真题
1 . 已知
是平面直角坐标系中的点集.设
是
中两点间距离的最大值,
是
表示的图形的面积,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbd4f6afbd0d32ee97a05e34948bb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
7日内更新
|
2493次组卷
|
8卷引用:2024年北京高考数学真题变式题6-10
(已下线)2024年北京高考数学真题变式题6-10专题03函数概念与基本初等函数(已下线)五年北京专题02函数概念与基本初等函数(已下线)三年北京专题02函数概念与基本初等函数(已下线)五年北京专题01集合、常用逻辑与不等式2024年北京高考数学真题专题02函数(已下线)平面解析几何-综合测试卷B卷
2 . 我国南北朝的伟大科学教祖暅于5世纪提出了著名的祖暅原理,意思就是:夹在两个平行平面之间的两个几何体,被平行于这两个平面的任意平面所截,如果截得的两个几截面的面积总相等,那么这两个几何体的体积相等.如图1,为了求半球的体积,可以构造一个底面半径和高都与半球的半径相等的圆柱,与半球放置在同一平面上,然后在圆柱内挖去一个以圆柱下底面圆心为顶点,圆柱上底面为底面的圆锥后得到一个新几何体,用任何一个平行底面的平面去截它们时,两个截面面积总相等.如图2,某个清代陶瓷容器的上、下底面为互相平行的圆面(上底面开口,下底面封闭),侧面为球面的一部分,上、下底面圆半径都为6cm,且它们的距离为24cm,则该容器的容积为______
(容器的厚度忽略不计).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d1d99afa158b4ba4fc0dae562fcc1.png)
您最近一年使用:0次
真题
3 . 设
与
是两个不同的无穷数列,且都不是常数列.记集合
,给出下列4个结论:
①若
与
均为等差数列,则M中最多有1个元素;
②若
与
均为等比数列,则M中最多有2个元素;
③若
为等差数列,
为等比数列,则M中最多有3个元素;
④若
为递增数列,
为递减数列,则M中最多有1个元素.
其中正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87d1659c66dd3286ae75a2603babbb3.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
其中正确结论的序号是
您最近一年使用:0次
4 . 设函数
,直线
是曲线
在点
处的切线.
(1)当
时,求
的单调区间.
(2)求证:
不经过点
.
(3)当
时,设点
,
,
,
为
与
轴的交点,
与
分别表示
与
的面积.是否存在点
使得
成立?若存在,这样的点
有几个?
(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417cb4681ede2fc845d8214e48b41bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0a205f3a39c7dcad9411c5d801f9a9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32832923ae26bd414843e4ca870d1c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abf9984cf7923373be05bbb2dfe41f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3998987160c168c3fc50cb2db66211f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c557708bf41b5fd4dbb8f04278e8a824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d166e13302046b25a2fa36af1e72f7a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f0f038ebe04ea9441bd5eedf069806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea05b8641371b1d221d9b4143ef3b37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e02569631057452e44347c1b8bcce37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e0d1953b7e72fac5593b4d7477b688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f07d589cd4bf0d4beb4c9f28bd2587.png)
您最近一年使用:0次
2024-06-15更新
|
2727次组卷
|
6卷引用:2024年北京高考数学真题变式题16-21
名校
解题方法
5 . 已知椭圆
的方程
,右焦点为
,且离心率为
.
(1)求椭圆
的方程;
(2)设
是椭圆
的左、右顶点,过
的直线
交
于
两点(其中
点在
轴上方),求
与
的面积之比的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25265fcbb10d34c23d98dc3c81525c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
您最近一年使用:0次
2024-05-21更新
|
511次组卷
|
9卷引用:信息必刷卷03(北京专用)
(已下线)信息必刷卷03(北京专用)(已下线)数学(全国卷文科02)(已下线)云南、广西、贵州2024届“3+3+3”高考备考诊断性联考(二)数学试题变式题16-19云南、广西、贵州2024届“3+3+3”高考备考诊断性联考(二)数学试卷云南、广西、贵州2024届“3+3+3”高考备考诊断性联考(二)数学试卷(已下线)第一套 艺体生新高考全真模拟 (二模重组卷)(已下线)第一套 艺体生新高考全真模拟 (二模重组卷1)宁夏回族自治区石嘴山市第三中学2024届高三下学期第三次模拟考试文科数学试题(已下线)模块5 三模重组卷 第1套 全真模拟卷
2024·全国·模拟预测
解题方法
6 . 中国的农历七月初七被称为“七夕节”,象征着爱情与美好.某商场为了迎接“七夕节”的到来,特推出了购物抽奖活动.如图是由一个正方形与正三角形构成的图形,在点
处各安装了一盏灯,每次只有一处的灯亮起.初始状态是点
处的灯亮起,输入程序运行次数的上限
,然后按下开始按钮,程序开始运行,下一次是与
相邻点处的其中一盏灯随机亮起,再下一次是与上一次灯亮处相邻点的其中一盏灯随机亮起.若在运行过程中,点
处的灯再次亮起,则游戏结束,否则运行
次后游戏自动结束.在程序运行过程中,若点
处的灯再次亮起,则顾客获奖.现顾客小王参与抽奖活动.
,求小王获奖的概率.
(2)若
,记游戏结束时程序运行的次数为
,求
的分布列与期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d75df9d80ce1e0b7cb50464e293864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511d1fa76a49c3a367f87d5dfbe6091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
您最近一年使用:0次
2024高三下·北京·专题练习
解题方法
7 . 设函数
,函数
.则下列说法正确的有____
①.当
时,函数
有3个零点 ②.当
时,函数
只有1个零点
③.当
时,函数
有5个零点 ④.存在实数
,使得函数
没有零点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5082bc7546d2327aeb79ed9fb0203d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541ca543427de0dafb2c1a1254f277d3.png)
①.当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
③.当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293d639e67df2da17966a567db2656e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2024高三下·北京·专题练习
解题方法
8 . 已知函数
,则下列说法正确的有_______________
①.
的单调减区间为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77eb16f9707bcfaa5230d32ac7494ddc.png)
②.若
有三个不同实数根
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c30aef5126a03682afce26e0135d0d9.png)
③.若
恒成立,则实数
的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b6a5f28db1e6005c45b1acc9c53b730.png)
④.对任意的
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
,不等式
恒成立
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c659985e45ef900e6878b66a55a92a.png)
①.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77eb16f9707bcfaa5230d32ac7494ddc.png)
②.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce90064385c4633056784c1ae375a2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c30aef5126a03682afce26e0135d0d9.png)
③.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7a54ead79841d64b18c5ea1a09ae4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b6a5f28db1e6005c45b1acc9c53b730.png)
④.对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eea38b035412ba24495d42dde3ea859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063223b5d1fc1b45ad67c449b330a064.png)
您最近一年使用:0次
9 . 已知函数
,曲线
在点
处的切线为
,记
.
(1)当
时,求切线
的方程;
(2)在(1)的条件下,求函数
的零点并证明
;
(3)当
时,直接写出函数
的零点个数.(结论不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be6b7c590b12db1b6cbe451ad18c4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd817a1014876a72ad1971548ed6f52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db57c256dac51842864d269d5cdab520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909736dad505d81be43aef91e6309bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)在(1)的条件下,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a93aef9c6c4b64df420c39ef19d1551.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe8dc8e5def7d46b88535453ae1fd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次