一、选择题:本大题共10小题,每小题5分,共50分,在每小题给出的四个选项中,只有一项是符合题目要求的
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1.
1.若集合
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfenced+open%3D%22%7B%22+close%3D%22%7D%22%3E%3Cmrow%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
(
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ei%3C%2Fmi%3E%3C%2Fmath%3E)
是虚数单位),
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfenced+open%3D%22%7B%22+close%3D%22%7D%22%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmo%3E%E2%88%A9%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
等于 ( )
-
-
3.
若双曲线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmo%3E%EF%BC%9A%3C%2Fmo%3E%3Cmfrac%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmfrac%3E%3Cmsup%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmn%3E16%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmath%3E)
的左、右焦点分别为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
点P在双曲线E上,且
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfenced+open%3D%22%7C%22+close%3D%22%7C%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmsub%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
=3,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfenced+open%3D%22%7C%22+close%3D%22%7C%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmsub%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
等于( )
A . 11
B . 9
C . 5
D . 3
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4.
为了解某社区居民的家庭年收入所年支出的关系,随机调查了该社区5户家庭,得到如下统计数据表:
收入x(万元) | 8.2 | 8.6 | 10.0 | 11.3 | 11.9 |
支出y(万元) | 6.2 | 7.5 | 8.0 | 8.5 | 9.8 |
根据上表可得回归直线方程
=
, 其中
,
,据此估计,该社区一户收入为15万元家庭年支出为( )
A . 11.4万元
B . 11.8万元
C . 12.0万元
D . 12.2万元
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5.
若变量x,y 满足约束条件
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfenced+open%3D%22%7B%22+close%3D%22%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ez%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
的最小值等于 ( )
A .
B . -2
C .
D . 2
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6.
阅读如图所示的程序框图,运行相应的程序,则输出的结果为( )
![](//tikupic.21cnjy.com/2021/07/30/b8d64386a5b8b6a41f8ce644a90a0ac4.png)
A . 2
B . 1
C . 0
D . -1
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7.
若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3El%3C%2Fmi%3E%3C%2Fmath%3E)
, m 是两条不同的直线,m 垂直于平面
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3E%CE%B1%3C%2Fmi%3E%3C%2Fmath%3E)
,则“
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3El%3C%2Fmi%3E%3Cmo%3E%E2%8A%A5%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
”是“
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3El%3C%2Fmi%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmi%3E%CE%B1%3C%2Fmi%3E%3C%2Fmath%3E)
" 的 ( )
A . 充分而不必要条件
B . 必要而不充分条件
C . 充分必要条件
D . 既不充分也不必要条件
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8.
若a,b 是函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eq%3C%2Fmi%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmi%3Eq%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
的两个不同的零点,且a,b,-2 这三个数可适当排序后成等差数列,也可适当排序后成等比数列,则p+q 的值等于( )
A . 6
B . 7
C . 8
D . 9
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9.
已知
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%E2%8A%A5%3C%2Fmo%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
=
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
=t若P 点是
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%96%B3%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
所在平面内一点,且
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
=
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmfenced+open%3D%22%7C%22+close%3D%22%7C%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmfenced%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
+
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmrow%3E%3Cmfenced+open%3D%22%7C%22+close%3D%22%7C%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmfenced%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
·
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
的最大值等于( )
A . 13
B . 15
C . 19
D . 21
-
10.
若定义在R上的函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
满足
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmfenced%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
=-1,其导函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmo%3E%27%3C%2Fmo%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
满足
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmo%3E%27%3C%2Fmo%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmath%3E)
,则下列结论中一定错误的是( )
二、填空题:本大题共5小题,每小题4分,共20分,把答案填在答题卡相应的位置
-
11.
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
的展开式中,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
的系数等于
.(用数字作答)
-
12.
若锐角
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%96%B3%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
的面积为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E10%3C%2Fmn%3E%3Cmsqrt%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsqrt%3E%3C%2Fmath%3E)
, 且AB=5,AC=8,则BC等于
。
-
13.
如图,点A的坐标(1,0),点C的坐标为(2,4),函数f(x)=
, 若在矩形ABCD内随机取一点,则此点取自阴影部分的概率等于 .
![](//tikupic.21cnjy.com/3b/14/3b14a674f63a1cf485e31031796e8840.png)
-
14.
若函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfenced+open%3D%22%7B%22+close%3D%22%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsub%3E%3Cmi+mathvariant%3D%22normal%22%3Elog%3C%2Fmi%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
(a>0且a≠1)的值域[4,+
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%9E%3C%2Fmo%3E%3C%2Fmath%3E)
),则实数a的取值范围是
。
-
15.
一个二元码是由0和1组成的数字
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmsub%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo%3E%E2%88%88%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3EN%3C%2Fmi%3E%3Cmo%3E%2A%3C%2Fmo%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
其中
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmsub%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
称为第k位码元,二元码是通信中常用的码,但在通信过程中有时会发生码元错误(即码元由0变为1,或者由1变为0)已知某中二元码
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的码元满足如下校验方程组:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfenced+open%3D%22%7B%22+close%3D%22%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E.%3C%2Fmo%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
其中运算
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3C%2Fmath%3E)
定义为:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%E2%8A%95%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E.%3C%2Fmo%3E%3C%2Fmath%3E)
现已知一个这种二元码在通信过程中仅在第k位发生码元错误后变成了1101101,那么利用上述校验方程组可判定k等于
。
三、解答题:本大题共6小题,共60分,解答应写出文字说明,证明过程或演算步骤
-
16.
某银行规定,一张银行卡若在一天内出现3次密码尝试错误,该银行卡将被锁定,小王到银行取钱时,发现自己忘记了银行卡的密码,但是可以确定该银行卡的正确密码是他常用的6个密码之一,小王决定从中不重复地随机选择1个进行尝试.若密码正确,则结束尝试;否则继续尝试,直至该银行卡被锁定.
-
-
(2)
设当天小王用该银行卡尝试密码次数为X,求X的分布列和数学期望.
-
17.
如图,在几何体ABCDE中,四边形ABCD是矩形,AB⊥平面BEC,BE⊥EC,AB=BE=EC=2,G,F分别是线段BE,DC的中点.
(Ⅰ)求证:BE//平面ADE ;
(Ⅱ)求平面AEF与平面BEC所成锐二面角的余弦值.
![](//tikupic.21cnjy.com/2021/07/30/2ec1eed3d0fee53cc42230d72b78630e_164x239.png)
-
18.
已知椭圆
(a>b>0)过点(0,
),且离心率为
。
![](//tikupic.21cnjy.com/62/e2/62e2120eb8d75d64b8132761d3c6cff6.png)
(Ⅰ)求椭圆E的方程;
(II)设直线x my 1,(m R)交椭圆E与A,B两点,判断点G(-
, 0)与以线段AB为直径的圆的位置关系,并说明理由。
-
19.
已知函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
的图像是由函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Ecos%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
的图像经如下变换得到:先将
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
图像上所有点的纵坐标伸长到原来的2倍(横坐标不变),再将所得到的图像向右平移
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmi+mathvariant%3D%22normal%22%3E%CF%80%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
个单位长度.
-
(1)
求函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
的解析式,并求其图像的对称轴方程;
-
(2)
已知关于X的方程
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmfenced%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfenced%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
在
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%5B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3E%CF%80%3C%2Fmi%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
内有两个不同的解
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3E%CE%B1%3C%2Fmi%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3E%CE%B2%3C%2Fmi%3E%3C%2Fmath%3E)
.
(1)求实数M的取值范围:
(2)证明:
。
四、选考题:每小题7分,任选两题作答,共14分
-
20.
已知
, 函数
的最小值为4.
-
(1)
求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmath%3E)
的值;
-
(2)
求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmsup%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmsup%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
的最小值.
-
21.
选修4-4:坐标系与参数方程
在平面直角坐标系xOy中,圆C的参数方程为
.在极坐标系(与平面直角坐标系xOy取相同的长度单位,且以原点O为极点,以x轴非负半轴为极轴)中,直线l的方程为![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsqrt%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsqrt%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Esin%3C%2Fmi%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3E%CE%B8%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmfrac%3E%3Cmi+mathvariant%3D%22normal%22%3E%CF%80%3C%2Fmi%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%E2%88%88%3C%2Fmo%3E%3Cmi%3ER%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmo%3E.%3C%2Fmo%3E%3C%2Fmath%3E)
-
-
-
22.
本题设有三个选考题,请考生任选2题作答.
选修4-2:矩阵与变换
已知矩阵![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfenced%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfenced%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
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(1)
求A的逆矩阵
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
;
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