planet/高考数学/2022年全国高考甲卷数学理科试题.tm

<TeXmacs|2.1.2>

<style|<tuple|exam|std-latex|chinese>>

<\body>
  <doc-data|<doc-title|2022\<#5E74\>\<#6570\>\<#5B66\>\<#5168\>\<#56FD\>\<#7532\>\<#5377\>\<#FF08\>\<#7406\>\<#79D1\>\<#FF09\>>>

  <strong|\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>12\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>60\<#5206\>\<#FF09\>

  <\enumerate-numeric>
    <item>\<#82E5\><math|z=-1+<sqrt|3><math-up|i>>\<#FF0C\>\<#5219\><math|<frac|z|z<wide|z|\<bar\>>-1>=>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|-1+<sqrt|3><math-up|i>>>|<cell|B.
    <math|-1-<sqrt|3><math-up|i>>>|<cell|C.
    <math|-<frac|1|3>+<frac|<sqrt|3>|3><math-up|i>>>|<cell|D.
    <math|-<frac|1|3>-<frac|<sqrt|3>|3><math-up|i>>>>>>>

    <item>\<#67D0\>\<#793E\>\<#533A\>\<#901A\>\<#8FC7\>\<#516C\>\<#76CA\>\<#8BB2\>\<#5EA7\>\<#4EE5\>\<#666E\>\<#53CA\>\<#793E\>\<#533A\>\<#5C45\>\<#6C11\>\<#7684\>\<#5783\>\<#573E\>\<#5206\>\<#7C7B\>\<#77E5\>\<#8BC6\>\<#FF0E\>\<#4E3A\>\<#4E86\>\<#89E3\>\<#8BB2\>\<#5EA7\>\<#6548\>\<#679C\>\<#FF0C\>\<#968F\>\<#673A\>\<#62BD\>\<#53D6\><math|10>\<#4F4D\>\<#793E\>\<#533A\>\<#5C45\>\<#6C11\>\<#FF0C\>\<#8BA9\>\<#4ED6\>\<#4EEC\>\<#5728\>\<#8BB2\>\<#5EA7\>\<#524D\>\<#548C\>\<#8BB2\>\<#5EA7\>\<#540E\>\<#5404\>\<#56DE\>\<#7B54\>\<#4E00\>\<#4EFD\>\<#5783\>\<#573E\>\<#5206\>\<#7C7B\>\<#77E5\>\<#8BC6\>\<#95EE\>\<#5377\>\<#FF0C\>\<#8FD9\><math|10>\<#4F4D\>\<#793E\>\<#533A\>\<#5C45\>\<#6C11\>\<#5728\>\<#8BB2\>\<#5EA7\>\<#524D\>\<#548C\>\<#8BB2\>\<#5EA7\>\<#540E\>\<#95EE\>\<#5377\>\<#7B54\>\<#9898\>\<#7684\>\<#6B63\>\<#786E\>\<#7387\>\<#5982\>\<#4E0B\>\<#56FE\>\<#FF1A\>

    <image|<tuple|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

    \<#5219\>

    A. \<#8BB2\>\<#5EA7\>\<#524D\>\<#95EE\>\<#5377\>\<#7B54\>\<#9898\>\<#7684\>\<#6B63\>\<#786E\>\<#7387\>\<#7684\>\<#4E2D\>\<#4F4D\>\<#6570\>\<#5C0F\>\<#4E8E\><math|70><with|font-family|rm|\<#FF05\>>

    B. \<#8BB2\>\<#5EA7\>\<#540E\>\<#95EE\>\<#5377\>\<#7B54\>\<#9898\>\<#7684\>\<#6B63\>\<#786E\>\<#7387\>\<#7684\>\<#5E73\>\<#5747\>\<#6570\>\<#5927\>\<#4E8E\><math|85><with|font-family|rm|\<#FF05\>>

    C. \<#8BB2\>\<#5EA7\>\<#524D\>\<#95EE\>\<#5377\>\<#7B54\>\<#9898\>\<#7684\>\<#6B63\>\<#786E\>\<#7387\>\<#7684\>\<#6807\>\<#51C6\>\<#5DEE\>\<#5C0F\>\<#4E8E\>\<#8BB2\>\<#5EA7\>\<#540E\>\<#6B63\>\<#786E\>\<#7387\>\<#7684\>\<#6807\>\<#51C6\>\<#5DEE\>

    D. \<#8BB2\>\<#5EA7\>\<#540E\>\<#95EE\>\<#5377\>\<#7B54\>\<#9898\>\<#7684\>\<#6B63\>\<#786E\>\<#7387\>\<#7684\>\<#6781\>\<#5DEE\>\<#5927\>\<#4E8E\>\<#8BB2\>\<#5EA7\>\<#524D\>\<#6B63\>\<#786E\>\<#7387\>\<#7684\>\<#6781\>\<#5DEE\>

    <item>\<#8BBE\>\<#5168\>\<#96C6\><math|U=<around|{|-2,-1,0,1,2,3|}>>\<#FF0C\>\<#96C6\>\<#5408\><math|A=<around|{|-1,2|}>,B=<around*|{|x\<mid\>x<rsup|2>-4*x+3=0|}>>\<#FF0C\>\<#5219\><math|\<complement\><rsub|U>*<around|(|A\<cup\>B|)>=>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|<around|{|1,3|}>>>|<cell|B. <math|<around|{|0,3|}>>>|<cell|C.
    <math|<around|{|-2,1|}>>>|<cell|D. <math|<around|{|-2,0|}>>>>>>>

    <item>\<#5982\>\<#56FE\>\<#FF0C\>\<#7F51\>\<#683C\>\<#7EB8\>\<#4E0A\>\<#7ED8\>\<#5236\>\<#7684\>\<#662F\>\<#4E00\>\<#4E2A\>\<#591A\>\<#9762\>\<#4F53\>\<#7684\>\<#4E09\>\<#89C6\>\<#56FE\>\<#FF0C\>\<#7F51\>\<#683C\>\<#5C0F\>\<#6B63\>\<#65B9\>\<#5F62\>\<#7684\>\<#8FB9\>\<#957F\>\<#4E3A\><math|1>\<#FF0C\>\<#5219\>\<#8BE5\>\<#591A\>\<#9762\>\<#4F53\>\<#7684\>\<#4F53\>\<#79EF\>\<#4E3A\>

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    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|8>>|<cell|B. <math|12>>|<cell|C. <math|16>>|<cell|D. <math|20>>>>>>

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    x>\<#5728\>\<#533A\>\<#95F4\><math|<around*|[|-<frac|\<pi\>|2>,<frac|\<pi\>|2>|]>>\<#7684\>\<#56FE\>\<#8C61\>\<#5927\>\<#81F4\>\<#4E3A\>

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    <math|<frac|1|2>>>|<cell|D. <math|1>>>>>>

    <item>\<#5728\>\<#957F\>\<#65B9\>\<#4F53\><math|A*B*C*D-A<rsub|1>*B<rsub|1>*C<rsub|1>*D<rsub|1>>\<#4E2D\>\<#FF0C\>\<#5DF2\>\<#77E5\><math|B<rsub|1>*D>\<#4E0E\>\<#5E73\>\<#9762\><math|A*B*C*D>\<#548C\>\<#5E73\>\<#9762\><math|A*A<rsub|1>*B<rsub|1>*B>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#5747\>\<#4E3A\><math|30<rsup|\<circ\>>>\<#FF0C\>\<#5219\>

    A. <math|A*B=2*A*D>

    B. <math|A*B>\<#4E0E\>\<#5E73\>\<#9762\><math|A*B<rsub|1>*C<rsub|1>*D>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|30<rsup|\<circ\>>>

    C. <math|A*C=C*B<rsub|1>>

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

    <item>\<#6C88\>\<#62EC\>\<#7684\><with|font-family|rm|\<#300A\>>\<#68A6\>\<#6EAA\>\<#7B14\>\<#8C08\><with|font-family|rm|\<#300B\>>\<#662F\>\<#4E2D\>\<#56FD\>\<#53E4\>\<#4EE3\>\<#79D1\>\<#6280\>\<#53F2\>\<#4E0A\>\<#7684\>\<#6770\>\<#4F5C\>\<#FF0C\>\<#5176\>\<#4E2D\>\<#6536\>\<#5F55\>\<#4E86\>\<#8BA1\>\<#7B97\>\<#5706\>\<#5F27\>\<#957F\>\<#5EA6\>\<#7684\>``\<#4F1A\>\<#5706\>\<#672F\>''\<#FF0C\>\<#5982\>\<#56FE\>\<#FF0C\><math|<wide|A*B|\<invbreve\>>>\<#662F\>\<#4EE5\><math|O>\<#4E3A\>\<#5706\>\<#5FC3\>\<#FF0C\><math|O*A>\<#4E3A\>\<#534A\>\<#5F84\>\<#7684\>\<#5706\>\<#5F27\>\<#FF0C\><math|C>\<#662F\>\<#7684\><math|A*B>\<#4E2D\>\<#70B9\>\<#FF0C\><math|D>\<#5728\><math|<wide|A*B|\<invbreve\>>>\<#4E0A\>\<#FF0C\>``\<#4F1A\>\<#5706\>\<#672F\>''\<#7ED9\>\<#51FA\><math|<wide|A*B|\<invbreve\>>>\<#7684\>\<#5F27\>\<#957F\>\<#7684\>\<#8FD1\>\<#4F3C\>\<#503C\><math|s>\<#7684\>\<#8BA1\>\<#7B97\>\<#516C\>\<#5F0F\>\<#FF1A\><math|s=A*B+<frac|C*D<rsup|2>|O*A>>.\<#5F53\><math|O
    A=2,\<angle\>A O B=60<rsup|\<circ\>>>\<#65F6\>\<#FF0C\><math|s=>

    <image|<tuple|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

    <tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A.
    <math|<frac|11-3*<sqrt|3>|2>>>|<cell|B.
    <math|<frac|11-4*<sqrt|3>|2>>>|<cell|C.
    <math|<frac|9-3*<sqrt|3>|2>>>|<cell|D. <math|<frac|9-4*<sqrt|3>|2>>>>>>>

    <item>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#4E2A\>\<#5706\>\<#9525\>\<#7684\>\<#6BCD\>\<#7EBF\>\<#957F\>\<#76F8\>\<#7B49\>\<#FF0C\>\<#4FA7\>\<#9762\>\<#5C55\>\<#5F00\>\<#56FE\>\<#7684\>\<#5706\>\<#5FC3\>\<#89D2\>\<#4E4B\>\<#548C\>\<#4E3A\><math|2*\<pi\>>\<#FF0C\>\<#4FA7\>\<#9762\>\<#79EF\>\<#5206\>\<#522B\>\<#4E3A\><math|S<rsub|<math-up|\<#7532\>>>>\<#548C\><math|S<rsub|<math-up|\<#4E59\>>>>\<#FF0C\>\<#4F53\>\<#79EF\>\<#5206\>\<#522B\>\<#4E3A\><math|V<rsub|<math-up|\<#7532\>>>>\<#548C\><math|V<rsub|<math-up|\<#4E59\>>>>.\<#82E5\><math|<frac|S<rsub|<math-up|\<#7532\>>>|S<rsub|<math-up|\<#4E59\>>>><with|math-font-family|rm|=>2>\<#FF0C\>\<#5219\><math|<frac|V<rsub|<math-up|\<#7532\>>>|V<rsub|<math-up|\<#4E59\>>>><with|math-font-family|rm|=>>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|<sqrt|5>>>|<cell|B. <math|2*<sqrt|2>>>|<cell|C.
    <math|<sqrt|10>>>|<cell|D. <math|<frac|5*<sqrt|10>|4>>>>>>>

    <item>\<#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|)>>\<#7684\>\<#5DE6\>\<#9876\>\<#70B9\>\<#4E3A\><math|A>\<#FF0C\>\<#70B9\><math|P>\<#FF0C\><math|Q>\<#5747\>\<#5728\><math|C>\<#4E0A\>\<#FF0C\>\<#4E14\>\<#5173\>\<#4E8E\><math|y>\<#8F74\>\<#5BF9\>\<#79F0\>\<#FF0E\>\<#82E5\>\<#76F4\>\<#7EBF\><math|A*P,A*Q>\<#7684\>\<#659C\>\<#7387\>\<#4E4B\>\<#79EF\>\<#4E3A\><math|<frac|1|4>>\<#FF0C\>\<#5219\><math|C>\<#7684\>\<#79BB\>\<#5FC3\>\<#7387\>\<#4E3A\>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|<frac|<sqrt|3>|2>>>|<cell|B. <math|<frac|<sqrt|2>|2>>>|<cell|C.
    <math|<frac|1|2>>>|<cell|D. <math|<frac|1|3>>>>>>>

    <item>\<#8BBE\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<math-up|sin><around*|(|\<omega\>*x+<frac|\<pi\>|3>|)>>\<#5728\>\<#533A\>\<#95F4\><math|<around|(|0,\<pi\>|)>>\<#6070\>\<#6709\>\<#4E09\>\<#4E2A\>\<#6781\>\<#503C\>\<#70B9\>\<#3001\>\<#4E24\>\<#4E2A\>\<#96F6\>\<#70B9\>\<#FF0C\>\<#5219\><math|\<omega\>>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#662F\>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|<around*|[|<frac|5|3>,<frac|13|6>|)>>>|<cell|B.
    <math|<around*|[|<frac|5|3>,<frac|19|6>|)>>>|<cell|C.
    <math|<around*|(|<frac|13|6>,<frac|8|3>|]>>>|<cell|D.
    <math|<around*|(|<frac|13|6>,<frac|19|6>|]>>>>>>>

    <item>\<#5DF2\>\<#77E5\><math|a=<frac|31|32>,b=<math-up|cos><frac|1|4>,c=4<math-up|sin><frac|1|4>>\<#FF0C\>\<#5219\>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|c\<gtr\>b\<gtr\>a>>|<cell|B. <math|b\<gtr\>a\<gtr\>c>>|<cell|C.
    <math|a\<gtr\>b\<gtr\>c>>|<cell|D. <math|a\<gtr\>c\<gtr\>b>>>>>>
  </enumerate-numeric>

  \<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>4\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>20\<#5206\>\<#FF09\>

  <\enumerate-numeric>
    <assign|item-nr|12><item>\<#8BBE\>\<#5411\>\<#91CF\><math|<wide|a|\<wide-varrightarrow\>>>\<#FF0C\><math|<wide|b|\<wide-varrightarrow\>>>\<#7684\>\<#5939\>\<#89D2\>\<#7684\>\<#4F59\>\<#5F26\>\<#503C\>\<#4E3A\><math|<frac|1|3>>\<#FF0C\>\<#4E14\><math|<around*|\||<wide|a|\<wide-varrightarrow\>>|\|>=1>\<#FF0C\><math|<around*|\||<wide|a|\<wide-varrightarrow\>>|\|>=3>\<#FF0C\>\<#5219\><math|<around*|(|2*<wide|a|\<wide-varrightarrow\>>+<wide|b|\<wide-varrightarrow\>>|)>\<cdot\><wide|b|\<wide-varrightarrow\>>=><underline|<space|2cm>>\<#FF0E\>

    <item>\<#82E5\>\<#53CC\>\<#66F2\>\<#7EBF\><math|y<rsup|2>-<frac|x<rsup|2>|m<rsup|2>>=1*<around|(|m\<gtr\>0|)>>\<#7684\>\<#6E10\>\<#8FD1\>\<#7EBF\>\<#4E0E\>\<#5706\><math|x<rsup|2>+y<rsup|2>-4*y+3=0>\<#76F8\>\<#5207\>\<#FF0C\>\<#5219\><math|m=><underline|<space|2cm>>\<#FF0E\>

    <item>\<#4ECE\>\<#6B63\>\<#65B9\>\<#4F53\>\<#7684\><math|8>\<#4E2A\>\<#9876\>\<#70B9\>\<#4E2D\>\<#4EFB\>\<#9009\><math|4>\<#4E2A\>\<#FF0C\>\<#5219\>\<#8FD9\><math|4>\<#4E2A\>\<#70B9\>\<#5728\>\<#540C\>\<#4E00\>\<#4E2A\>\<#5E73\>\<#9762\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\>
    <underline|<space|2cm>>\<#FF0E\>

    <item>\<#5DF2\>\<#77E5\><math|\<vartriangle\>*A*B*C>\<#4E2D\>\<#FF0C\>\<#70B9\><math|D>\<#5728\>\<#8FB9\><math|B*C>\<#4E0A\>\<#FF0C\><math|\<angle\>*A*D*B=120<rsup|\<circ\>>,A*D=2,C*D=2*B*D>.\<#5F53\><math|<frac|A*C|A*B>>\<#53D6\>\<#5F97\>\<#6700\>\<#5C0F\>\<#503C\>\<#65F6\>\<#FF0C\><math|B*D=><underline|<space|2cm>>\<#FF0E\>
  </enumerate-numeric>

  \<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>7\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>80\<#5206\>\<#FF09\>

  \ (\<#4E00\>) \ \<#5FC5\>\<#8003\>\<#9898\>\<#FF1A\>\<#5171\> 60 \<#5206\>.

  <\enumerate-numeric>
    <assign|item-nr|16><item>\<#8BB0\><math|S<rsub|n>>\<#4E3A\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#524D\><math|n>\<#9879\>\<#548C\>\<#FF0E\>\<#5DF2\>\<#77E5\><math|<frac|2*S<rsub|n>|n>+n=2*a<rsub|n>+1>\<#FF0E\>

    (1)\<#8BC1\>\<#660E\>\<#FF1A\><math|<around*|{|a<rsub|n>|}>>\<#662F\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>\<#FF1B\>

    (2)\<#82E5\><math|a<rsub|4>,a<rsub|7>,a<rsub|9>>\<#6210\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\>\<#FF0C\>\<#6C42\><math|S<rsub|n>>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#FF0E\><vspace|5cm>

    <item>\<#5728\>\<#56DB\>\<#68F1\>\<#9525\><math|P-A*B*C*D>\<#4E2D\>\<#FF0C\><math|P*D*\<bot\>>\<#5E95\>\<#9762\><math|A*B*C*D,C*D//A*B,A*D=D*C=C*B=1,A*B=2,D*P=<sqrt|3>>\<#FF0E\>

    (1)\<#8BC1\>\<#660E\>\<#FF1A\><math|B*D*\<bot\>*P*A>\<#FF1B\>

    (2)\<#6C42\><math|P*D>\<#4E0E\>\<#5E73\>\<#9762\><math|P*A*B>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#7684\>\<#6B63\>\<#5F26\>\<#503C\>\<#FF0E\>

    <image|<tuple|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

    <item>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#4E2A\>\<#5B66\>\<#6821\>\<#8FDB\>\<#884C\>\<#4F53\>\<#80B2\>\<#6BD4\>\<#8D5B\>\<#FF0C\>\<#6BD4\>\<#8D5B\>\<#5171\>\<#8BBE\>\<#4E09\>\<#4E2A\>\<#9879\>\<#76EE\>\<#FF0C\>\<#6BCF\>\<#4E2A\>\<#9879\>\<#76EE\>\<#80DC\>\<#65B9\>\<#5F97\><math|10>\<#5206\>\<#FF0C\>\<#8D1F\>\<#65B9\>\<#5F97\><math|0>\<#5206\>\<#FF0C\>\<#6CA1\>\<#6709\>\<#5E73\>\<#5C40\>\<#FF0E\>\<#4E09\>\<#4E2A\>\<#9879\>\<#76EE\>\<#6BD4\>\<#8D5B\>\<#7ED3\>\<#675F\>\<#540E\>\<#FF0C\>\<#603B\>\<#5F97\>\<#5206\>\<#9AD8\>\<#7684\>\<#5B66\>\<#6821\>\<#83B7\>\<#5F97\>\<#51A0\>\<#519B\>\<#FF0E\>\<#5DF2\>\<#77E5\>\<#7532\>\<#5B66\>\<#6821\>\<#5728\>\<#4E09\>\<#4E2A\>\<#9879\>\<#76EE\>\<#4E2D\>\<#83B7\>\<#80DC\>\<#7684\>\<#6982\>\<#7387\>\<#5206\>\<#522B\>\<#4E3A\><math|5>\<#FF0C\><math|0.4>\<#FF0C\><math|0.8>\<#FF0C\>\<#5404\>\<#9879\>\<#76EE\>\<#7684\>\<#6BD4\>\<#8D5B\>\<#7ED3\>\<#679C\>\<#76F8\>\<#4E92\>\<#72EC\>\<#7ACB\>\<#FF0E\>

    (1)\<#6C42\>\<#7532\>\<#5B66\>\<#6821\>\<#83B7\>\<#5F97\>\<#51A0\>\<#519B\>\<#7684\>\<#6982\>\<#7387\>\<#FF1B\>

    (2)\<#7528\><math|X>\<#8868\>\<#793A\>\<#4E59\>\<#5B66\>\<#6821\>\<#7684\>\<#603B\>\<#5F97\>\<#5206\>\<#FF0C\>\<#6C42\><math|X>\<#7684\>\<#5206\>\<#5E03\>\<#5217\>\<#4E0E\>\<#671F\>\<#671B\>\<#FF0E\><vspace|5cm>

    <item>\<#8BBE\>\<#629B\>\<#7269\>\<#7EBF\><math|C:y<rsup|2>=2*p*x*<around|(|p\<gtr\>0|)>>\<#7684\>\<#7126\>\<#70B9\>\<#4E3A\><math|F>\<#FF0C\>\<#70B9\><math|D*<around|(|p,0|)>>\<#FF0C\>\<#8FC7\><math|F>\<#7684\>\<#76F4\>\<#7EBF\>\<#4EA4\><math|C>\<#4E8E\><math|M>\<#FF0C\><math|N>\<#4E24\>\<#70B9\>\<#FF0E\>\<#5F53\>\<#76F4\>\<#7EBF\><math|M*D>\<#5782\>\<#76F4\>\<#4E8E\><math|x>\<#8F74\>\<#65F6\>\<#FF0C\><math|<around|\||M*F|\|>=3>\<#FF0E\>

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

    (2)\<#8BBE\>\<#76F4\>\<#7EBF\><math|M*D,N*D>\<#4E0E\><math|C>\<#7684\>\<#53E6\>\<#4E00\>\<#4E2A\>\<#4EA4\>\<#70B9\>\<#5206\>\<#522B\>\<#4E3A\><math|A>\<#FF0C\><math|B>\<#FF0C\>\<#8BB0\>\<#76F4\>\<#7EBF\><math|M*N,A*B>\<#7684\>\<#503E\>\<#659C\>\<#89D2\>\<#5206\>\<#522B\>\<#4E3A\><math|\<alpha\>,\<beta\>>.\<#5F53\><math|\<alpha\>-\<beta\>>\<#53D6\>\<#5F97\>\<#6700\>\<#5927\>\<#503C\>\<#65F6\>\<#FF0C\>\<#6C42\>\<#76F4\>\<#7EBF\><math|A*B>\<#7684\>\<#65B9\>\<#7A0B\>\<#FF0E\><vspace|5cm>

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=<frac|e<rsup|x>|x>-<math-up|ln>x+x-a>\<#FF0E\>

    (1)\<#82E5\><math|f<around*|(|x|)>\<ge\>0>\<#FF0C\>\<#6C42\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#FF1B\>

    (2)\<#8BC1\>\<#660E\>\<#FF1A\>\<#82E5\><math|f<around*|(|x|)>>\<#6709\>\<#4E24\>\<#4E2A\>\<#96F6\>\<#70B9\><math|x<rsub|1>,x<rsub|2>>\<#FF0C\>\<#5219\><math|x<rsub|1>*x<rsub|2>\<less\>1>\<#FF0E\><vspace|5cm>

    \;
  </enumerate-numeric>

  (\<#4E8C\>) \<#9009\>\<#8003\>\<#9898\>\<#FF1A\>\<#5171\> 10 \<#5206\>

  <\enumerate>
    <assign|item-nr|21><item>\<#5728\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#7CFB\><math|x*O*y>\<#4E2D\>\<#FF0C\>\<#66F2\>\<#7EBF\><math|C<rsub|1>>\<#7684\>\<#53C2\>\<#6570\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|<around*|{|<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|1|1|cell-rborder|0ln>|<table|<row|<cell|x=<frac|2+t|6>>>|<row|<cell|y=<sqrt|t>>>>>>|\<nobracket\>>(t>\<#4E3A\>\<#53C2\>\<#6570\><math|>)\<#FF0C\>\<#66F2\>\<#7EBF\><math|C<rsub|2>>\<#7684\>\<#53C2\>\<#6570\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|<around*|{|<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|1|1|cell-rborder|0ln>|<table|<row|<cell|x=-<frac|2+s|6>>>|<row|<cell|y=-<sqrt|s>>>>>>|\<nobracket\>>(s>\<#4E3A\>\<#53C2\>\<#6570\><math|>)\<#FF0E\>

    (1)\<#5199\>\<#51FA\><math|C<rsub|1>>\<#7684\>\<#666E\>\<#901A\>\<#65B9\>\<#7A0B\>\<#FF1B\>

    (2)\<#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<rsub|3>>\<#7684\>\<#6781\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|2<math-up|cos>\<theta\>-<math-up|sin>\<theta\>=0>\<#FF0C\>\<#6C42\><math|C<rsub|3>>\<#4E0E\><math|C<rsub|1>>\<#4EA4\>\<#70B9\>\<#7684\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#FF0C\>\<#53CA\><math|C<rsub|3>>\<#4E0E\><math|C<rsub|2>>\<#4EA4\>\<#70B9\>\<#7684\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#FF0E\><vspace|5cm>

    <item>\<#5DF2\>\<#77E5\><math|a>\<#FF0C\><math|b>\<#FF0C\><math|c>\<#5747\>\<#4E3A\>\<#6B63\>\<#6570\>\<#FF0C\>\<#4E14\><math|a<rsup|2>+b<rsup|2>+4*c<rsup|2>=3>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\>

    (1)<math|a+b+2*c\<le\>3>\<#FF1B\>

    (2)\<#82E5\><math|b=2*c>\<#FF0C\>\<#5219\><math|<frac|1|a>+<frac|1|c>\<ge\>3>\<#FF0E\><vspace|5cm>
  </enumerate>
</body>

<initial|<\collection>
</collection>>