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<TeXmacs|2.1.3>
高考数学：十份试题 (#3)
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<style|<tuple|generic|chinese>>
<\body>
<doc-data|<doc-title|2021<with|font|Songti
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SC|年全国新高考>Ⅰ<with|font|Songti SC|卷数学试题>>>
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<with|font-series|bold|<with|font|Songti SC|一>、<with|font|Songti
SC|单选题>>
高考数学：十份试题 (#3)
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1<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|设集合><math|A=<around*|{|x*<around*|\||-2\<less\>x\<less\>4|\<nobracket\>>|}>><with|font|Hiragino
Kaku Gothic ProN|，><math|B=<around*|{|2,3,4,5|}>><with|font|Hiragino Kaku
Gothic ProN|，><with|font|Songti SC|则><math|A\<cap\>B=>（<space|1.2em>）
高考数学：十份试题 (#3)
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><math|<around*|{|2|}>>>|<cell|B<with|font|Hiragino
Kaku Gothic ProN|．><math|<around*|{|2,3|}>>>|<cell|C<with|font|Hiragino
Kaku Gothic ProN|．><math|<around*|{|3,4|}>>>|<cell|D<with|font|Hiragino
Kaku Gothic ProN|．><math|<around*|{|2,3,4|}>>>>>>>\
高考数学：十份试题 (#3)
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2<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知><math|z=2-i><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|则><math|z*<around*|(|<wide|z|\<bar\>>+i|)>=>（<space|1.2em>）
高考数学：十份试题 (#3)
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><math|6-2*i>>|<cell|B<with|font|Hiragino Kaku Gothic
ProN|．><math|4-2*i>>|<cell|C<with|font|Hiragino Kaku Gothic
ProN|．><math|6+2*i>>|<cell|D<with|font|Hiragino Kaku Gothic
ProN|．><math|4+2*i>>>>>>\
3<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知圆锥的底面半径为><math|<sqrt|2>><with|font|Hiragino Kaku
Gothic ProN|，><with|font|Songti SC|其侧面展开图为一个半圆><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|则该圆锥的母线长为>（<space|1.2em>）
高考数学：十份试题 (#3)
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><math|2>>|<cell|B<with|font|Hiragino Kaku Gothic
ProN|．><math|2*<sqrt|2>>>|<cell|C<with|font|Hiragino Kaku Gothic
ProN|．><math|4>>|<cell|D<with|font|Hiragino Kaku Gothic
ProN|．><math|4*<sqrt|2>>>>>>>\
4<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|下列区间中><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|函数><math|f<around|(|x|)>=7*sin
高考数学：十份试题 (#3)
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<around*|(|x-<frac|\<pi\>|6>|)>><with|font|Songti
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SC|单调递增的区间是>（<space|1.2em>）
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><math|<around*|(|0,<frac|\<pi\>|2>|)>>
高考数学：十份试题 (#3)
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>|<cell|B<with|font|Hiragino Kaku Gothic
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ProN|．><math|<around*|(|<frac|\<pi\>|2>,\<pi\>|)>>>|<cell|C<with|font|Hiragino
Kaku Gothic ProN|．><math|<around*|(|\<pi\>,<frac|3*\<pi\>|2>|)>>>|<cell|D<with|font|Hiragino
Kaku Gothic ProN|．><math|<around*|(|<frac|3*\<pi\>|2>,2*\<pi\>|)>>>>>>>
高考数学：十份试题 (#3)
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\
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5<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知><math|F<rsub|1>><with|font|Hiragino Kaku Gothic
ProN|，><math|F<rsub|2>><with|font|Songti
SC|是椭圆><math|C><with|font|Hiragino Kaku Gothic
ProN|：><math|<frac|x<rsup|2>|9>+<frac|y<rsup|2>|4>=1><with|font|Songti
SC|的两个焦点><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|点><math|M><with|font|Songti
SC|在><math|C><with|font|Songti SC|上><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|则><math|<around*|\||M*F<rsub|1>|\|>\<cdot\><around*|\||M*F<rsub|2>|\|>>（<space|1.2em>）
高考数学：十份试题 (#3)
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．>13>|<cell|B<with|font|Hiragino Kaku Gothic
ProN|．>12>|<cell|C<with|font|Hiragino Kaku Gothic
ProN|．>9>|<cell|D<with|font|Hiragino Kaku Gothic ProN|．>6>>>>> \ \
6<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|若><math|tan \<theta\>=-2><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|则><math|<frac|sin
高考数学：十份试题 (#3)
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\<theta\>*<around*|(|1+sin 2*\<theta\>|)>|sin \<theta\>+cos
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\<theta\>>=>（<space|1.2em>）
高考数学：十份试题 (#3)
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><math|-<frac|6|5>>>|<cell|B<with|font|Hiragino Kaku
Gothic ProN|．><math|-<frac|2|5>>>|<cell|C<with|font|Hiragino Kaku Gothic
ProN|．><math|<frac|2|5>>>|<cell|D<with|font|Hiragino Kaku Gothic
ProN|．><math|<frac|6|5>>>>>>>\
7<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|若过点><math|<around|(|a,b|)>><with|font|Songti
SC|可以作曲线><math|y=e<rsup|x>><with|font|Songti
SC|的两条切线><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|则>（<space|1.2em>）
高考数学：十份试题 (#3)
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><math|e<rsup|b>\<less\>a>>|<cell|B<with|font|Hiragino
Kaku Gothic ProN|．><math|e<rsup|a>\<less\>b>>|<cell|C<with|font|Hiragino
Kaku Gothic ProN|．><math|0\<less\>a\<less\>e<rsup|b>>>|<cell|D<with|font|Hiragino
Kaku Gothic ProN|．><math|0\<less\>b\<less\>e<rsup|a>>>>>>>\
8<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|有>6<with|font|Songti SC|个相同的球><with|font|Hiragino Kaku
Gothic ProN|，><with|font|Songti SC|分别标有数字>1<with|font|Hiragino
Kaku Gothic ProN|，>2<with|font|Hiragino Kaku Gothic
ProN|，>3<with|font|Hiragino Kaku Gothic ProN|，>4<with|font|Hiragino
Kaku Gothic ProN|，>5<with|font|Hiragino Kaku Gothic
ProN|，>6<with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|从中有放回的随机取两次><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|每次取>1<with|font|Songti
SC|个球><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|甲表示事件>\P<with|font|Songti SC|第一次取出的球的数字是>1\Q<with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|乙表示事件>\P<with|font|Songti
SC|第二次取出的球的数字是>2\Q<with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|丙表示事件>\P<with|font|Songti
SC|两次取出的球的数字之和是>8\Q<with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|丁表示事件>\P<with|font|Songti
SC|两次取出的球的数字之和是>7\Q<with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|则>（<space|1.2em>）
高考数学：十份试题 (#3)
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><with|font|Songti SC|甲与丙相互独立>>|<cell|B<with|font|Hiragino
Kaku Gothic ProN|．><with|font|Songti SC|甲与丁相互独立>>>|<row|<cell|C<with|font|Hiragino
Kaku Gothic ProN|．><with|font|Songti SC|乙与丙相互独立>>|<cell|D<with|font|Hiragino
Kaku Gothic ProN|．><with|font|Songti SC|丙与丁相互独立>>>>>>
高考数学：十份试题 (#3)
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\;
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<with|font-series|bold|<with|font|Songti SC|二>、<with|font|Songti
SC|多选题>>
9<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|有一组样本数据><math|x<rsub|1>><with|font|Hiragino Kaku Gothic
ProN|，><math|x<rsub|2>><with|font|Hiragino Kaku Gothic
ProN|，>...<with|font|Hiragino Kaku Gothic
ProN|，><math|x<rsub|n>><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|由这组数据得到新样本数据><math|y<rsub|1>><with|font|Hiragino
Kaku Gothic ProN|，><math|y<rsub|2>><with|font|Hiragino Kaku Gothic
ProN|，>...<with|font|Hiragino Kaku Gothic
ProN|，><math|y<rsub|n>><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|其中><math|y<rsub|i>=x<rsub|i>+c>
高考数学：十份试题 (#3)
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<math|<around|(|i=1,2,\<cdot\>\<cdot\>\<cdot\>,n|)>,c><with|font|Songti
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SC|为非零常数><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|则>（<space|1.2em>）
高考数学：十份试题 (#3)
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A<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|两组样本数据的样本平均数相同>
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B<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|两组样本数据的样本中位数相同>
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C<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|两组样本数据的样本标准差相同>
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D<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|两组样数据的样本极差相同>
高考数学：十份试题 (#3)
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10<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知><math|O><with|font|Songti SC|为坐标原点><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|点><math|P<rsub|1>*<around*|(|cos
\<alpha\>,sin \<alpha\>|)>><with|font|Hiragino Kaku Gothic
ProN|，><math|P<rsub|2>*<around*|(|cos \<beta\>,-sin
高考数学：十份试题 (#3)
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\<beta\>|)>><with|font|Hiragino Kaku Gothic
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ProN|，><math|P<rsub|3>*<around*|(|cos <around|(|\<alpha\>+\<beta\>|)>,sin
<around|(|\<alpha\>+\<beta\>|)>|)>><with|font|Hiragino Kaku Gothic
ProN|，><math|A*<around|(|1,0|)>><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|则>（<space|1.2em>）
高考数学：十份试题 (#3)
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><math|<around*|\||<wide|O*P<rsub|1>|\<wide-varrightarrow\>>|\|>=<around*|\||<wide|O*P<rsub|2>|\<wide-varrightarrow\>>|\|>>>|<cell|B<with|font|Hiragino
Kaku Gothic ProN|．><math|<around*|\||<wide|A*P<rsub|1>|\<wide-varrightarrow\>>|\|>=<around*|\||<wide|A*P<rsub|2>|\<wide-varrightarrow\>>|\|>>>>|<row|<cell|C<with|font|Hiragino
Kaku Gothic ProN|．><math|<wide|O*A|\<wide-varrightarrow\>>\<cdot\><wide|O*P|\<wide-varrightarrow\>><rsub|3>=<wide|O*P<rsub|1>|\<wide-varrightarrow\>>\<cdot\><wide|O*P<rsub|2>|\<wide-varrightarrow\>>>>|<cell|D<with|font|Hiragino
Kaku Gothic ProN|．><math|<wide|O*A|\<wide-varrightarrow\>>\<cdot\><wide|O*P<rsub|1>|\<wide-varrightarrow\>>=<wide|O*P<rsub|2>|\<wide-varrightarrow\>>\<cdot\><wide|O*P<rsub|3>|\<wide-varrightarrow\>>>>>>>>
高考数学：十份试题 (#3)
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\
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11<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知点><math|P><with|font|Songti SC|在圆><math|<around|(|x-5|)><rsup|2>+<around|(|y-5|)><rsup|2>=16><with|font|Songti
SC|上><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|点><math|A*<around|(|4,0|)>>、<math|B*<around|(|0,2|)>><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|则>（<space|1.2em>）
A<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|点><math|P><with|font|Songti SC|到直线><math|A*B><with|font|Songti
SC|的距离小于><math|10>
B<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|点><math|P><with|font|Songti SC|到直线><math|A*B><with|font|Songti
SC|的距离大于><math|2>
C<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|当><math|\<angle\>*P*B*A><with|font|Songti
SC|最小时><with|font|Hiragino Kaku Gothic
ProN|，><math|<around|\||P*B|\|>=3*<sqrt|2>>
D<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|当><math|\<angle\>*P*B*A><with|font|Songti
SC|最大时><with|font|Hiragino Kaku Gothic
ProN|，><math|<around|\||P*B|\|>=3*<sqrt|2>>
12<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|在正三棱柱><math|A*B*C-A<rsub|1>*B<rsub|1>*C<rsub|1>><with|font|Songti
SC|中><with|font|Hiragino Kaku Gothic ProN|，><math|A*B=A*A<rsub|1>=1><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|点><math|P><with|font|Songti
SC|满足><math|<wide|B*P|\<wide-varrightarrow\>>=\<lambda\><wide|B*C|\<wide-varrightarrow\>>+\<mu\><wide|B*B<rsub|1>|\<wide-varrightarrow\>>><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|其中><math|\<lambda\>\<in\><around|[|0,1|]>>，<math|\<mu\>\<in\><around|[|0,1|]>><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|则>（<space|1.2em>）
A<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|当><math|\<lambda\>=1><with|font|Songti SC|时><with|font|Hiragino Kaku
Gothic ProN|，><math|<big|triangleup>A*B<rsub|1>*P><with|font|Songti
SC|的周长为定值>
B<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|当><math|\<mu\>=1><with|font|Songti SC|时><with|font|Hiragino Kaku
Gothic ProN|，><with|font|Songti SC|三棱锥><math|P-A<rsub|1>*B*C><with|font|Songti
SC|的体积为定值>
C<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|当><math|\<lambda\>=<frac|1|2>><with|font|Songti
SC|时><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|有且仅有一个点><math|P><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|使得><math|A<rsub|1>*P*\<bot\>*B*P>
D<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|当><math|\<mu\>=<frac|1|2>><with|font|Songti SC|时><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|有且仅有一个点><math|P><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|使得><math|A<rsub|1>*B*\<bot\>><with|font|Songti
SC|平面><math|A*B<rsub|1>*P>
<with|font-series|bold|<with|font|Songti SC|三>、<with|font|Songti
SC|填空题>>
13<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知函数><math|f<around|(|x|)>=x<rsup|3>*<around*|(|a\<cdot\>2<rsup|x>-2<rsup|-x>|)>><with|font|Songti
SC|是偶函数><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|则><math|a=><underline|<space|2cm>>．
14<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知><math|O><with|font|Songti SC|为坐标原点><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|抛物线><math|C><with|font|Hiragino
Kaku Gothic ProN|：><math|y<rsup|2>=2*p*x>
(<math|p\<gtr\>0>)<with|font|Songti SC|的焦点为><math|F><with|font|Hiragino
Kaku Gothic ProN|，><math|P><with|font|Songti
SC|为><math|C><with|font|Songti SC|上一点><with|font|Hiragino Kaku
Gothic ProN|，><math|P*F><with|font|Songti
SC|与><math|x><with|font|Songti SC|轴垂直><with|font|Hiragino Kaku
Gothic ProN|，><math|Q><with|font|Songti SC|为><math|x><with|font|Songti
SC|轴上一点><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|且><math|P*Q*\<bot\>*O*P><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|若><math|<around|\||F*Q|\|>=6><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|则><math|C><with|font|Songti
SC|的准线方程为><underline|<space|2cm>>．
15<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|函数><math|f<around|(|x|)>=<around|\||2*x-1|\|>-2*ln
x><with|font|Songti SC|的最小值为><underline|<space|2cm>>．
<with|font-series|bold|<with|font|Songti SC|四>、<with|font|Songti
SC|双空题>>
16<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|某校学生在研究民间剪纸艺术时><with|font|Hiragino Kaku
Gothic ProN|，><with|font|Songti SC|发现剪纸时经常会沿纸的某条对称轴把纸对折><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|规格为><math|20<text|dm>\<times\>12>dm<with|font|Songti
SC|的长方形纸><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|对折>1<with|font|Songti
SC|次共可以得到><math|10<text|dm>\<times\>12>dm<with|font|Hiragino
Kaku Gothic ProN|，><math|20<text|dm>\<times\>6>dm<with|font|Songti
SC|两种规格的图形><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|它们的面积之和><math|S<rsub|1>=240<text|dm><rsup|2>><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|对折>2<with|font|Songti
SC|次共可以得到><math|5<text|dm>\<times\>12>dm<with|font|Hiragino
Kaku Gothic ProN|，><math|10<text|dm>\<times\>6>dm<with|font|Hiragino Kaku
Gothic ProN|，><math|20<text|dm>\<times\>3>dm<with|font|Songti
SC|三种规格的图形><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|它们的面积之和><math|S<rsub|2>=180<text|dm><rsup|2>><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|以此类推><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|则对折>4<with|font|Songti
SC|次共可以得到不同规格图形的种数为><underline|<space|2cm>><with|font|Hiragino
Kaku Gothic ProN|；><with|font|Songti SC|如果对折><math|n><with|font|Songti
SC|次><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|那么><math|<big|sum><rsub|k=1><rsup|n>S<rsub|k>=><underline|<space|2cm>>dm<rsup|<math|2>>.
<with|font-series|bold|<with|font|Songti SC|五>、<with|font|Songti
SC|解答题>>
17<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知数列><math|<around*|{|a<rsub|n>|}>><with|font|Songti
SC|满足><math|a<rsub|1>=1><with|font|Hiragino Kaku Gothic
ProN|，><math|a<rsub|n+1>=><choice|<tformat|<table|<row|<cell|a<rsub|n>+1,n<with|font|Songti
SC|为奇数>,>>|<row|<cell|a<rsub|n>+2,n<with|font|Songti
SC|为偶数>.>>>>>
<with|font|Hiragino Kaku Gothic ProN|（>1<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|记><math|b<rsub|n>=a<rsub|2*n>><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|写出><math|b<rsub|1>><with|font|Hiragino
Kaku Gothic ProN|，><math|b<rsub|2>><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|并求数列><math|<around*|{|b<rsub|n>|}>><with|font|Songti
SC|的通项公式><with|font|Hiragino Kaku Gothic ProN|；>
<with|font|Hiragino Kaku Gothic ProN|（>2<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|求><math|<around*|{|a<rsub|n>|}>><with|font|Songti
SC|的前>20<with|font|Songti SC|项和>.<vspace|3cm>
18<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|某学校组织>\P<with|font|Songti SC|一带一路>\Q<with|font|Songti
SC|知识竞赛><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|有><em|A><with|font|Hiragino Kaku Gothic
ProN|，><em|B><with|font|Songti SC|两类问题><with|font|Hiragino Kaku
Gothic ProN|，><with|font|Songti SC|每位参加比赛的同学先在两类问题中选择一类并从中随机抽取一个问题回答><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|若回答错误则该同学比赛结束><with|font|Hiragino
Kaku Gothic ProN|；><with|font|Songti SC|若回答正确则从另一类问题中再随机抽取一个问题回答><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|无论回答正确与否><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|该同学比赛结束>.<em|A><with|font|Songti
SC|类问题中的每个问题回答正确得>20<with|font|Songti
SC|分><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|否则得>0<with|font|Songti SC|分><with|font|Hiragino Kaku Gothic
ProN|；><em|B><with|font|Songti SC|类问题中的每个问题回答正确得>80<with|font|Songti
SC|分><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|否则得>0<with|font|Songti SC|分><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|己知小明能正确回答><em|A><with|font|Songti
SC|类问题的概率为>0.8<with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|能正确回答><em|B><with|font|Songti
SC|类问题的概率为>0.6<with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|且能正确回答问题的概率与回答次序无关>.
<with|font|Hiragino Kaku Gothic ProN|（>1<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|若小明先回答><em|A><with|font|Songti
SC|类问题><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|记><math|X><with|font|Songti SC|为小明的累计得分><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|求><math|X><with|font|Songti
SC|的分布列><with|font|Hiragino Kaku Gothic ProN|；>
<with|font|Hiragino Kaku Gothic ProN|（>2<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|为使累计得分的期望最大><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|小明应选择先回答哪类问题><with|font|Hiragino
Kaku Gothic ProN|？><with|font|Songti SC|并说明理由>.<vspace|3cm>
19<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|记><math|\<triangle\>A B C><with|font|Songti
SC|是内角><math|<math|A>，<math|B>，<math|C>><with|font|Songti
SC|的对边分别为><math|a>，<math|b>，<math|c>.<with|font|Songti
SC|已知><math|b<rsup|2>=a*c>，<with|font|Songti
SC|点><math|D><with|font|Songti SC|在边><math|A*C><with|font|Songti
SC|上>， <math|B*D*sin \<angle\>*A*B*C=a*sin C>.
<with|font|Hiragino Kaku Gothic ProN|（>1<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|证明><with|font|Hiragino Kaku Gothic
ProN|：><math|B*D=b><with|font|Hiragino Kaku Gothic ProN|；>
<with|font|Hiragino Kaku Gothic ProN|（>2<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|若><math|A*D=2*D*C><with|font|Hiragino Kaku
Gothic ProN|，><with|font|Songti SC|求><math|cos
高考数学：十份试题 (#3)
2022-05-15 15:50:23 +08:00
\<angle\>*A*B*C>.<vspace|3cm>
Upgrade to Mogan v1.1.0
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20<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|如图><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|在三棱锥><math|A-B*C*D><with|font|Songti SC|中><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|平面><math|A*B*D*\<bot\>><with|font|Songti
SC|平面><math|B*C*D><with|font|Hiragino Kaku Gothic
ProN|，><math|A*B=A*D><with|font|Hiragino Kaku Gothic
ProN|，><math|O><with|font|Songti SC|为><math|B*D><with|font|Songti
SC|的中点>.
高考数学：十份试题 (#3)
2022-05-15 15:50:23 +08:00
<center|<image|<tuple|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
Upgrade to Mogan v1.1.0
2022-08-29 19:24:27 +08:00
<with|font|Hiragino Kaku Gothic ProN|（>1<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|证明><with|font|Hiragino Kaku Gothic
ProN|：><math|O*A*\<bot\>*C*D><with|font|Hiragino Kaku Gothic ProN|；>
<with|font|Hiragino Kaku Gothic ProN|（>2<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|若><math|<big|triangleup>O*C*D><with|font|Songti
SC|是边长为>1<with|font|Songti SC|的等边三角形><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|点><math|E><with|font|Songti
SC|在棱><math|A*D><with|font|Songti SC|上><with|font|Hiragino Kaku
Gothic ProN|，><math|D*E=2*E*A><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|且二面角><math|E-B*C-D><with|font|Songti
SC|的大小为><math|45<rsup|\<circ\>>><with|font|Hiragino Kaku Gothic
ProN|，><with|font|Songti SC|求三棱锥><math|A-B*C*D><with|font|Songti
SC|的体积>.<vspace|3cm>
21<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|在平面直角坐标系><math|x*O*y><with|font|Songti
SC|中><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|已知点><math|F<rsub|1>*<around*|(|-<sqrt|17>,0|)>>、<math|F<rsub|2>*<around*|(|<sqrt|17>,0|)><with|font|Hiragino
Kaku Gothic ProN|，><around*|\||M*F<rsub|1>|\|>-<around*|\||M*F<rsub|2>|\|>=2><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|点><math|M><with|font|Songti
SC|的轨迹为><math|C>.
<with|font|Hiragino Kaku Gothic ProN|（>1<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|求><math|C><with|font|Songti
SC|的方程><with|font|Hiragino Kaku Gothic ProN|；>
<with|font|Hiragino Kaku Gothic ProN|（>2<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|设点><math|T><with|font|Songti
SC|在直线><math|x=<frac|1|2>><with|font|Songti
SC|上><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|过><math|T><with|font|Songti SC|的两条直线分别交><math|C><with|font|Songti
SC|于><math|A>、<math|B><with|font|Songti
SC|两点和><math|P><with|font|Hiragino Kaku Gothic
ProN|，><math|Q><with|font|Songti SC|两点><with|font|Hiragino Kaku
Gothic ProN|，><with|font|Songti SC|且><math|<around|\||T*A|\|>\<cdot\><around|\||T*B|\|>=<around|\||T*P|\|>\<cdot\><around|\||T*Q|\|>><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|求直线><math|A*B><with|font|Songti
SC|的斜率与直线><math|P*Q><with|font|Songti
SC|的斜率之和>.<vspace|3cm>
22<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
SC|已知函数><math|f<around|(|x|)>=x*<around*|(|1-ln x|)>>.
<with|font|Hiragino Kaku Gothic ProN|（>1<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|讨论><math|f<around|(|x|)>><with|font|Songti
SC|的单调性><with|font|Hiragino Kaku Gothic ProN|；>
<with|font|Hiragino Kaku Gothic ProN|（>2<with|font|Hiragino Kaku Gothic
ProN|）><with|font|Songti SC|设><math|a><with|font|Hiragino Kaku Gothic
ProN|，><math|b><with|font|Songti SC|为两个不相等的正数><with|font|Hiragino
Kaku Gothic ProN|，><with|font|Songti SC|且><math|b*ln a-a*ln
b=a-b><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
SC|证明><with|font|Hiragino Kaku Gothic
ProN|：><math|2\<less\><frac|1|a>+<frac|1|b>\<less\>>e.
高考数学：十份试题 (#3)
2022-05-15 15:50:23 +08:00
</body>
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