planet/高考数学/2022年全国新高考一卷数学试题.tm

<TeXmacs|2.1.2>

<style|<tuple|exam|chinese>>

<\body>
  <doc-data|<doc-title|2022\<#5E74\>\<#6570\>\<#5B66\>\<#65B0\>\<#9AD8\>\<#8003\>I\<#5377\>>>

  <strong|\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\><with|font-series|bold|8>\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\><with|font-series|bold|40>\<#5206\>\<#FF09\>

  <\enumerate-numeric>
    <item>\<#82E5\>\<#96C6\>\<#5408\><math|M=<around|{|x\|<sqrt|x>\<less\>4|}>>\<#FF0C\><math|N=<around|{|x\|3*x\<geq\>1|}>>\<#FF0C\>\<#5219\><math|M\<cap\>N=>(<space|2em>)

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<around|{|x\|0\<leq\>x\<less\>2|}>>
      </cell>|<\cell>
        B. <math|<around|{|x\|<frac|1|3>\<leq\>x\<less\>2|}>>
      </cell>|<\cell>
        C. <math|<around|{|x\|3\<leq\>x\<less\>16|}>>
      </cell>|<\cell>
        D. <math|<around|{|x\|<frac|1|3>\<leq\>x\<less\>16|}>>
      </cell>>>>
    </wide-tabular>

    <item>\<#82E5\><math|i*<around|(|1-z|)>=1>\<#FF0C\>\<#5219\><math|z+<wide|z|\<bar\>>=>(<space|2em>)

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

    <item>\<#5728\><math|\<vartriangle\>A*B*C>\<#4E2D\>\<#FF0C\>\<#70B9\><math|D>\<#5728\>\<#8FB9\><math|A*B>\<#4E0A\>\<#FF0C\><math|B*D=2*D*A>.\<#8BB0\><math|<wide|C*A|\<wide-varrightarrow\>>=<wide|m|\<wide-varrightarrow\>>>\<#FF0C\><math|<wide|C*D|\<wide-varrightarrow\>>=<wide|n|\<wide-varrightarrow\>>>\<#FF0C\>\<#5219\><math|<wide|C*B|\<wide-varrightarrow\>>=>(<space|2em>)

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|3*<wide|m|\<wide-varrightarrow\>>-2*<wide|n|\<wide-varrightarrow\>>>
      </cell>|<\cell>
        B. <math|-2*<wide|m|\<wide-varrightarrow\>>+3*<wide|n|\<wide-varrightarrow\>>>
      </cell>|<\cell>
        C. <math|3*<wide|m|\<wide-varrightarrow\>>+2*<wide|n|\<wide-varrightarrow\>>>
      </cell>|<\cell>
        D. <math|2*<wide|m|\<wide-varrightarrow\>>+3*<wide|n|\<wide-varrightarrow\>>>
      </cell>>>>
    </wide-tabular>

    <item>\<#5357\>\<#6C34\>\<#5317\>\<#8C03\>\<#5DE5\>\<#7A0B\>\<#7F13\>\<#89E3\>\<#4E86\>\<#5317\>\<#65B9\>\<#4E00\>\<#4E9B\>\<#5730\>\<#533A\>\<#6C34\>\<#8D44\>\<#6E90\>\<#77ED\>\<#7F3A\>\<#95EE\>\<#9898\>\<#FF0C\>\<#5176\>\<#4E2D\>\<#4E00\>\<#90E8\>\<#5206\>\<#6C34\>\<#84C4\>\<#5165\>\<#67D0\>\<#6C34\>\<#5E93\>.\<#5DF2\>\<#77E5\>\<#8BE5\>\<#6C34\>\<#5E93\>\<#6C34\>\<#4F4D\>\<#4E3A\>\<#6D77\>\<#62D4\>148.5m\<#65F6\>\<#FF0C\>\<#76F8\>\<#5E94\>\<#6C34\>\<#9762\>\<#7684\>\<#9762\>\<#79EF\>\<#4E3A\><math|140.0*km<rsup|2>>;\<#6C34\>\<#4F4D\>\<#4E3A\>\<#6D77\>\<#62D4\><math|157.5>m\<#65F6\>\<#FF0C\>\<#76F8\>\<#5E94\>\<#6C34\>\<#9762\>\<#7684\>\<#9762\>\<#79EF\>\<#4E3A\><math|180.0*km<rsup|2>>.\<#5C06\>\<#8BE5\>\<#6C34\>\<#5E93\>\<#5728\>\<#8FD9\>\<#4E24\>\<#4E2A\>\<#6C34\>\<#4F4D\>\<#95F4\>\<#7684\>\<#5F62\>\<#72B6\>\<#770B\>\<#4F5C\>\<#4E00\>\<#4E2A\>\<#68F1\>\<#53F0\>\<#FF0C\>\<#5219\>\<#8BE5\>\<#6C34\>\<#5E93\>\<#6C34\>\<#4F4D\>\<#4ECE\>\<#6D77\>\<#62D4\><math|148.5*>m\<#4E0A\>\<#5347\>\<#5230\><math|157.5*>m\<#65F6\>\<#FF0C\>\<#589E\>\<#52A0\>\<#7684\>\<#6C34\>\<#91CF\>\<#7EA6\>\<#4E3A\><math|<around*|(|<sqrt|7>\<approx\>2.65|)>>(<space|2em>)

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|1.0\<times\>10<rsup|9>*m<rsup|3>>
      </cell>|<\cell>
        B. <math|1.2\<times\>10<rsup|9>*m<rsup|3>>
      </cell>|<\cell>
        C. <math|1.4\<times\>10<rsup|9>*m<rsup|3>>
      </cell>|<\cell>
        D. <math|1.6\<times\>10<rsup|9>*m<rsup|3>>
      </cell>>>>
    </wide-tabular>

    <item>\<#4ECE\><math|2>\<#81F3\><math|8>\<#7684\><math|7>\<#4E2A\>\<#6574\>\<#6570\>\<#4E2D\>\<#968F\>\<#673A\>\<#53D6\><math|2>\<#4E2A\>\<#4E0D\>\<#540C\>\<#7684\>\<#6570\>\<#FF0C\>\<#5219\>\<#8FD9\><math|2>\<#4E2A\>\<#6570\>\<#4E92\>\<#8D28\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\>(<space|2em>)

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

    <item>\<#8BB0\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=sin
    <around|(|\<omega\>*x+<frac|\<pi\>|4>|)>+b*<around|(|\<omega\>\<gtr\>0|)>>\<#7684\>\<#6700\>\<#5C0F\>\<#6B63\>\<#5468\>\<#671F\>\<#4E3A\><math|T>.\<#82E5\><math|<frac|2*\<pi\>|3>\<less\>T\<less\>\<pi\>>\<#FF0C\>\<#4E14\><math|y=f<around|(|x|)>>\<#7684\>\<#56FE\>\<#50CF\>\<#5173\>\<#4E8E\>\<#70B9\><math|<around|(|<frac|3*\<pi\>|2>,2|)>>\<#4E2D\>\<#5FC3\>\<#5BF9\>\<#79F0\>\<#FF0C\>\<#5219\><math|f<around|(|<frac|\<pi\>|2>|)>=>(<space|2em>)

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

    <item>\<#8BBE\><math|a=0.1*e<rsup|0.1>>\<#FF0C\><math|b=<frac|1|9>>\<#FF0C\><math|c=-ln
    0.9>\<#FF0C\>\<#5219\>(<space|2em>)

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|a\<less\>b\<less\>c>
      </cell>|<\cell>
        B. <math|c\<less\>b\<less\>a>
      </cell>|<\cell>
        C. <math|c\<less\>a\<less\>b>
      </cell>|<\cell>
        D. <math|a\<less\>c\<less\>b>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\>\<#6B63\>\<#56DB\>\<#68F1\>\<#9525\>\<#7684\>\<#4FA7\>\<#68F1\>\<#957F\>\<#4E3A\><math|l>\<#FF0C\>\<#5176\>\<#5404\>\<#9876\>\<#70B9\>\<#90FD\>\<#5728\>\<#540C\>\<#4E00\>\<#4E2A\>\<#7403\>\<#9762\>\<#4E0A\>\<#FF0C\>\<#82E5\>\<#8BE5\>\<#7403\>\<#7684\>\<#4F53\>\<#79EF\>\<#4E3A\><math|36*\<pi\>>\<#FF0C\>\<#4E14\><math|3\<leq\>l\<leq\>3*<sqrt|3>>\<#FF0C\>\<#5219\>\<#8BE5\>\<#6B63\>\<#56DB\>\<#68F1\>\<#9525\>\<#4F53\>\<#79EF\>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#662F\>(<space|2em>)

    <\wide-tabular>
      <tformat|<table|<row|A. <math|<around|[|18,<frac|81|4>|]>>|<\cell>
        B. <math|<around|[|<frac|27|4>,<frac|81|4>|]>>
      </cell>|<\cell>
        C. <math|<around|[|<frac|27|4>,<frac|64|3>|]>>
      </cell>|<\cell>
        D. <math|<around|[|18,27|]>>
      </cell>>>>
    </wide-tabular>
  </enumerate-numeric>

  <strong|\<#4E8C\>\<#3001\>\<#591A\>\<#9009\>\<#9898\>>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\><with|font-series|bold|4>\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\><with|font-series|bold|20>\<#5206\>\<#FF09\>

  <\enumerate>
    <assign|item-nr|8><item>\<#5DF2\>\<#77E5\>\<#6B63\>\<#65B9\>\<#4F53\><math|A*B*C*D-A<rsub|1>*B<rsub|1>*C<rsub|1>*D<rsub|1>>\<#FF0C\>\<#5219\>(<space|2em>)

    A. \<#76F4\>\<#7EBF\><math|B*C<rsub|1>>\<#4E0E\><math|D*A<rsub|1>>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|90<rsup|\<circ\>>>

    B. \<#76F4\>\<#7EBF\><math|B*C<rsub|1>>\<#4E0E\><math|C*A<rsub|1>>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|90<rsup|\<circ\>>>

    C. \<#76F4\>\<#7EBF\><math|B*C<rsub|1>>\<#4E0E\>\<#5E73\>\<#9762\><math|B*B<rsub|1>*D<rsub|1>*D>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|45<rsup|\<circ\>>>

    D. \<#76F4\>\<#7EBF\><math|B*C<rsub|1>>\<#4E0E\>\<#5E73\>\<#9762\><math|A*B*C*D>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|45<rsup|\<circ\>>>

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=x<rsup|3>-x+1>\<#FF0C\>\<#5219\>(<space|2em>)

    A. <math|f<around|(|x|)>>\<#6709\>\<#4E24\>\<#4E2A\>\<#6781\>\<#503C\>\<#70B9\>

    B. <math|f<around|(|x|)>>\<#6709\>\<#4E09\>\<#4E2A\>\<#96F6\>\<#70B9\>

    C. \<#70B9\><math|<around|(|0,1|)>>\<#662F\>\<#66F2\>\<#7EBF\><math|y=f<around|(|x|)>>\<#7684\>\<#5BF9\>\<#79F0\>\<#4E2D\>\<#5FC3\>

    D. \<#76F4\>\<#7EBF\><math|y=2*x>\<#662F\>\<#66F2\>\<#7EBF\><math|y=f<around|(|x|)>>\<#7684\>\<#5207\>\<#7EBF\>

    <item>\<#5DF2\>\<#77E5\><math|O>\<#4E3A\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#FF0C\>\<#70B9\><math|A*<around|(|1,1|)>>\<#5728\>\<#629B\>\<#7269\>\<#7EBF\><math|C:x<rsup|2>=2p*y*<around|(|p\<gtr\>0|)>>\<#4E0A\>\<#FF0C\>\<#8FC7\>\<#70B9\><math|B*<around|(|0,-1|)>>\<#7684\>\<#76F4\>\<#7EBF\>\<#4EA4\><math|C>\<#4E8E\><math|P>\<#FF0C\><math|Q>\<#4E24\>\<#70B9\>\<#FF0C\>\<#5219\>(<space|2em>)

    A. <math|C>\<#7684\>\<#51C6\>\<#7EBF\>\<#4E3A\><math|y=-1>\ 

    B. \<#76F4\>\<#7EBF\><math|A*B>\<#4E0E\><math|C>\<#76F8\>\<#5207\>

    C. <math|<around|\||O*P|\|>\<cdot\><around|\||O*Q|\|>\<gtr\><around|\||O*A|\|><rsup|2>>\ 

    D. <math|<around|\||B*P|\|>\<cdot\><around|\||B*Q|\|>\<gtr\><around|\||B*A|\|><rsup|2>>

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>>\<#53CA\>\<#5176\>\<#5BFC\>\<#51FD\>\<#6570\><math|f<rprime|'><around|(|x|)>>\<#7684\>\<#5B9A\>\<#4E49\>\<#57DF\>\<#4E3A\><math|R>\<#FF0C\>\<#8BB0\><math|g<around|(|x|)>=f<rprime|'><around|(|x|)>>.\<#82E5\><math|f*<around|(|<frac|3|2>-2*x|)>>\<#FF0C\><math|g*<around|(|2+x|)>>\<#5747\>\<#4E3A\>\<#5076\>\<#51FD\>\<#6570\>\<#FF0C\>\<#5219\>(<space|2em>)

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|f<around|(|0|)>=0>
      </cell>|<\cell>
        B. <math|g*<around|(|-<frac|1|2>|)>=0>
      </cell>|C. <math|f*<around|(|-1|)>=f<around|(|4|)>>|<\cell>
        D. <math|g*<around|(|-1|)>=g<around|(|2|)>>
      </cell>>>>
    </wide-tabular>
  </enumerate>

  <strong|\<#4E09\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\><with|font-series|bold|4>\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\><with|font-series|bold|20>\<#5206\>\<#FF09\>

  <\enumerate>
    <assign|item-nr|12><item><math|<around|(|1-<frac|y|x>|)>*<around|(|x+y|)><rsup|8>>\<#7684\>\<#5C55\>\<#5F00\>\<#5F0F\>\<#4E2D\><math|x<rsup|2>*y<rsup|6>>\<#7684\>\<#7CFB\>\<#6570\>\<#4E3A\><underline|<space|2cm>>
    (\<#7528\>\<#6570\>\<#5B57\>\<#4F5C\>\<#7B54\>)\<#FF0E\>

    <item>\<#5199\>\<#51FA\>\<#4E0E\>\<#5706\><math|x<rsup|2>+y<rsup|2>=1>\<#548C\><math|<around|(|x-3|)><rsup|2>+<around|(|y-4|)><rsup|2>=16>\<#90FD\>\<#76F8\>\<#5207\>\<#7684\>\<#4E00\>\<#6761\>\<#76F4\>\<#7EBF\>\<#7684\>\<#65B9\>\<#7A0B\><underline|<space|2cm>>\<#FF0E\>

    <item>\<#82E5\>\<#66F2\>\<#7EBF\><math|y=<around|(|x+a|)>*e<rsup|x>>\<#6709\>\<#4E24\>\<#6761\>\<#8FC7\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#7684\>\<#5207\>\<#7EBF\>\<#FF0C\>\<#5219\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#662F\><underline|<space|2cm>>\<#FF0E\>

    <item>\<#5DF2\>\<#77E5\>\<#692D\>\<#5706\><math|C:<frac|x<rsup|2>|a<rsup|2>>+<frac|y<rsup|2>|b<rsup|2>>=1*<around|(|a\<gtr\>b\<gtr\>0|)>>\<#FF0C\><math|C>\<#7684\>\<#4E0A\>\<#9876\>\<#70B9\>\<#4E3A\><math|A>\<#FF0C\>\<#4E24\>\<#4E2A\>\<#7126\>\<#70B9\>\<#4E3A\><math|F<rsub|1>>\<#FF0C\><math|F<rsub|2>>\<#FF0C\>\<#79BB\>\<#5FC3\>\<#7387\>\<#4E3A\><math|<frac|1|2>>\<#FF0C\>\<#8FC7\><math|F<rsub|1>>\<#4E14\>\<#5782\>\<#76F4\>\<#4E8E\><math|A*F<rsub|2>>\<#7684\>\<#76F4\>\<#7EBF\>\<#4E0E\><math|C>\<#4EA4\>\<#4E8E\><math|D>\<#FF0C\><math|E>\<#4E24\>\<#70B9\>\<#FF0C\><math|<around|\||D*E|\|>=6>\<#FF0C\>\<#5219\>\<vartriangle\>\<#7684\>\<#5468\>\<#957F\>\<#662F\><underline|<space|2cm>>\<#FF0E\>
  </enumerate>

  <strong|\<#56DB\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\><with|font-series|bold|6>\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\><with|font-series|bold|70>\<#5206\>\<#FF09\>

  <\enumerate>
    <assign|item-nr|16><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|1>=1>\<#FF0C\><math|<around*|{|<frac|S<rsub|n>|a<rsub|n>>|}>>\<#662F\>\<#516C\>\<#5DEE\>\<#4E3A\><math|<frac|1|3>>\<#7684\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>\<#FF0E\>

    <math|<around|(|1|)>>\<#6C42\><math|<around|{|a<rsub|n>|}>>\<#7684\>\<#901A\>\<#9879\>\<#516C\>\<#5F0F\><math|;<around|(|2|)>>\<#8BC1\>\<#660E\>\<#FF1A\><math|<frac|1|a<rsub|1>>+<frac|1|a<rsub|2>>+\<cdots\>+<frac|1|a<rsub|n>>\<less\>2>\<#FF0E\><vspace|5cm>

    <item>\<#8BB0\><math|\<vartriangle\>A*B*C>\<#7684\>\<#5185\>\<#89D2\><math|A>\<#FF0C\><math|B>\<#FF0C\><math|C>\<#7684\>\<#5BF9\>\<#8FB9\>\<#5206\>\<#522B\>\<#4E3A\><math|a>\<#FF0C\><math|b>\<#FF0C\><math|c>\<#FF0C\>\<#5DF2\>\<#77E5\><math|<frac|cos
    A|1+sin A>=<frac|sin 2*B|1+cos 2*B>>\<#FF0E\>

    <math|<around|(|1|)>>\<#82E5\><math|C=<frac|2*\<pi\>|3>>\<#FF0C\>\<#6C42\><math|B;<around|(|2|)>>\<#6C42\><math|<frac|a<rsup|2>+b<rsup|2>|c<rsup|2>>>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#FF0E\><vspace|5cm>

    <item>\<#5982\>\<#56FE\>\<#FF0C\>\<#76F4\>\<#4E09\>\<#68F1\>\<#67F1\><math|A*B*C-A<rsub|1>*B<rsub|1>*C<rsub|1>>\<#7684\>\<#4F53\>\<#79EF\>\<#4E3A\><math|4>\<#FF0C\><math|\<vartriangle\>A<rsub|1>B
    C>\<#7684\>\<#9762\>\<#79EF\>\<#4E3A\><math|2<sqrt|2>>\<#FF0E\>

    <math|<around|(|1|)>>\<#6C42\><math|A>\<#5230\>\<#5E73\>\<#9762\><math|A<rsub|1>*B*C>\<#7684\>\<#8DDD\>\<#79BB\>;

    <around|(|2|)>\<#8BBE\><math|D>\<#4E3A\><math|A<rsub|1>*C>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\><math|A*A<rsub|1>=A*B>\<#FF0C\>\<#5E73\>\<#9762\><math|A<rsub|1>*B*C*\<bot\>>\<#5E73\>\<#9762\><math|A*B*B<rsub|1>*A<rsub|1>>\<#FF0C\>\<#6C42\>\<#4E8C\>\<#9762\>\<#89D2\><math|A-B*D-C>\<#7684\>\<#6B63\>\<#5F26\>\<#503C\>\<#FF0E\>

    <image|<tuple|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

    <item>\<#4E00\>\<#652F\>\<#533B\>\<#7597\>\<#56E2\>\<#961F\>\<#7814\>\<#7A76\>\<#67D0\>\<#5730\>\<#7684\>\<#4E00\>\<#79CD\>\<#5730\>\<#65B9\>\<#6027\>\<#75BE\>\<#75C5\>\<#4E0E\>\<#5F53\>\<#5730\>\<#5C45\>\<#6C11\>\<#7684\>\<#536B\>\<#751F\>\<#4E60\>\<#60EF\><math|(>\<#536B\>\<#751F\>\<#4E60\>\<#60EF\>\<#5206\>\<#4E3A\>\<#826F\>\<#597D\>\<#548C\>\<#4E0D\>\<#591F\>\<#826F\>\<#597D\>\<#4E24\>\<#7C7B\><math|)>\<#7684\>\<#5173\>\<#7CFB\>\<#FF0C\>\<#5728\>\<#5DF2\>\<#60A3\>\<#8BE5\>\<#75BE\>\<#75C5\>\<#7684\>\<#75C5\>\<#4F8B\>\<#4E2D\>\<#968F\>\<#673A\>\<#8C03\>\<#67E5\>\<#4E86\><math|100>\<#4F8B\><math|(>\<#79F0\>\<#4E3A\>\<#75C5\>\<#4F8B\>\<#7EC4\><math|)>\<#FF0C\>\<#540C\>\<#65F6\>\<#5728\>\<#672A\>\<#60A3\>\<#8BE5\>\<#75BE\>\<#75C5\>\<#7684\>\<#4EBA\>\<#7FA4\>\<#4E2D\>\<#968F\>\<#673A\>\<#8C03\>\<#67E5\>\<#4E86\><math|100>\<#4EBA\><math|(>\<#79F0\>\<#4E3A\>\<#5BF9\>\<#7167\>\<#7EC4\><math|)>\<#FF0C\>\<#5F97\>\<#5230\>\<#5982\>\<#4E0B\>\<#6570\>\<#636E\>\<#FF1A\>

    <center|<center|><block*|<tformat|<table|<row|<cell|>|<cell|\<#4E0D\>\<#591F\>\<#826F\>\<#597D\>>|<cell|\<#826F\>\<#597D\>>>|<row|<cell|\<#75C5\>\<#4F8B\>\<#7EC4\>>|<cell|40>|<cell|60>>|<row|<cell|\<#5BF9\>\<#7167\>\<#7EC4\>>|<cell|10>|<cell|90>>>>>>

    <math|<around|(|1|)>>\<#80FD\>\<#5426\>\<#6709\><math|99%>\<#7684\>\<#628A\>\<#63E1\>\<#8BA4\>\<#4E3A\>\<#60A3\>\<#8BE5\>\<#75BE\>\<#75C5\>\<#7FA4\>\<#4F53\>\<#4E0E\>\<#672A\>\<#60A3\>\<#8BE5\>\<#75BE\>\<#75C5\>\<#7FA4\>\<#4F53\>\<#7684\>\<#536B\>\<#751F\>\<#4E60\>\<#60EF\>\<#6709\>\<#5DEE\>\<#5F02\>\<cdot\>

    <around|(|2|)>\<#4ECE\>\<#8BE5\>\<#5730\>\<#7684\>\<#4EBA\>\<#7FA4\>\<#4E2D\>\<#4EFB\>\<#9009\>\<#4E00\>\<#4EBA\>\<#FF0C\><math|A>\<#8868\>\<#793A\>\<#4E8B\>\<#4EF6\>``\<#9009\>\<#5230\>\<#7684\>\<#4EBA\>\<#536B\>\<#751F\>\<#4E60\>\<#60EF\>\<#4E0D\>\<#591F\>\<#826F\>\<#597D\>''\<#FF0C\><math|B>\<#8868\>\<#793A\>\<#4E8B\>\<#4EF6\>``\<#9009\>\<#5230\>\<#7684\>\<#4EBA\>\<#60A3\>\<#6709\>\<#8BE5\>\<#75BE\>\<#75C5\>''\<#FF0C\><math|<frac|P<around|(|B\|A|)>|P<around|(|<wide|B|\<bar\>>\|A|)>>>\<#4E0E\><math|<frac|P<around|(|B\|<wide|A|\<bar\>>|)>|P<around|(|<wide|B|\<bar\>>\|<wide|A|\<bar\>>|)>>>\<#7684\>\<#6BD4\>\<#503C\>\<#662F\>\<#536B\>\<#751F\>\<#4E60\>\<#60EF\>\<#4E0D\>\<#591F\>\<#826F\>\<#597D\>\<#5BF9\>\<#60A3\>\<#8BE5\>\<#75BE\>\<#75C5\>\<#98CE\>\<#9669\>\<#7A0B\>\<#5EA6\>\<#7684\>\<#4E00\>\<#9879\>\<#5EA6\>\<#91CF\>\<#6307\>\<#6807\>\<#FF0C\>\<#8BB0\>\<#8BE5\>\<#6307\>\<#6807\>\<#4E3A\><math|R>\<#FF0E\>

    <math|<around|(|<math|i>|)>>\<#8BC1\>\<#660E\>\<#FF1A\><math|R=<frac|P<around|(|A\|B|)>|P<around|(|<wide|A|\<bar\>>\|B|)>>>\<#FF0E\><frac|P<around|(|<wide|A|\<bar\>>\|<wide|B|\<bar\>>|)>|P<around|(|A\|<wide|B|\<bar\>>|)>>;

    <around|(|ii|)>\<#5229\>\<#7528\>\<#8BE5\>\<#8C03\>\<#67E5\>\<#6570\>\<#636E\>\<#FF0C\>\<#7ED9\>\<#51FA\><math|P<around|(|A\|B|)>>\<#FF0C\><math|P<around|(|A\|<wide|B|\<bar\>>|)>>\<#7684\>\<#4F30\>\<#8BA1\>\<#503C\>\<#FF0C\>\<#5E76\>\<#5229\>\<#7528\><math|<around|(|i|)>>\<#7684\>\<#7ED3\>\<#679C\>\<#7ED9\>\<#51FA\><math|R>\<#7684\>\<#4F30\>\<#8BA1\>\<#503C\>\<#FF0E\>

    \<#9644\>\<#FF1A\><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|)>>>\<#FF0C\><block|<tformat|<cwith|2|2|1|1|cell-halign|c>|<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>>>>><vspace|5cm>

    <item>\<#5DF2\>\<#77E5\>\<#70B9\><math|A*<around|(|2,1|)>>\<#5728\>\<#53CC\>\<#66F2\>\<#7EBF\><math|C:<frac|x<rsup|2>|a<rsup|2>>-<frac|y<rsup|2>|a<rsup|2>-1>=1*<around|(|a\<gtr\>1|)>>\<#4E0A\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|l>\<#4EA4\><math|C>\<#4E8E\><math|P>\<#FF0C\><math|Q>\<#4E24\>\<#70B9\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|A*P>\<#FF0C\><math|A*Q>\<#7684\>\<#659C\>\<#7387\>\<#4E4B\>\<#548C\>\<#4E3A\><math|0>\<#FF0E\>

    <math|<around|(|1|)>>\<#6C42\><math|l>\<#7684\>\<#659C\>\<#7387\><math|;<around|(|2|)>>\<#82E5\><math|tan
    \<angle\>*P*A*Q=2<sqrt|2>>\<#FF0C\>\<#6C42\><math|\<vartriangle\>P*A*Q>\<#7684\>\<#9762\>\<#79EF\>\<#FF0E\><vspace|5cm>

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=e<rsup|x>-a*x>\<#548C\><math|g<around|(|x|)>=a*x-ln
    x>\<#6709\>\<#76F8\>\<#540C\>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#FF0E\>

    <math|<around|(|1|)>>\<#6C42\><math|a>;

    <around|(|2|)>\<#8BC1\>\<#660E\>\<#FF1A\>\<#5B58\>\<#5728\><math|y=b>\<#76F4\>\<#7EBF\>\<#FF0C\>\<#5176\>\<#4E0E\>\<#4E24\>\<#6761\>\<#66F2\>\<#7EBF\><math|y=f<around|(|x|)>>\<#548C\><math|y=g<around|(|x|)>>\<#5171\>\<#6709\>\<#4E09\>\<#4E2A\>\<#4E0D\>\<#540C\>\<#7684\>\<#4EA4\>\<#70B9\>\<#FF0C\>\<#5E76\>\<#4E14\>\<#4ECE\>\<#5DE6\>\<#5230\>\<#53F3\>\<#7684\>\<#4E09\>\<#4E2A\>\<#4EA4\>\<#70B9\>\<#7684\>\<#6A2A\>\<#5750\>\<#6807\>\<#6210\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>\<#FF0E\><vspace|5cm>
  </enumerate>

  \;
</body>

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