名校
1 . 设函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若
,当
时,求证:
.
(3)若函数
在区间
上存在唯一零点,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ef7de45c7c920dff0762e81aaf70cf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb9374a0245ffdcb4b23bd8bd5b662a.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
您最近一年使用:0次
名校
解题方法
2 . 在学期末,为了解学生对食堂用餐满意度情况,某兴趣小组按性别采用分层抽样的方法,从全校学生中抽取容量为200的样本进行调查.被抽中的同学分别对食堂进行评分,满分为100分.调查结果显示:最低分为51分,最高分为100分.随后,兴趣小组将男、女生的评分结果按照相同的分组方式分别整理成了频数分布表和频率分布直方图,图表如下:
男生评分结果的频数分布表
为了便于研究,兴趣小组将学生对食堂的评分转换成了“满意度情况”,二者的对应关系如下:
(1)求a的值;
(2)为进一步改善食堂状况,从评分在
的男生中随机抽取3人进行座谈,记这3人中对食堂“不满意”的人数为X,求X的分布列;
(3)以调查结果的频率估计概率,从该校所有学生中随机抽取两名学生,求有且只有一人对食堂“比较满意”的概率.
男生评分结果的频数分布表
分数区间 | 频数 |
3 | |
3 | |
16 | |
38 | |
20 |
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/23/f358481a-027b-4a07-bf75-f34b40c9e65a.png?resizew=210)
为了便于研究,兴趣小组将学生对食堂的评分转换成了“满意度情况”,二者的对应关系如下:
分数 | |||||
满意度情况 | 不满意 | 一般 | 比较满意 | 满意 | 非常满意 |
(1)求a的值;
(2)为进一步改善食堂状况,从评分在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1060d57931930bf800beaeaf5e8c18e.png)
(3)以调查结果的频率估计概率,从该校所有学生中随机抽取两名学生,求有且只有一人对食堂“比较满意”的概率.
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解题方法
3 . 对于定义在
上的函数
,及区间
,记
,若
,则称
为
的“
区间对”.已知函数
给出下列四个结论:①若
和
是
的“
区间对”,则
的取值范围是
;②若
和
不是
的“
区间对”,则对任意
和
也不是
的“
区间对”;③存在实数
,使得对任意
和
都是
的“
区间对”;④对任意
,都存在实数
,使得
和
不是
的“
区间对”;其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c7469ee8a8f2794feb43d308e6740a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34827631412485924690f6ae624f9004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a51ba7093704585a09bdee86ca844b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0248166f5a50eb4fe7f8a02a2d8e397e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad956ebc88c7fa82b268e47a361392b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e58768fc0df02f60aa54d00fe063c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be381da62d4a042476aa11dbd5824e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e58768fc0df02f60aa54d00fe063c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f310064412024a4947291dc7b03ef61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574bdac28b1dcbf03f0fb903e8d0b49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22aee79f09d487b7867fefb973675cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c0d0b38c9c2222aae8d00ed437b61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d760d2028fcb9bd149c721c3fe6187b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c0d0b38c9c2222aae8d00ed437b61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)当
时,求曲线
在
处的切线方程;
(2)当
时,求
的极大值点和极小值点的个数;
(3)若对任意
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e2eb5502a6126eb88958cb2509b432.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb95a2f0119be29f08999179a1b3a74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
5 . 已知函数
给出下列四个结论:
①当
时,
的最小值为0;
②当
时,
不存在最小值;
③
零点个数为
,则函数
的值域为
;
④当
时,对任意
,
,
.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423eeca486904505933ac5748901acce.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3e0bb22d4ccc0dde74072134e1d48f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a7b7c834d06f3e28a339db94690172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a7b7c834d06f3e28a339db94690172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e565001c699e5e221ed616dd7be2bb83.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c08bc45e2e0c7554ff9079c03f5f71.png)
其中所有正确结论的序号是
您最近一年使用:0次
2023-12-13更新
|
662次组卷
|
5卷引用:北京市第一六一中学2024届高三上学期12月阶段测试数学试题
名校
解题方法
6 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdc384aa20e27b9289497e741e35554.png)
过点
,焦距为2.
(1)求椭圆E的方程;
(2)设椭圆E的右焦点为点F,右顶点为点A.过点F的直线l交椭圆E于不同的两点
,直线
与y轴分别交于点
.当
时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdc384aa20e27b9289497e741e35554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
(1)求椭圆E的方程;
(2)设椭圆E的右焦点为点F,右顶点为点A.过点F的直线l交椭圆E于不同的两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f37c4b4e3ed0694229810c951b227c6.png)
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7 . 已知函数
的定义域为
,若
在
上为增函数,则称
为“一阶比增函数”.
(1)若
是“一阶比增函数”,求实数
的取值范围;
(2)若
是“一阶比增函数”,求证:
,
,
;
(3)若
是“一阶比增函数”,且
有零点,求证:
有解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e82cc461b9607e08a8b31597f6d26df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbd41b395876a630b360b2a34acbcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1a5699410baa270f3fa8153ab346e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe66bbf8d1c5647038819e31d88015.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b244b324e93c98de88fbffa52fc103f1.png)
您最近一年使用:0次
名校
8 . 在平面直角坐标系中,到两个点
和
的距离之积等于4的轨迹记作曲线
,对于曲线
及其上一点P,有下列四个结论:
①曲线
关于x轴对称;
②曲线上有且仅有一点P,满足
;
③曲线
上所有的点的横坐标
,纵坐标
;
④
的取值范围是
.
其中,所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
②曲线上有且仅有一点P,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f30acc34f4ee1077532ae6808af2ab2.png)
③曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6580fe48f2a7406c9dedc306a680fea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd6915d4f1cf4364a681af96b603424.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979f27823cdcba516dfa885d8afe19d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8302f6fd5631625b5ce279377d30fa.png)
其中,所有正确结论的序号是
您最近一年使用:0次
2023-11-14更新
|
236次组卷
|
4卷引用:北京市西城区北京师范大学附属实验中学2023-2024学年高二上学期期中考试数学试题
北京市西城区北京师范大学附属实验中学2023-2024学年高二上学期期中考试数学试题北京市北京师范大学附属中学2023-2024学年高二上学期数学期中考试数学试题(已下线)2.5 曲线与方程(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)专题19 曲线与方程4种常见考法归类-【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)
9 . 已知椭圆
经过
,
两点.
为坐标原点,且
的面积为
,过点
且斜率为
的直线
与椭圆
有两个不同的交点
,
.且直线
,
分别与
轴交于点
,
.
(1)求椭圆
的方程;
(2)若以
为直径的圆经过坐标原点,求直线
的方程;
(3)设
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c09615735d331befd07664aa47cb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893d4e8d70ea2c716ac7b6c1777a77f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accc443b1900c02b55e0f991ce35fbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23df39598e5f9baef2b7d41fffc31afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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2023-11-13更新
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618次组卷
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3卷引用:北京市西城区2023-2024学年高二上学期期末模拟练习数学试题
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解题方法
10 . 已知椭圆
的右焦点为
,M点的坐标为
,O为坐标原点,
是等腰直角三角形.
(1)求椭圆C的方程;
(2)经过点
作直线AB交椭圆C于A,B两点,求
面积的最大值;
(3)是否存在直线l交椭圆于P,Q两点,使点F为
的垂心?若存在,求出直线l的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad29801f799532ee7dda9658c30e373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c3b743769d19231c2165ec275bab1b.png)
(1)求椭圆C的方程;
(2)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c41b2f7ca11db3aaea46c69286adbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)是否存在直线l交椭圆于P,Q两点,使点F为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1f167ece5d18225840af97b39af9e4.png)
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