名校
解题方法
1 . 某班拟从2名男学生和1名女学生中随机选派2名学生去参加一项活动,则恰有一名女学生和一名男学生去参加活动的概率是______ .
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2024-02-27更新
|
255次组卷
|
2卷引用:江西省萍乡市2023-2024学年高一上学期期末考试数学试题
2 . 记
表示不超过x的最大整数,例如
,
.已知函数
,若函数
恰有2个零点,则实数a的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0582aa1aa68e686d214659b220d2f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a090ab1d3413d618f80e175c28d0b04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47b26eb3415753b4fcb356efc31826c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc4c82dfc61859116cecdbcf7a48531.png)
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解题方法
3 . 从某学校800名男生中随机抽取50名测量身高,被测学生身高全部介于155cm和195cm之间,将测量结果按如下方式分成八组:第一组
,第二组
,…,第八组
,下图是按上述分组方法得到的频率分布直方图的一部分,已知第六组的人数为4.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/87c19e5b-7b7a-4760-ba10-71e92f3dcf93.png?resizew=286)
(1)求第七组的频率;
(2)估计该校800名男生身高的中位数;
(3)从样本身高属于第六组和第八组的男生中随机抽取两名,若他们的身高分别为x,y,记
为事件E,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d2570a8c8d1a740a91e4b5facf9123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439f8009ecaf546e38642730be395ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea01a998ab857ec93b27e3659cb16eac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/87c19e5b-7b7a-4760-ba10-71e92f3dcf93.png?resizew=286)
(1)求第七组的频率;
(2)估计该校800名男生身高的中位数;
(3)从样本身高属于第六组和第八组的男生中随机抽取两名,若他们的身高分别为x,y,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e285efadcf684ae0c1dc99be24e4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018621a7f453480c26c99bcc9d654757.png)
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4 . 若把函数
的图象平移,可以使图象上的点
变换成点
,则函数
的图象经此平移变换后所得的图象大致形状为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db929d2a696f5143d789726e28159560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ecfca4a090b78015210871850538361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c61bf7032d0198ab25955d45ef9b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知关于x的一元二次不等式
的解集为
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12158455e91292363be593868e0a05eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba317690c72a1d29babd8c6d303b0eaa.png)
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6 . 已知函数
,若函数
与函数
的零点相同,则
的取值可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0be340e9d80b212b03debec931515cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276b142a9d9f0a87425a668dd6501f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ec08be6e5edde3502faba89bb505e0.png)
A.2 | B.![]() | C.0 | D.4 |
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解题方法
7 . 如图,
是边长为4的正方形,
平面
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/0f4ffa94-cd65-4404-8b0f-ebaac56bcefa.png?resizew=155)
(1)证明:
平面
;
(2)线段
上是否存在一点
,使得点
到平面
的距离为
?若存在,求线段
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8139d9fd5c670c91aa7dc485366dd1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba02c4ed0787d5032dcf194304a1ab0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/0f4ffa94-cd65-4404-8b0f-ebaac56bcefa.png?resizew=155)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e748de03fae345643615176b133bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
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解题方法
8 . 曲线
:
,直线
:
与
:
,下列结论错误 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32285bed39ecfeb20c074ecea537f4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0634f28147dae91b847f54ecf9b72185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2b0ac2954599b70a920377119a8cc9.png)
A.曲线![]() ![]() | B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() | D.若![]() ![]() ![]() ![]() |
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解题方法
9 . 如图,正方体
边长为1,
是线段
的中点,
是线段
上的动点,下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/963da2cd-0de0-4cc5-bee1-cc295a06f2f9.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/963da2cd-0de0-4cc5-bee1-cc295a06f2f9.png?resizew=152)
A.![]() |
B.三棱锥![]() ![]() |
C.直线![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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解题方法
10 . 如图,椭圆
:
(
)的上顶点为
,右顶点为
,离心率
,
、
是椭圆上的两个动点,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/5568a94c-36c5-4c83-98d9-a35abf4db1fd.png?resizew=93)
(1)求椭圆
的标准方程;
(2)试判断直线
与
的斜率之积是否为定值?若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc35409c8054fe18431c70e6fea0334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb898663f98b8400a897913b4d3102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8328c021c9a815bf28a443563931aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/5568a94c-36c5-4c83-98d9-a35abf4db1fd.png?resizew=93)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)试判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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