planet/高考数学/2022年浙江省高考数学试题.tm

<TeXmacs|2.1.2>

<style|<tuple|generic|chinese|doc>>

<\body>
  <doc-data|<doc-title|2022\<#5E74\>\<#666E\>\<#901A\>\<#9AD8\>\<#7B49\>\<#5B66\>\<#6821\>\<#62DB\>\<#751F\>\<#5168\>\<#56FD\>\<#7EDF\>\<#4E00\>\<#8003\>\<#8BD5\>>|<doc-subtitle|<with|font|AR
  PL UMing CN|font-base-size|16|\<#6570\><space|2em>\<#5B66\>>>>

  <space|2em>\<#672C\>\<#8BD5\>\<#9898\>\<#5377\>\<#5206\>\<#9009\>\<#62E9\>\<#9898\>\<#548C\>\<#975E\>\<#9009\>\<#62E9\>\<#9898\>\<#4E24\>\<#90E8\>\<#5206\>\<#3002\>\<#5168\>\<#5377\>\<#5171\>4\<#9875\>\<#FF0C\>\<#9009\>\<#62E9\>\<#9898\>\<#90E8\>\<#5206\>1\<#81F3\>3\<#9875\>\<#FF1B\>\<#975E\>\<#9009\>\<#62E9\>\<#9898\>\<#90E8\>\<#5206\>3\<#81F3\>4\<#9875\>\<#3002\>\<#6EE1\>\<#5206\>150\<#5206\>\<#FF0C\>\<#8003\>\<#8BD5\>\<#65F6\>\<#95F4\>120\<#5206\>\<#949F\>\<#3002\>

  \;

  <strong|\<#8003\>\<#751F\>\<#6CE8\>\<#610F\>\<#FF1A\>>

  <\enumerate>
    <item>\<#7B54\>\<#9898\>\<#524D\>\<#FF0C\>\<#8BF7\>\<#52A1\>\<#5FC5\>\<#5C06\>\<#81EA\>\<#5DF1\>\<#7684\>\<#59D3\>\<#540D\>\<#3001\>\<#51C6\>\<#8003\>\<#8BC1\>\<#53F7\>\<#7528\>\<#9ED1\>\<#8272\>\<#5B57\>\<#8FF9\>\<#7684\>\<#7B7E\>\<#5B57\>\<#7B14\>\<#6216\>\<#94A2\>\<#7B14\>\<#5206\>\<#522B\>\<#586B\>\<#5199\>\<#5728\>\<#8BD5\>\<#9898\>\<#5377\>\<#548C\>\<#7B54\>\<#9898\>\<#7EB8\>\<#89C4\>\<#5B9A\>\<#7684\>\<#4F4D\>\<#7F6E\>\<#4E0A\>\<#3002\>

    <item>\<#7B54\>\<#9898\>\<#65F6\>\<#FF0C\>\<#8BF7\>\<#6309\>\<#7167\>\<#7B54\>\<#9898\>\<#7EB8\>\<#4E0A\>\P\<#6CE8\>\<#610F\>\<#4E8B\>\<#9879\>\Q\<#7684\>\<#8981\>\<#6C42\>\<#FF0C\>\<#5728\>\<#7B54\>\<#9898\>\<#7EB8\>\<#76F8\>\<#5E94\>\<#7684\>\<#4F4D\>\<#7F6E\>\<#4E0A\>\<#89C4\>\<#8303\>\<#4F5C\>\<#7B54\>\<#FF0C\>\<#5728\>\<#672C\>\<#8BD5\>\<#9898\>\<#5377\>\<#4E0A\>\<#7684\>\<#4F5C\>\<#7B54\>\<#4E00\>\<#5F8B\>\<#65E0\>\<#6548\>\<#3002\>
  </enumerate>

  \;

  <\with|par-columns|2>
    <strong|\<#53C2\>\<#8003\>\<#516C\>\<#5F0F\>\<#FF1A\>>

    \<#82E5\>\<#4E8B\>\<#4EF6\>A,B\<#4E92\>\<#65A5\>\<#FF0C\>\<#5219\>

    <math|P<around*|(|A+B|)>=P<around*|(|A|)>+P<around*|(|B|)>>

    \<#82E5\>\<#4E8B\>\<#4EF6\>A,B\<#76F8\>\<#4E92\>\<#72EC\>\<#7ACB\>\<#FF0C\>\<#5219\>

    <math|P<around*|(|AB|)>=P<around*|(|A|)>*P<around*|(|B|)>>

    \<#82E5\>\<#4E8B\>\<#4EF6\>A\<#5728\>\<#4E00\>\<#6B21\>\<#8BD5\>\<#9A8C\>\<#4E2D\>\<#53D1\>\<#751F\>\<#7684\>\<#6982\>\<#7387\>\<#662F\><math|p>\<#FF0C\>\<#5219\><math|n>\<#6B21\>\<#72EC\>\<#7ACB\>\<#91CD\>\<#590D\>\<#8BD5\>\<#9A8C\>\<#4E2D\>\<#4E8B\>\<#4EF6\><math|A>\<#6070\>\<#597D\>\<#53D1\>\<#751F\><math|k>\<#6B21\>\<#7684\>\<#6982\>\<#7387\>

    <math|P<rsub|n><around*|(|k|)>=C<rsup|k><rsub|n>*p<rsup|k><around*|(|1-p|)><rsup|n-k><around*|(|k=0,1,2,\<ldots\>,n|)>>

    \<#53F0\>\<#4F53\>\<#7684\>\<#4F53\>\<#79EF\>\<#516C\>\<#5F0F\>

    <math|V=<frac|1|3><around*|(|S<rsub|1>+<sqrt|S<rsub|1>S<rsub|2>>+S<rsub|2>|)>*h>

    \<#5176\>\<#4E2D\><math|S<rsub|1>>,<math|S<rsub|2>>\<#5206\>\<#522B\>\<#8868\>\<#793A\>\<#53F0\>\<#4F53\>\<#7684\>\<#4E0A\>\<#3001\>\<#4E0B\>\<#5E95\>\<#9762\>\<#79EF\>\<#FF0C\><math|h>\<#8868\>\<#793A\>\<#53F0\>\<#4F53\>\<#7684\>\<#9AD8\>

    \<#67F1\>\<#4F53\>\<#7684\>\<#4F53\>\<#79EF\>\<#516C\>\<#5F0F\>

    <math|V=S*h>

    \<#5176\>\<#4E2D\><math|S>\<#8868\>\<#793A\>\<#67F1\>\<#4F53\>\<#7684\>\<#5E95\>\<#9762\>\<#79EF\>\<#FF0C\>h\<#8868\>\<#793A\>\<#67F1\>\<#4F53\>\<#7684\>\<#9AD8\>

    \<#9525\>\<#4F53\>\<#7684\>\<#4F53\>\<#79EF\>\<#516C\>\<#5F0F\>

    <math|V=<frac|1|3>S*h>

    \<#5176\>\<#4E2D\><math|S>\<#8868\>\<#793A\>\<#9525\>\<#4F53\>\<#7684\>\<#5E95\>\<#9762\>\<#79EF\>\<#FF0C\><math|h>\<#8868\>\<#793A\>\<#9525\>\<#4F53\>\<#7684\>\<#9AD8\>

    \<#7403\>\<#7684\>\<#8868\>\<#9762\>\<#79EF\>\<#516C\>\<#5F0F\>

    <math|S=4*\<pi\>*R<rsup|2>>

    \<#7403\>\<#7684\>\<#4F53\>\<#79EF\>\<#516C\>\<#5F0F\>

    <math|V=<frac|4|3>*\<pi\>*R<rsup|3>>

    \<#5176\>\<#4E2D\><math|R>\<#8868\>\<#793A\>\<#7403\>\<#7684\>\<#534A\>\<#5F84\>
  </with>

  \;

  \;

  <\with|par-mode|center>
    <strong|<with|font|AR PL UMing CN|font-base-size|14|\<#9009\>\<#62E9\>\<#9898\>\<#90E8\>\<#5206\>\<#FF08\>\<#5171\>40\<#5206\>\<#FF09\>>>
  </with>

  \;

  <strong|\<#4E00\>\<#3001\>\<#9009\>\<#62E9\>\<#9898\>\<#FF1A\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>10\<#5C0F\>\<#9898\>\<#FF0C\>\<#6BCF\>\<#5C0F\>\<#9898\>4\<#5206\>\<#FF0C\>\<#5171\>40\<#5206\>\<#3002\>\<#5728\>\<#6BCF\>\<#5C0F\>\<#9898\>\<#7ED9\>\<#51FA\>\<#7684\>\<#56DB\>\<#4E2A\>\<#9009\>\<#9879\>\<#4E2D\>\<#FF0C\>\<#53EA\>\<#6709\>\<#4E00\>\<#9879\>\<#662F\>\<#7B26\>\<#5408\>\<#9898\>\<#76EE\>\<#8981\>\<#6C42\>\<#7684\>\<#3002\>>

  <\enumerate>
    <item>\<#8BBE\>\<#96C6\>\<#5408\><math|A=<around*|{|1,2|}>,B=<around*|{|2,4,6|}>>\<#FF0C\>\<#5219\><math|A\<cup\>B=>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|2>
      </cell>|<\cell>
        B. <math|<around*|{|1,2|}>>
      </cell>|<\cell>
        C. <math|<around*|{|2,4,6|}>>
      </cell>|<\cell>
        D. <math|<around*|{|1,2,4,6|}>>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\><math|a,b\<in\>\<bbb-R\>,a+3*i=<around*|(|b+i|)>*i>\<#FF08\><math|i>\<#4E3A\>\<#865A\>\<#6570\>\<#5355\>\<#4F4D\>\<#FF09\>\<#FF0C\>\<#5219\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|a=1,b=-3>
      </cell>|<\cell>
        B. <math|a=-1,b=3>
      </cell>|<\cell>
        C. <math|a=-1,b=-3>
      </cell>|<\cell>
        D. <math|a=1,b=3>
      </cell>>>>
    </wide-tabular>

    <item>\<#82E5\>\<#5B9E\>\<#6570\><math|x,y>\<#6EE1\>\<#8DB3\>\<#7EA6\>\<#675F\>\<#6761\>\<#4EF6\><math|<with|math-display|true|<choice|<tformat|<table|<row|<cell|x-2\<geqslant\>0,>>|<row|<cell|2*x+y-7\<leqslant\>0,>>|<row|<cell|x-y-2\<leqslant\>0,>>>>>>>\<#5219\><math|z=3*x+4*y>\<#7684\>\<#6700\>\<#5927\>\<#503C\>\<#662F\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|20>
      </cell>|<\cell>
        B. <math|18>
      </cell>|<\cell>
        C. <math|13>
      </cell>|<\cell>
        D. <math|6>
      </cell>>>>
    </wide-tabular>

    <item>\<#8BBE\><math|x\<in\>\<bbb-R\>>\<#FF0C\>\<#5219\>\<#201C\><math|sin
    x=1>\<#201D\>\<#662F\>\<#201C\><math|cos x=0>\<#201D\>\<#7684\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. \<#5145\>\<#5206\>\<#4E0D\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>
      </cell>>|<row|<\cell>
        B. \<#5FC5\>\<#8981\>\<#4E0D\>\<#5145\>\<#5206\>\<#6761\>\<#4EF6\>
      </cell>>|<row|<\cell>
        C. \<#5145\>\<#5206\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>
      </cell>>|<row|<\cell>
        D. \<#65E2\>\<#4E0D\>\<#5145\>\<#5206\>\<#4E5F\>\<#4E0D\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>
      </cell>>>>
    </wide-tabular>

    <item>\<#67D0\>\<#51E0\>\<#4F55\>\<#4F53\>\<#7684\>\<#4E09\>\<#89C6\>\<#56FE\>\<#5982\>\<#56FE\>\<#6240\>\<#793A\>\<#FF08\>\<#5355\>\<#4F4D\>\<#FF1A\>cm\<#FF09\>\<#FF0C\>\<#5219\>\<#8BE5\>\<#51E0\>\<#4F55\>\<#4F53\>\<#7684\>\<#4F53\>\<#79EF\>\<#FF08\>\<#5355\>\<#4F4D\>\<#FF1A\><math|cm<rsup|3>>\<#FF09\>\<#662F\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|22\<pi\>>
      </cell>|<\cell>
        B. <math|8\<pi\>>
      </cell>>|<row|<\cell>
        C. <math|<frac|22|3>\<pi\>>
      </cell>|<\cell>
        D. <math|<frac|16|3>\<pi\>>
      </cell>>>>
    </wide-tabular>

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    <item>\<#4E3A\>\<#4E86\>\<#5F97\>\<#5230\>\<#51FD\>\<#6570\><math|y=2*sin
    3*x>\<#7684\>\<#56FE\>\<#8C61\>\<#FF0C\>\<#53EA\>\<#8981\>\<#628A\>\<#51FD\>\<#6570\><math|y=2*sin<around*|(|3*x+<frac|\<pi\>|5>|)>>\<#56FE\>\<#8C61\>\<#4E0A\>\<#6240\>\<#6709\>\<#7684\>\<#70B9\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. \<#5411\>\<#5DE6\>\<#5E73\>\<#79FB\><math|<frac|\<pi\>|5>>\<#4E2A\>\<#5355\>\<#4F4D\>\<#957F\>\<#5EA6\>
      </cell>|<\cell>
        B. \<#5411\>\<#53F3\>\<#5E73\>\<#79FB\><math|<frac|\<pi\>|5>>\<#4E2A\>\<#5355\>\<#4F4D\>\<#957F\>\<#5EA6\>
      </cell>>|<row|<\cell>
        C. \<#5411\>\<#5DE6\>\<#5E73\>\<#79FB\><math|<frac|\<pi\>|15>>\<#4E2A\>\<#5355\>\<#4F4D\>\<#957F\>\<#5EA6\>
      </cell>|<\cell>
        D. \<#5411\>\<#53F3\>\<#5E73\>\<#79FB\><math|<frac|\<pi\>|15>>\<#4E2A\>\<#5355\>\<#4F4D\>\<#957F\>\<#5EA6\>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\><math|2<rsup|a>=5,log<rsub|8>3=b>\<#FF0C\>\<#5219\><math|4<rsup|a-3b>=>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|25>
      </cell>|<\cell>
        B. <math|5>
      </cell>>|<row|<\cell>
        C. <math|<frac|25|9>>
      </cell>|<\cell>
        D. <math|<frac|5|3>>
      </cell>>>>
    </wide-tabular>

    <item>\<#5982\>\<#56FE\>\<#FF0C\>\<#5DF2\>\<#77E5\>\<#6B63\>\<#4E09\>\<#68F1\>\<#67F1\><math|<math-it|ABC>-A<rsub|1>B<rsub|1>C<rsub|1>,<math-it|AC>=<math-it|AA<rsub|1>>>\<#FF0C\><math|E,F>\<#5206\>\<#522B\>\<#662F\>\<#68F1\><math|<math-it|BC>>\<#FF0C\><math|A<rsub|1>C<rsub|1>>\<#4E0A\>\<#7684\>\<#70B9\>.\<#8BB0\><math|<math-it|EF>>\<#4E0E\><math|A<math-it|A<rsub|1>>>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|\<alpha\>>\<#FF0C\><math|<math-it|EF>>\<#4E0E\>\<#5E73\>\<#9762\><math|<math-it|ABC>>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|\<beta\>>\<#FF0C\>\<#4E8C\>\<#9762\>\<#89D2\><math|F-<math-it|BC>-A>\<#7684\>\<#5E73\>\<#9762\>\<#89D2\>\<#4E3A\><math|\<gamma\>>\<#FF0C\>\<#5219\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|\<alpha\>\<leqslant\>\<beta\>\<leqslant\>\<gamma\>>
      </cell>|<\cell>
        B. <math|\<beta\>\<leqslant\>\<alpha\>\<leqslant\>\<gamma\>>
      </cell>>|<row|<\cell>
        C. <math|\<beta\>\<leqslant\>\<gamma\>\<less\>\<alpha\>>
      </cell>|<\cell>
        D. <math|\<alpha\>\<leqslant\>\<gamma\>\<less\>\<beta\>>
      </cell>>>>
    </wide-tabular>

    <with|figure-sep||<\render-small-figure||>
      <with|gr-mode|<tuple|group-edit|edit-props>|gr-frame|<tuple|scale|1cm|<tuple|0.5gw|0.5gh>>|gr-geometry|<tuple|geometry|0.386691par|0.386676par|center>|gr-grid|<tuple|empty>|gr-edit-grid-aspect|<tuple|<tuple|axes|none>|<tuple|1|none>|<tuple|10|none>>|gr-edit-grid|<tuple|empty>|gr-dash-style|11100|gr-grid-old|<tuple|cartesian|<point|0|0>|1>|gr-edit-grid-old|<tuple|cartesian|<point|0|0>|1>|gr-auto-crop|true|<graphics||<line|<point|-1.4|0>|<point|0.0|-0.6>>|<line|<point|0|-0.6>|<point|0.6000000000000002|0.0>>|<line|<point|-1.4|2>|<point|-1.4|0.0>>|<line|<point|0.6|2>|<point|0.6000000000000002|0.0>>|<line|<point|-1.4|2>|<point|0.0|1.4>>|<line|<point|0|1.4>|<point|0.6000000000000002|2.0>>|<line|<point|-1.4|2>|<point|0.6000000000000002|2.0>>|<with|dash-style|11100|<line|<point|-1.4|0>|<point|0.6000000000000002|0.0>>>|<with|dash-style|11100|<line|<point|-1.1|2>|<point|0.4000000000000003|-0.1999999999999999>>>|<math-at|B<rsub|1>|<point|0.2|1.3>>|<math-at|B|<point|-0.1999999999999999|-1.0>>|<math-at|E|<point|0.3999999999999998|-0.5>>|<math-at|C|<point|0.7|-0.2>>|<math-at|C<rsub|1>|<point|0.7|2.146774944823396>>|<math-at|F|<point|-1.2488419205418728|2.1>>|<math-at|A<rsub|1>|<point|-1.8605437551586161|2.1>>|<math-at|A|<point|-1.8|-0.2>>|<line|<point|0|1.4>|<point|0.0|-0.6>>>>
    </render-small-figure|\<#FF08\>\<#7B2C\>8\<#9898\>\<#56FE\>\<#FF09\>>>

    <item>\<#5DF2\>\<#77E5\><math|a,b\<in\>\<bbb-R\>>\<#FF0C\>\<#82E5\>\<#5BF9\>\<#4EFB\>\<#610F\><math|x\<in\>\<bbb-R\>>\<#FF0C\><math|a*<around*|\||x-b|\|>+<around*|\||x-4|\|>-<around*|\||2*x-5|\|>\<geqslant\>0>\<#FF0C\>\<#5219\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|a\<leqslant\>1,b\<geqslant\>3>
      </cell>|<\cell>
        B. <math|a\<leqslant\>1,b\<leqslant\>3>
      </cell>>|<row|<\cell>
        C. <math|a\<geqslant\>1,b\<geqslant\>3>
      </cell>|<\cell>
        D. <math|a\<geqslant\>1,b\<leqslant\>3>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#6EE1\>\<#8DB3\><with|math-display|true|<math|a<rsub|1>=1,a<rsub|n+1>=a<rsub|n>-<frac|1|3>a<rsub|n><rsup|2><around*|(|n\<in\>\<bbb-N\><rsup|\<ast\>>|)>>>\<#FF0C\>\<#5219\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<with|math-display|true|2\<less\>100*a<rsub|100>\<less\><frac|5|2>>>
      </cell>|<\cell>
        B. <with|math-display|true|<math|<frac|5|2>\<less\>100*a<rsub|100>\<less\>3>>
      </cell>>|<row|<\cell>
        C. <with|math-display|true|<math|3\<less\>100*a<rsub|100>\<less\><frac|7|2>>>
      </cell>|<\cell>
        D. <math|<with|math-display|true|<frac|7|2>\<less\>100*a<rsub|100>\<less\>4>>
      </cell>>>>
    </wide-tabular>
  </enumerate>

  \;

  \;

  \;

  <\with|par-mode|center>
    <strong|<\with|font|AR PL UMing CN|font-base-size|14>
      \<#975E\>\<#9009\>\<#62E9\>\<#9898\>\<#90E8\>\<#5206\>\<#FF08\>\<#5171\>110\<#5206\>\<#FF09\>
    </with>>
  </with>

  \;

  <strong|\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>\<#FF1A\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>7\<#5C0F\>\<#9898\>\<#FF0C\>\<#5355\>\<#7A7A\>\<#9898\>\<#6BCF\>\<#9898\>4\<#5206\>\<#FF0C\>\<#591A\>\<#7A7A\>\<#9898\>\<#6BCF\>\<#7A7A\>3\<#5206\>\<#FF0C\>\<#5171\>36\<#5206\>\<#3002\>>

  <\enumerate>
    <assign|item-nr|10><item>\<#6211\>\<#56FD\>\<#5357\>\<#5B8B\>\<#8457\>\<#540D\>\<#6570\>\<#5B66\>\<#53EB\>\<#79E6\>\<#4E5D\>\<#97F6\>\<#FF0C\>\<#53D1\>\<#73B0\>\<#4E86\>\<#4ECE\>\<#4E09\>\<#89D2\>\<#5F62\>\<#4E09\>\<#8FB9\>\<#6C42\>\<#9762\>\<#79EF\>\<#7684\>\<#516C\>\<#5F0F\>\<#FF0C\>\<#4ED6\>\<#628A\>\<#8FD9\>\<#79CD\>\<#65B9\>\<#6CD5\>\<#79F0\>\<#4E3A\>\<#201C\>\<#4E09\>\<#659C\>\<#6C42\>\<#79EF\>\<#201D\>\<#FF0C\>\<#5B83\>\<#586B\>\<#8865\>\<#4E86\>\<#6211\>\<#56FD\>\<#4F20\>\<#7EDF\>\<#6570\>\<#5B66\>\<#7684\>\<#4E00\>\<#4E2A\>\<#7A7A\>\<#767D\>.
    \<#5982\>\<#679C\>\<#628A\>\<#8FD9\>\<#4E2A\>\<#65B9\>\<#6CD5\>\<#5199\>\<#6210\>\<#516C\>\<#5F0F\>\<#FF0C\>\<#5C31\>\<#662F\><math|<with|math-display|true|S=<sqrt|<frac|1|4><around*|[|c<rsup|2>a<rsup|2>-<around*|(|<frac|c<rsup|2>+a<rsup|2>-b<rsup|2>|2>|)><rsup|2>|]>>>>\<#FF0C\>\<#5176\>\<#4E2D\><math|a,b,c>\<#662F\>\<#4E09\>\<#89D2\>\<#5F62\>\<#7684\>\<#4E09\>\<#8FB9\>\<#FF0C\><math|S>\<#662F\>\<#4E09\>\<#89D2\>\<#5F62\>\<#7684\>\<#9762\>\<#79EF\>.
    \<#8BBE\>\<#67D0\>\<#4E09\>\<#89D2\>\<#5F62\>\<#7684\>\<#4E09\>\<#8FB9\><math|a=<sqrt|2>,b=<sqrt|3>,c=2>\<#FF0C\>\<#5219\>\<#8BE5\>\<#4E09\>\<#89D2\>\<#5F62\>\<#7684\>\<#9762\>\<#79EF\><math|S=><underline|<space|3em>>.

    <item>\<#5DF2\>\<#77E5\>\<#591A\>\<#9879\>\<#5F0F\><math|<with|math-display|true|<around*|(|x+2|)><around*|(|x-1|)><rsup|4>=a<rsub|0>+a<rsub|1>*x+a<rsub|2>*x<rsup|2>+a<rsub|3>*x<rsup|3>+a<rsub|4>*x<rsup|4>+a<rsub|5>*x<rsup|5>>>\<#FF0C\>\<#5219\><math|a<rsub|2>=><underline|<space|3em>>,<math|a<rsub|1>+a<rsub|2>+a<rsub|3>+a<rsub|4>+a<rsub|5>=><underline|<space|3em>>.

    <item>\<#82E5\><math|<with|math-display|true|3*sin \<alpha\>-sin
    \<beta\>=<sqrt|10>,\<alpha\>+\<beta\>=<frac|\<pi\>|2>>>\<#FF0C\>\<#5219\><math|sin
    \<alpha\>=><underline|<space|3em>>\<#FF0C\><math|cos
    2*\<beta\>=><underline|<space|3em>>.

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|<with|math-display|true|f<around*|(|x|)>=<choice|<tformat|<table|<row|<cell|-x<rsup|2>+2,>|<cell|x\<leqslant\>1,>>|<row|<cell|x+<frac|1|x>-1,>|<cell|x\<gtr\>1,>>>>>>>\<#5219\><math|f<around*|(|f<around*|(|<frac|1|2>|)>|)>=><underline|<space|3em>>\<#FF1B\>\<#82E5\>\<#5F53\><math|x\<in\><around*|[|a,b|]>>\<#65F6\>\<#FF0C\><math|1\<leqslant\>f<around*|(|x|)>\<leqslant\>3>\<#FF0C\>\<#5219\><math|b-a>\<#7684\>\<#6700\>\<#5927\>\<#503C\>\<#662F\><underline|<space|3em>>.

    <item>\<#73B0\>\<#6709\> 7 \<#5F20\>\<#5361\>\<#7247\>\<#FF0C\>\<#5206\>\<#522B\>\<#5199\>\<#4E0A\>\<#6570\>\<#5B57\>1,2,3,4,5,6.
    \<#4ECE\>\<#8FD9\>7\<#5F20\>\<#5361\>\<#7247\>\<#4E2D\>\<#968F\>\<#673A\>\<#62BD\>\<#53D6\>3\<#5F20\>\<#FF0C\>\<#8BB0\>\<#6240\>\<#62BD\>\<#53D6\>\<#5361\>\<#7247\>\<#4E0A\>\<#6570\>\<#5B57\>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#4E3A\><math|\<xi\>>\<#FF0C\>\<#5219\><math|P<around*|(|\<xi\>=2|)>=><underline|<space|3em>>\<#FF0C\><math|E<around*|(|\<xi\>|)>=><underline|<space|3em>>.

    <item>\<#5DF2\>\<#77E5\>\<#53CC\>\<#66F2\>\<#7EBF\><math|<with|math-display|true|<frac|x<rsup|2>|a<rsup|2>>-<frac|y<rsup|2>|b<rsup|2>>=1<around*|(|a\<gtr\>0,b\<gtr\>0|)>>>\<#7684\>\<#5DE6\>\<#7126\>\<#70B9\>\<#4E3A\><math|F>\<#FF0C\>\<#8FC7\><math|F>\<#4E14\>\<#659C\>\<#7387\>\<#4E3A\><math|<with|math-display|true|<frac|b|4a>>>\<#7684\>\<#76F4\>\<#7EBF\>\<#4EA4\>\<#53CC\>\<#66F2\>\<#7EBF\>\<#4E8E\>\<#70B9\><math|A<around*|(|x<rsub|1>,y<rsub|1>|)>>\<#FF0C\>\<#4EA4\>\<#53CC\>\<#66F2\>\<#7EBF\>\<#7684\>\<#6E10\>\<#8FD1\>\<#7EBF\>\<#4E8E\>\<#70B9\><math|B<around*|(|x<rsub|2>,y<rsub|2>|)>>\<#4E14\><math|x<rsub|1>\<less\>0\<less\>x<rsub|2>>.
    \<#82E5\><math|<around*|\||FB|\|>=3*<around*|\||FA|\|>>\<#FF0C\>\<#5219\>\<#53CC\>\<#66F2\>\<#7EBF\>\<#7684\>\<#79BB\>\<#5FC3\>\<#7387\>\<#662F\><underline|<space|3em>>.

    <item>\<#8BBE\>\<#70B9\><math|P>\<#5728\>\<#5355\>\<#4F4D\>\<#5706\>\<#7684\>\<#5185\>\<#63A5\>\<#6B63\>\<#516B\>\<#8FB9\>\<#5F62\><math|A<rsub|1>A<rsub|2>\<ldots\>A<rsub|8>>\<#7684\>\<#8FB9\><math|A<rsub|1>A<rsub|2>>\<#4E0A\>\<#FF0C\>\<#5219\><math|<wide|PA<rsub|1>|\<vect\>><rsup|2>+<wide|PA<rsub|2>|\<vect\>><rsup|2>+\<cdots\>+<wide|PA<rsub|8>|\<vect\>><rsup|2>>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#662F\><underline|<space|3em>>.
  </enumerate>

  \;

  \;

  \;

  \;

  \;

  <strong|\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>\<#FF1A\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>5\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>74\<#5206\>\<#3002\>\<#89E3\>\<#7B54\>\<#5E94\>\<#5199\>\<#51FA\>\<#6587\>\<#5B57\>\<#8BF4\>\<#660E\>\<#3001\>\<#8BC1\>\<#660E\>\<#8FC7\>\<#7A0B\>\<#6216\>\<#6F14\>\<#7B97\>\<#6B65\>\<#9AA4\>\<#3002\>>

  <\enumerate>
    <assign|item-nr|17><item>\<#FF08\>\<#672C\>\<#9898\>\<#6EE1\>\<#5206\>14\<#5206\>\<#FF09\>\<#5728\><math|\<triangle\><math-it|ABC>>\<#4E2D\>\<#FF0C\>\<#89D2\><math|A,B,C>\<#6240\>\<#5BF9\>\<#7684\>\<#8FB9\>\<#5206\>\<#522B\>\<#4E3A\><math|a,b,c>.
    \<#5DF2\>\<#77E5\><math|4*a=<sqrt|5>*c,cos C=<frac|3|5>>.

    (I) \<#6C42\><math|sin A>\<#7684\>\<#503C\>\<#FF1B\>

    (II) \<#82E5\><math|b=11>\<#FF0C\>\<#6C42\><math|\<triangle\><math-it|ABC>>\<#7684\>\<#9762\>\<#79EF\>.

    <item>\<#FF08\>\<#672C\>\<#9898\>\<#6EE1\>\<#5206\>15\<#5206\>\<#FF09\>\<#5982\>\<#56FE\>\<#FF0C\>\<#5DF2\>\<#77E5\><math|<math-it|ABCD>>\<#548C\><math|<math-it|CDEF>>\<#90FD\>\<#662F\>\<#76F4\>\<#89D2\>\<#68AF\>\<#5F62\>\<#FF0C\><math|<math-it|AB>//<math-it|DC>,<math-it|DC>//<math-it|EF>,<math-it|AB>=5,<math-it|DC>=3,<math-it|EF>=1,\<angle\><math-it|BAD>=\<angle\><math-it|CDE>=60<rsup|\<circ\>>>\<#FF0C\>\<#4E8C\>\<#9762\>\<#89D2\><math|F-<math-it|DC>-B>\<#7684\>\<#5E73\>\<#9762\>\<#89D2\>\<#4E3A\><math|60<rsup|\<circ\>>>\<#FF0C\>\<#8BBE\><math|M>\<#FF0C\><math|N>\<#5206\>\<#522B\>\<#4E3A\><math|<math-it|AE>>\<#FF0C\><math|<math-it|BC>>\<#7684\>\<#4E2D\>\<#70B9\>.

    <\with|par-columns-sep|1fn|par-columns|2>
      (I) \<#8BC1\>\<#660E\>\<#FF1A\><math|<math-it|FN>\<perp\><math-it|AD>>\<#FF1B\>

      (II) \<#6C42\>\<#76F4\>\<#7EBF\><math|<math-it|BM>>\<#4E0E\>\<#5E73\>\<#9762\><math|<math-it|ADE>>\<#6240\>\<#6210\>\<#89D2\>\<#7684\>\<#6B63\>\<#5F26\>\<#503C\>.

      <\with|par-columns-sep|1fn>
        <render-small-figure|||<with|gr-mode|<tuple|group-edit|edit-props>|gr-geometry|<tuple|geometry|0.66668par|0.466672par|center>|gr-grid|<tuple|empty>|gr-grid-old|<tuple|cartesian|<point|0|0>|1>|gr-edit-grid-aspect|<tuple|<tuple|axes|none>|<tuple|1|none>|<tuple|10|none>>|gr-edit-grid|<tuple|empty>|gr-edit-grid-old|<tuple|cartesian|<point|0|0>|1>|gr-frame|<tuple|scale|0.749988cm|<tuple|0.507498gw|0.529997gh>>|gr-dash-style|11100|gr-snap|<tuple|control
        point|grid point|grid curve point|curve-grid
        intersection>|gr-auto-crop|true|magnify|0.75|<graphics|<line|<point|-2.72172|-1.18147>|<point|-1.98948|0.140131>>|<line|<point|-2.72172|-1.18147>|<point|2.36824|-1.12789>>|<line|<point|-1.98948|0.140131>|<point|0.6537239999999997|1.80106>>|<line|<point|0.653724|1.80106>|<point|1.7074299999999998|1.78321>>|<line|<point|1.70743|1.78321>|<point|2.36824|-1.12789>>|<line|<point|-0.953631|0.318726>|<point|-2.72172|-1.18147>>|<line|<point|-0.953631|0.318726>|<point|0.6537239999999997|1.80106>>|<line|<point|-0.953631|0.318726>|<point|2.36824|-1.12789>>|<with|dash-style|11100|<line|<point|-1.98948|0.140131>|<point|1.0823500000000004|0.17584999999999998>>>|<with|dash-style|11100|<line|<point|1.70743|1.78321>|<point|1.0823500000000004|0.17584999999999998>>>|<with|dash-style|11100|<line|<point|1.08235|0.17585>|<point|2.36824|-1.12789>>>|<with|dash-style|11100|<line|<point|1.70743|1.78321>|<point|1.6717200000000008|-0.413514>>>|<math-at|D|<point|-2.3427495078714125|0.13503837055166024>>|<math-at|A|<point|-3.041258056621246|-1.4524858433655243>>|<math-at|B|<point|2.377452987167615|-1.431307053843101>>|<math-at|F|<point|1.8059537531419505|1.9765543008334432>>|<math-at|E|<point|0.19726555099880957|1.9553815848657232>>|<math-at|C|<point|1.2979562045244082|0.1562053222119325>>|<math-at|N|<point|1.7987252969969574|-0.4558476404286283>>|<math-at|M|<point|-0.6917415036380471|0.28320544450324114>>>>|\<#FF08\>\<#7B2C\>19\<#9898\>\<#56FE\>\<#FF09\>>
      </with>
    </with>

    <item>\<#FF08\>\<#672C\>\<#9898\>\<#6EE1\>\<#5206\>15\<#5206\>\<#FF09\>\<#5DF2\>\<#77E5\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#9996\>\<#9879\><math|a<rsub|1>=-1>\<#FF0C\>\<#516C\>\<#5DEE\><math|d\<gtr\>1>.
    \<#8BB0\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#524D\><math|n>\<#9879\>\<#548C\>\<#4E3A\><math|S<rsub|n><around*|(|n\<in\>\<bbb-N\><rsup|\<ast\>>|)>>.

    (I) \<#82E5\><math|S<rsub|4>-2a<rsub|2>a<rsub|3>+6>\<#FF0C\>\<#6C42\><math|S<rsub|n>>\<#FF1B\>

    (II) \<#82E5\>\<#5BF9\>\<#4E8E\>\<#6BCF\>\<#4E2A\><math|n\<in\>\<bbb-N\><rsup|\<ast\>>>\<#FF0C\>\<#5B58\>\<#5728\>\<#5B9E\>\<#6570\><math|c<rsub|n>>\<#FF0C\>\<#4F7F\><math|a<rsub|n>+c<rsub|n>,a<rsub|n+1>+4*c<rsub|n>,a<rsub|n+2>+15*c<rsub|n>>\<#6210\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\>\<#FF0C\>\<#6C42\><math|d>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>.

    <item>\<#FF08\>\<#672C\>\<#9898\>\<#6EE1\>\<#5206\>15\<#5206\>\<#FF09\>\<#5982\>\<#56FE\>\<#FF0C\>\<#5DF2\>\<#77E5\>\<#692D\>\<#5706\><with|math-display|true|<math|<frac|x<rsup|2>|12>+y<rsup|2>=1>>.
    \<#8BBE\><math|A,B>\<#662F\>\<#692D\>\<#5706\>\<#4E0A\>\<#5F02\>\<#4E0E\><math|P<around*|(|0,1|)>>\<#7684\>\<#4E24\>\<#70B9\>\<#FF0C\>\<#4E14\>\<#70B9\><math|Q<around*|(|0,<frac|1|2>|)>>\<#5728\>\<#7EBF\>\<#6BB5\><math|<math-it|AB>>\<#4E0A\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|<math-it|PA>,<math-it|PB>>\<#5206\>\<#522B\>\<#4EA4\>\<#76F4\>\<#7EBF\><math|<with|math-display|true|y=-<frac|1|2>x+3>>\<#4E8E\><math|C,D>\<#4E24\>\<#70B9\>.

    <\with|par-columns|2>
      (I) \<#6C42\>\<#70B9\><math|P>\<#5230\>\<#692D\>\<#5706\>\<#4E0A\>\<#70B9\>\<#7684\>\<#8DDD\>\<#79BB\>\<#7684\>\<#6700\>\<#5927\>\<#503C\>\<#FF1B\>

      (II) \<#6C42\><math|<around*|\||<math-it|CD>|\|>>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>.

      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    </with>

    <item>\<#FF08\>\<#672C\>\<#9898\>\<#6EE1\>\<#5206\>15\<#5206\>\<#FF09\>\<#8BBE\>\<#51FD\>\<#6570\><math|<with|math-display|true|f<around*|(|x|)>=<frac|\<mathe\>|2*x>+ln
    x<around*|(|x\<gtr\>0|)>>>.

    <\enumerate-Roman>
      <item>\<#6C42\><math|f<around*|(|x|)>>\<#7684\>\<#5355\>\<#8C03\>\<#533A\>\<#95F4\>\<#FF1B\>

      <item>\<#5DF2\>\<#77E5\><math|a,b\<in\>\<bbb-R\>>\<#FF0C\>\<#66F2\>\<#7EBF\><math|y=f<around*|(|x|)>>\<#4E0A\>\<#4E0D\>\<#540C\>\<#7684\>\<#4E09\>\<#70B9\><math|<around*|(|x<rsub|1>,f<around*|(|x<rsub|1>|)>|)>,<around*|(|x<rsub|2>,f<around*|(|x<rsub|2>|)>|)>,<around*|(|x<rsub|3>,f<around*|(|x<rsub|3>|)>|)>>\<#5904\>\<#7684\>\<#5207\>\<#7EBF\>\<#90FD\>\<#7ECF\>\<#8FC7\>\<#70B9\><math|<around*|(|a,b|)>>.
      \<#8BC1\>\<#660E\>\<#FF1A\>

      <\enumerate-roman>
        <item>\<#82E5\><math|a\<gtr\>\<mathe\>>\<#FF0C\>\<#5219\><math|<with|math-display|true|0\<less\>b-f<around*|(|a|)>\<less\><frac|1|2><around*|(|<frac|a|e>-1|)>>>\<#FF1B\>

        <item>\<#82E5\><math|0\<less\>a\<less\>\<mathe\>,x<rsub|1>\<less\>x<rsub|2>\<less\>x<rsub|3>>\<#FF0C\>\<#5219\><with|math-display|true|<math|<frac|2|\<mathe\>>+<frac|\<mathe\>-a|6*\<mathe\><rsup|2>>\<less\><frac|1|x<rsub|1>>+<frac|1|x<rsub|3>>\<less\><frac|2|a>-<frac|\<mathe\>-a|6e<rsup|2>>>>.
      </enumerate-roman>
    </enumerate-Roman>

    \<#FF08\>\<#6CE8\>\<#FF1A\><math|e=2.71828\<ldots\>>\<#662F\>\<#81EA\>\<#7136\>\<#5BF9\>\<#6570\>\<#7684\>\<#5E95\>\<#6570\>\<#FF09\>
  </enumerate>

  \;
</body>

<\initial>
  <\collection>
    <associate|figure-sep|<macro|>>
    <associate|page-even-footer|<htab|5mm><strong|Z\<#6570\>\<#5B66\>\<#8BD5\>\<#9898\>\<#7B2C\><page-the-page>\<#9875\>\<#FF08\>\<#5171\>4\<#9875\>\<#FF09\>\<#4F7F\>\<#7528\>\<#58A8\>\<#5E72\>\<#7406\>\<#5DE5\>\<#5957\>\<#4EF6\>\<#5236\>\<#4F5C\>><htab|5mm>>
    <associate|page-even-header|>
    <associate|page-medium|paper>
    <associate|page-odd-footer|<htab|5mm><strong|Z\<#6570\>\<#5B66\>\<#8BD5\>\<#9898\>\<#7B2C\><page-the-page>\<#9875\>\<#FF08\>\<#5171\>4\<#9875\>\<#FF09\>\<#4F7F\>\<#7528\>\<#58A8\>\<#5E72\>\<#7406\>\<#5DE5\>\<#5957\>\<#4EF6\>\<#5236\>\<#4F5C\>><htab|5mm>>
    <associate|page-odd-header|>
    <associate|page-screen-margin|false>
    <associate|par-columns|1>
  </collection>
</initial>

<\references>
  <\collection>
    <associate|auto-1|<tuple|8|2>>
    <associate|auto-2|<tuple|19|4>>
  </collection>
</references>

<\auxiliary>
  <\collection>
    <\associate|>
      <tuple|normal|\<#FF08\>\<#7B2C\>8\<#9898\>\<#56FE\>\<#FF09\>|<pageref|auto-1>>

      <tuple|normal|\<#FF08\>\<#7B2C\>19\<#9898\>\<#56FE\>\<#FF09\>|<pageref|auto-2>>
    </associate>
  </collection>
</auxiliary>