planet/高考数学/2022年全国新高考二卷数学试题.tm

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  <doc-data|<doc-title|2022年数学新高考2卷>>

  一、单选题（本大题共8小题，共40分）

  <\enumerate-numeric>
    <item>已知集合<math|A=<around|{|-1,1,2,4|}>>，<math|B=<around|{|x\|<around|\||x-1|\|>\<leq\>1|}>>，则<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|{|-1,2|}>>>|<cell|B. <math|<around|{|1,2|}>>>|<cell|C.
    <math|<around|{|1,4|}>>>|<cell|D. <math|<around|{|-1,4|}>>>>>>>

    <item><math|<around|(|2+2*i|)>*<around|(|1-2*i|)>=>

    <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|-2+4*i>>|<cell|B. <math|-2-4*i>>|<cell|C. <math|6+2*i>>|<cell|D.
    <math|6-2*i>>>>>>

    <item>中国的古建筑不仅是挡风遮雨的住处，更是美学和哲学的体现.
    如图是某古建筑物的剖面图，
    <math|A*A<rprime|'>>，<math|B*B<rprime|'>>，<math|C*C<rprime|'>>，<math|D*D<rprime|'>>是桁，
    <math|D*D<rsub|1>>，<math|C*C<rsub|1>>，<math|B*B<rsub|1>>，<math|A*A<rsub|1>>是脊，
    <math|O*D<rsub|1>>，<math|D*C<rsub|1>>，<math|C*B<rsub|1>>，<math|B*A<rsub|1>>是相等的步，
    相邻桁的脊步的比分别为<math|<frac|D*D<rsub|1>|O*D<rsub|1>>=0.5>，<math|<frac|C*C<rsub|1>|D*C<rsub|1>>=k<rsub|1>>，<math|<frac|B*B<rsub|1>|C*B<rsub|1>>=k<rsub|2>>，<math|<frac|A*A<rsub|1>|B*A<rsub|1>>=k<rsub|3>>，若<math|k<rsub|1>>，<math|k<rsub|2>>，<math|k<rsub|3>>是公差为<math|0.1>的等差数列，直线<math|O*A>的斜率为<math|0.725>，则<math|k<rsub|3>=>

    <image|<tuple|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
    <image|<tuple|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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|0.75>>|<cell|B. <math|0.8>>|<cell|C. <math|0.85>>|<cell|D.
    <math|0.9>>>>>>

    <item>已知向量<math|<wide|a|\<wide-varrightarrow\>>=<around|(|3,4|)>>，<math|<wide|b|\<wide-varrightarrow\>>=<around|(|1,0|)>>，<math|<wide|c|\<wide-varrightarrow\>>=<wide|a|\<wide-varrightarrow\>>+t<wide|b|\<wide-varrightarrow\>>>，若<math|\<less\><wide|a|\<wide-varrightarrow\>>,<wide|c|\<wide-varrightarrow\>>\<gtr\>=\<less\><wide|b|\<wide-varrightarrow\>>,<wide|c|\<wide-varrightarrow\>>\<gtr\>>，则实数<math|t=>

    <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|-6>>|<cell|B. <math|-5>>|<cell|C. <math|5>>|<cell|D. <math|6>>>>>>

    <item>甲乙丙丁戊<math|5>名同学站成一排参加文艺汇演，若甲不站在两端，丙和丁相邻的不同排列方式有

    <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|12>种>|<cell|B. <math|24>种>|<cell|C. <math|36>种>|<cell|D.
    <math|48>种>>>>>

    <item>若<math|<math-up|sin><around|(|\<alpha\>+\<beta\>|)>+<math-up|cos><around|(|\<alpha\>+\<beta\>|)>=2*<sqrt|2><math-up|cos><around|(|\<alpha\>+<frac|\<pi\>|4>|)><math-up|sin>\<beta\>>，则

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|2|2|1|2|cell-valign|c>|<cwith|1|-1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    <math|<math-up|tan><around|(|\<alpha\>+\<beta\>|)>=-1>>|<cell|B.
    <math|<math-up|tan><around|(|\<alpha\>+\<beta\>|)>=1>>>|<row|<cell|C.
    <math|<math-up|tan><around|(|\<alpha\>-\<beta\>|)>=-1>>|<cell|D.
    <math|<math-up|tan><around|(|\<alpha\>-\<beta\>|)>=1>>>>>>

    <item>已知正三棱台的高为<math|1>，上下底面的边长分别为<math|3*<sqrt|3>>和<math|4*<sqrt|3>>，其顶点都在同一球面上，则该球的表面积为

    <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|100*\<pi\>>>|<cell|B. <math|128*\<pi\>>>|<cell|C.
    <math|144*\<pi\>>>|<cell|D. <math|192*\<pi\>>>>>>>

    <item>若函数<math|f<around|(|x|)>>的定义域为<math|R>，且<math|f*<around|(|x+y|)>+f*<around|(|x-y|)>=f<around|(|x|)>*f<around|(|y|)>>，<math|f=1>，则<math|<big|int><rsup|22><rsub|k=1>f<around|(|k|)>=>

    <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|-3>>|<cell|B. <math|-2>>|<cell|C. <math|0>>|<cell|D. <math|1>>>>>>
  </enumerate-numeric>

  二、多选题（本大题共4小题，共20分）

  <\enumerate-numeric>
    <assign|item-nr|8><item>已知函数<math|f<around|(|x|)>=<math-up|sin><around|(|2*x+\<varphi\>|)>*<around|(|0\<less\>\<varphi\>\<less\>\<pi\>|)>>的图象关于点<math|<around|(|<frac|2*\<pi\>|3>,0|)>>对称，则

    A. <math|f<around|(|x|)>>在<math|<around|(|0,<frac|5*\<pi\>|12>|)>>单调递减

    B. <math|f<around|(|x|)>>在<math|<around|(|-<frac|\<pi\>|12>,<frac|11*\<pi\>|12>|)>>有两个极值点

    C. 直线<math|x=<frac|7*\<pi\>|6>>是曲线<math|y=f<around|(|x|)>>的一条对称轴

    D. 直线<math|y=<frac|<sqrt|3>|2>-x>是曲线<math|y=f<around|(|x|)>>的一条切线

    <item>已知<math|O>为坐标原点，过抛物线<math|C:y<rsup|2>=2*p*x*<around|(|p\<gtr\>0|)>>的焦点<math|F>的直线与<math|C>交于<math|A>，<math|B>两点，点<math|A>在第一象限，点<math|M*<around|(|p,0|)>>，若<math|<around|\||A*F|\|>=<around|\||A*M|\|>>，则

    <tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|2|2|1|2|cell-valign|c>|<cwith|1|-1|1|-1|cell-halign|l>|<table|<row|<cell|A.
    直线<math|A*B>的斜率为<math|2*<sqrt|6>>>|<cell|B.
    <math|<around|\||O*B|\|>=<around|\||O*F|\|>>>>|<row|<cell|C.
    <math|<around|\||A*B|\|>\<gtr\>4*<around|\||O*F|\|>>>|<cell|D.
    <math|\<angle\>*O*A*M+\<angle\>*O*B*M\<less\>180*\<degree\>>>>>>>

    <item>如图，四边形<math|A*B*C*D>为正方形，<math|E*D*\<bot\>>平面<math|A*B*C*D>，<math|F*B//E*D>，
    <math|A*B=E*D=2*F*B>，记三棱锥<math|E-A*B*C>，<math|E-A*C*F>，<math|F-A*B*C>的体积分别为<math|V<rsub|1>>，<math|V<rsub|2>>，<math|V<rsub|3>>，则

    <image|<tuple|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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|V<rsub|3>=2*V<rsub|2>>>|<cell|B.
    <math|V<rsub|3>=2*V<rsub|1>>>|<cell|C.
    <math|V<rsub|3>=V<rsub|1>+V<rsub|2>>>|<cell|D.
    <math|2*V<rsub|3>=3*V<rsub|1>>>>>>>

    <item>若实数<math|x>，<math|y>满足<math|x<rsup|2>+y<rsup|2>-x*y=1>，则

    <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|x+y\<leq\>1>>|<cell|B. <math|x+y\<geq\>-2>>|<cell|C.
    <math|x<rsup|2>+y<rsup|2>\<geq\>1>>|<cell|D.
    <math|x<rsup|2>+y<rsup|2>\<leq\>2>>>>>>
  </enumerate-numeric>

  三、填空题（本大题共4小题，共20分）

  <\enumerate-numeric>
    <assign|item-nr|12><item>随机变量<math|X>服从正态分布<math|N*<around|(|2,\<sigma\><rsup|2>|)>>，若<math|P*<around|(|2\<less\>x\<leq\>2.5|)>=0.36>，则<math|P*<around|(|X\<gtr\>2.5|)>=><underline|<space|2cm>>．

    <item>曲线<math|y=<math-up|ln><around|\||x|\|>>经过坐标原点的两条切线方程分别为<underline|<space|1cm>>，<underline|<space|1cm>>．

    <item>设点<math|A*<around|(|-2,3|)>>，<math|B*<around|(|0,a|)>>，直线<math|A*B>关于直线<math|y=a>的对称直线为<math|l>，已知<math|l>与圆<math|C:<around|(|x+3|)><rsup|2>+<around|(|y+2|)><rsup|2>=1>有公共点，则<math|a>的取值范围为<underline|<space|2cm>>．

    <item>已知直线<math|l>与椭圆<math|<frac|x<rsup|2>|6>+<frac|y<rsup|2>|3>=1>在第一象限交于<math|A>，<math|B>两点，<math|l>与<math|x>轴<math|y>轴分别相交于<math|M>，<math|N>两点，且<math|<around|\||M*A|\|>=<around|\||N*B|\|>>，<math|<around|\||M*N|\|>=2*<sqrt|3>>，则直线<math|l>的方程为<underline|<space|2cm>>．
  </enumerate-numeric>

  四、解答题（本大题共6小题，共70分）

  <\enumerate-numeric>
    <assign|item-nr|16><item>已知<math|<around|{|a<rsub|n>|}>>为等差数列，<math|<around|{|b<rsub|n>|}>>为公比为<math|2>的等比数列，且<math|a<rsub|2>-b<rsub|2>=a<rsub|3>-b<rsub|3>=b<rsub|4>-a<rsub|4>>．

    (1)证明：<math|a<rsub|1>=b<rsub|1>>;

    (2)求集合<math|<around|{|k\|b<rsub|k>=a<rsub|m>+a<rsub|1>,1\<leq\>m\<leq\>500|}>>中元素个数．<vspace|5cm>

    <item>记<math|\<bigtriangleup\>*A*B*C>的三个内角分别为<math|A>，<math|B>，<math|C>，其对边分别为<math|a>，<math|b>，<math|c>，分别以<math|a>，<math|b>，<math|c>为边长的三个正三角形的面积依次为<math|S<rsub|1>>，<math|S<rsub|2>>，<math|S<rsub|3>>，且<math|S<rsub|1>-S<rsub|2>+S<rsub|3>=<frac|<sqrt|3>|2>>，<math|<math-up|sin>B=<frac|1|3>>．

    (1)求<math|\<bigtriangleup\>*A*B*C>的面积;

    (2)若<math|<math-up|sin>A<math-up|sin>C=<frac|<sqrt|2>|3>>，求<math|b>．<vspace|5cm>

    <item>在某地区进行某种疾病调查，随机调查了<math|100>位这种疾病患者的年龄，得到如下样本数据频率分布直方图．

    <image|<tuple|<#89504E470D0A1A0A0000000D49484452000001B5000001040806000000AF3CAA0D000000E16943435073524742000018956360603CCD00044C0E0C0CB979254541EE4E0A1191510A0C482031B9B8800137606460F8760D4432305CD60D2C61E5C7A3161BE02C025A08A43F00B1483A98CDC802622741D81220767949410990AD036227171481D8401733F01485043903D93E40B6423A123B09899D925A9C0C64E700D9F108BFE5CF6760B0F8C2C0C03C112196348D81617B3B0383C41D8498CA420606FE5606866D9711629FFDC1FE65143B54925A510212F1D3776428482C4A044B338302342D8D81E1D3720606DE480606E10B0C0C5CD1107780016B3130A0490C2742000072D83684A31F47B3000000097048597300000EC400000EC401952B0E1B0000001974455874536F667477617265004D6963726F736F6674204F66666963657FED35710000200049444154789CECDD777C5455FEFFF1D7BD7726BD0742482021844028A117055DE908BA828D262B5264592902BAF416504445D7F25304890A2245A90A28A0204DA5F784D00221819084407A32EDFEFEC837F7CB98E877D7D50D3B7C9E8F878F879CCF9C3BE7CE4DF29E73EFB9338AAEEB3A779003070E909A9ACA134F3CF18B8FB97EFD3A797979C4C4C4FCE263EC763BB9B9B9040505FDE2635252525014853A75EAFCE6F1161414E0E6E6869B9BDB6FDE861042887FDF9C39731453550FE2E73EF9E4137EF8E1875F0DB51D3B76B079F366962F5F4E4646065F7EF925D5AA55A3B8B898F3E7CFD3B871632E5FBECCC1830779F7DD77A95EBD7AA5DB090808A05FBF7EC4C7C773EFBDF7FEA6F10E1D3A94F6EDDB336EDC380A0A0AD8B3670F414141A8AA8AA22864666672F2E449468F1E8DB7B7B7D1EFF0E1C3141515E1E9E989AEEB242626D2BD7B77323232D0340D6F6F6F745D475555BEFFFE7BFCFCFC7EF535114208017754A8DDBA758B0D1B3670EDDA350E1E3C489B366D9CEA274F9E242D2D0D5555A957AF1EC5C5C5949696D2B56B57020202D8B97327BB77EF66C4881174EBD68D91234762369B01C8CCCCE4F8F1E3F8F8F818B32A4F4F4F6AD7AECD8F3FFE888787070E87034551F8F2CB2FF1F0F060D2A449288A623CBFAEEB6CD9B285071E78001F1F1F525353B97EFD3A7DFAF401C06AB5F2F6DB6F336AD42802020230994C242626B262C50A468F1EEDB42FCB962D233030909E3D7B929999C9BBEFBE4BF7EEDD79EFBDF7888A8AA24D9B36D86C365455C56AB502E070385055F50F7BFD8510E2BFDD1D156A5F7EF925D7AE5D03E0E38F3FAE106AC9C9C9ECDAB58B871F7E98D3A74FF3C1071F00306AD428344DC366B3316AD4286AD4A8415E5E1E050505D4A851030093C984878707F5EBD7C76AB5A2691AEBD6ADE3DCB973CC9D3B172F2F2F4A4A4A5014853E7DFA50AD5AB50AE33B77EE1CEBD6ADA3478F1E00AC5FBF9EA79E7A8A3A75EAF0EDB7DF12161646CD9A35E9DEBD3BEEEEEE405910EEDFBFDF6996563E9E7BEEB98776EDDA919F9FCFDAB56B090909C16C36D3A3470F5AB76EFDFBBEB842087117B8A3DEF6BFFFFEFBC6FF2F5DBA94ECEC6CA77AB56AD568DEBC39269389C8C848468F1ECDF8F1E3F9E4934F18316204376FDEC4E170B069D32666CC98C184091328BF64181414C4850B1758BD7A35A1A1A1B8BBBB939898C8FBEFBF8FBFBF3F7FFFFBDFF1F3F3E3C2850B4C9A34097F7F7FA7591AC0AE5DBBB8E79E7B30994CE4E5E571E3C60D468C18416A6A2A43860C21232303777777A7D994AAAAD8EDF60AFBAA288AB17D93C984DD6EC76EB7A3280A858585D86C36E3BF9B376F56BA0D218410CEEE9899DA8E1D3B70381C3CF2C823DCB8710393C9C4679F7DC6F3CF3F0F407E7E3E191919A4A7A713101080A2285CBB768D949414B2B3B3F1F5F565E4C89124272753BB766DB2B3B3B970E182533075EFDE9D3FFFF9CF4445459190904083060DC8CFCF67D8B061D4A851832B57AEB066CD1A264E9C5861660570EAD429C68C1983C3E1E0D5575FC5DFDF9F63C78EF1CA2BAF3072E4481E78E001DE7AEB2DD6AC59436060209AA6B17FFF7E1C0E47856D959696B27DFB762C160B376EDCE0C2850B58AD56745DE7D8B163689A86AEEB141717337FFE7CDE7EFB6DE2E2E2FEB8032084102EE08E09B59A356BF2DD77DFB17CF9727EF8E107962E5DCAB163C78CFA962D5BB870E102616161ECDDBB97E2E262B66DDB465E5E1EC5C5C5F8F8F800F0E28B2F3275EA540202028CEB69E5C2C2C2D8B56B17D7AE5DA363C78EB46DDB96C58B17D3A04103E2E3E33974E81053A74EADF4D4637272321E1E1ED4AB570F5DD7494A4A223636969F7EFA89FCFC7C264E9C68AC848C8A8A32667A57AE5CA930E383B280F5F2F2E2830F3EA07BF7EEBCF9E69B78797961B7DB69D3A60DEDDBB707E0C68D1BF8FBFB131616F67BBEDC4208E192EE98506BD8B02150B644BEA8A808555569D9B2A551EFD7AF1F50B61863E1C2855CBA7489E1C38703F08F7FFC838C8C0C00DCDCDCA857AF1EA9A9A95476B7C289132728292961F4E8D16CDFBE9DFEFDFBD3B2654BBEF9E61BEEBBEF3E3EF8E00302030319346890715D0C60CF9E3D3469D204283B75F8C5175FA0691A63C78EE5E5975FC66C36535252829797172D5AB430FAE6E4E4B069D326A731381C0E6AD4A841CB962DD9B87123CD9A35233A3ADA18EFCF4F5F7A7878A069DABFF7020B21C45DE08EBAA656AEB2990D94CDD6FEF297BF505454848F8F0FBAAEB36DDB368A8B8B319BCDE8BA4E7E7E3E2693A9C2768E1E3D4AFFFEFD397CF8307171710C1A3488850B1772EBD62DF6EDDBC7F4E9D359BA7429FDFAF563E1C285BCFDF6DB46DFF253827

    (1)估计该地区这种疾病患者的平均年龄;(同一组数据用该区间的中点值作代表<math|)>;

    (2)估计该地区以为这种疾病患者年龄位于区间<math|<around|[|20,70|)>>的概率;

    (3)已知该地区这种疾病患者的患病率为<math|0.1%>，该地区年龄位于区间<math|<around|[|40,50|)>>的人口数占该地区总人口数的<math|16%>，从该地区选出<math|1>人，若此人的年龄位于区间<math|<around|[|40,50|)>>，求此人患这种疾病的概率<math|(>精确到<math|0.0001)>．<vspace|5cm>

    <item>如图，<math|P*O>是三棱锥<math|P-A*B*C>的高，<math|P*A=P*B>，<math|A*B*\<bot\>*A*C>，<math|E>是<math|P*B>的中点．

    (1)证明：<math|O*E//>平面<math|P*A*C>;

    (2)若<math|\<angle\>*A*B*O=\<angle\>*C*B*O=30*\<degree\>>，<math|P*O=3>，<math|P*A=5>，求二面角<math|C-A*E-B>正弦值．

    <image|<tuple|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

    <vspace|5cm>

    <item>设双曲线<math|C:<frac|x<rsup|2>|a<rsup|2>>-<frac|y<rsup|2>|b<rsup|2>>=1*<around|(|a\<gtr\>0,b\<gtr\>0|)>>的右焦点为<math|F*<around|(|2,0|)>>，渐近线方程为<math|y=<sqrt|3>*x>.

    (1)求<math|C>的方程;

    (2)经过<math|F>的直线与<math|C>的渐近线分别交于<math|A>，<math|B>两点，点<math|P*<around|(|x<rsub|1>,y<rsub|1>|)>>，<math|Q<around|(|x<rsub|2>,y<rsub|2>|)>>在<math|C>上，且<math|x<rsub|1>\<gtr\>x<rsub|2>\<gtr\>0>，<math|y<rsub|1>\<gtr\>0>.过<math|P>且斜率为<math|-<sqrt|3>>的直线与过<math|Q>且斜率为<math|<sqrt|3>>的直线交于点<math|M>，从下面三个条件①②③中选择两个条件，证明另一个条件成立：<math-up|①><math|M>在<math|A*B>上<math|;<math-up|②>P*Q//A*B;<math-up|③><around|\||A*M|\|>=<around|\||B*M|\|>>．<vspace|5cm>

    <item>已知函数<math|f<around|(|x|)>=x*e<rsup|a*x>-e<rsup|x>>．

    (1)当<math|a=1>时，讨论<math|f<around|(|x|)>>的单调性;

    (2)当<math|x\<gtr\>0>时，<math|f<around|(|x|)>\<less\>-1>，求实数<math|a>的取值范围;

    (3)设<math|n\<in\>N<rsup|\<ast\>>>，证明：<math|<frac|1|<sqrt|1<rsup|2>+1>>+<frac|1|<sqrt|2<rsup|2>+2>>+\<cdots\>+<frac|1|<sqrt|n<rsup|2>+n>>\<gtr\><math-up|ln><around|(|n+1|)>>．<vspace|5cm>
  </enumerate-numeric>
</body>