名校
解题方法
1 . 已知椭圆
的长轴长是短轴长的2倍,焦距是
.
(1)求椭圆C的方程;
(2)若直线l:
与椭圆C交于两个不同点D,E,以线段
为直径的圆经过原点,求实数
的值;
(3)设A,B为椭圆C的左、右顶点,
为椭圆C上除A,B外任意一点,线段
的垂直平分线分别交直线
和直线
于点P和点Q,分别过点P和Q作
轴的垂线,垂足分别为M和N,求证:线段MN的长为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆C的方程;
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67e4b79aaab10cccde470d408ec9f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设A,B为椭圆C的左、右顶点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2022-04-14更新
|
447次组卷
|
5卷引用:北京市大兴区2020-2021学年度高二上学期期末检测试卷数学试题
名校
2 . 如图为某年6月份北京空气质量指数
历史数据折线图,以下结论不正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/12/29/2883192538456064/2883452336791552/STEM/1adadeb1601e468a861298a71da8d848.png?resizew=511)
指数数值与等级水平表:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948bb5009ca5364aed257353af37e90b.png)
![](https://img.xkw.com/dksih/QBM/2021/12/29/2883192538456064/2883452336791552/STEM/1adadeb1601e468a861298a71da8d848.png?resizew=511)
指数数值与等级水平表:
指数 | 0~50 | 51~100 | 101~150 | 151~200 | 201~300 | ![]() |
等级 | 一级优 | 二级良 | 三级轻度污染 | 四级中度污染 | 五级重度污染 | 六级严重污染 |
A.6月份空气质量为优的天数为8天 |
B.6月份连续2天出现中度污染的概率为![]() |
C.6月份北京空气质量指数![]() |
D.北京6月4至7日这4天的空气质量逐渐变好 |
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2021-12-31更新
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321次组卷
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3卷引用:北京十一学校2020-2021学年高二上期末数学试题
3 . 已知抛物线
,O为坐标原点.
(1)过点O作两相互垂直的弦
,设M的横坐标为m,用m表示
的面积,并求
面积的最小值;
(2)过抛物线上一点
引圆
的两条切线
,分别交抛物线于点B,C,连接
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ad7c068b9b7c0fd764cf7746407079.png)
(1)过点O作两相互垂直的弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f65dbed884e2248ec075655c684aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
(2)过抛物线上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c99e40c95d7029c040c66fce3d23d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ecf7a6913d90c2df051d608011cc57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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4 . 已知椭圆C的标准方程是
.
(1)求椭圆C的顶点坐标;
(2)若抛物线
的焦点是椭圆C的右顶点,求抛物线
的标准方程;
(3)若双曲线
的右焦点是椭圆C的右顶点,且其离心率
,求双曲线
的渐近线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c86c0fe04600e6225c4951ce8dd6002b.png)
(1)求椭圆C的顶点坐标;
(2)若抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(3)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0276541c12707b24d2f06ea3d976cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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5 . 在某次数学考试中,整个年级的数学成绩取值只有
这n个数,这些值的频率分别为
,若年级的平均成绩记为
,则下面结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351e486570290f0433ace7d0ecf2d473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d9cf284a6d151f05fc8fe80d36c4b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d80da4a6cb5f102be334006d875a7.png)
A.![]() | B.![]() | C.![]() | D.无法判断![]() ![]() |
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名校
6 . 已知在
中,有
,则下列说法中:
①
为钝角三角形;
②
;
③
.
正确说法的序号是_______________ .(填上所有正确说法的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a3afce08e60c0307602c47dccb20e4.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/537cbf6768befe0354ee668a7a5614e7.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77a62fe16fe5bf112b20b3d120b299a.png)
正确说法的序号是
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2021-10-29更新
|
719次组卷
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4卷引用:北京市中国农业大学附属中学2020-2021学年高一下学期期末数学试题
北京市中国农业大学附属中学2020-2021学年高一下学期期末数学试题北京市第五中学2021-2022学年高一3月第一次阶段检测数学试题北京市第五中学2021-2022学年高一下学期期中考试数学试题(已下线)考点13 三角函数与三角恒等变换-2022年高考数学一轮复习小题多维练(新高考版)
7 . 已知集合
.集合
含有
个元素的子集分别记为
,
,
,
,
,其中
,
,
.当
,
时,设
,且
.定义:
;
.
(1)若
,
(i)写出满足
的一个集合
,并写出
的最大值;
(ii)求
的值;
(2)若存在唯一的
,使得
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2b3a23d2f1fec50e17559f1636fc68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df852270b85104c0bd2d0de2830ffd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640d4cb502dfb924620e30dbf7546241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf73e41a26910357acba6dd83b558af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65b7b76ec96df162672fcdf653b9e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7601dbefa6836756e3d2731b79af0126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694b52596fdfcc391b23b3894ad85ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338947df86eb08f890be799504afe309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43c0c1f79b6b55d45a56087f42b9aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07eeb1c770bde4ee79af5abfd298dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2021769c50f01848cb89311c71659b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca99f1104c0f7c014ab87496a892d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b096b7a7ab6364001a6fbc0d8b53291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba05bc733cdab0d9fbb6ebcfcef5c011.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
(i)写出满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6faa41c5bd313f84d10c09d19c4abc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c325086d711b98fc89fe38b65e1b0e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe19c7c063c09c9c3740109ff526c757.png)
(2)若存在唯一的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b99d124d29ec453459d80f079d9a442e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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8 . 数列
,
,
,
,
;
,
,
,
,
,定义数列
,
,
,
,
,
,
,
.
①设
,
,
,则数列
的所有项的和等于___________ ;
②设
,
,
,则数列
与
有___________ 个公共项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fa96cac16e6f21878dcb01a1d29729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e47de0244d73bed64914273a162011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608acdaf41e570166be4e5fa45a636c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fcc69dc28bc11b22f5c9bec9e2aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd71bc7e6668f90f259ad0b06dd60c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da64ba18b8515e6f0a9c54fe28823209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcb936b1197e44381d13b31dbfd8072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bce36f7108e3c7eb6af848a10463f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd82720241ad17c930a170e13e1a81fc.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20971e1595679f81553245a7d2f0055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138a7462e3a4a4aac4a083a8e87cab58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bce36f7108e3c7eb6af848a10463f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd82720241ad17c930a170e13e1a81fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7577e674d14cb355d912949f8e39cb31.png)
您最近一年使用:0次
9 . 已知四棱锥
的
条棱长都相等,任取其中
条棱的中点作平面,截该四棱锥所得的平面图形可能是 ______ (写出所有正确结论的序号).
①等腰三角形;②等腰梯形;③正方形;④正五边形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
①等腰三角形;②等腰梯形;③正方形;④正五边形.
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10 . 设集合
.若
中的任意三个元素均不构成等差数列,则
中的元素最多有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be04deb0bce0f0b5f61b0d1ec844a36c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-08-16更新
|
135次组卷
|
2卷引用:北京市延庆区2020-2021学年高二下学期期末考试数学试题