名校
解题方法
1 . 已知函数
,其中
为常数.
(1)当
时,解不等式
的解集;
(2)当
时,写出函数
的单调区间;
(3)若在
上存在
个不同的实数
,
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db58afeac1cfe83233a8887e16f59b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940adbf54e96ecb2bb2637e5f976a3b0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e946baf1316ac1f219398ecedadf6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c84367e55e896aee2b24cb90a9ba829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5341c6040416a2bc0732121a35918d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02b2a2459a73f0fdee1247ae6d3ac30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-11-17更新
|
304次组卷
|
2卷引用:广东省肇庆市第一中学2023-2024学年高一上学期学科能力竞赛数学试题
名校
解题方法
2 . 已知双曲线
的左、右焦点分别为
,
,点
在双曲线
上.
(1)求
的方程;
(2)过
作两条相互垂直的直线
和
,与
的右支分别交
,
两点和
,
两点,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813f9a2814013e2407b5b1c216159359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8ba2b1920103e0879cff3de727a90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/2a30f3a8b673cc28bd90c50cf1a35281.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-11-16更新
|
1335次组卷
|
10卷引用:广东省肇庆市第一中学2023-2024学年高二上学期学科能力竞赛数学试题
广东省肇庆市第一中学2023-2024学年高二上学期学科能力竞赛数学试题湖南省长沙市雅礼中学2023-2024学年高二上学期期中数学试题湖南省长沙市雨花区雅礼教育集团2023-2024学年高二上学期期中数学试题浙江省温州市温州中学2023-2024学年高二上学期12月月考数学试题(已下线)3.2.2 双曲线的几何性质(8大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)(已下线)第3章:圆锥曲线与方程章末重点题型复习-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)(已下线)第三章:圆锥曲线的方程章末重点题型复习-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)(已下线)第7讲:圆锥曲线的模型【练】(已下线)通关练16 双曲线13考点精练(100题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)专题26 直线与圆锥曲线的位置关系5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)
名校
3 . 已知点
,圆
.
(1)求圆
过点
的切线方程;
(2)
为圆
与
轴正半轴的交点,过点
作直线
与圆
交于两点
、
,设
、
的斜率分别为
、
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21b59d92c33a3b451d6cc13878c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f25834d8218c53cb975c2a2fe7442a.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
2023-11-14更新
|
774次组卷
|
4卷引用:广东省肇庆市第一中学2023-2024学年高二上学期学科能力竞赛数学试题
解题方法
4 . 在
中,角
、
、
所对的边分别为
、
、
,已知
.
(1)证明:
;
(2)若
,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ebfe064c4a9b8ea80be67616f42d38.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2264c134952d41fb9bcb90e6c72c83.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6beb17d468d0e90f9c08a8dbbc05541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1659bc969a9689f94a1d5a567fb29394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2023-11-09更新
|
1449次组卷
|
5卷引用:广东省汕头市潮阳区棉城中学2023-2024学年高二上学期数学竞赛试题
广东省汕头市潮阳区棉城中学2023-2024学年高二上学期数学竞赛试题广东省珠海市金砖四校2024届高三上学期11月联考数学试题浙江省宁波市2024届高三上学期高考模拟考试数学试题(已下线)专题02 解三角形大题(已下线)专题03 三角函数与解三角形
5 . 如图,直四棱柱
的底面是正方形,
,E,F分别为BC,
的中点.
(1)证明:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/12d21a85-ebae-417d-8b82-d0c5e108835b.png?resizew=137)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ae72f5e5891249caa10c43224da89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9857316a93ee2289a32a3ef3c589e9b3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349e524d28d7458b033a0759ae171c0f.png)
您最近一年使用:0次
2023-10-12更新
|
567次组卷
|
3卷引用:广东省汕头市潮阳区棉城中学2023-2024学年高二上学期数学竞赛试题
名校
解题方法
6 . 已知点
,点
和点
为椭圆
上不同的三个点.当点
,点B和点C为椭圆的顶点时,△ABC恰好是边长为2的等边三角形.
(1)求椭圆
标准方程;
(2)若
为原点,且满足
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157943bb1e22bc07255f9139ce8d18b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2023-03-30更新
|
3039次组卷
|
6卷引用:广东省肇庆市第一中学2023-2024学年高二上学期学科能力竞赛数学试题
广东省肇庆市第一中学2023-2024学年高二上学期学科能力竞赛数学试题广东省部分学校2023届高三下学期3月模拟数学试题广东省2023届高考一模数学试题专题20平面解析几何(解答题)(已下线)第84练 计算速度训练4(已下线)第7讲:圆锥曲线的模型【练】
解题方法
7 . 如图,在平面四边形
中,
为正三角形,设
的中点为
.
![](https://img.xkw.com/dksih/QBM/2023/12/29/3399731396272128/3399821954179072/STEM/97dd858fe2844991b8c68ba314f47da2.png?resizew=138)
(1)求证:
的面积为定值,并求出该值;
(2)求
的正切值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fc779c4d22f15d835b51b2277c94e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2023/12/29/3399731396272128/3399821954179072/STEM/97dd858fe2844991b8c68ba314f47da2.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2281cb6df0c3c518ce5ed19a02b57e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76bc8e50eeccced1d7f3bc52e09a7d03.png)
您最近一年使用:0次
解题方法
8 . 设实数
,函数
.
(1)若
的最小正周期是
,求
在
上的最大值与最小值;
(2)若
在
上有且仅有2个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eaa6cbe72e34aab6c31a1f651a51397.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad1dfb10a0ad4195a890223f40a2147.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d6a66a015ddd2a8076f35ed191927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
您最近一年使用:0次
2023-12-29更新
|
981次组卷
|
2卷引用:广东省佛山市顺德区2020-2021学年高一下学期竞赛数学试题
解题方法
9 . 如图,在正方体
中,
分别为棱
的中点.
的截面.(只需写出作图过程,不用证明)
(2)请求出截面分正方体上下两部分的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ae536809b1161fd4e83fdc7f42be96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548d64146122e344b7d30bf0dbedb374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba446c8c4a5f93fa23dc21acd4cb1920.png)
(2)请求出截面分正方体上下两部分的体积之比.
您最近一年使用:0次
名校
解题方法
10 . 已知四棱锥
中,底面ABCD是正方形,
平面ABCD,
,E是PB的中点.
(1)求直线BD与直线PC所成角的余弦值;
(2)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58cc09c1d62eb8850ca32dcbac40910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/25/fe8dd620-60a4-4b7d-b93e-34bb02906a10.png?resizew=169)
(1)求直线BD与直线PC所成角的余弦值;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2023-07-21更新
|
2058次组卷
|
6卷引用:广东省汕头市潮阳区棉城中学2023-2024学年高二上学期数学竞赛试题
广东省汕头市潮阳区棉城中学2023-2024学年高二上学期数学竞赛试题北京市第三十五中学2022-2023学年高二上学期期中数学试题北京市顺义区第一中学2023-2024学年高二上学期10月考试数学试题陕西省西安市田家炳中学2023-2024学年高二上学期9月月考数学试题北京市怀柔区青苗学校2023-2024学年高二上学期期中考试数学试题(已下线)专题06 用空间向量研究距离、夹角问题10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A版2019选择性必修第一册)