planet/高考数学/2021年全国高考乙卷数学文科试题.tm

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<\body>
  <doc-data|<doc-title|2021\<#5E74\>\<#5168\>\<#56FD\>\<#9AD8\>\<#8003\>\<#4E59\>\<#5377\>\<#6570\>\<#5B66\>\<#FF08\>\<#6587\>\<#FF09\>\<#8BD5\>\<#5377\>>>

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

  <\enumerate>
    <item>\<#5DF2\>\<#77E5\>\<#5168\>\<#96C6\><math|U=<around*|{|1,2,3,4,5|}>>\<#FF0C\>\<#96C6\>\<#5408\><math|M=<around*|{|1,2|}>,N=<around*|{|3,4|}>>\<#FF0C\>\<#5219\><math|C<rsub|u><around*|(|M\<cup\>N|)>=><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<around*|{|5|}>>
      </cell>|<\cell>
        B. <math|<around*|{|1,2|}>>
      </cell>|<\cell>
        C. <math|<around*|{|3,4|}>>
      </cell>|<\cell>
        D. <math|<around*|{|1,2,3,4|}>>
      </cell>>>>
    </wide-tabular>

    <item>\<#8BBE\><math|i*z=4+3*i>\<#FF0C\>\<#5219\><math|z=><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|-3-4*i>
      </cell>|<\cell>
        B. <math|-3+4*i>
      </cell>|<\cell>
        C. <math|3-4*i>
      </cell>|<\cell>
        D. <math|3+4*i>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\>\<#547D\>\<#9898\><math|p>\<#FF1A\><math|\<exists\>x\<in\>\<bbb-R\>,sin
    x\<less\>1>\<#FF1B\>\<#547D\>\<#9898\><math|q>\<#FF1A\><math|\<forall\>x\<in\>\<bbb-R\>,e<rsup|<around*|\||x|\|>>\<geqslant\>1>\<#FF0C\>\<#5219\>\<#4E0B\>\<#5217\>\<#547D\>\<#9898\>\<#4E2D\>\<#4E3A\>\<#771F\>\<#547D\>\<#9898\>\<#7684\>\<#662F\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|p\<wedge\>q>
      </cell>|<\cell>
        B. <math|\<neg\>p\<wedge\>q>
      </cell>|<\cell>
        C. <math|p\<wedge\>\<neg\>q>
      </cell>|<\cell>
        D. <math|\<neg\><around*|(|p\<vee\>q|)>>
      </cell>>>>
    </wide-tabular>

    <item>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=sin
    <frac|x|3>+cos<frac|x|3>>\<#7684\>\<#6700\>\<#5C0F\>\<#6B63\>\<#5468\>\<#671F\>\<#548C\>\<#6700\>\<#5927\>\<#503C\>\<#5206\>\<#522B\>\<#662F\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|3\<pi\>>\<#548C\><math|<sqrt|2>>
      </cell>|<\cell>
        B. <math|3*\<pi\>>\<#548C\>2
      </cell>|<\cell>
        C. <math|6*\<pi\>>\<#548C\><math|<sqrt|2>>
      </cell>|<\cell>
        D. <math|6*\<pi\>>\<#548C\>2
      </cell>>>>
    </wide-tabular>

    <item>\<#82E5\><math|x>\<#FF0C\><math|y>\<#6EE1\>\<#8DB3\>\<#7EA6\>\<#675F\>\<#6761\>\<#4EF6\><with|math-display|true|<choice|<tformat|<table|<row|<cell|<math|x+y\<geqslant\>4>,>>|<row|<cell|<math|x-y\<leqslant\>2>,>>|<row|<cell|<math|y\<leqslant\>3>,>>>>>>\<#5219\><math|z=3*x+y>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#4E3A\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. 18
      </cell>|<\cell>
        B. 10
      </cell>|<\cell>
        C. 6
      </cell>|<\cell>
        D. 4
      </cell>>>>
    </wide-tabular>

    <item><math|cos<rsup|2><frac|\<pi\>|12>-cos<rsup|2><frac|5*\<pi\>|12>=><underline|<space|3em>>

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

    <item>\<#5728\>\<#533A\>\<#95F4\>0, <math|<frac|1|2>>\<#968F\>\<#673A\>\<#53D6\>1\<#4E2A\>\<#6570\>\<#FF0C\>\<#5219\>\<#53D6\>\<#5230\>\<#7684\>\<#6570\>\<#5C0F\>\<#4E8E\><math|<frac|1|3>>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<frac|3|4>>
      </cell>|<\cell>
        B. <math|<frac|2|3>>
      </cell>|<\cell>
        C. <math|<frac|1|3>>
      </cell>|<\cell>
        D. <math|<frac|1|6>>
      </cell>>>>
    </wide-tabular>

    <item>\<#4E0B\>\<#5217\>\<#51FD\>\<#6570\>\<#4E2D\>\<#6700\>\<#5C0F\>\<#503C\>\<#4E3A\>4\<#7684\>\<#662F\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|y=x<rsup|2>+2*x+4>
      </cell>|<\cell>
        B. <math|y=<around*|\||sin x|\|>+<frac|4|<around*|\||sin x|\|>>>
      </cell>>|<row|<\cell>
        C. <math|y=2<rsup|x>+2<rsup|2-x>>
      </cell>|<\cell>
        D. <math|y=ln x+<frac|4|ln x>>
      </cell>>>>
    </wide-tabular>

    <item>\<#8BBE\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=<frac|1-x|1+x>>\<#FF0C\>\<#5219\>\<#4E0B\>\<#5217\>\<#51FD\>\<#6570\>\<#4E2D\>\<#4E3A\>\<#5947\>\<#51FD\>\<#6570\>\<#7684\>\<#662F\><underline|<space|3em>>.

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|f<around*|(|x-1|)>-1>
      </cell>|<\cell>
        B. <math|f<around*|(|x-1|)>+1>
      </cell>|<\cell>
        C. <math|f<around*|(|x+1|)>-1>
      </cell>|<\cell>
        D. <math|f<around*|(|x+1|)>+1>
      </cell>>>>
    </wide-tabular>

    <item>\<#5728\>\<#6B63\>\<#65B9\>\<#4F53\><math|ABCD-A<rsub|1>B<rsub|1>C<rsub|1>D<rsub|1>>\<#4E2D\>\<#FF0C\><math|P>\<#4E3A\><math|B<rsub|1>D<rsub|1>>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><math|PB>\<#4E0E\><math|AD<rsub|1>>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<frac|\<pi\>|2>>
      </cell>|<\cell>
        B. <math|<frac|\<pi\>|3>>
      </cell>|<\cell>
        C. <math|<frac|\<pi\>|4>>
      </cell>|<\cell>
        D. <math|<frac|\<pi\>|6>>
      </cell>>>>
    </wide-tabular>

    <item>\<#8BBE\><math|B>\<#662F\>\<#692D\>\<#5706\><math|C:<frac|x<rsup|2>|5>+y=1>\<#7684\>\<#4E0A\>\<#9876\>\<#70B9\>\<#FF0C\>\<#70B9\><math|P>\<#5728\><math|C>\<#4E0A\>\<#FF0C\>\<#5219\><math|<around*|\||PB|\|>>\<#7684\>\<#6700\>\<#5927\>\<#503C\>\<#4E3A\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<frac|5|2>>
      </cell>|<\cell>
        B. <math|<sqrt|6>>
      </cell>|<\cell>
        C. <math|<sqrt|5>>
      </cell>|<\cell>
        D. 2
      </cell>>>>
    </wide-tabular>

    <item>\<#8BBE\><math|a\<neq\>0>\<#FF0C\>\<#82E5\><math|x=a>\<#4E3A\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=a*<around*|(|x-a|)><rsup|2><around*|(|x-b|)>>\<#7684\>\<#6781\>\<#5927\>\<#503C\>\<#70B9\>\<#FF0C\>\<#5219\><underline|<space|3em>>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|a\<less\>b>
      </cell>|<\cell>
        B. <math|a\<gtr\>b>
      </cell>|<\cell>
        C. <math|a*b\<less\>a<rsup|2>>
      </cell>|<\cell>
        D. <math|a*b\<gtr\>a<rsup|2>>
      </cell>>>>
    </wide-tabular>
  </enumerate>

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

  <\enumerate>
    <assign|item-nr|12><item>\<#5DF2\>\<#77E5\>\<#5411\>\<#91CF\><math|<wide|a|\<vect\>>=<around*|(|2,5|)>,<wide|b|\<vect\>>=<around*|(|\<lambda\>,4|)>>\<#FF0C\>\<#82E5\><math|<wide|a|\<vect\>>//<wide|b|\<vect\>>>\<#FF0C\>\<#5219\><math|\<lambda\>=><underline|<space|3em>>.

    <item>\<#53CC\>\<#66F2\>\<#7EBF\><math|<frac|x<rsup|2>|4>-<frac|y<rsup|2>|5>=1>\<#7684\>\<#53F3\>\<#7126\>\<#70B9\>\<#5230\>\<#76F4\>\<#7EBF\><math|x+2*y-8=0>\<#7684\>\<#8DDD\>\<#79BB\>\<#4E3A\><underline|<space|3em>>.

    <item>\<#8BB0\><math|\<triangle\>ABC>\<#7684\>\<#5185\>\<#89D2\><math|A>\<#FF0C\><math|B>\<#FF0C\><math|C>\<#7684\>\<#5BF9\>\<#8FB9\>\<#5206\>\<#522B\>\<#4E3A\>a\<#FF0C\>b\<#FF0C\>c\<#FF0C\>\<#9762\>\<#79EF\>\<#4E3A\><math|<sqrt|3>>\<#FF0C\><math|B=60<rsup|\<circ\>>>\<#FF0C\><math|a<rsup|2>+c<rsup|2>=3*a*c>\<#FF0C\>\<#5219\><math|b=><underline|<space|3em>>.

    <item>\<#4EE5\>\<#56FE\>\<#2460\>\<#4E3A\>\<#6B63\>\<#89C6\>\<#56FE\>\<#FF0C\>\<#5728\>\<#56FE\>\<#2461\>\<#2462\>\<#2463\>\<#2464\>\<#4E2D\>\<#9009\>\<#4E24\>\<#4E2A\>\<#5206\>\<#522B\>\<#4F5C\>\<#4E3A\>\<#4FA7\>\<#89C6\>\<#56FE\>\<#548C\>\<#4FEF\>\<#89C6\>\<#56FE\>\<#FF0C\>\<#7EC4\>\<#6210\>\<#67D0\>\<#4E2A\>\<#4E09\>\<#68F1\>\<#9525\>\<#7684\>\<#4E09\>\<#89C6\>\<#56FE\>\<#FF0C\>\<#5219\>\<#6240\>\<#9009\>\<#4FA7\>\<#89C6\>\<#56FE\>\<#548C\>\<#4FEF\>\<#89C6\>\<#56FE\>\<#7684\>\<#7F16\>\<#53F7\>\<#4F9D\>\<#6B21\>\<#4E3A\><underline|<space|3em>>\<#FF08\>\<#5199\>\<#51FA\>\<#7B26\>\<#5408\>\<#8981\>\<#6C42\>\<#7684\>\<#4E00\>\<#7EC4\>\<#7B54\>\<#6848\>\<#5373\>\<#53EF\>\<#FF09\>\<#FF0E\>

    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  </enumerate>

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

  <\enumerate>
    <assign|item-nr|16><item>\<#67D0\>\<#5382\>\<#7814\>\<#5236\>\<#4E86\>\<#4E00\>\<#79CD\>\<#751F\>\<#4EA7\>\<#9AD8\>\<#7CBE\>\<#4EA7\>\<#54C1\>\<#7684\>\<#8BBE\>\<#5907\>\<#FF0C\>\<#4E3A\>\<#68C0\>\<#9A8C\>\<#65B0\>\<#8BBE\>\<#5907\>\<#751F\>\<#4EA7\>\<#4EA7\>\<#54C1\>\<#7684\>\<#67D0\>\<#9879\>\<#6307\>\<#6807\>\<#6709\>\<#65E0\>\<#63D0\>\<#9AD8\>\<#FF0C\>\<#7528\>\<#4E00\>\<#53F0\>\<#65E7\>\<#8BBE\>\<#5907\>\<#548C\>\<#4E00\>\<#53F0\>\<#65B0\>\<#8BBE\>\<#5907\>\<#5404\>\<#751F\>\<#4EA7\>\<#4E86\>10\<#4EF6\>\<#4EA7\>\<#54C1\>\<#FF0C\>\<#5F97\>\<#5230\>\<#5404\>\<#4EF6\>\<#4EA7\>\<#54C1\>\<#8BE5\>\<#9879\>\<#6307\>\<#6807\>\<#6570\>\<#636E\>\<#5982\>\<#4E0B\>\<#FF1A\>

    <block*|<tformat|<cwith|1|1|1|1|cell-valign|b>|<cwith|2|2|6|6|cell-halign|r>|<table|<row|<cell|\<#65E7\>\<#8BBE\>\<#5907\>>|<cell|9.8>|<cell|10.3>|<cell|10.0>|<cell|10.2>|<cell|9.9>|<cell|9.8>|<cell|10.0>|<cell|10.1>|<cell|10.2>|<cell|9.7>>|<row|<cell|\<#65B0\>\<#8BBE\>\<#5907\>>|<cell|10.1>|<cell|10.4>|<cell|10.1>|<cell|10.0>|<cell|10.1>|<cell|10.3>|<cell|10.6>|<cell|10.5>|<cell|10.4>|<cell|10.5>>>>>

    \<#65E7\>\<#8BBE\>\<#5907\>\<#548C\>\<#65B0\>\<#8BBE\>\<#5907\>\<#751F\>\<#4EA7\>\<#4EA7\>\<#54C1\>\<#7684\>\<#8BE5\>\<#9879\>\<#6307\>\<#6807\>\<#7684\>\<#6837\>\<#672C\>\<#5E73\>\<#5747\>\<#6570\>\<#5206\>\<#522B\>\<#8BB0\>\<#4E3A\>\<#548C\>\<#FF0C\>\<#6837\>\<#672C\>\<#65B9\>\<#5DEE\>\<#5206\>\<#522B\>\<#8BB0\>\<#4E3A\>\<#548C\>\<#FF0E\>

    \<#FF08\>1\<#FF09\>\<#6C42\><math|<wide|x|\<bar\>>,<wide|y|\<bar\>>,s<rsup|2><rsub|1>,s<rsup|2><rsub|2>>\<#FF1B\>

    \<#FF08\>2\<#FF09\>\<#5224\>\<#65AD\>\<#65B0\>\<#8BBE\>\<#5907\>\<#751F\>\<#4EA7\>\<#4EA7\>\<#54C1\>\<#7684\>\<#8BE5\>\<#9879\>\<#6307\>\<#6807\>\<#7684\>\<#5747\>\<#503C\>\<#8F83\>\<#65E7\>\<#8BBE\>\<#5907\>\<#662F\>\<#5426\>\<#6709\>\<#663E\>\<#8457\>\<#63D0\>\<#9AD8\>\<#FF08\>\<#5982\>\<#679C\><math|<wide|y|\<bar\>>-<wide|x|\<bar\>>\<geqslant\>2<sqrt|<frac|s<rsup|2><rsub|1>+s<rsup|2><rsub|2>|10>>>\<#FF0C\>\<#5219\>\<#8BA4\>\<#4E3A\>\<#65B0\>\<#8BBE\>\<#5907\>\<#751F\>\<#4EA7\>\<#4EA7\>\<#54C1\>\<#7684\>\<#8BE5\>\<#9879\>\<#6307\>\<#6807\>\<#7684\>\<#5747\>\<#503C\>\<#8F83\>\<#65E7\>\<#8BBE\>\<#5907\>\<#6709\>\<#663E\>\<#8457\>\<#63D0\>\<#9AD8\>\<#FF0C\>\<#5426\>\<#5219\>\<#4E0D\>\<#8BA4\>\<#4E3A\>\<#6709\>\<#663E\>\<#8457\>\<#63D0\>\<#9AD8\>\<#FF09\>\<#FF0E\>

    <item>\<#5982\>\<#56FE\>\<#FF0C\>\<#56DB\>\<#68F1\>\<#9525\><math|P-ABCD>\<#7684\>\<#5E95\>\<#9762\>\<#662F\>\<#77E9\>\<#5F62\>\<#FF0C\><math|PD\<perp\>\<#5E95\>\<#9762\>ABCD>\<#FF0C\><math|M>\<#4E3A\><math|BC>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\>\<#4E14\><math|PB\<perp\>AM>.

    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    \<#FF08\>2\<#FF09\>\<#82E5\><math|PD=DC=1>\<#FF0C\>\<#6C42\>\<#56DB\>\<#68F1\>\<#9525\><math|P-ABCD>\<#7684\>\<#4F53\>\<#79EF\>.

    <item>\<#8BBE\><math|<around*|{|a<rsub|n>|}>>\<#662F\>\<#9996\>\<#9879\>\<#4E3A\>1\<#7684\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\>\<#FF0C\>\<#6570\>\<#5217\><math|<around*|{|b<rsub|n>|}>>\<#6EE1\>\<#8DB3\><math|b<rsub|n>=<frac|n*a<rsub|n>|3>>.
    \<#5DF2\>\<#77E5\><math|a<rsub|1>>\<#FF0C\><math|3*a<rsub|2>>\<#FF0C\><math|9*a<rsub|3>>\<#6210\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>.

    \<#FF08\>1\<#FF09\>\<#6C42\><math|<around*|{|a<rsub|n>|}>>\<#548C\><math|<around*|{|b<rsub|n>|}>>\<#7684\>\<#901A\>\<#9879\>\<#516C\>\<#5F0F\>\<#FF1B\>

    \<#FF08\>2\<#FF09\>\<#8BB0\><math|S<rsub|n>>\<#548C\><math|T<rsub|n>>\<#5206\>\<#522B\>\<#4E3A\><math|<around*|{|a<rsub|n>|}>>\<#548C\><math|<around*|{|b<rsub|n>|}>>\<#7684\>\<#524D\><math|n>\<#9879\>\<#548C\>.
    \<#8BC1\>\<#660E\>\<#FF1A\><math|T<rsub|n>\<less\><frac|S<rsub|n>|2>>.

    <item>\<#5DF2\>\<#77E5\>\<#629B\>\<#7269\>\<#7EBF\><math|C>\<#FF1A\><math|y<rsup|2>=2*p*x<around*|(|p\<gtr\>0|)>>\<#7684\>\<#7126\>\<#70B9\><math|F>\<#5230\>\<#51C6\>\<#7EBF\>\<#7684\>\<#8DDD\>\<#79BB\>\<#4E3A\>2.

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

    \<#FF08\>2\<#FF09\>\<#5DF2\>\<#77E5\><math|O>\<#4E3A\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#FF0C\>\<#70B9\><math|P>\<#5728\><math|C>\<#4E0A\>\<#FF0C\>\<#70B9\><math|Q>\<#6EE1\>\<#8DB3\><math|<wide|PQ|\<vect\>>=9<wide|QF|\<vect\>>>\<#FF0C\>\<#6C42\>\<#76F4\>\<#7EBF\><math|OQ>\<#659C\>\<#7387\>\<#7684\>\<#6700\>\<#5927\>\<#503C\>.

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

    \<#FF08\>1\<#FF09\>\<#8BA8\>\<#8BBA\><math|f<around*|(|x|)>>\<#7684\>\<#5355\>\<#8C03\>\<#6027\>\<#FF1B\>

    \<#FF08\>2\<#FF09\>\<#6C42\>\<#66F2\>\<#7EBF\><math|y=f<around*|(|x|)>>\<#8FC7\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#7684\>\<#5207\>\<#7EBF\>\<#4E0E\>\<#66F2\>\<#7EBF\><math|y=f<around*|(|x|)>>\<#7684\>\<#516C\>\<#5171\>\<#70B9\>\<#7684\>\<#5750\>\<#6807\>.

    <item>\<#5728\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#7CFB\><math|x O
    y>\<#4E2D\>\<#FF0C\><math|\<odot\>C>\<#7684\>\<#5706\>\<#5FC3\>\<#4E3A\><math|C<around*|(|2,1|)>>\<#FF0C\>\<#534A\>\<#5F84\>\<#4E3A\>1.

    \<#FF08\>1\<#FF09\>\<#5199\>\<#51FA\><math|\<odot\>C>\<#7684\>\<#4E00\>\<#4E2A\>\<#53C2\>\<#6570\>\<#65B9\>\<#7A0B\>\<#FF1B\>

    \<#FF08\>2\<#FF09\>\<#8FC7\>\<#70B9\><math|F<around*|(|4,1|)>>\<#4F5C\><math|\<odot\>C>\<#7684\>\<#4E24\>\<#6761\>\<#5207\>\<#7EBF\>\<#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\>\<#6C42\>\<#8FD9\>\<#4E24\>\<#6761\>\<#5207\>\<#7EBF\>\<#7684\>\<#6781\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>.

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|<with|math-display|true|<frac|<around*|\||OB|\|>|<around*|\||OA|\|>>=<frac|\<rho\><rsub|1>|\<rho\><rsub|2>>=<frac|1|4>\<times\>2*sin
    \<alpha\><around*|(|<sqrt|3>*cos \<alpha\>+sin
    \<alpha\>|)>=<frac|1|4><around*|[|2*sin<around*|(|2*\<alpha\>-<frac|\<pi\>|6>|)>+1|]>>>.

    \<#FF08\>1\<#FF09\>\<#5F53\><math|a=1>\<#65F6\>\<#FF0C\>\<#6C42\>\<#4E0D\>\<#7B49\>\<#5F0F\><math|f<around*|(|x|)>\<geqslant\>6>\<#7684\>\<#89E3\>\<#96C6\>\<#FF1B\>

    \<#FF08\>2\<#FF09\>\<#82E5\><math|f<around*|(|x|)>\<gtr\>-\<alpha\>>\<#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|2>>
  </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>