名校
1 . 如图甲,在菱形
与等腰直角
中,
,
,
,现将
沿
旋转,点
旋转到点
,如图乙,若
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/ff4d58a3-3259-46de-857c-c3f8cbda9eeb.png?resizew=315)
(1)求证:
;
(2)求二面角
平面角的余弦的绝对值,并据此求出平面
在平面
上投影的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1c122603b60b6f1a1334ddb56c3fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755b2bcf7516eedb26a27ad73657216.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/ff4d58a3-3259-46de-857c-c3f8cbda9eeb.png?resizew=315)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
解题方法
2 . 我国古代数学家祖暅提出一条原理:“幂势既同,则积不容异”,即两个等高的几何体若在所有等高处的水平截面的面积相等,则这两个几何体的体积相等.利用该原理可以证明:一个底面半径和高都等于R的圆柱,挖去一个以上底面为底面,下底面圆心为顶点的圆锥后,所得的几何体的体积与一个半径为R的半球的体积相等.现有一个半径为R的球,被一个距离球心为d(
)的平面截成两部分,记两部分的体积分别为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6505c58d9042136851439f35dba0081a.png)
A.![]() | B.![]() |
C.当![]() ![]() | D.当![]() ![]() |
您最近一年使用:0次
2024-01-26更新
|
659次组卷
|
5卷引用:云南省大理州祥云县部分高中(云·上联盟五校协作体)2024届高三下学期复习摸底诊断联合测评数学试题
云南省大理州祥云县部分高中(云·上联盟五校协作体)2024届高三下学期复习摸底诊断联合测评数学试题江苏省南通市2024届高三第一次调研测试数学试题(已下线)第二章 立体几何中的计算 专题三 空间体积的计算 微点4 四面体体积公式拓展综合训练【培优版】(已下线)专题6 立体几何与数学文化【讲】河北省石家庄二中润德中学2023-2024学年高二下学期第一次月考数学试题
名校
3 . 基本不等式是高中数学的重要内容之一,我们可以应用其解决数学中的最值问题.
(1)已知
,
R,证明
;
(2)已知
,
,
,
R,证明
,并指出等号成立的条件;
(3)已知
,
,
,
,证明:
,并指出等号成立的条件.
(4)应用(2)(3)两个结论解决以下两个问题:
①已知
,证明:
;
②已知
,
,且
,求
的最小值.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1f5facca1d0db44613d7c690bc90aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267cd7062303bbe8d8a4bd8dd48fef2e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7701d084d2b153bbea08cfbf63413a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61d582437402db050313612348dfa27.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d51126fd77ba262607809563550b48f.png)
(4)应用(2)(3)两个结论解决以下两个问题:
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5acd1467c10c7ff14caca53feea7a540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d49468bf449d201b533f5f8f9e9add1.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983154ee44321cef8eb8213bd862c70d.png)
您最近一年使用:0次
2024-02-10更新
|
141次组卷
|
2卷引用:云南省昆明市官渡区第五中学2023-2024学年高一上学期期中测试数学试卷
名校
解题方法
4 . 已知二元关系
,曲线
,曲线E过点
,直线
,若Q为l上的动点,A,B为E与x轴的交点,且点A在点B的左侧,
与E的另一个交点为
与E的另一个交点为N.
(1)求a,b;
(2)求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7725c9a664d423a6f8616e014bc9ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a9b73f1e23e741d223eb5306670f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f7a37ba6d79633e03aa5377e07ef44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11449658adfc07dcf4fc0b25e7ed7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549a99a086d5ed39749fc158ed7c2ba5.png)
(1)求a,b;
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
名校
解题方法
5 . 悬链线的原理运用于悬索桥、架空电缆、双曲拱桥、拱坝等工程.通过适当建立坐标系,悬链线可为双曲余弦函数
的图象,类比三角函数的三种性质:①平方关系:①
,②和角公式:
,③导数:
定义双曲正弦函数
.
(1)直接写出
,
具有的类似①、②、③的三种性质(不需要证明);
(2)若当
时,
恒成立,求实数a的取值范围;
(3)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bb273b5a350968453b96f948fcded4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af7ca3fcd9a43d520ed650b80ef2dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089d529ef22e4f75f91a4657dedcaf37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4d4c6c322c65c32e15cf2ad012560a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2cb91e9953f005f9d72f892466b8fd2.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b8f5a1a76374ad5712b4ecafb64b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0379c458448d37a46ae0d25e65ab6258.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9957a339be7094158adb4b156a31d40.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e1e3e51b8ae3bebb72439b409ee6b96.png)
您最近一年使用:0次
2024-01-27更新
|
2030次组卷
|
7卷引用:云南省昆明市第一中学2024届高三上学期第六次考前基础强化数学试题
云南省昆明市第一中学2024届高三上学期第六次考前基础强化数学试题2024届高三新改革适应性模拟测试数学试卷一(九省联考题型)浙江省湖州市第一中学2024届高三下学期新高考数学模拟试题(已下线)压轴题函数与导数新定义题(九省联考第19题模式)练(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编江苏省常州高级中学2023-2024学年高二下学期第一次调研考试数学试题2024届山西省平遥县第二中学校高三冲刺调研押题卷数学(二)
6 . 如图:在平行四边形
的边
,
上截取
,
,使得
,连接
,点
,
是线段
上两点,且
,连接
,
.
(1)求证:
;
(2)若
,
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c581dab991aeadf06d972e47673ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a74fa1d77910529e4eda3b2d70f40a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/55e0d838-89da-4cfa-9dda-8e4e571d1bda.png?resizew=225)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c883ea424e7bc9db19d5e35a6ec63134.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760d7546f3f4f788eabf9c493fcdc867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f898fd9009607f692cddda426d179427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bcb22ca5b9cdfeebca14bdfad0b8f29.png)
您最近一年使用:0次
名校
7 . 已知
(
且
,
),
(
),
.
(1)当
有两个根时,求
的取值范围;
(2)当
时,求证:
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d76ee3b131ecd6aa1aacf7fb7b3eb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c4473159277aed64ea96c4af087954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609c5160caf691be852310f8f6970c88.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b08f5fa971bb6852cf15acd85ea3061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f66d78b2928071b238928dd87a45bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
您最近一年使用:0次
8 . 某商场拟在周末进行促销活动,为吸引消费者,特别推出“玩游戏,送礼券”的活动,游戏规则如下:该游戏进行10轮,若在10轮游戏中,参与者获胜5次就送2000元礼券,并且游戏结束:否则继续游戏,直至10轮结束.已知该游戏第一次获胜的概率是
,若上一次获胜则下一次获胜的概率也是
,若上一次失败则下一次成功的概率是
.记消费者甲第
次获胜的概率为
,数列
的前
项和
,且
的实际意义为前
次游戏中平均获胜的次数.
(1)求消费者甲第2次获胜的概率
;
(2)证明:
为等比数列;并估计要获得礼券,平均至少要玩几轮游戏才可能获奖.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0c67506bfdded2b8aeff3b60d9c788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求消费者甲第2次获胜的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ff17a82cafb5d0ee8e5dc6f4e36802.png)
您最近一年使用:0次
2023-10-13更新
|
1512次组卷
|
9卷引用:黄金卷04
(已下线)黄金卷04广东省广州市天河区2024届高三上学期普通高中毕业班综合测试(一)数学试题(已下线)山东省实验中学2024届高三第一次诊断考试数学试题变式题19-22广东省广州市第六十五中学2024届高三上学期11月月考数学试题(已下线)考点19 概率中的数列 2024届高考数学考点总动员(已下线)大招3 概率结合数列模型(已下线)专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)湖南省长郡中学2023-2024学年高二下学期寒假检测(开学考试)数学试题(已下线)专题3.5马尔科夫链模型(强化训练)-2023-2024学年高二数学下学期重难点突破及混淆易错规避(人教A版2019)
9 . 已知实数m,n满足
.令
,
,记动点
的轨迹为E.
(1)求E的方程,并说明E是什么曲线;
(2)过点
作相互垂直的两条直线
和
,
和
与E分别交于A、B和C、D,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656c9f0000b55609d0b4451d7a8bdca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/017488660cd2e871bf26ff3ec1745a59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183fedbd8ccd264784a57e1089613578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
(1)求E的方程,并说明E是什么曲线;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495021c7da1c77e6ed1d1dd30e0be7bc.png)
您最近一年使用:0次
2023-10-07更新
|
492次组卷
|
4卷引用:云南省昆明市第二十四中学2024届高三上学期月考数学试题(一)
云南省昆明市第二十四中学2024届高三上学期月考数学试题(一)河南省郑州市第四高级中学2023-2024学年高二上学期期中数学试题(已下线)考点14 直线与圆锥曲线相交问题 2024届高考数学考点总动员【练】(已下线)第三章 圆锥曲线的方程【单元提升卷】-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
10 . 设
的定义域为
,若
,都有
,则称函数
为“H函数”.
(1)若
在
上单调递增,证明
是“H函数”;
(2)已知函数
.
①证明
是
上的奇函数,并判断
是否为“H函数”(无需证明);
②解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8625151f40f341575c1a71992e485188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2bfd103090863fbcc1bd10618cff0c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0c77ba1db113cb10f711a0a42325bc.png)
①证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3ca700dbdfefffcc21eb9eb9dc22a8.png)
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