名校
1 . 双曲线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5baeb1ed0d7e530b0299c289ca4a726.png)
(1)已知双曲线
的实轴长为
,渐近线方程为
.求双曲线
的标准方程;
(2)若双曲线
与直线
交于
、
两点,且
(
为原点),求证:行列式
的值为常数;
(3)可以证明:函数
的图像是由双曲线
的图像逆时针旋转
得到的.用类似的方法可以得出:函数
的图像也是双曲线.按教材对双曲线的性质的研究,请列出双曲线
的性质(不必证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5baeb1ed0d7e530b0299c289ca4a726.png)
(1)已知双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6bb019e2d7c6d17d15ec4d9043f5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0fb02846c1f030d0a4a7415a4aa788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594a6b2d1e35eb06e35887ceab681380.png)
(3)可以证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5848e50805496263d52dcbde9671a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e952a01fa0e4ab0a4f3ccc40d4ba6e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e952a01fa0e4ab0a4f3ccc40d4ba6e6b.png)
您最近一年使用:0次
名校
2 . 完成下列证明:
(Ⅰ)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5de8eb289fde19705d3ebf005cc36e8.png)
;
(Ⅱ)若
,求证:
.
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5de8eb289fde19705d3ebf005cc36e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de4ddc6ed5fc0f34fe195115a391ca4.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2f4630b66f80a5f2b7f186e49b321e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da586544943f6fb62344a58f9e645f70.png)
您最近一年使用:0次
2019-09-12更新
|
1116次组卷
|
3卷引用:江西省吉安市2018-2019学年高二下学期期末数学(理)试题
3 . 设向量
,
(
为正整数),函数
在
上的最小值与最大值的和为
.又数列
满足:
.
(1)求证:
;
(2)求
的表达式;
(3)若
,试问数列
中,是否存在正整数
,使得对于任意的正整数
,都有
成立?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4f40def777e1d7c7ced828899ed593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecd0618a94b609ba39648aee5078ad7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3001a6338718284f7d39dc9a0c9b1ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f422217788237b19729bece6bbc07687.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc193f718a5f5fa18880eedfe45b24d2.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4957e76e086cebb2ceb534b6a3dd907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f69e2573d086fa7cfbd7e4f5a162c1.png)
您最近一年使用:0次
4 . 如图所示,在四棱锥
中,四边形
是正方形,点
分别是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/684f0061-f471-44fa-b0ef-91fd3df2774a.png?resizew=140)
(1)求证:
;
(2)线段
上是否存在一点
,使得面
面
,若存在,请找出点
并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1e038b4e76b3a368731d3331522b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a003de8409231a347edebc8284be186c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85de410d85be189dfa5aabb33410b896.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/684f0061-f471-44fa-b0ef-91fd3df2774a.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4cd5cd0de37a81455262f96acaca01.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f32299ca54d8b38967931d69a218c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
您最近一年使用:0次
2019-01-26更新
|
2609次组卷
|
19卷引用:【全国百强校】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(理科)试题
【全国百强校】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(理科)试题【校级联考】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(文科)试题四川省眉山市2022-2023学年高二上学期期末教学质量检测数学(文)试题四川省眉山市2022-2023学年高二上学期期末教学质量检测理科数学试题四川省眉山市2022-2023学年高二上学期期末数学(理)试题安徽省皖北名校2020-2021学年高二上学期第一次联考数学试题安徽省合肥市肥东县第二中学2020-2021学年高二上学期第一次月考数学(理)试题四川省峨眉第二中学校2022-2023学年高二上学期10月月考文科数学试题(已下线)2.2.4 平面与平面平行的性质-2020-2021学年高一数学课时同步练(人教A版必修2)福建省厦门一中2020-2021学年高一下学期期中考数学试题湖南省郴州市嘉禾县第一中学2020-2021学年高一下学期第二次月考数学试题湖北省鄂东南三校联考2021-2022学年高一下学期阶段考试(二)数学试题安徽省芜湖市华星学校2021-2022学年高一下学期期中数学试题陕西省西安市鄠邑区2022-2023学年高一下学期期中数学试题陕西省渭南市韩城市新蕾中学2020-2021学年高一上学期第三次月考数学试题云南省红河州开远市第一中学校2022-2023学年高一下学期4月月考数学试题浙江省嘉兴八校联盟2020-2021学年高一下学期期中联考数学试题(已下线)核心考点07空间直线、平面的平行-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)江苏省无锡市江阴市三校联考2023-2024学年高一下学期4月期中数学试题
名校
5 . 用反证法证明命题①:“已知
,求证:
”时,可假设“
”;命题②:“若
,则
或
”时,可假设“
或
”.以下结论正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937559aeec06323cde8861b17024fc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be100015cff38b6dfba5080fa94d128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44dcfbe7130c760acae3703469dd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2053e1f50472a9fed67d4c84d9cb938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc335ee14fc0b1130900cb82bcb3061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d09b9fc9719ff6faf32254b9d48713.png)
A.①与②的假设都错误 | B.①与②的假设都正确 |
C.①的假设正确,②的假设错误 | D.①的假设错误,②的假设正确 |
您最近一年使用:0次
2018-07-12更新
|
760次组卷
|
9卷引用:【全国市级联考】福建省三明市2017-2018学年高二下学期期末考试数学(文)试题
【全国市级联考】福建省三明市2017-2018学年高二下学期期末考试数学(文)试题湖北省咸宁市2018-2019学年高二下学期期末数学(文)试题四川省仁寿第一中学校北校区2020-2021学年高二6月期末数学(文)试题安徽省宣城市郎溪中学2020-2021学年高二下学期第一次月考理科数学试题广西河池市九校2020-2021学年高二下学期第二次联考数学(理)试题河南省灵宝市第五高级中学2021-2022学年高二下学期第一次月考数学文科试题黑龙江省大庆实验中学2021届高三得分训练(二)数学(理)试题(已下线)考点43 直接证明与间接证明-备战2022年高考数学(理)一轮复习考点微专题(已下线)数学(上海B卷)
名校
6 . 如图,在边长为
的正方形
中,点
是
的中点,点
是
的中点,点
是
上的点,且
.将△AED,△DCF分别沿
,
折起,使
,
两点重合于
,连接
,
.
![](https://img.xkw.com/dksih/QBM/2018/7/16/1989574276603904/1989768106516480/STEM/88df25c0416e4c0fbd0694a6e48537a8.png?resizew=318)
(Ⅰ)求证:
;
(Ⅱ)试判断
与平面
的位置关系,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1df842ffd4121b27c70a8d0b1f78b173.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2018/7/16/1989574276603904/1989768106516480/STEM/88df25c0416e4c0fbd0694a6e48537a8.png?resizew=318)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6969b9971ceae406072933356189a897.png)
(Ⅱ)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc704b98f4ed2c7359a7a5b6498b5290.png)
您最近一年使用:0次
2018-07-16更新
|
689次组卷
|
3卷引用:【全国市级联考】四川省攀枝花市2017-2018学年高二下学期期末调研检测数学(理)试题
名校
解题方法
7 . 如图,在四棱锥
中,
,
,
,平面
平面
.
平面
;
(2)设
,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8ef58be8708144272538ee427fb92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7812ef34a2b02f9ce73952d5db2eee35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d1553f6806c1eee3b17b94d23f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04f300403bc4c84663b06e8534f6576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29373112b7e2448686d95d88b2d44045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dd9f16a5c7a66e62e52fd66f4449ee.png)
您最近一年使用:0次
2024-01-15更新
|
320次组卷
|
5卷引用:陕西省西安市长安区第一中学2022-2023学年高二上学期期末文科数学试题
陕西省西安市长安区第一中学2022-2023学年高二上学期期末文科数学试题四川省宜宾市翠屏区宜宾市第四中学校2022-2023学年高二下学期期末数学(文)试题(已下线)期末真题必刷易错60题(32个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)(已下线)专题8.8 空间中的线面位置关系大题专项训练【七大题型】-举一反三系列(已下线)专题08 立体几何异面直线所成角、线面角、面面角及平行和垂直的证明 -《期末真题分类汇编》(北师大版(2019))
解题方法
8 . 端午节吃粽子,用箬竹叶包裹而成的三角粽是上海地区常见的一种粽子,假设其形状是一个正四面体,如图记作正四面体A-BCD,设棱长为a.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d72a007e3c4a134956b0e3fbde5f46.png)
(2)求箬竹叶折出的二面角
的大小;
(3)用绳子捆扎三角粽,要求绳子经过正四面体的每一个面、不经过顶点,并且绳子的起点和终点重合.请设计一种捆扎三角粽的方案,使绳子长度最短(不计打结用的绳子),请在图中作出绳子捆扎的路径,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d72a007e3c4a134956b0e3fbde5f46.png)
(2)求箬竹叶折出的二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
(3)用绳子捆扎三角粽,要求绳子经过正四面体的每一个面、不经过顶点,并且绳子的起点和终点重合.请设计一种捆扎三角粽的方案,使绳子长度最短(不计打结用的绳子),请在图中作出绳子捆扎的路径,并说明理由.
您最近一年使用:0次
9 . 已知数列
的前n项和为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
(1)证明:
是等比数列,并求出
的通项公式;
(2)已知
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0e184b6489ceb9fa3e3068bf91a855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d13e4dc9e1494ace25f8f1ca08e40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
解题方法
10 . 已知函数
,
的零点分别是
与
.
(1)若
,解不等式
;
(2)已知
,
①证明:
;
②若
,
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3023e7cb9c12cd7789dd5babcbc81bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460fb23be742df604c9e3acbadb975d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97b49ac1c01655ddceb48cc71585f62.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d755a0a76e2102eb6e29db34df0903dd.png)
②若
![](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/123371927e0a2f94563eb7321039dfbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
您最近一年使用:0次