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>

    <image|<tuple|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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\>.

      <image|<tuple|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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>