planet/高考数学/2022年全国高考甲卷数学文科试题.tm

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

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  <doc-data|<doc-title|2022\<#5E74\>\<#6570\>\<#5B66\>\<#5168\>\<#56FD\>\<#7532\>\<#5377\>\<#FF08\>\<#6587\>\<#79D1\>\<#FF09\>>>

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

  <\enumerate-numeric>
    <item>\<#8BBE\>\<#96C6\>\<#5408\><math|A=<around|{|-2,-1,0,1,2|}>>\<#FF0C\><math|B=<around|{|x\|0\<leq\>x\<less\><frac|5|2>|}>>\<#FF0C\>\<#5219\><math|A\<cap\>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|{|0,1,2|}>>>|<cell|B. <math|<around|{|-2,-1,0|}>>>|<cell|C.
    <math|<around|{|0,1|}>>>|<cell|D. <math|<around|{|1,2|}>>>>>>>

    <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>\<#82E5\><math|z=1+i>\<#FF0C\>\<#5219\><math|<around|\||i*z+3*<wide|z|\<bar\>>|\|>=>

    <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|4*<sqrt|5>>>|<cell|B. <math|4*<sqrt|2>>>|<cell|C.
    <math|2*<sqrt|5>>>|<cell|D. <math|2*<sqrt|2>>>>>>>

    <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>>>>>>

    <item>\<#5C06\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<math-up|sin><around|(|\<omega\>*x+<frac|\<pi\>|3>|)>*<around|(|\<omega\>\<gtr\>0|)>>\<#7684\>\<#56FE\>\<#50CF\>\<#5411\>\<#5DE6\>\<#5E73\>\<#79FB\><math|<frac|\<pi\>|2>>\<#4E2A\>\<#5355\>\<#4F4D\>\<#957F\>\<#5EA6\>\<#540E\>\<#5F97\>\<#5230\>\<#66F2\>\<#7EBF\><math|C>\<#FF0C\>\<#82E5\><math|C>\<#5173\>\<#4E8E\><math|y>\<#8F74\>\<#5BF9\>\<#79F0\>\<#FF0C\>\<#5219\><math|\<omega\>>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#662F\>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A.
    <math|<frac|1|6>>>|<cell|B. <math|<frac|1|4>>>|<cell|C.
    <math|<frac|1|3>>>|<cell|D. <math|<frac|1|2>>>>>>>

    <item>\<#4ECE\>\<#5206\>\<#522B\>\<#5199\>\<#6709\><math|1>\<#FF0C\><math|2>\<#FF0C\><math|3>\<#FF0C\><math|4>\<#FF0C\><math|5>\<#FF0C\><math|6>\<#7684\><math|6>\<#5F20\>\<#5361\>\<#7247\>\<#4E2D\>\<#65E0\>\<#653E\>\<#56DE\>\<#968F\>\<#673A\>\<#62BD\>\<#53D6\><math|2>\<#5F20\>\<#FF0C\>\<#5219\>\<#62BD\>\<#5230\>\<#7684\><math|2>\<#5F20\>\<#5361\>\<#7247\>\<#4E0A\>\<#7684\>\<#6570\>\<#5B57\>\<#4E4B\>\<#79EF\>\<#662F\><math|4>\<#7684\>\<#500D\>\<#6570\>\<#7684\>\<#6982\>\<#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|1|5>>>|<cell|B. <math|<frac|1|3>>>|<cell|C.
    <math|<frac|2|5>>>|<cell|D. <math|<frac|2|3>>>>>>>

    <item>\<#51FD\>\<#6570\><math|y=<around*|(|3<rsup|x>-3<rsup|-x>|)><math-up|cos>
    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>\<#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|<with|math-font-family|rm|font-family|rm|\<#7532\>>>>\<#548C\><math|S<rsub|<with|math-font-family|rm|font-family|rm|\<#4E59\>>>>\<#FF0C\>\<#4F53\>\<#79EF\>\<#5206\>\<#522B\>\<#4E3A\><math|V<rsub|<with|math-font-family|rm|font-family|rm|\<#7532\>>>>\<#548C\><math|V<rsub|<with|math-font-family|rm|font-family|rm|\<#4E59\>>>>.\<#82E5\><math|<frac|S<rsub|<with|math-font-family|rm|font-family|rm|\<#7532\>>>|S<rsub|<with|math-font-family|rm|font-family|rm|\<#4E59\>>>><with|math-font-family|rm|=>2>\<#FF0C\>\<#5219\><math|<frac|V<rsub|<with|math-font-family|rm|font-family|rm|\<#7532\>>>|V<rsub|<with|math-font-family|rm|font-family|rm|\<#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>\<#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|)>>\<#7684\>\<#79BB\>\<#5FC3\>\<#7387\>\<#4E3A\><math|<frac|1|3>>\<#FF0C\><math|A<rsub|1>>\<#FF0C\><math|A<rsub|2>>\<#5206\>\<#522B\>\<#4E3A\><math|C>\<#7684\>\<#5DE6\>\<#3001\>\<#53F3\>\<#9876\>\<#70B9\>\<#FF0C\><math|B>\<#4E3A\><math|C>\<#7684\>\<#4E0A\>\<#9876\>\<#70B9\>.\<#82E5\><math|<wide|B*A<rsub|1>|\<vect\>>\<cdot\><wide|B*A<rsub|2>|\<vect\>>=-1>\<#FF0C\>\<#5219\><math|C>\<#7684\>\<#65B9\>\<#7A0B\>\<#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|x<rsup|2>|18>+<frac|y<rsup|2>|16>=1>>|<cell|B.
    <math|<frac|x<rsup|2>|9>+<frac|y<rsup|2>|8>=1>>|<cell|C.
    <math|<frac|x<rsup|2>|3>+<frac|y<rsup|2>|2>=1>>|<cell|D.
    <math|<frac|x<rsup|2>|2>+y<rsup|2>=1>>>>>>

    <item>\<#5DF2\>\<#77E5\><math|9<rsup|m>=10>\<#FF0C\><math|a=10<rsup|m>-11>\<#FF0C\><math|b=8<rsup|m>-9>\<#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|a\<gtr\>0\<gtr\>b>>|<cell|B. <math|a\<gtr\>b\<gtr\>0>>|<cell|C.
    <math|b\<gtr\>a\<gtr\>0>>|<cell|D. <math|b\<gtr\>0\<gtr\>a>>>>>>
  </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>\<#5DF1\>\<#77E5\>\<#5411\>\<#91CF\><math|<wide|a|\<vect\>>=<around|(|m,3|)>>\<#FF0C\><math|<wide|b|\<vect\>>=<around|(|1,m+1|)>>.\<#82E5\><math|<wide|a|\<vect\>>\<bot\><wide|b|\<vect\>>>\<#FF0C\>\<#5219\><math|m=><underline|<space|2cm>>\<#FF0E\>

    <item>\<#8BBE\>\<#70B9\><math|M>\<#5728\>\<#76F4\>\<#7EBF\><math|2*x+y-1=0>\<#4E0A\>\<#FF0C\>\<#70B9\><math|<around|(|3,0|)>>\<#548C\><math|<around|(|0,1|)>>\<#5747\>\<#5728\><math|\<varodot\>*M>\<#4E0A\>\<#FF0C\>\<#5219\><math|\<varodot\>*M>\<#7684\>\<#65B9\>\<#7A0B\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>

    <item>\<#8BB0\>\<#53CC\>\<#66F2\>\<#7EBF\><math|C:<frac|x<rsup|2>|a<rsup|2>>-<frac|y<rsup|2>|b<rsup|2>>=1*<around|(|a\<gtr\>0,b\<gtr\>0|)>>\<#7684\>\<#79BB\>\<#5FC3\>\<#7387\>\<#4E3A\><math|e>\<#FF0C\>\<#5199\>\<#51FA\>\<#6EE1\>\<#8DB3\>\<#6761\>\<#4EF6\>``\<#76F4\>\<#7EBF\><math|y=2*x>\<#4E0E\><math|C>\<#65E0\>\<#516C\>\<#5171\>\<#70B9\>''\<#7684\><math|e>\<#7684\>\<#4E00\>\<#4E2A\>\<#503C\><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>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#57CE\>\<#4E4B\>\<#95F4\>\<#7684\>\<#957F\>\<#9014\>\<#5BA2\>\<#8F66\>\<#5747\>\<#7531\><math|A>\<#548C\><math|B>\<#4E24\>\<#5BB6\>\<#516C\>\<#53F8\>\<#8FD0\>\<#8425\>\<#FF0C\>\<#4E3A\>\<#4E86\>\<#4E86\>\<#89E3\>\<#8FD9\>\<#4E24\>\<#5BB6\>\<#516C\>\<#53F8\>\<#957F\>\<#9014\>\<#5BA2\>\<#8F66\>\<#7684\>\<#8FD0\>\<#884C\>\<#60C5\>\<#51B5\>\<#FF0C\>\<#968F\>\<#673A\>\<#8C03\>\<#67E5\>\<#4E86\>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#57CE\>\<#4E4B\>\<#95F4\>\<#7684\><math|500>\<#4E2A\>\<#73ED\>\<#6B21\>\<#FF0C\>\<#5F97\>\<#5230\>\<#4E0B\>\<#9762\>\<#5217\>\<#8054\>\<#8868\>\<#FF1A\>

    <block*|<tformat|<table|<row|<cell|>|<cell|\<#51C6\>\<#70B9\>\<#73ED\>\<#6B21\>\<#6570\>>|<cell|\<#672A\>\<#51C6\>\<#70B9\>\<#73ED\>\<#6B21\>\<#6570\>>>|<row|<cell|A>|<cell|240>|<cell|20>>|<row|<cell|B>|<cell|210>|<cell|30>>>>>

    (1)\<#6839\>\<#636E\>\<#4E0A\>\<#8868\>\<#FF0C\>\<#5206\>\<#522B\>\<#4F30\>\<#8BA1\>\<#8FD9\>\<#4E24\>\<#5BB6\>\<#516C\>\<#53F8\>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#57CE\>\<#4E4B\>\<#95F4\>\<#7684\>\<#957F\>\<#9014\>\<#5BA2\>\<#8F66\>\<#51C6\>\<#70B9\>\<#7684\>\<#6982\>\<#7387\>;

    (2)\<#80FD\>\<#5426\>\<#6709\><math|90%>\<#7684\>\<#628A\>\<#63E1\>\<#8BA4\>\<#4E3A\>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#57CE\>\<#4E4B\>\<#95F4\>\<#7684\>\<#957F\>\<#9014\>\<#5BA2\>\<#8F66\>\<#662F\>\<#5426\>\<#51C6\>\<#70B9\>\<#4E0E\>\<#5BA2\>\<#8F66\>\<#6240\>\<#5C5E\>\<#516C\>\<#53F8\>\<#6709\>\<#5173\>?

    \<#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|0.100>|<cell|0.050>|<cell|0.010>>|<row|<cell|<math|k>>|<cell|2.706>|<cell|3.841>|<cell|6.635>>>>><vspace|5cm>

    <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>\<#5C0F\>\<#660E\>\<#540C\>\<#5B66\>\<#53C2\>\<#52A0\>\<#7EFC\>\<#5408\>\<#5B9E\>\<#8DF5\>\<#6D3B\>\<#52A8\>\<#FF0C\>\<#8BBE\>\<#8BA1\>\<#4E86\>\<#4E00\>\<#4E2A\>\<#5C01\>\<#95ED\>\<#7684\>\<#5305\>\<#88C5\>\<#76D2\>.
    \<#5305\>\<#88C5\>\<#76D2\>\<#5982\>\<#56FE\>\<#6240\>\<#793A\>\<#FF1A\>
    \<#5E95\>\<#9762\><math|A*B*C*D>\<#662F\>\<#8FB9\>\<#957F\>\<#4E3A\><math|8(>\<#5355\>\<#4F4D\>\<#FF1A\><math|c*m>)
    \<#7684\>\<#6B63\>\<#65B9\>\<#5F62\>\<#FF0C\>
    <math|\<bigtriangleup\>*E*A*B>\<#FF0C\>
    <math|\<bigtriangleup\>*F*B*C>\<#FF0C\>
    <math|\<bigtriangleup\>*G*C*D>\<#FF0C\><math|\<bigtriangleup\>*H*D*A>\<#5747\>\<#4E3A\>\<#6B63\>\<#4E09\>\<#89D2\>\<#5F62\>\<#FF0C\>\<#4E14\>\<#5B83\>\<#4EEC\>\<#6240\>\<#5728\>\<#7684\>\<#5E73\>\<#9762\>\<#90FD\>\<#4E0E\>\<#5E73\>\<#9762\><math|A*B*C*D>\<#5782\>\<#76F4\>\<#FF0E\>

    (1)\<#8BC1\>\<#660E\>\<#FF1A\><math|E*F//>\<#5E73\>\<#9762\><math|A*B*C*D>;

    (2)\<#6C42\>\<#8BE5\>\<#5305\>\<#88C5\>\<#76D2\>\<#7684\>\<#5BB9\>\<#79EF\>(<math|>\<#4E0D\>\<#8BA1\>\<#5305\>\<#88C5\>\<#76D2\>\<#6750\>\<#6599\>\<#7684\>\<#539A\>\<#5EA6\><math|>)\<#FF0E\>

    <image|<tuple|<#89504E470D0A1A0A0000000D49484452000000A30000009608030000008505C8AC000000E16943435073524742000018956360603CCD00044C0E0C0CB979254541EE4E0A1191510A0C482031B9B8800137606460F8760D4432305CD60D2C61E5C7A3161BE02C025A08A43F00B1483A98CDC802622741D81220767949410990AD036227171481D8401733F01485043903D93E40B6423A123B09899D925A9C0C64E700D9F108BFE5CF6760B0F8C2C0C03C112196348D81617B3B0383C41D8498CA420606FE5606866D9711629FFDC1FE65143B54925A510212F1D3776428482C4A044B338302342D8D81E1D3720606DE480606E10B0C0C5CD1107780016B3130A0490C2742000072D83684A31F47B3000002FA504C54450000000000001919190202021A1A1A0101010F0F0F1C1C1C1414141717170404041313130606061616160E0E0E0505050909091212120303031B1B1B0808081010101515150C0C0C0707071F1F1F1111111818180A0A0A0B0B0B2525252323232727272E2E2E3F3F3F3C3C3C2929293B3B3B3737373E3E3E2626263535353838383030302A2A2A2121212B2B2B3131313333333636363D3D3D2424243939392D2D2D3A3A3A3232322F2F2F2C2C2C2222222020203434342828284646465757575A5A5A4040405959595858584545454242424444444141415454544C4C4C4F4F4F5050505C5C5C4A4A4A4747475353534949494B4B4B5B5B5B5151515D5D5D4E4E4E5656564343435252524848485555555E5E5E4D4D4D5F5F5F7979796C6C6C6F6F6F6E6E6E6969696767676565656D6D6D7171716060607C7C7C7474746666667676766A6A6A6464646262627E7E7E7070706363637F7F7F6868687373737878787A7A7A7777776161616B6B6B7B7B7B7272727575757D7D7D8383838989898282829494949C9C9C9696969A9A9A8080808686869090908C8C8C9393938484848787879292929E9E9E8B8B8B8E8E8E9999999595959F9F9F8181818F8F8F9191919797978D8D8D8888889B9B9B8585859D9D9D9898988A8A8AAAAAAAABABABACACACA6A6A6BCBCBCBEBEBEA4A4A4A9A9A9BABABAA0A0A0B9B9B9B7B7B7BFBFBFADADADA3A3A3B0B0B0BBBBBBB8B8B8AFAFAFA2A2A2B4B4B4B2B2B2A8A8A8B6B6B6B1B1B1A1A1A1BDBDBDA7A7A7AEAEAEB3B3B3A5A5A5B5B5B5D8D8D8D5D5D5D9D9D9D4D4D4CECECEC8C8C8C6C6C6CACACADFDFDFC4C4C4CCCCCCD0D0D0DCDCDCD3D3D3D2D2D2C7C7C7C9C9C9CDCDCDD1D1D1DDDDDDC0C0C0DADADACFCFCFDEDEDECBCBCBD6D6D6C5C5C5C2C2C2C1C1C1D7D7D7C3C3C3DBDBDBF8F8F8F9F9F9E2E2E2F7F7F7F3F3F3E0E0E0E9E9E9F6F6F6FEFEFEE8E8E8FDFDFDF1F1F1FBFBFBE4E4E4EAEAEAFAFAFAE5E5E5EDEDEDF4F4F4FCFCFCE1E1E1E3E3E3F5F5F5E7E7E7EFEFEFEEEEEEF2F2F2EBEBEBF0F0F0ECECECE6E6E6FFFFFF3BB853910000000174524E530040E6D866000000097048597300000EC400000EC401952B0E1B0000001974455874536F667477617265004D6963726F736F6674204F66666963657FED35710000132049444154789CED5C07541449DE77DCBB5DF7C2BABB1777BFEF4018014551191516D44194A42841508C98100326CC892818103388BBB78A8A6244C5EC8A01155811105430CE90646486308CC0A060BD77D53DA943754FCF00DEDD7BF77B8FAEAE40F76FBAD23F757701FFF1E8D2E5D3DC475C6AFCFF7E1A8E07C3232203236F19F9DF9F82639970FAEDF28AE4AE9546FEFF27E0F8C664069E46551979814FC0D1C9144F246F8DBD40E773BCC38B86C76AF82731F20A9DCF71232F131E33C387C7488DBC42E7738CE595C1A36CE66735FFB9CFF110EF2E96388F30FA0A9DCFB1E23723E151FADBC3465FE113CCEB7B3D661D49996D566BF4053EC51A2E3D1ABEE9A0B113067CBAFDBA3DE8748E7577370F7739DAAE4B742EC75BD141E6FC399FF77475BBDF8EAB741EC7FA63C1EE161E5BB24A532DAD8E6F359B9B6DF4953A8763ED89C05196A3E7A5C8B14CDCC953F3C19B05BD228C15213B9E6343CE364FBE4BC869AA08F1AB676F2397C88EE5287B103FC6DA7DE1995C64EDB13E637F35E6AA1DC83177FB2273AB31510F15A4D26379D8F1DD19EC58BAA36F508DE117EE208E8D69C15E96DE11F79AA81577BEC03936DB9CC2B3658BFBEDAC33F4E21DC0517976898F8557ECB916445D9D6FA0EA24BAFF7BD549BE70C079036FD04E8E4D05114EB6C2A5C9650CF5B5E334CC431F69CAD207F8DD35E826EDE0A828DCE52F700E3D5E64E83F362D1B38E303B5F07DF2968DC7B7472FCBA1B767E0F8F6C2B18B5270E7F4E1C7E5E8FB3C39BCC07DD098DD4F658612C4511C3A7827796A01C5255E74E1D392E55B3973AC58C4BB2C061F6CBEC8ACA657BEB9B2C2C5627C440E037D1D5AF6107FC2A5DB84CC632BBB73E4C6BBBA6193A9E621678EC0C3151E145F6CA3DDF6C85E3F7BDF9527384983F37C88BF7095905479B5BF279134104E80D35E2AA33C5E168E0D5F46C163D6EF1E100B4BB312BC2D02661EE4BAC43DB47946CC96FFB08754AD0CE9B55AA9CDBDFF7DF0D3E4850DA8EB30707CCEBB9C5D541662A3EBABCCE83502C19AEDB791CDD1885E42CEA7CDA7347832AEE746CD79CA1F76A60B6622AFC3C071C91F13E313F7755DAECA351E9EE36AE791F8C8C0098218CA545CB60B48519DCD7000E0EE0B4338DACF8207E9578700687D1938B6B747F84B25B25DFB71981F8AEDEE12871970A6A267219A6359F78BF078ECEBB7E096E967218FE5C6DCFCF1637A59E5715A51D1265EB74698747FC9782534C7E3DFB4C2A3BF395C3078B69EA78CA1586E768C5E58EF788D982D3E3

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=x<rsup|3>-x>\<#FF0C\><math|g<around|(|x|)>=x<rsup|2>+a>\<#FF0C\>\<#66F2\>\<#7EBF\><math|y=f<around|(|x|)>>\<#5728\>\<#70B9\><math|<around|(|x<rsub|1>,f<around|(|x<rsub|1>|)>|)>>\<#5904\>\<#7684\>\<#5207\>\<#7EBF\>\<#4E5F\>\<#662F\>\<#66F2\>\<#7EBF\><math|y=g<around|(|x|)>>\<#7684\>\<#5207\>\<#7EBF\>\<#FF0E\>

    (1)\<#82E5\><math|x<rsub|1>=-1>\<#FF0C\>\<#6C42\><math|a>;

    (2)\<#6C42\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#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>
  </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\<leq\>3>\<#FF1B\>

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

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