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2022年浙江省高考数学试题 (#3) 2022年浙江省高考数学试题
2022-06-11 12:48:38 +08:00
<TeXmacs|2.1.1>
<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|<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>
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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>
修正2022年浙江省高考数学试题第7题，感谢V2EX用户Maddox
2022-06-17 23:28:23 +08:00
<item>\<#5DF2\>\<#77E5\><math|2<rsup|a>=5,log<rsub|8>3=b>\<#FF0C\>\<#5219\><math|4<rsup|a-3b>=>
2022年浙江省高考数学试题 (#3) 2022年浙江省高考数学试题
2022-06-11 12:48:38 +08:00
<\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|ABC-A<rsub|1>B<rsub|1>C<rsub|1>,AC=AA<rsub|1>>\<#FF0C\><math|E,F>\<#5206\>\<#522B\>\<#662F\>\<#68F1\><math|BC>\<#FF0C\><math|A<rsub|1>C<rsub|1>>\<#4E0A\>\<#7684\>\<#70B9\>.\<#8BB0\><math|EF>\<#4E0E\><math|AA<rsub|1>>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|\<alpha\>>\<#FF0C\><math|EF>\<#4E0E\>\<#5E73\>\<#9762\><math|ABC>\<#6240\>\<#6210\>\<#7684\>\<#89D2\>\<#4E3A\><math|\<beta\>>\<#FF0C\>\<#4E8C\>\<#9762\>\<#89D2\><math|F-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>
<image|<tuple|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
<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.
修正2022年浙江省高考数学试题第15题 (#4) 修正2022年浙江省高考数学试题第15题
2022-06-12 16:11:20 +08:00
\<#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>>.
2022年浙江省高考数学试题 (#3) 2022年浙江省高考数学试题
2022-06-11 12:48:38 +08:00
<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\>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\>ABC>\<#7684\>\<#9762\>\<#79EF\>.
<item>\<#FF08\>\<#672C\>\<#9898\>\<#6EE1\>\<#5206\>15\<#5206\>\<#FF09\>\<#5982\>\<#56FE\>\<#FF0C\>\<#5DF2\>\<#77E5\><math|ABCD>\<#548C\><math|CDEF>\<#90FD\>\<#662F\>\<#76F4\>\<#89D2\>\<#68AF\>\<#5F62\>\<#FF0C\><math|AB//DC,DC//EF,AB=5,DC=3,EF=1,\<angle\>BAD=\<angle\>CDE=60<rsup|\<circ\>>>\<#FF0C\>\<#4E8C\>\<#9762\>\<#89D2\><math|F-DC-B>\<#7684\>\<#5E73\>\<#9762\>\<#89D2\>\<#4E3A\><math|60<rsup|\<circ\>>>\<#FF0C\>\<#8BBE\><math|M>\<#FF0C\><math|N>\<#5206\>\<#522B\>\<#4E3A\><math|AE>\<#FF0C\><math|BC>\<#7684\>\<#4E2D\>\<#70B9\>.
<\with|par-columns|2>
(I) \<#8BC1\>\<#660E\>\<#FF1A\><math|FN\<perp\>AD>\<#FF1B\>
(II) \<#6C42\>\<#76F4\>\<#7EBF\><math|BM>\<#4E0E\>\<#5E73\>\<#9762\><math|ADE>\<#6240\>\<#6210\>\<#89D2\>\<#7684\>\<#6B63\>\<#5F26\>\<#503C\>.
<image|<tuple|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
</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|AB>\<#4E0A\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|PA,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\>P\<#5230\>\<#692D\>\<#5706\>\<#4E0A\>\<#70B9\>\<#7684\>\<#8DDD\>\<#79BB\>\<#7684\>\<#6700\>\<#5927\>\<#503C\>\<#FF1B\>
(II) \<#6C42\><math|<around*|\||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>
\;
<\note*>
\<#672C\>\<#8BD5\>\<#9898\>\<#7531\>B\<#7AD9\>UP\<#4E3B\><hlink|<strong|\<#6C88\>\<#6D6A\>\<#718A\>\<#732B\>\<#513F\>>|https://space.bilibili.com/28058658>\<#4E8E\>2022\<#5E74\>6\<#6708\>10\<#65E5\>\<#82B1\>\<#8D39\>2\<#5C0F\>\<#65F6\>\<#7EAF\>\<#624B\>\<#5DE5\>\<#8F93\>\<#5165\>\<#5236\>\<#4F5C\>\<#3002\>\<#4E0B\>\<#8F7D\>\<#58A8\>\<#5E72\>\<#7F16\>\<#8F91\>\<#5668\>\<#FF0C\>\<#901A\>\<#8FC7\>\<#83DC\>\<#5355\><menu|help|planet>\<#53EF\>\<#4EE5\>\<#5F97\>\<#5230\>\<#672C\>\<#8BD5\>\<#9898\>\<#7684\>\<#53EF\>\<#7F16\>\<#8F91\>\<#6587\>\<#6863\>\<#3002\>
</note*>
\;
\;
</body>
<\initial>
<\collection>
<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\>\<#7F16\>\<#8F91\>\<#5668\>\<#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\>\<#7F16\>\<#8F91\>\<#5668\>\<#5236\>\<#4F5C\>><htab|5mm>>
<associate|page-odd-header|>
</collection>
</initial>
<\references>
<\collection>
<associate|auto-1|<tuple|ii|4>>
</collection>
</references>
<\auxiliary>
<\collection>
<\associate|idx>
<tuple|<tuple|<with|font-family|<quote|ss>|\<#5E2E\>\<#52A9\>>|<with|font-family|<quote|ss>|\<#58A8\>\<#5BA2\>\<#661F\>\<#7403\>>>|<pageref|auto-1>>
</associate>
</collection>
</auxiliary>