \<alpha\>>>\<#FF0C\>\<#5219\><math|tan \<alpha\>=><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<frac|<sqrt|15>|15>>
      </cell>|<\cell>
        B. <math|<frac|<sqrt|5>|5>>
      </cell>|<\cell>
        C. <math|<frac|<sqrt|5>|3>>
      </cell>|<\cell>
        D. <math|<frac|<sqrt|15>|3>>
      </cell>>>>
    </wide-tabular>

    <item>\<#8BBE\><math|f<around*|(|x|)>>\<#662F\>\<#5B9A\>\<#4E49\>\<#57DF\>\<#4E3A\><math|R>\<#7684\>\<#5947\>\<#51FD\>\<#6570\>\<#FF0C\>\<#4E14\><math|f<around*|(|1+x|)>=f<around*|(|-x|)>>.
    \<#82E5\><math|f<around*|(|-<frac|1|3>|)>=<frac|1|3>>\<#FF0C\>\<#5219\><math|f<around*|(|<frac|5|3>|)>=><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|-<frac|5|3>>
      </cell>|<\cell>
        B. <math|-<frac|1|3>>
      </cell>|<\cell>
        C. <math|<frac|1|3>>
      </cell>|<\cell>
        D. <math|<frac|5|3>>
      </cell>>>>
    </wide-tabular>
  </enumerate>

  <subsubsection*|\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>>

  <\enumerate>
    <assign|item-nr|12><item>\<#82E5\>\<#5411\>\<#91CF\><math|<around*|\||<wide|a|\<vect\>>|\|>=3>\<#FF0C\><math|<around*|\||<wide|a|\<vect\>>-<wide|b|\<vect\>>|\|>=5>\<#FF0C\><math|<wide|a|\<vect\>>\<cdot\><wide|b|\<vect\>>=1>\<#FF0C\>\<#5219\><math|<around*|\||<wide|b|\<vect\>>|\|>=><underline|<space|3em>>.

    <item>\<#5DF2\>\<#77E5\>\<#4E00\>\<#4E2A\>\<#5706\>\<#9525\>\<#7684\>\<#5E95\>\<#9762\>\<#534A\>\<#5F84\>\<#4E3A\>6\<#FF0C\>\<#5176\>\<#4F53\>\<#79EF\>\<#4E3A\><math|30\<pi\>>\<#FF0C\>\<#5219\>\<#8BE5\>\<#5706\>\<#9525\>\<#7684\>\<#4FA7\>\<#9762\>\<#79EF\>\<#4E3A\><underline|<space|3em>>.

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=2*cos<around*|(|\<omega\>*x+\<varphi\>|)>>\<#7684\>\<#90E8\>\<#5206\>\<#56FE\>\<#50CF\>\<#5982\>\<#56FE\>\<#6240\>\<#793A\>\<#FF0C\>\<#5219\><math|f<around*|(|<frac|\<pi\>|2>|)>=><underline|<space|3em>>.

    <image|<tuple|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

    <item>\<#5DF2\>\<#77E5\><math|F<rsub|1>,F<rsub|2>>\<#4E3A\>\<#692D\>\<#5706\>C:
    <with|math-display|true|<math|<frac|x<rsup|2>|16>+<frac|x<rsup|2>|4>=1>>\<#7684\>\<#4E24\>\<#4E2A\>\<#7126\>\<#70B9\>\<#FF0C\><math|P>\<#FF0C\><math|Q>\<#4E3A\><math|C>\<#4E0A\>\<#5173\>\<#4E8E\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#5BF9\>\<#79F0\>\<#7684\>\<#4E24\>\<#70B9\>\<#FF0C\>\<#4E14\><math|<around*|\||PQ|\|>=<around*|\||F<rsub|1>F<rsub|2>|\|>>\<#FF0C\>\<#5219\>\<#56DB\>\<#8FB9\>\<#5F62\><math|PF<rsub|1>QF<rsub|2>>\<#7684\>\<#9762\>\<#79EF\>\<#4E3A\><underline|<space|3em>>.
  </enumerate>

  <subsubsection*|\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>>

  <\enumerate>
    <assign|item-nr|16><item>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#53F0\>\<#673A\>\<#5E8A\>\<#751F\>\<#4EA7\>\<#540C\>\<#79CD\>\<#4EA7\>\<#54C1\>\<#FF0C\>\<#4EA7\>\<#54C1\>\<#6309\>\<#8D28\>\<#91CF\>\<#5206\>\<#4E3A\>\<#4E00\>\<#7EA7\>\<#54C1\>\<#548C\>\<#4E8C\>\<#7EA7\>\<#54C1\>\<#FF0C\>\<#4E3A\>\<#4E86\>\<#6BD4\>\<#8F83\>\<#4E24\>\<#53F0\>\<#673A\>\<#5E8A\>\<#4EA7\>\<#54C1\>\<#7684\>\<#8D28\>\<#91CF\>\<#FF0C\>\<#5206\>\<#522B\>\<#7528\>\<#4E24\>\<#53F0\>\<#673A\>\<#5E8A\>\<#5404\>\<#751F\>\<#4EA7\>\<#4E86\>200\<#4EF6\>\<#4EA7\>\<#54C1\>\<#FF0C\>\<#4EA7\>\<#54C1\>\<#7684\>\<#8D28\>\<#91CF\>\<#60C5\>\<#51B5\>\<#7EDF\>\<#8BA1\>\<#5982\>\<#4E0B\>\<#8868\>\<#FF1A\>

    <\wide-block>
      <tformat|<cwith|1|1|2|2|cell-halign|c>|<cwith|1|1|3|3|cell-halign|c>|<cwith|1|1|4|4|cell-halign|c>|<cwith|2|2|2|2|cell-halign|c>|<cwith|2|2|3|3|cell-halign|c>|<cwith|2|2|4|4|cell-halign|c>|<cwith|3|3|2|-1|cell-halign|c>|<cwith|3|3|2|2|cell-valign|b>|<cwith|2|-1|1|1|cell-halign|c>|<cwith|4|4|3|3|cell-halign|c>|<cwith|4|4|2|2|cell-halign|c>|<cwith|4|4|4|4|cell-halign|c>|<table|<row|<\cell>
        \;
      </cell>|<\cell>
        \<#4E00\>\<#7EA7\>\<#54C1\>
      </cell>|<\cell>
        \<#4E8C\>\<#7EA7\>\<#54C1\>
      </cell>|<\cell>
        \<#4E09\>\<#7EA7\>\<#54C1\>
      </cell>>|<row|<\cell>
        \<#7532\>\<#673A\>\<#5E8A\>
      </cell>|<\cell>
        150
      </cell>|<\cell>
        50
      </cell>|<\cell>
        200
      </cell>>|<row|<\cell>
        \<#4E59\>\<#673A\>\<#5E8A\>
      </cell>|<\cell>
        120
      </cell>|<\cell>
        80
      </cell>|<\cell>
        200
      </cell>>|<row|<\cell>
        \<#5408\>\<#8BA1\>
      </cell>|<\cell>
        270
      </cell>|<\cell>
        130
      </cell>|<\cell>
        400
      </cell>>>>
    </wide-block>

    \<#FF08\>1\<#FF09\>\<#7532\>\<#673A\>\<#5E8A\>\<#3001\>\<#4E59\>\<#673A\>\<#5E8A\>\<#751F\>\<#4EA7\>\<#7684\>\<#4EA7\>\<#54C1\>\<#4E2D\>\<#4E00\>\<#7EA7\>\<#54C1\>\<#7684\>\<#9891\>\<#7387\>\<#5206\>\<#522B\>\<#662F\>\<#591A\>\<#5C11\>\<#FF1F\>

    \<#FF08\>2\<#FF09\>\<#80FD\>\<#5426\>\<#6709\>99%\<#7684\>\<#628A\>\<#63E1\>\<#8BA4\>\<#4E3A\>\<#7532\>\<#673A\>\<#5E8A\>\<#7684\>\<#4EA7\>\<#54C1\>\<#8D28\>\<#91CF\>\<#4E0E\>\<#4E59\>\<#673A\>\<#5E8A\>\<#7684\>\<#4EA7\>\<#54C1\>\<#8D28\>\<#91CF\>\<#6709\>\<#5DEE\>\<#5F02\>?

    \<#9644\>\<#FF1A\><with|math-display|true|<math|K<rsup|2>=<frac|n*<around*|(|a*d-b*c|)><rsup|2>|<around*|(|a+b|)>*<around*|(|c+d|)>*<around*|(|a+c|)>*<around*|(|b+d|)>>>>

    <block*|<tformat|<table|<row|<cell|<math|P<around*|(|K<rsup|2>\<geqslant\>K|)>>>|<cell|0.050>|<cell|0.010>|<cell|0.001>>|<row|<cell|<math|k>>|<cell|3.841>|<cell|6.635>|<cell|10.828>>>>>

    <item>\<#8BB0\><math|S<rsub|n>>\<#4E3A\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#524D\><math|n>\<#9879\>\<#548C\>\<#FF0C\>\<#5DF2\>\<#77E5\><math|a<rsub|n>\<gtr\>0>\<#FF0C\><math|a<rsub|2>=3*a<rsub|1>>\<#FF0C\>\<#4E14\>\<#6570\>\<#5217\><math|<around*|{|<sqrt|S<rsub|n>>|}>>\<#662F\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\><math|<around*|{|a<rsub|n>|}>>\<#662F\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>.

    <item>\<#5DF2\>\<#77E5\>\<#76F4\>\<#4E09\>\<#68F1\>\<#67F1\><math|ABC-A<rsub|1>B<rsub|1>C<rsub|1>>\<#4E2D\>\<#FF0C\>\<#4FA7\>\<#9762\><math|AA<rsub|1>B<rsub|1>B>\<#4E3A\>\<#6B63\>\<#65B9\>\<#5F62\>\<#FF0C\><math|AB=BC=2>\<#FF0C\><math|E>\<#FF0C\><math|F>\<#5206\>\<#522B\>\<#4E3A\><math|AC>\<#548C\><math|CC<rsub|1>>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\><math|BF\<perp\>A<rsub|1>B<rsub|1>>.

    <image|<tuple|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

    (1) \<#6C42\>\<#4E09\>\<#68F1\>\<#9525\><math|F-EBC>\<#7684\>\<#4F53\>\<#79EF\>\<#FF1B\>

    (2) \<#5DF2\>\<#77E5\><math|D>\<#4E3A\>\<#68F1\><math|A<rsub|1>B<rsub|1>>\<#4E0A\>\<#7684\>\<#70B9\>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\><math|BF\<perp\>DE>.

    <item>\<#8BBE\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=a<rsup|2>x<rsup|2>+a*x-3*ln
    x+1>\<#FF0C\>\<#5176\>\<#4E2D\><math|a\<gtr\>0>.

    (1) \<#8BA8\>\<#8BBA\><math|f<around*|(|x|)>>\<#7684\>\<#5355\>\<#8C03\>\<#6027\>\<#FF1B\>

    (2) \<#82E5\><math|y=f<around*|(|x|)>>\<#7684\>\<#56FE\>\<#50CF\>\<#4E0E\><math|x>\<#8F74\>\<#6CA1\>\<#6709\>\<#516C\>\<#5171\>\<#70B9\>\<#FF0C\>\<#6C42\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>.

    <item>\<#629B\>\<#7269\>\<#7EBF\><math|C>\<#7684\>\<#9876\>\<#70B9\>\<#4E3A\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\><math|O>\<#FF0E\>\<#7126\>\<#70B9\>\<#5728\><math|x>\<#8F74\>\<#4E0A\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|l:x=1>\<#4EA4\>C\<#4E8E\>P\<#FF0C\>Q\<#4E24\>\<#70B9\>\<#FF0C\>\<#4E14\><math|OP\<perp\>OQ>.\<#5DF2\>\<#77E5\>\<#70B9\><math|M<around*|(|2,0|)>>\<#FF0C\>\<#4E14\><math|\<odot\>M>\<#4E0E\><math|l>\<#76F8\>\<#5207\>.

    \<#FF08\>1\<#FF09\>\<#6C42\>C\<#FF0C\><math|\<odot\>M>\<#7684\>\<#65B9\>\<#7A0B\>\<#FF1B\>

    \<#FF08\>2\<#FF09\>\<#8BBE\><math|A<rsub|1>,A<rsub|2>,A<rsub|3>>\<#662F\>C\<#4E0A\>\<#7684\>\<#4E09\>\<#4E2A\>\<#70B9\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|A<rsub|1>A<rsub|2>,A<rsub|1>A<rsub|3>>\<#5747\>\<#4E0E\><math|\<odot\>M>\<#76F8\>\<#5207\>\<#FF0E\>\<#5224\>\<#65AD\>\<#76F4\>\<#7EBF\><math|A<rsub|2>A<rsub|3>>\<#4E0E\><math|\<odot\>M>\<#7684\>\<#4F4D\>\<#7F6E\>\<#5173\>\<#7CFB\>\<#FF0C\>\<#5E76\>\<#8BF4\>\<#660E\>\<#7406\>\<#7531\>\<#FF0E\>

    <item>\<#5728\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#7CFB\><math|x O
    y>\<#4E2D\>\<#FF0C\>\<#4EE5\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#4E3A\>\<#6781\>\<#70B9\>\<#FF0C\><math|x>\<#8F74\>\<#6B63\>\<#534A\>\<#8F74\>\<#4E3A\>\<#6781\>\<#8F74\>\<#5EFA\>\<#7ACB\>\<#6781\>\<#5750\>\<#6807\>\<#7CFB\>\<#FF0C\>\<#66F2\>\<#7EBF\><math|C>\<#7684\>\<#6781\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|\<rho\>=2<sqrt|2>*cos
    \<theta\>>.

    \<#FF08\>1\<#FF09\>\<#5C06\><math|C>\<#7684\>\<#6781\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>\<#5316\>\<#4E3A\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>\<#FF1B\>

    \<#FF08\>2\<#FF09\>\<#8BBE\>\<#70B9\>A\<#7684\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#4E3A\><math|<around*|(|1,0|)>>\<#FF0C\>M\<#4E3A\>C\<#4E0A\>\<#7684\>\<#52A8\>\<#70B9\>\<#FF0C\>\<#70B9\>P\<#6EE1\>\<#8DB3\><math|<wide|AP|\<vect\>>=<sqrt|2><wide|AM|\<vect\>>>\<#FF0C\>\<#5199\>\<#51FA\>\<#420\>\<#7684\>\<#8F68\>\<#8FF9\><math|C<rsub|1>>\<#7684\>\<#53C2\>\<#6570\>\<#65B9\>\<#7A0B\>\<#FF0C\>\<#5E76\>\<#5224\>\<#65AD\>C\<#4E0E\><math|C<rsub|1>>\<#662F\>\<#5426\>\<#6709\>\<#516C\>\<#5171\>\<#70B9\>.

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=<around*|\||x-2|\|>>\<#FF0C\><math|g<around*|(|x|)>=<around*|\||2*x+3|\|>-<around*|\||2*x-1|\|>>.

    <image|<tuple|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

    (1) \<#753B\>\<#51FA\><math|y=f<around*|(|x|)>>\<#548C\><math|y=g<around*|(|x|)>>\<#7684\>\<#56FE\>\<#50CF\>\<#FF1B\>

    (2) \<#82E5\><math|f<around*|(|x+a|)>\<geqslant\>g<around*|(|x|)>>\<#FF0C\>\<#6C42\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>.
  </enumerate>

  \;
</body>

<\initial>
  <\collection>
    <associate|page-medium|paper>
  </collection>
</initial>

<\references>
  <\collection>
    <associate|auto-1|<tuple|?|1>>
    <associate|auto-2|<tuple|12|2>>
    <associate|auto-3|<tuple|16|3>>
  </collection>
</references>

<\auxiliary>
  <\collection>
    <\associate|toc>
      <with|par-left|<quote|2tab>|\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-1>>

      <with|par-left|<quote|2tab>|\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-2>>

      <with|par-left|<quote|2tab>|\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-3>>
    </associate>
  </collection>
</auxiliary>