四川省南充市2024届高三上学期1月高考适应性考试(一诊)数学(理)试题
来源:出卷网 日期:2024-03-08 类型:数学高考模拟 学期:高考阶段 查看:10
单项选择题:本题共12小题,每小题5分,共60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。
抛物线
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
的准线方程为( )
当
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
时,复数
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmi%3Ei%3C%2Fmi%3E%3C%2Fmath%3E)
在复平面内对应的点位于( )
A. 第一象限 B. 第二象限 C. 第三象限 D. 第四象限
已知正方形
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
的边长为1,则
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%3D%3C%2Fmo%3E%3C%2Fmath%3E)
( )
A. 0 B.
C.
D. 4 已知直线m,n和平面
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo%3E%E2%8A%82%3C%2Fmo%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmenclose+notation%3D%22updiagonalstrike%22%3E%3Cmo%3E%E2%8A%82%3C%2Fmo%3E%3C%2Fmenclose%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3C%2Fmath%3E)
, 则“
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmtext%3E%E2%88%A5%3C%2Fmtext%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmath%3E)
”是“
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmtext%3E%E2%88%A5%3C%2Fmtext%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3C%2Fmath%3E)
”的( ___ )条件
A. 充分不必要 B. 必要不充分 C. 充分必要 D. 既不充分也不必要
已知全集
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EU%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3ER%3C%2Fmi%3E%3C%2Fmath%3E)
, 集合
![](https://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%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmn%3El%3C%2Fmn%3E%3Cmn%3Eo%3C%2Fmn%3E%3Cmsub%3E%3Cmrow%3E%3Cmn%3Eg%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%7D%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](https://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%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%7D%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 则能表示A,B,U关系的图是( ___ )
某商品的地区经销商对2023年1月到5月该商品的销售情况进行了调查,得到如下统计表.发现销售量y(万件)与时间x(月)成线性相关,根据表中数据,利用最小二乘法求得y与x的回归直线方程为:
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%5E%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmath%3E)
. 则下列说法错误的是( )
时间x(月) | 1 | 2 | 3 | 4 | 5 |
销售量y(万件) | 1 | 1.6 | 2.0 | a | 3 |
A. 由回归方程可知2024年1月份该地区的销售量为6.8万件 B. 表中数据的样本中心点为
C.
D. 由表中数据可知,y和x成正相关 二项式
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
的展开式中常数项为( )
A.
B. 60 C. 210 D. ![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
已知:
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 则下列说法中错误的是( ___ )
如图,正方体
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的棱长为2,E,F分别为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的中点,则平面
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
截正方体所得的截面面积为( )
![](http://tikupic.21cnjy.com/2024/02/21/74/4d/744d73ff10a444fddb57459d015a72ec.png)
A.
B.
C. 9 D. 18 已知双曲线
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%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
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
, 左右顶点分别为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
, P为双曲线在第一象限上的一点,若
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3Ec%3C%2Fmn%3E%3Cmn%3Eo%3C%2Fmn%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 则
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%E2%8B%85%3C%2Fmo%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%3D%3C%2Fmo%3E%3C%2Fmath%3E)
( ___ )
A.
B. 2 C. 5 D. ![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmath%3E)
已知函数
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3El%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
(
![](https://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%26lt%3B%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmath%3E)
)有两个不同的零点
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
(
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
),下列关于
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的说法正确的有( ___ )个
①
②
③
④![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmath%3E)
A. 1 B. 2 C. 3 D. 4
填空题:本题共4小题,每小题5分,共20分。
满足约束条件
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ex%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%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的平面区域的面积为___.
已知圆台
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的上下底面半径分别为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3C%2Fmath%3E)
和
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3C%2Fmath%3E)
, 若存在一个球同时与该圆台的上、下底面及侧面都相切,则该圆台的体积为___.
附:圆台体积公式为:![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EV%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3E%E4%B8%8A%3C%2Fmtext%3E%3Cmtext%3E%26nbsp%3B%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3E%E4%B8%8A%3C%2Fmtext%3E%3Cmtext%3E%26nbsp%3B%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3E%E4%B8%8B%3C%2Fmtext%3E%3Cmtext%3E%26nbsp%3B%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3E%E4%B8%8B%3C%2Fmtext%3E%3Cmtext%3E%26nbsp%3B%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmi%3Eh%3C%2Fmi%3E%3C%2Fmath%3E)
如图,在
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%96%B3%3C%2Fmtext%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
中,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmath%3E)
, P为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%96%B3%3C%2Fmtext%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
内一点,且
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3C%2Fmath%3E)
, 则
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3Et%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3C%2Fmath%3E)
___.
![](http://tikupic.21cnjy.com/2024/02/21/17/51/175186489b1a152e7fe05651872ce0aa.png)
解答题:共70分.解答应写出文字说明、证明过程或演算步骤,第17~21题为必考题,每个试题考生都必须作答.第22、23题为选考题,考生根据要求作答.必考题:共60分
2023年秋季,支原体肺炎在全国各地流行,该疾病的主要感染群体为青少年和老年人,某市医院传染病科在该市各医院某段时间就医且年龄在70岁以上的老年人中随机抽查了200人的情况,并将调查结果整理如下:
| 有慢性疾病 | 没有慢性疾病 | 合计 |
未感染支原体肺炎 | 60 | 80 | 140 |
感染支原体肺炎 | 40 | 20 | 60 |
合计 | 100 | 100 | 200 |
附表:
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3EK%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmtext%3E%E2%A9%BE%3C%2Fmtext%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
| 0.15 | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 |
k | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
参考公式:
(其中
)
设函数
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ee%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
(e为自然对数的底数),函数
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
与函数
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
的图象关于直线
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
对称.
如图,椭圆
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmn%3E%EF%BC%9A%3C%2Fmn%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmath%3E)
的四个顶点为A,B,C,D,过左焦点
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
且斜率为k的直线交椭圆E于M,N两点.
![](http://tikupic.21cnjy.com/2024/02/21/ae/71/ae7166e6e0ee42b2b135db37f76ef989.png)
在直角坐标系
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmi%3EO%3C%2Fmi%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
中,直线
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的参数方程为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmn%3Ec%3C%2Fmn%3E%3Cmn%3Eo%3C%2Fmn%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmn%3Ei%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(t为参数,
![](https://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%26lt%3B%3C%2Fmo%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmtext%3E%CF%80%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
),把
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
绕坐标原点逆时针旋转
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmtext%3E%CF%80%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
得到
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
, 以坐标原点O为极点,x轴正半轴为极轴,取相同的单位长度建立极坐标系.
已知函数
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
.