planet/高考数学/2021年全国高考甲卷数学文科试题.tm

<TeXmacs|2.1.2>

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<\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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        A. 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        B. 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      </cell>>|<row|<\cell>
        C. <image|<tuple|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|png>|80pt|80pt||>
      </cell>|<\cell>
        D. <image|<tuple|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|png>|80pt|80pt||>
      </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>>.

    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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>>.

    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    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|\|>>.

    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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\>.
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      <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>>
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