mirror of https://gitee.com/XmacsLabs/planet.git
190 lines
140 KiB
Tcl
190 lines
140 KiB
Tcl
<TeXmacs|2.1.2>
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<style|<tuple|exam|std-latex|chinese>>
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<\body>
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<doc-data|<doc-title|2022\<#5E74\>\<#6570\>\<#5B66\>\<#5317\>\<#4EAC\>\<#5377\>>>
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<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\>
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<\enumerate-numeric>
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<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=>
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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.
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<math|<around*|(|-2,1|]>>>|<cell|B. <math|<around|(|-3,-2|)>\<cup\><around|[|1,3|)>>>|<cell|C.
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<math|<around*|[|-2,1|)>>>|<cell|D. <math|<around|(|-3,-2|]>\<cup\><around|(|1,3|)>>>>>>>
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<item>\<#82E5\>\<#590D\>\<#6570\><math|z>\<#6EE1\>\<#8DB3\><math|i\<cdot\>z=3-4*i>\<#FF0C\>\<#5219\><math|<around*|\||z|\|>=>
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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.
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1>|<cell|B. 5>|<cell|C. 7>|<cell|D. 25>>>>>
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<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=>
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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.
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<math|<frac|1|2>>>|<cell|B. <math|-<frac|1|2>>>|<cell|C. 1>|<cell|D.
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<math|-1>>>>>>
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<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\>
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<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.
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<math|f*<around*|(|-x|)>+f<around*|(|x|)>=0>>|<cell|B.
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<math|f*<around*|(|-x|)>-f<around*|(|x|)>=0>>>|<row|<cell|C.
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<math|f*<around*|(|-x|)>+f<around*|(|x|)>=1>>|<cell|D.
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<math|f*<around*|(|-x|)>-f<around*|(|x|)>=<frac|1|3>>>>>>>
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<item>\<#5DF1\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=cos<rsup|2>
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x-sin<rsup|2> x>\<#FF0C\>\<#5219\>
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A. <math|f<around*|(|x|)>>\<#5728\><math|<around*|(|-<frac|\<pi\>|2>,-<frac|\<pi\>|6>|)>>\<#4E0A\>\<#5355\>\<#8C03\>\<#9012\>\<#589E\>
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B. <math|f<around*|(|x|)>>\<#5728\><math|<around*|(|-<frac|\<pi\>|4>,<frac|\<pi\>|12>|)>>\<#4E0A\>\<#5355\>\<#8C03\>\<#9012\>\<#589E\>
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C. <math|f<around*|(|x|)>>\<#5728\><math|<around*|(|0,<frac|\<pi\>|3>|)>>\<#4E0A\>\<#5355\>\<#8C03\>\<#9012\>\<#51CF\>
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D. <math|f<around*|(|x|)>>\<#5728\><math|<around*|(|<frac|\<pi\>|4>,<frac|7*\<pi\>|12>|)>>\<#4E0A\>\<#5355\>\<#8C03\>\<#9012\>\<#589E\>
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<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\>
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<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.
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\<#5145\>\<#5206\>\<#800C\>\<#4E0D\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>>|<cell|B.
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\<#5FC5\>\<#8981\>\<#800C\>\<#4E0D\>\<#5145\>\<#5206\>\<#6761\>\<#4EF6\>>>|<row|<cell|C.
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\<#5145\>\<#5206\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>>|<cell|D.
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\<#65E2\>\<#4E0D\>\<#5145\>\<#5206\>\<#4E5F\>\<#4E0D\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>>>>>>
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<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\>
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A. \<#5F53\><math|T=220>\<#FF0C\><math|P=1026>\<#65F6\>\<#FF0C\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#5904\>\<#4E8E\>\<#6DB2\>\<#6001\>
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B. \<#5F53\><math|T=270>\<#FF0C\><math|P=128>\<#65F6\>\<#FF0C\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#5904\>\<#4E8E\>\<#6C14\>\<#6001\>
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C. \<#5F53\><math|T=300>\<#FF0C\><math|P=9987>\<#65F6\>\<#FF0C\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#5904\>\<#4E8E\>\<#8D85\>\<#4E34\>\<#754C\>\<#72B6\>\<#6001\>
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D. \<#5F53\><math|T=360>\<#FF0C\><math|P=729>\<#65F6\>\<#FF0C\>\<#4E8C\>\<#6C27\>\<#5316\>\<#78B3\>\<#5904\>\<#4E8E\>\<#8D85\>\<#4E34\>\<#754C\>\<#72B6\>\<#6001\>
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|png>|.5par|||>
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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>=>
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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.
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40>|<cell|B. 41>|<cell|C. <math|-40>>|<cell|D. <math|-41>>>>>>
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<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|}
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>5|}>>\<#FF0C\>\<#5219\><math|T>\<#8868\>\<#793A\>\<#7684\>\<#533A\>\<#57DF\>\<#7684\>\<#9762\>\<#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.
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<math|<frac|3*\<pi\>|4>>>|<cell|B. <math|\<pi\>>>|<cell|C.
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<math|2*\<pi\>>>|<cell|D. <math|3*\<pi\>>>>>>>
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<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\>
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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.
|
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<math|<around*|[|-5,3|]>>>|<cell|B. <math|<around*|[|-3,5|]>>>|<cell|C.
|
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<math|<around*|[|-6,4|]>>>|<cell|D. <math|<around*|[|-4,6|]>>>>>>>
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</enumerate-numeric>
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<strong|\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>>\<#FF08\>\<#5171\>5\<#5C0F\>\<#9898\>\<#FF0C\>\<#6BCF\>\<#5C0F\>\<#9898\>5\<#5206\>\<#FF0C\>\<#5171\>25\<#5206\>\<#3002\>\<#FF09\>
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<\enumerate-numeric>
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<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\>
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<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\>
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<item>\<#82E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=A*sin
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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\>
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<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\>
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<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\>
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\<#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\>
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\<#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\>
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\<#5176\>\<#4E2D\>\<#6240\>\<#6709\>\<#6B63\>\<#786E\>\<#7ED3\>\<#8BBA\>\<#7684\>\<#5E8F\>\<#53F7\>\<#662F\><underline|<space|2cm>>\<#FF0E\>
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</enumerate-numeric>
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<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\>)
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<\enumerate-numeric>
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<assign|item-nr|15><item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>13\<#5206\>\<#FF09\>
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\<#5728\><with|font-family|rm|\<triangle\>><math|A*B*C>\<#4E2D\>\<#FF0C\><math|sin
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2*C=<sqrt|3>*sin C>\<#FF0E\>
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\<#FF08\>I\<#FF09\>\<#6C42\><math|\<angle\>*C>\<#FF1A\>
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\<#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>
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<item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>14\<#5206\>\<#FF09\>
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\<#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\>
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\<#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\>
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\<#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\>
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\<#76F4\>\<#7EBF\><math|A*B>\<#4E0E\>\<#5E73\>\<#9762\><math|B*M*N>\<#6240\>\<#6210\>\<#89D2\>\<#7684\>\<#6B63\>\<#5F26\>\<#503C\>\<#3002\>
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\<#6761\>\<#4EF6\>\<#2460\>\<#FF1A\><math|A*B*\<bot\>*M*N>\<#FF1B\>
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\<#6761\>\<#4EF6\>\<#2461\>\<#FF1A\><math|B*M=M*N>\<#FF0E\>
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\<#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\>
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<vspace|5cm>
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\<#7532\>\<#FF1A\>9.80, 9.70, 9.55, 9.54, 9.48, 9.42, 9.40, 9.35, 9.30,
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9.25\<#FF1B\>
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\<#4E59\>\<#FF1A\>9.78, 9.56, 9.51, 9.36, 9.32, 9.23\<#FF1B\>
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\<#4E19\>\<#FF1A\>9.85, 9.65, 9.20, 9.16\<#FF0E\>
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\<#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\>
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\<#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\>
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\<#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>
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<item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>15\<#5206\>\<#FF09\>
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\<#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\>
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\<#FF08\>I\<#FF09\>\<#6C42\>\<#692D\>\<#5706\><math|E>\<#7684\>\<#65B9\>\<#7A0B\>\<#FF1A\>
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\<#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>
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<item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>15\<#5206\>\<#FF09\>
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\<#5DF1\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=e<rsup|x><math-up|ln><around*|(|1+x|)>>\<#FF0E\>
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\<#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\>
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\<#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\>
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\<#FF08\>III\<#FF09\>\<#8BC1\>\<#660E\>\<#FF1A\>\<#5BF9\>\<#4EFB\>\<#610F\>\<#7684\><math|s,t\<in\><around|(|0,+\<infty\>|)>><with|font-family|rm|<space|0.27em>
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>\<#FF0C\>\<#6709\><math|f*<around|(|s+t|)>\<gtr\>f<around|(|s|)>+f<around|(|t|)>>\<#FF0E\><vspace|5cm>
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<item>\<#FF08\>\<#672C\>\<#5C0F\>\<#9898\>15\<#5206\>\<#FF09\>
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\<#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\>
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\<#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\>
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\<#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\>
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\<#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>
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</enumerate-numeric>
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</body>
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<initial|<\collection>
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</collection>> |