planet/高考数学/2022年北京市高考数学试题.tm

<TeXmacs|2.1.2>

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

<\body>
  <doc-data|<doc-title|2022\<#5E74\>\<#6570\>\<#5B66\>\<#5317\>\<#4EAC\>\<#5377\>>>

  <strong|\<#4E00\>\<#3001\>\<#9009\>\<#62E9\>\<#9898\>>\<#FF08\>\<#5171\>10\<#5C0F\>\<#9898\>\<#FF0C\>\<#6BCF\>\<#5C0F\>\<#9898\>4\<#5206\>\<#FF0C\>\<#5171\>40\<#5206\>\<#3002\>\<#5728\>\<#6BCF\>\<#5C0F\>\<#9898\>\<#5217\>\<#51FA\>\<#7684\>\<#56DB\>\<#4E2A\>\<#9009\>\<#9879\>\<#4E2D\>\<#FF0C\>\<#9009\>\<#51FA\>\<#7B26\>\<#5408\>\<#9898\>\<#76EE\>\<#8981\>\<#6C42\>\<#7684\>\<#4E00\>\<#9879\>\<#3002\>\<#FF09\>

  <\enumerate-numeric>
    <item>\<#5DF2\>\<#77E5\>\<#5168\>\<#96C6\><math|U=<around*|{|<around*|\<nobracket\>|x|\|>-3\<less\>x\<less\>3|}>>\<#FF0C\>\<#96C6\>\<#5408\><math|A=<around*|{|<around*|\<nobracket\>|x|\|>-2\<less\>x\<le\>1|}>>\<#FF0C\>\<#5219\><math|C<rsub|U>*A=>

    <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*|(|-2,1|]>>>|<cell|B. <math|<around|(|-3,-2|)>\<cup\><around|[|1,3|)>>>|<cell|C.
    <math|<around*|[|-2,1|)>>>|<cell|D. <math|<around|(|-3,-2|]>\<cup\><around|(|1,3|)>>>>>>>

    <item>\<#82E5\>\<#590D\>\<#6570\><math|z>\<#6EE1\>\<#8DB3\><math|i\<cdot\>z=3-4*i>\<#FF0C\>\<#5219\><math|<around*|\||z|\|>=>

    <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.
    1>|<cell|B. 5>|<cell|C. 7>|<cell|D. 25>>>>>

    <item>\<#82E5\>\<#76F4\>\<#7EBF\><math|2*x+y-1=0>\<#662F\>\<#5706\><math|<around*|(|x-a|)><rsup|2>+y<rsup|2>=1>\<#7684\>\<#4E00\>\<#6761\>\<#5BF9\>\<#79F0\>\<#8F74\>\<#FF0C\>\<#5219\><math|a=>

    <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|2>>>|<cell|B. <math|-<frac|1|2>>>|<cell|C. 1>|<cell|D.
    <math|-1>>>>>>

    <item>\<#5DF1\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<frac|1|1+2<rsup|x>>>,\<#5219\>\<#5BF9\>\<#4EFB\>\<#610F\>\<#5B9E\>\<#6570\><math|x>\<#FF0C\>\<#6709\>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<cwith|2|2|1|2|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|-1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|f*<around*|(|-x|)>+f<around*|(|x|)>=0>>|<cell|B.
    <math|f*<around*|(|-x|)>-f<around*|(|x|)>=0>>>|<row|<cell|C.
    <math|f*<around*|(|-x|)>+f<around*|(|x|)>=1>>|<cell|D.
    <math|f*<around*|(|-x|)>-f<around*|(|x|)>=<frac|1|3>>>>>>>

    <item>\<#5DF1\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=cos<rsup|2>
    x-sin<rsup|2> x>\<#FF0C\>\<#5219\>

    A. <math|f<around*|(|x|)>>\<#5728\><math|<around*|(|-<frac|\<pi\>|2>,-<frac|\<pi\>|6>|)>>\<#4E0A\>\<#5355\>\<#8C03\>\<#9012\>\<#589E\>

    B. <math|f<around*|(|x|)>>\<#5728\><math|<around*|(|-<frac|\<pi\>|4>,<frac|\<pi\>|12>|)>>\<#4E0A\>\<#5355\>\<#8C03\>\<#9012\>\<#589E\>

    C. <math|f<around*|(|x|)>>\<#5728\><math|<around*|(|0,<frac|\<pi\>|3>|)>>\<#4E0A\>\<#5355\>\<#8C03\>\<#9012\>\<#51CF\>

    D. <math|f<around*|(|x|)>>\<#5728\><math|<around*|(|<frac|\<pi\>|4>,<frac|7*\<pi\>|12>|)>>\<#4E0A\>\<#5355\>\<#8C03\>\<#9012\>\<#589E\>

    <item>\<#8BBE\><math|<around*|{|a<rsub|n>|}>>\<#662F\>\<#516C\>\<#5DEE\>\<#4E0D\>\<#4E3A\>0\<#7684\>\<#65E0\>\<#7A77\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>\<#FF0C\>\<#5219\>``<math|<around*|{|a<rsub|n>|}>>\<#4E3A\>\<#9012\>\<#589E\>\<#6570\>\<#5217\>''\<#662F\>``\<#5B58\>\<#5728\>\<#6B63\>\<#6574\>\<#6570\><math|N<rsub|0>>\<#FF0C\>\<#5F53\><math|n\<gtr\>N<rsub|0>>\<#65F6\>\<#FF0C\><math|a<rsub|n>\<gtr\>0>''\<#7684\>

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<cwith|2|2|1|2|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|-1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    \<#5145\>\<#5206\>\<#800C\>\<#4E0D\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>>|<cell|B.
    \<#5FC5\>\<#8981\>\<#800C\>\<#4E0D\>\<#5145\>\<#5206\>\<#6761\>\<#4EF6\>>>|<row|<cell|C.
    \<#5145\>\<#5206\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>>|<cell|D.
    \<#65E2\>\<#4E0D\>\<#5145\>\<#5206\>\<#4E5F\>\<#4E0D\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>>>>>>

    <item>\<#5728\>\<#5317\>\<#4EAC\>\<#51AC\>\<#5965\>\<#4F1A\>\<#4E0A\>\<#FF0C\>\<#56FD\>\<#5BB6\>\<#901F\>\<#6ED1\>\<#9986\>``\<#51B0\>\<#4E1D\>\<#5E26\>''\<#4F7F\>\<#7528\>\<#9AD8\>\<#6548\>\<#73AF\>\<#4FDD\>\<#7684\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#8DE8\>\<#4E34\>\<#754C\>\<#76F4\>\<#51B7\>\<#5236\>\<#51B0\>\<#6280\>\<#672F\>\<#FF0C\>\<#4E3A\>\<#5B9E\>\<#73B0\>\<#7EFF\>\<#8272\>\<#51AC\>\<#5965\>\<#4F5C\>\<#51FA\>\<#4E86\>\<#8D21\>\<#732E\>\<#FF0C\>\<#5982\>\<#56FE\>\<#63CF\>\<#8FF0\>\<#4E86\>\<#4E00\>\<#5B9A\>\<#6761\>\<#4EF6\>\<#4E0B\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#6240\>\<#5904\>\<#7684\>\<#72B6\>\<#6001\>\<#4E0E\><math|T>\<#548C\><math|1*g*P>\<#7684\>\<#5173\>\<#7CFB\>\<#FF0C\>\<#5176\>\<#4E2D\><math|T>\<#8868\>\<#793A\>\<#6E29\>\<#5EA6\>\<#FF0C\>\<#5355\>\<#4F4D\>\<#662F\><math|K>\<#FF1B\><math|P>\<#8868\>\<#793A\>\<#538B\>\<#5F3A\>\<#FF0C\>\<#5355\>\<#4F4D\>\<#662F\>bar\<#FF0C\>\<#4E0B\>\<#5217\>\<#7ED3\>\<#8BBA\>\<#4E2D\>\<#6B63\>\<#786E\>\<#7684\>\<#662F\>

    A. \<#5F53\><math|T=220>\<#FF0C\><math|P=1026>\<#65F6\>\<#FF0C\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#5904\>\<#4E8E\>\<#6DB2\>\<#6001\>

    B. \<#5F53\><math|T=270>\<#FF0C\><math|P=128>\<#65F6\>\<#FF0C\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#5904\>\<#4E8E\>\<#6C14\>\<#6001\>

    C. \<#5F53\><math|T=300>\<#FF0C\><math|P=9987>\<#65F6\>\<#FF0C\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#5904\>\<#4E8E\>\<#8D85\>\<#4E34\>\<#754C\>\<#72B6\>\<#6001\>

    D. \<#5F53\><math|T=360>\<#FF0C\><math|P=729>\<#65F6\>\<#FF0C\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#5904\>\<#4E8E\>\<#8D85\>\<#4E34\>\<#754C\>\<#72B6\>\<#6001\>

    <image|<tuple|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

    <item>\<#82E5\><math|<around|(|2*x-1|)><rsup|4>=a<rsub|4>*x<rsup|4>+a<rsub|3>*x<rsup|3>+a<rsub|2>*x<rsup|2>+a<rsub|1>*x+a<rsub|0>>\<#FF0C\>\<#5219\><math|a<rsub|0>+a<rsub|2>+a<rsub|4>=>

    <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.
    40>|<cell|B. 41>|<cell|C. <math|-40>>|<cell|D. <math|-41>>>>>>

    <item>\<#5DF2\>\<#77E5\>\<#6B63\>\<#4E09\>\<#68F1\>\<#9525\><math|P-A*B*C>\<#7684\>\<#516D\>\<#6761\>\<#68F1\>\<#957F\>\<#5747\>\<#4E3A\>6\<#FF0C\><math|S>\<#662F\><with|font-family|rm|\<triangle\>><math|A*B*C>\<#53CA\>\<#5176\>\<#5185\>\<#90E8\>\<#7684\>\<#70B9\>\<#6784\>\<#6210\>\<#7684\>\<#96C6\>\<#5408\>\<#FF0C\>\<#8BBE\>\<#96C6\>\<#5408\><math|T=<around|{|Q\<in\><around*|\<nobracket\>|S|\|>*P*Q<math-up|}
    >5|}>>\<#FF0C\>\<#5219\><math|T>\<#8868\>\<#793A\>\<#7684\>\<#533A\>\<#57DF\>\<#7684\>\<#9762\>\<#79EF\>\<#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|3*\<pi\>|4>>>|<cell|B. <math|\<pi\>>>|<cell|C.
    <math|2*\<pi\>>>|<cell|D. <math|3*\<pi\>>>>>>>

    <item>\<#5728\><with|font-family|rm|\<triangle\>><math|A*B*C>\<#4E2D\>\<#FF0C\><math|A*C=3>\<#FF0C\><math|B*C=4>\<#FF0C\><math|\<angle\>*C=90<rsup|\<circ\>>>\<#FF0E\><math|P>\<#4E3A\><with|font-family|rm|\<triangle\>><math|A*B*C>\<#6240\>\<#5728\>\<#5E73\>\<#9762\>\<#5185\>\<#7684\>\<#52A8\>\<#70B9\>\<#FF0C\>\<#4E14\><math|P*C=1>\<#FF0C\>\<#5219\><math|<wide|P*A|\<wide-varrightarrow\>>\<cdot\><wide|P*B|\<wide-varrightarrow\>>>\<#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*|[|-5,3|]>>>|<cell|B. <math|<around*|[|-3,5|]>>>|<cell|C.
    <math|<around*|[|-6,4|]>>>|<cell|D. <math|<around*|[|-4,6|]>>>>>>>
  </enumerate-numeric>

  <strong|\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>>\<#FF08\>\<#5171\>5\<#5C0F\>\<#9898\>\<#FF0C\>\<#6BCF\>\<#5C0F\>\<#9898\>5\<#5206\>\<#FF0C\>\<#5171\>25\<#5206\>\<#3002\>\<#FF09\>

  <\enumerate-numeric>
    <assign|item-nr|10><item>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=<frac|1|x>+<sqrt|1-x>>\<#7684\>\<#5B9A\>\<#4E49\>\<#57DF\>\<#662F\><underline|<space|2cm>>\<#FF0E\>

    <item>\<#5DF2\>\<#77E5\>\<#53CC\>\<#66F2\>\<#7EBF\><math|y<rsup|2>+<frac|x<rsup|2>|m>=1>\<#7684\>\<#6E10\>\<#8FD1\>\<#7EBF\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|y=\<pm\><frac|<sqrt|3>|3>*x>\<#FF0C\>\<#5219\><math|m=><underline|<space|2cm>>\<#FF0E\>

    <item>\<#82E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=A*sin
    x-<sqrt|3>*cos x>\<#7684\>\<#4E00\>\<#4E2A\>\<#96F6\>\<#70B9\>\<#4E3A\><math|<frac|\<pi\>|3>>\<#FF0C\>\<#5219\><math|A=><underline|<space|2cm>>\<#FF1B\><math|f<around*|(|<frac|\<pi\>|12>|)>=><underline|<space|2cm>>\<#FF0E\>

    <item>\<#8BBE\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<around*|{|<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|2|2|cell-halign|l>|<cwith|1|-1|2|2|cell-rborder|0ln>|<table|<row|<cell|-a*x+1,>|<cell|x\<less\>a>>|<row|<cell|<around|(|x-2|)><rsup|2>,>|<cell|x\<geqslant\>a>>>>>|\<nobracket\>>>\<#FF0C\>\<#82E5\><math|f<around*|(|x|)>>\<#5B58\>\<#5728\>\<#6700\>\<#5C0F\>\<#503C\>\<#FF0C\>\<#5219\><math|a>\<#7684\>\<#4E00\>\<#4E2A\>\<#53D6\>\<#503C\>\<#4E3A\><underline|<space|2cm>>\<#FF1B\><math|a>\<#7684\>\<#6700\>\<#5927\>\<#503C\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>

    <item>\<#5DF2\>\<#77E5\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#5404\>\<#9879\>\<#5747\>\<#4E3A\>\<#6B63\>\<#6570\>\<#FF0C\>\<#5176\>\<#524D\><math|n>\<#9879\>\<#548C\><math|S<rsub|n>>\<#FF0C\>\<#6EE1\>\<#8DB3\><math|a<rsub|n>\<cdot\>S<rsub|n>=9*<around|(|n=1,2,\<cdots\>|)>>\<#7ED9\>\<#51FA\>\<#4E0B\>\<#5217\>\<#56DB\>\<#4E2A\>\<#7ED3\>\<#8BBA\>\<#FF1A\>

    \<#2460\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#7B2C\>2\<#9879\>\<#5C0F\>\<#4E8E\>3\<#FF1B\>\<#2461\><math|<around*|{|a<rsub|n>|}>>\<#4E3A\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\>\<#FF1B\>

    \<#2462\><math|<around*|{|a<rsub|n>|}>>\<#4E3A\>\<#9012\>\<#51CF\>\<#6570\>\<#5217\>\<#FF1B\>\<#2463\><math|<around*|{|a<rsub|n>|}>>\<#4E2D\>\<#5B58\>\<#5728\>\<#5C0F\>\<#4E8E\><math|<frac|1|100>>\<#7684\>\<#9879\>\<#3002\>

    \<#5176\>\<#4E2D\>\<#6240\>\<#6709\>\<#6B63\>\<#786E\>\<#7ED3\>\<#8BBA\>\<#7684\>\<#5E8F\>\<#53F7\>\<#662F\><underline|<space|2cm>>\<#FF0E\>
  </enumerate-numeric>

  <strong|\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>>(\<#5171\>6\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>85\<#5206\>\<#3002\>\<#89E3\>\<#7B54\>\<#5E94\>\<#5199\>\<#51FA\>\<#6587\>\<#5B57\>\<#8BF4\>\<#660E\>\<#FF0C\>\<#6F14\>\<#7B97\>\<#6B65\>\<#9AA4\>\<#6216\>\<#8BC1\>\<#660E\>\<#8FC7\>\<#7A0B\>\<#3002\>)

  <\enumerate-numeric>
    <assign|item-nr|15><item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>13\<#5206\>\<#FF09\>

    \<#5728\><with|font-family|rm|\<triangle\>><math|A*B*C>\<#4E2D\>\<#FF0C\><math|sin
    2*C=<sqrt|3>*sin C>\<#FF0E\>

    \<#FF08\>I\<#FF09\>\<#6C42\><math|\<angle\>*C>\<#FF1A\>

    \<#FF08\>II\<#FF09\>\<#82E5\><math|b=6>\<#FF0C\>\<#4E14\><with|font-family|rm|\<triangle\>><math|A*B*C>\<#7684\>\<#9762\>\<#79EF\>\<#4E3A\><math|6*<sqrt|3>>\<#FF0C\>\<#6C42\><with|font-family|rm|\<triangle\>><math|A*B*C>\<#7684\>\<#5468\>\<#957F\>\<#FF0E\><vspace|5cm>

    <item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>14\<#5206\>\<#FF09\>

    \<#5982\>\<#56FE\>\<#FF0C\>\<#5728\>\<#4E09\>\<#68F1\>\<#67F1\><math|A*B*C-A<rsub|1>*B<rsub|1>*C<rsub|1>>\<#4E2D\>\<#FF0C\>\<#4FA7\>\<#9762\><math|B*C*C<rsub|1>*B<rsub|1>>\<#4E3A\>\<#6B63\>\<#65B9\>\<#5F62\>\<#FF0C\>\<#5E73\>\<#9762\><math|B*C*C<rsub|1>*B<rsub|1>*\<bot\>>\<#5E73\>\<#9762\><math|A*B*B<rsub|1>*A<rsub|1>>\<#FF0C\><math|A*B=B*C=2>\<#FF0C\><math|M,N>\<#5206\>\<#522B\>\<#4E3A\><math|A<rsub|1>*B<rsub|1>>\<#FF0C\><math|A*C>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0E\>

    \<#FF08\>I\<#FF09\>\<#6C42\>\<#8BC1\>\<#FF1A\><math|M*N><with|font-family|rm|//>\<#5E73\>\<#9762\><math|B*C*C<rsub|1>*B<rsub|1>>\<#FF1B\>

    \<#FF08\>II\<#FF09\>\<#518D\>\<#4ECE\>\<#6761\>\<#4EF6\>\<#2460\>\<#3001\>\<#6761\>\<#4EF6\>\<#2461\>\<#8FD9\>\<#4E24\>\<#4E2A\>\<#6761\>\<#4EF6\>\<#4E2D\>\<#9009\>\<#62E9\>\<#4E00\>\<#4E2A\>\<#4F5C\>\<#4E3A\>\<#5DF2\>\<#77E5\>\<#FF0C\>\<#6C42\>

    \<#76F4\>\<#7EBF\><math|A*B>\<#4E0E\>\<#5E73\>\<#9762\><math|B*M*N>\<#6240\>\<#6210\>\<#89D2\>\<#7684\>\<#6B63\>\<#5F26\>\<#503C\>\<#3002\>

    \<#6761\>\<#4EF6\>\<#2460\>\<#FF1A\><math|A*B*\<bot\>*M*N>\<#FF1B\>

    \<#6761\>\<#4EF6\>\<#2461\>\<#FF1A\><math|B*M=M*N>\<#FF0E\>

    \<#6CE8\>\<#FF1A\>\<#5982\>\<#679C\>\<#9009\>\<#62E9\>\<#6761\>\<#4EF6\>\<#2460\>\<#548C\>\<#6761\>\<#4EF6\>\<#2461\>\<#5206\>\<#522B\>\<#89E3\>\<#7B54\>\<#FF0C\>\<#6309\>\<#7B2C\>\<#4E00\>\<#4E2A\>\<#89E3\>\<#7B54\>\<#8BA1\>\<#5206\>\<#3002\>

    <image|<tuple|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

    <vspace|5cm>

    <item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>13\<#5206\>\<#FF09\>

    \<#5728\>\<#6821\>\<#8FD0\>\<#52A8\>\<#4F1A\>\<#4E0A\>\<#FF0C\>\<#53EA\>\<#6709\>\<#7532\>\<#3001\>\<#4E59\>\<#3001\>\<#4E19\>\<#4E09\>\<#540D\>\<#540C\>\<#5B66\>\<#53C2\>\<#52A0\>\<#94C5\>\<#7403\>\<#6BD4\>\<#8D5B\>\<#FF0C\>\<#6BD4\>\<#8D5B\>\<#6210\>\<#7EE9\>\<#8FBE\>\<#5230\>9.50m\<#4EE5\>\<#4E0A\>\<#FF08\>\<#542B\>9.50m\<#FF09\>\<#7684\>\<#540C\>\<#5B66\>\<#5C06\>\<#83B7\>\<#5F97\>\<#4F18\>\<#79C0\>\<#5956\>\<#FF0C\>\<#4E3A\>\<#9884\>\<#6D4B\>\<#83B7\>\<#5F97\>\<#4F18\>\<#79C0\>\<#5956\>\<#7684\>\<#4EBA\>\<#6570\>\<#53CA\>\<#51A0\>\<#519B\>\<#5F97\>\<#4E3B\>\<#FF0C\>\<#6536\>\<#96C6\>\<#4E86\>\<#7532\>\<#3001\>\<#4E59\>\<#3001\>\<#4E19\>\<#4EE5\>\<#5F80\>\<#7684\>\<#6BD4\>\<#8D5B\>\<#6210\>\<#7EE9\>\<#FF0C\>\<#5E76\>\<#6574\>\<#7406\>\<#5F97\>\<#5230\>\<#5982\>\<#4E0B\>\<#6570\>\<#636E\>\<#FF08\>\<#5355\>\<#4F4D\>\<#FF1A\>m\<#FF09\>\<#FF1A\>

    \<#7532\>\<#FF1A\>9.80, 9.70, 9.55, 9.54, 9.48, 9.42, 9.40, 9.35, 9.30,
    9.25\<#FF1B\>

    \<#4E59\>\<#FF1A\>9.78, 9.56, 9.51, 9.36, 9.32, 9.23\<#FF1B\>

    \<#4E19\>\<#FF1A\>9.85, 9.65, 9.20, 9.16\<#FF0E\>

    \<#5047\>\<#8BBE\>\<#7528\>\<#9891\>\<#7387\>\<#4F30\>\<#8BA1\>\<#6982\>\<#7387\>\<#FF0C\>\<#4E14\>\<#7532\>\<#3001\>\<#4E59\>\<#3001\>\<#4E19\>\<#7684\>\<#6BD4\>\<#8D5B\>\<#6210\>\<#7EE9\>\<#76F8\>\<#4E92\>\<#72EC\>\<#7ACB\>

    \<#FF08\>I\<#FF09\>\<#4F30\>\<#8BA1\>\<#7532\>\<#5728\>\<#6821\>\<#8FD0\>\<#52A8\>\<#4F1A\>\<#94C5\>\<#7403\>\<#6BD4\>\<#8D5B\>\<#4E2D\>\<#83B7\>\<#5F97\>\<#4F18\>\<#79C0\>\<#5956\>\<#7684\>\<#6982\>\<#7387\>\<#FF1B\>

    \<#FF08\>II\<#FF09\>\<#8BBE\>X\<#662F\>\<#7532\>\<#3001\>\<#4E59\>\<#3001\>\<#4E19\>\<#5728\>\<#6821\>\<#8FD0\>\<#52A8\>\<#4F1A\>\<#94C5\>\<#7403\>\<#6BD4\>\<#8D5B\>\<#4E2D\>\<#83B7\>\<#5F97\>\<#4F18\>\<#79C0\>\<#5956\>\<#7684\>\<#603B\>\<#4EBA\>\<#6570\>\<#FF0C\>\<#4F30\>\<#8BA1\><math|X>\<#7684\>\<#6570\>\<#5B66\>\<#671F\>\<#671B\><math|E*X>\<#FF1B\>

    \<#FF08\>III\<#FF09\>\<#5728\>\<#6821\>\<#8FD0\>\<#52A8\>\<#4F1A\>\<#94C5\>\<#7403\>\<#6BD4\>\<#8D5B\>\<#4E2D\>\<#FF0C\>\<#7532\>\<#3001\>\<#4E59\>\<#3001\>\<#4E19\>\<#8C01\>\<#83B7\>\<#5F97\>\<#51A0\>\<#519B\>\<#7684\>\<#6982\>\<#7387\>\<#4F30\>\<#8BA1\>\<#503C\>\<#6700\>\<#5927\>\<#FF1F\>\<#FF08\>\<#7ED3\>\<#8BBA\>\<#4E0D\>\<#8981\>\<#6C42\>\<#8BC1\>\<#660E\>\<#FF09\><vspace|5cm>

    <item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>15\<#5206\>\<#FF09\>

    \<#5DF2\>\<#77E5\>\<#692D\>\<#5706\><math|E:<frac|x<rsup|2>|a<rsup|2>>+<frac|y<rsup|2>|b<rsup|2>>=1*<around|(|a\<gtr\>b\<gtr\>0|)>>\<#7684\>\<#4E00\>\<#4E2A\>\<#9876\>\<#70B9\>\<#4E3A\><math|A*<around*|(|0,1|)>>\<#FF0C\>\<#7126\>\<#8DDD\>\<#4E3A\><math|2*<sqrt|3>>\<#FF0E\>

    \<#FF08\>I\<#FF09\>\<#6C42\>\<#692D\>\<#5706\><math|E>\<#7684\>\<#65B9\>\<#7A0B\>\<#FF1A\>

    \<#FF08\>Il\<#FF09\>\<#8FC7\>\<#70B9\><math|P*<around*|(|-2,1|)>>\<#4F5C\>\<#659C\>\<#7387\>\<#4E3A\><math|k>\<#7684\>\<#76F4\>\<#7EBF\>\<#4E0E\>\<#692D\>\<#5706\><math|E>\<#4EA4\>\<#4E8E\>\<#4E0D\>\<#540C\>\<#7684\>\<#4E24\>\<#70B9\><math|B,C>\<#FF0C\>\<#76F4\>\<#7EBF\><math|A*B,A*C>\<#5206\>\<#522B\>\<#4E0E\><math|x>\<#8F74\>\<#4EA4\>\<#4E8E\>\<#70B9\><math|M,N>\<#FF0C\>\<#5F53\><math|<around*|\||M*N|\|>=2>\<#65F6\>\<#FF0C\>\<#6C42\><math|k>\<#7684\>\<#503C\>\<#3002\><vspace|5cm>

    <item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>15\<#5206\>\<#FF09\>

    \<#5DF1\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=e<rsup|x><math-up|ln><around*|(|1+x|)>>\<#FF0E\>

    \<#FF08\>I\<#FF09\>\<#6C42\>\<#66F2\>\<#7EBF\><math|y=f<around*|(|x|)>>\<#5728\>\<#70B9\><math|<around*|(|0,f<around*|(|0|)>|)>>\<#5904\>\<#7684\>\<#5207\>\<#7EBF\>\<#65B9\>\<#7A0B\>\<#FF1B\>

    \<#FF08\>I\<#FF09\>\<#8BBE\><math|g<around*|(|x|)>=f<rprime|'><around*|(|x|)>>\<#FF0C\>\<#8BA8\>\<#8BBA\>\<#51FD\>\<#6570\><math|g<around*|(|x|)>>\<#5728\><math|<around*|[|0,+\<infty\>|)>>\<#4E0A\>\<#7684\>\<#5355\>\<#8C03\>\<#6027\>\<#FF1B\>

    \<#FF08\>III\<#FF09\>\<#8BC1\>\<#660E\>\<#FF1A\>\<#5BF9\>\<#4EFB\>\<#610F\>\<#7684\><math|s,t\<in\><around|(|0,+\<infty\>|)>><with|font-family|rm|<space|0.27em>
    >\<#FF0C\>\<#6709\><math|f*<around|(|s+t|)>\<gtr\>f<around|(|s|)>+f<around|(|t|)>>\<#FF0E\><vspace|5cm>

    <item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>15\<#5206\>\<#FF09\>

    \<#5DF1\>\<#77E5\><math|Q:a<rsub|1>,a<rsub|2>,\<cdots\>,a<rsub|k>>\<#4E3A\>\<#6709\>\<#7A77\>\<#6574\>\<#6570\>\<#6570\>\<#5217\>\<#FF0E\>\<#7ED9\>\<#5B9A\>\<#6B63\>\<#6574\>\<#6570\><math|m>\<#FF0C\>\<#82E5\>\<#5BF9\>\<#4EFB\>\<#610F\>\<#7684\><math|n\<in\><around|{|1,2,\<cdots\>,m|}>>\<#FF0C\>\<#5728\><math|Q>\<#4E2D\>\<#5B58\>\<#5728\><math|a<rsub|1>,a<rsub|i+1>,a<rsub|i+2>,\<cdots\>,a<rsub|i+j><around|(|j<math-up|\<sim\>>0|)>>\<#FF0C\>\<#4F7F\>\<#5F97\><math|a<rsub|i>+a<rsub|i+1>+a<rsub|i+2>+\<cdots\>+a<rsub|i+j>=n>\<#FF0C\>\<#5219\>\<#79F0\><math|Q>\<#4E3A\><math|m->\<#8FDE\>\<#7EED\>\<#53EF\>\<#8868\>\<#6570\>\<#5217\>\<#FF0E\>

    \<#FF08\>I\<#FF09\>\<#5224\>\<#65AD\><math|Q:2,1,4>\<#662F\>\<#5426\>\<#4E3A\>5-\<#8FDE\>\<#7EED\>\<#53EF\>\<#8868\>\<#6570\>\<#5217\>\<#FF1F\>\<#662F\>\<#5426\>\<#4E3A\><math|6->\<#8FDE\>\<#7EED\>\<#53EF\>\<#8868\>\<#6570\>\<#5217\>\<#FF1F\>\<#8BF4\>\<#660E\>\<#7406\>\<#7531\>\<#FF1B\>

    \<#FF08\>II\<#FF09\>\<#82E5\><math|Q:a<rsub|1>,a<rsub|2>,\<cdots\>,a<rsub|k>>\<#4E3A\><math|8->\<#8FDE\>\<#7EED\>\<#53EF\>\<#8868\>\<#6570\>\<#5217\>\<#FF0C\>\<#6C42\>\<#8BC1\>\<#FF1A\><math|k>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#4E3A\>4\<#FF1B\>

    \<#FF08\>III\<#FF09\>\<#82E5\><math|Q:a<rsub|1>,a<rsub|2>,\<cdots\>,a<rsub|k>>\<#4E3A\><math|20->\<#8FDE\>\<#7EED\>\<#53EF\>\<#8868\>\<#6570\>\<#5217\>\<#FF0C\><math|a<rsub|1>+a<rsub|2>+\<cdots\>+a<rsub|k>\<less\>20>\<#FF0C\>\<#6C42\>\<#8BC1\>\<#FF1A\><math|k\<ge\>7>\<#FF0E\><vspace|5cm>
  </enumerate-numeric>
</body>

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