planet/高考数学/2022年全国高考乙卷数学文科试题.tm

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  <doc-data|<doc-title|2022年数学全国乙卷（文科）>>

  一、单选题（本大题共12小题，共60分）

  <\enumerate-numeric>
    <item>集合<math|M=<around|{|2,4,6,8,10|}>>，<math|N=<around|{|x\|-1\<less\>x\<less\>6|}>>，则<math|M*\<cap\>*N=>

    <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|{|2,4|}>>>|<cell|B. <math|<around|{|2,4,6|}>>>|<cell|C.
    <math|<around|{|2,4,6,8|}>>>|<cell|D. <math|<around|{|2,4,6,8,10|}>>>>>>>

    <item>设<math|<around|(|1+2*i|)>*a+b=2*i>，其中<math|a>，<math|b>为实数，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>|<cwith|2|2|1|2|cell-valign|c>|<cwith|2|2|1|2|cell-halign|l>|<table|<row|<cell|A.
    <math|a=1>，<math|b=-2>>|<cell|B. <math|a=-1>，<math|b=2>>>|<row|<cell|C.
    <math|a=1>，<math|b=2>>|<cell|D. <math|a=-1>，<math|b=-2>>>>>>

    <item>已知向量<math|<wide|a|\<wide-varrightarrow\>>=<around|(|2,1|)>>，<math|<wide|b|\<wide-varrightarrow\>>=<around|(|-2,4|)>>，则<math|<around|\||<wide|a|\<wide-varrightarrow\>>-<wide|b|\<wide-varrightarrow\>>|\|>=>

    <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>>|<cell|B. <math|3>>|<cell|C. <math|4>>|<cell|D. <math|5>>>>>>

    <item>分别统计了甲、乙两位同学<math|16>周的各周课外体育运动时长(单位：h)，得如下茎叶图：

    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|png>|90pt|60pt||>

    则下列结论中错误的是

    A. 甲同学周课外体育运动时长的样本中位数为<math|7.4>

    B. 乙同学周课外体育运动时长的样本平均数大于<math|8>

    C. 甲同学周课外体育运动时长大于<math|8>的概率的估计值大于<math|0.4>

    D. 乙同学周课外体育运动时长大于<math|8>的概率的估计值大于<math|0.6>

    <item>若<math|x>，<math|y>满足约束条件<math|<around*|{|<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|1|1|cell-rborder|0ln>|<table|<row|<cell|x+y\<geq\>2,>>|<row|<cell|x+2*y\<leq\>4,>>|<row|<cell|y\<geq\>0,>>>>>|\<nobracket\>>>则<math|z=2*x-y>的最大值是

    <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>>|<cell|B. <math|4>>|<cell|C. <math|8>>|<cell|D. <math|12>>>>>>

    <item>设<math|F>为抛物线<math|C:y<rsup|2>=4*x>的焦点，点<math|A>在<math|C>上，点<math|B*<around|(|3,0|)>>，若<math|<around|\||A*F|\|>=<around|\||B*F|\|>>，则<math|<around|\||A*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|2>>|<cell|B. <math|2*<sqrt|2>>>|<cell|C. <math|3>>|<cell|D.
    <math|3*<sqrt|2>>>>>>>

    <item>执行右边的程序框图，输出的<math|n=>

    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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|3>>|<cell|B. <math|4>>|<cell|C. <math|5>>|<cell|D. <math|6>>>>>>

    <item>右图是下列四个函数中的某个函数在区间<math|<around|[|-3,3|]>>的大致图像，则该函数是

    <image|<tuple|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|png>|80pt|60pt||>

    <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|y=<frac|-x<rsup|3>+3*x|x<rsup|2>+1>>>|<cell|B.
    <math|y=<frac|x<rsup|3>-x|x<rsup|2>+1>>>|<cell|C.
    <math|y=<frac|2*x<math-up|cos>x|x<rsup|2>+1>>>|<cell|D.
    <math|y=<frac|2<math-up|sin>x|x<rsup|2>+1>>>>>>>

    <item>在正方体<math|A*B*C*D-A<rsub|1>*B<rsub|1>*C<rsub|1>*D<rsub|1>>中，<math|E>，<math|F>分别为<math|A*B>，<math|B*C>的中点，则

    <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.
    平面<math|B<rsub|1>*E*F*\<bot\>>平面<math|B*D*D<rsub|1>>>|<cell|B.
    平面<math|B<rsub|1>*E*F*\<bot\>>平面<math|A<rsub|1>*B*D>>>|<row|<cell|C.
    平面<math|B<rsub|1>*E*F//>平面<math|A<rsub|1>*A*C>>|<cell|D.
    平面<math|B<rsub|1>*E*F//>平面<math|A<rsub|1>*C<rsub|1>*D>>>>>>

    <item>已知等比数列<math|<around|{|a<rsub|n>|}>>的前<math|3>项和为<math|168>，<math|a<rsub|2>-a<rsub|5>=42>，则<math|a<rsub|6>=>

    <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|14>>|<cell|B. <math|12>>|<cell|C. <math|6>>|<cell|D. <math|3>>>>>>

    <item>函数<math|f<around|(|x|)>=<math-up|cos>x+<around|(|x+1|)><math-up|sin>x+1>在区间<math|<around|[|0,2*\<pi\>|]>>的最小值，最大值分别为

    <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|-<frac|\<pi\>|2>>，<math|<frac|\<pi\>|2>>>|<cell|B.
    <math|-<frac|3*\<pi\>|2>>，<math|<frac|\<pi\>|2>>>|<cell|C.
    <math|-<frac|\<pi\>|2>>，<math|<frac|\<pi\>|2>+2>>|<cell|D.
    <math|-<frac|3*\<pi\>|2>>，<math|<frac|\<pi\>|2>+2>>>>>>

    <item>已知球<math|O>的半径为<math|1>，四棱锥的顶点为<math|O>，底面的四个顶点均在球<math|O>的球面上，则当该四棱锥的体积最大时，其高为

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

  二、填空题（本大题共4小题，共20分）

  <\enumerate-numeric>
    <assign|item-nr|12><item>记<math|S<rsub|n>>为等差数列<math|<around|{|a<rsub|n>|}>>的前<math|n>项和.若<math|2*S<rsub|3>=3*S<rsub|2>+6>，则公差<math|d=><underline|<space|2cm>>．

    <item>从甲、乙等<math|5>名同学中随机选<math|3>名参加社区服务工作，则甲、乙都入选的概率为<underline|<space|2cm>>．

    <item>过四点<math|<around|(|0,0|)>>，<math|<around|(|4,0|)>>，<math|<around|(|-1,1|)>>，<math|<around|(|4,2|)>>中的三点的一个圆的方程为<underline|<space|2cm>>．

    <item>若<math|f<around|(|x|)>=<math-up|ln>\|a+<frac|1|1-x>\|+b>是奇函数，则<math|a=><underline|<space|2cm>>，<math|b=><underline|<space|2cm>>．
  </enumerate-numeric>

  三、解答题（本大题共7小题，共80.0分）

  \ (一) \ 必考题：共 60 分.

  <\enumerate-numeric>
    <assign|item-nr|16><item>记<math|\<bigtriangleup\>*A*B*C>的内角<math|A>，<math|B>，<math|C>的对边分别为<math|a>，<math|b>，<math|c>，已知<math|<math-up|sin>C<math-up|sin><around|(|A-B|)>=<math-up|sin>B<math-up|sin><around|(|C-A|)>>．

    (1)若<math|A=2*B>，求<math|C>:

    (2)证明：<math|2*a<rsup|2>=b<rsup|2>+c<rsup|2>>．<vspace|5cm>

    <item>如图，四面体<math|A*B*C*D>中，<math|A*D*\<bot\>*C*D>，<math|A*D=C*D>，<math|\<angle\>*A*D*B=\<angle\>*B*D*C>，<math|E>为<math|A*C>的中点．

    (1)证明：平面<math|B*E*D*\<bot\>>平面<math|A*C*D>;

    (2)设<math|A*B=B*D=2>，<math|\<angle\>*A*C*B=60<rsup|\<circ\>>>，点<math|F>在<math|B*D>上，当<math|\<bigtriangleup\>*A*F*C>的面积最小时，求<math|C*F>与平面<math|A*B*D>所成角的正弦值．

    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    <item>某地经过多年的环填治理，已将就山改造成了绿水青山.为估计一林区某种树木的总材积量，随机选取了<math|10>棵这种村木，测量每棵村的根部横截而积(心位：<math|m<rsup|2>>)和材积量<math|<around|(|m<rsup|3>|)>>，得到如下数据：

    <block*|<tformat|<table|<row|<cell|样本号<math|i>>|<cell|1>|<cell|2>|<cell|3>|<cell|4>|<cell|5>|<cell|6>|<cell|7>|<cell|8>|<cell|9>|<cell|10>|<cell|总和>>|<row|<cell|根部横截面积<math|x
    <rsub|i>>>|<cell|0.04>|<cell|0.06>|<cell|0.04>|<cell|0.08>|<cell|0.08>|<cell|0.05>|<cell|0.05>|<cell|0.07>|<cell|0.07>|<cell|0.06>|<cell|0.6>>|<row|<cell|材积量<math|y<rsub|i>>>|<cell|0.25>|<cell|0.40>|<cell|0.22>|<cell|0.54>|<cell|0.51>|<cell|0.34>|<cell|0.36>|<cell|0.46>|<cell|0.42>|<cell|0.40>|<cell|3.9>>>>>

    并计算得<math|<big|sum><rsup|10><rsub|i=1>x<rsub|i><rsup|2>=0.038>，<math|<big|sum><rsup|10><rsub|i=1>y<rsup|2><rsub|i>=1.6158>，<math|<big|sum><rsup|10><rsub|i=1>x<rsub|i>*y<rsub|i>=0.2474>．

    (1)估计该林区这种树木平均一棵的根部横截面积与平均一棵的材积量：

    (2)求该林区这种树木的根部横截面积与材积量的样本相关系数(精确到0.01);

    (3)现测量了该林区所有这种树木的根部横截面积，并得到所有这种树木的根部横截面积总和为<math|186*m<rsup|2>>.已知树木的材积量与其根部横截面积近似成正比.利用以上数据给出该林区这种树木的总材积量的估计值．

    附：相关系数<math|r=<frac|<big|sum><rsup|n><rsub|i=1><around*|(|x<rsub|i>-<wide|x|\<bar\>>|)>*<around*|(|y<rsub|i>-<wide|y|\<bar\>>|)>|<sqrt|<big|sum><rsup|n><rsub|i=1><around*|(|x<rsub|i>-<wide|x|\<bar\>>|)><rsup|2>*<big|sum><rsup|n><rsub|i=1><around*|(|y<rsub|i>-<wide|y|\<bar\>>|)><rsup|2>>>>，<math|<sqrt|1.896>\<approx\>1.377>．<vspace|5cm>

    <item>已知函数<math|f<around|(|x|)>=a*x-<frac|1|x>-<around|(|a+1|)><math-up|ln>x>.

    (1)当<math|a=0>时，求<math|f<around|(|x|)>>的最大值;

    (2)若<math|f<around|(|x|)>>恰有一个零点，求<math|a>的取值范围．<vspace|5cm>

    <item>已知椭圆<math|E>的中心为坐标原点，对称轴为<math|x>轴，<math|y>轴，且过<math|A*<around|(|0,-2|)>>，<math|B*<around|(|<frac|3|2>,-1|)>>两点

    (1)求<math|E>的方程;

    (2)设过点<math|P<around|(|1,-2|)>>的直线交<math|E>于<math|M>，<math|N>两点，过<math|M>且平行于<math|x>的直线与线段<math|A*B>交于点<math|T>，点<math|H>满足<math|<wide|M*T|\<wide-varrightarrow\>>=<wide|T*H|\<wide-varrightarrow\>>>，证明：直线<math|H*N>过定点．
  </enumerate-numeric>

  <vspace|5cm>

  (二) 选考题：共 10 分

  <\enumerate-numeric>
    <assign|item-nr|21><item>在直角坐标系<math|x*O*y>中，曲线<math|C>的方程为<math|<around*|{|<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|1|1|cell-rborder|0ln>|<table|<row|<cell|x=<sqrt|3><math-up|cos>2*t>>|<row|<cell|y=2<math-up|sin>t>>>>>|\<nobracket\>>(t>为参数<math|)>.以坐标原点为极点，

    <math|x>轴正半轴为极轴建立极坐标系，已知直线<math|l>的极坐标方程为<math|\<rho\><math-up|sin><around|(|\<theta\>+<frac|\<pi\>|3>|)>+m=0>．

    (1)写出<math|l>的直角坐标方程：

    (2)若<math|l>与<math|C>有公共点，求<math|m>的取值范围．<vspace|5cm>

    <item>已知<math|a.*b.*c>为正数，且<math|a<rsup|<frac|3|2>>+b<rsup|<frac|3|2>>+c<rsup|<frac|3|2>>=1>，证明：\ 

    <math|<around|(|1|)>*a*b*c\<leq\><frac|1|9>>;

    <math|<around|(|2|)><frac|a|b+c>+<frac|b|a+c>+<frac|c|a+b>\<leq\><frac|1|2*<sqrt|a*b*c>>>.
  </enumerate-numeric>

  <vspace|5cm>
</body>