名校
解题方法
1 . 已知
中,角A,B,C所对的边分别为a,b,c,且
.
(1)证明:
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa5d5cc749d8b8bad2ef0a5b4cd271e.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65c875691cec70bedee102d280f2f31.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06880757d57f2b12384eaf8443f74b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5201fc26d013f6fb889933c0e32f5c53.png)
您最近一年使用:0次
2024-02-14更新
|
1409次组卷
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10卷引用:河南省漯河市高级中学2023-2024学年高一下学期3月月考数学试题
河南省漯河市高级中学2023-2024学年高一下学期3月月考数学试题河南省焦作市2024届高三一模数学试题河南省安阳市2024届高三第一次模拟考试数学试卷天一大联考2024届高三毕业班阶段性测试(五) 数学试题(已下线)热点3-3 正弦定理与余弦定理(8题型+满分技巧+限时检测)陕西省安康市高新中学2024届高三下学期2月月考数学(文)试题陕西省安康市高新中学2023-2024学年高三下学期2月月考理科数学试题(已下线)专题1.12平面向量及其应用-重难点突破及混淆易错规避(人教A版2019必修第二册)陕西省咸阳市武功县普集高级中学2023-2024学年高一下学期第1次月考数学试题青海省西宁市第五中学2023-2024学年高一下学期4月月考数学试题
名校
2 . 已知函数
.
(1)若
时,
,求实数
的取值范围;
(2)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c96f8ad547da747b9f9ce65bbbcbc0e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c518b02c22538e6a9427e4e1a418199e.png)
您最近一年使用:0次
2024-01-20更新
|
1071次组卷
|
6卷引用:河南省漯河市高级中学2024届高三下学期3月检测数学试题(一)
名校
3 . 已知函数
.
(1)求证:
;
(2)若
是
的两个相异零点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba20f73926fa882b592848c085f060f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93296bd064e2c6ae84bc4fe7b22f1e4b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd625540579bf15a6465a2224c9d61.png)
您最近一年使用:0次
2024-06-11更新
|
139次组卷
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2卷引用:河南省漯河市高级中学2024届高三下学期三模数学试题
名校
解题方法
4 . 如图,四棱锥
的底面
是矩形,
平面
为
的中点,
为PA上一点,且
.
平面BDQ;
(2)若二面角
为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19210d688c39eb13fdf214dc517b1556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571c3a99cf0b5225444cc5d2d586874d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb178784aa857d4d4683e650273f054.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2386b1cb84295ef95039af00cc76772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4ccef06bd7c89746239123517347c3.png)
您最近一年使用:0次
2024-06-11更新
|
158次组卷
|
2卷引用:河南省漯河市高级中学2024届高三下学期三模数学试题
名校
解题方法
5 . 对于数列
,如果存在等差数列
和等比数列
,使得
,则称数列
是“优分解”的.
(1)证明:如果
是等差数列,则
是“优分解”的.
(2)记
,证明:如果数列
是“优分解”的,则
或数列
是等比数列.
(3)设数列
的前
项和为
,如果
和
都是“优分解”的,并且
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd84622d5883097a686797889192356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33119e0b8e033e27fde4505b90a1c3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238024e8fa2058c5cbbf2f757ce9a997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e274217ecbdfeea729eaa317359e77.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15ebc127b977d405b867a151696b163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2024-06-11更新
|
929次组卷
|
5卷引用:河南省漯河市高级中学2024届高三下学期三模数学试题
名校
解题方法
6 . 已知等差数列
的前
项和为
,
且
,数列
满足
,设
.
(1)求
的通项公式,并证明:
;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df84d425e294d81cc36912dab4656af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb14da5d8ba603dbb53af344a9fd84b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e3a1d52cf4a1abcb8da0ecc01c3867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6fc93e6615bf4c1a2115d318aff007.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd24f1d24e712436bb64c950c7e11ad8.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817c2cae1c70dfe804155469ede46b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
您最近一年使用:0次
2024-04-28更新
|
674次组卷
|
3卷引用:河南省漯河市高级中学2024届高三下学期4月强化拉练一数学试题
7 . 已知数列
满足
,
(
).
(1)求数列
的通项公式;
(2)记数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b29b1bb8d43a471007538194e0d6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5737f1f9cad2471f3ca53241b25a1eb9.png)
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2024-05-21更新
|
1630次组卷
|
4卷引用:河南省漯河市高级中学2024届高三下学期5月月考数学试题
河南省漯河市高级中学2024届高三下学期5月月考数学试题福建省福州市2023-2024学年高三下学期4月末质量检测数学试卷(已下线)专题2 考前押题大猜想6-10(已下线)4.3.2等比数列的前n项和公式(2)
名校
解题方法
8 . 已知四棱柱
如图所示,底面
为平行四边形,其中点
在平面
内的投影为点
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4ba8b53e76a625f3c70b89c46fcc6d.png)
.
平面
;
(2)已知点
在线段
上(不含端点位置),且平面
与平面
的夹角的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4ba8b53e76a625f3c70b89c46fcc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e95842967bd771494cc758fa29a1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31094f1b430f65336dfc222c91d9f35.png)
您最近一年使用:0次
2024-04-05更新
|
3887次组卷
|
7卷引用:河南省漯河市高级中学2024届高三下学期4月强化拉练一数学试题
2024·全国·模拟预测
9 . 已知离心率为
的椭圆
的左、右顶点分别为
,点
为椭圆
上的动点,且
面积的最大值为
.直线
与椭圆
交于
两点,点
,直线
分别交椭圆
于
两点,过点
作直线
的垂线,垂足为
.
(1)求椭圆
的方程.
(2)记直线
的斜率为
,证明:
为定值.
(3)试问:是否存在定点
,使
为定值?若存在,求出定点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4f4499c0501fd24a9d66e3c97b9038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d52429c8324350309f77e7209a5c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eebfdc6ba3ce5f137a749650e575f12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ab82c33e6c1f8b73628fa78e6868b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a77aa6c27acfffcc601d9ca7e6d4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce89b633e5d6bcf9406e3f9208fe06d.png)
(3)试问:是否存在定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2024-04-23更新
|
778次组卷
|
7卷引用:河南省漯河市高级中学2024届高三下学期5月月考数学试题
河南省漯河市高级中学2024届高三下学期5月月考数学试题(已下线)2024年普通高等学校招生全国统一考试·押题卷数学(一)重庆市开州中学2024届高三下学期高考模拟考试(二)数学试题(已下线)情境12 结论未知的证明命题(已下线)情境10 存在性探索命题河南省信阳市浉河区信阳高级中学2024届高三下学期三模数学试题(已下线)专题13 学科素养与综合问题(解答题18)
名校
10 . 在四棱锥
中,已知
,
,
,
,
,
是线段
上的点.
底面
;
(2)是否存在点
使得
与平面
所成角的余弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251dc163e6db632d7b0ed3ce94f43aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60964e720188e325eb18c9528b1fa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd3c2e2199cd4565c05b949bc21fc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85aeab3aeaf4367b711da8cde2e8bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2899e607479d8d1c47d954ae9ebb7144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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8卷引用:河南省漯河市高级中学2024届高三下学期3月检测数学试题(一)
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