名校
解题方法
1 . 数列
中,从第二项起,每一项与其前一项的差组成的数列
称为
的一阶差数列,记为
,依此类推,
的一阶差数列称为
的二阶差数列,记为
,….如果一个数列
的p阶差数列
是等比数列,则称数列
为p阶等比数列
.
(1)已知数列
满足
,
.
(ⅰ)求
,
,
;
(ⅱ)证明:
是一阶等比数列;
(2)已知数列
为二阶等比数列,其前5项分别为
,求
及满足
为整数的所有n值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c599a8303d934678c8cae0ed864b776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c599a8303d934678c8cae0ed864b776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5452a758da0f722da03128a5eb3ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f88267cbc5e8e016b1a92bcf0fb27d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281cde49dcc279bdc6b2a99edafe19da.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3998df04d0a8ded946c3f39d545fdc7e.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f94c7bb2d2afc4196b15f6879ddf86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e9e4a01bdaa1f768225e055b6c6d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13df1f8f074ab49fc065ed0da2d5aff.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0965cc6a58c25d9ba7876da319a8cae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
2024-05-07更新
|
892次组卷
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2卷引用:北京市中国人民大学附属中学2023-2024学年高二下学期统练3数学试题
名校
解题方法
2 . 已知
.
(1)求展开式第3项的二项式系数;
(2)求
的值;
(3)求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bad5be4a5a6fd913b5ad547d813763.png)
(1)求展开式第3项的二项式系数;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d59728ea7f7ac72ffe5e508bcd17d0.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed70cf593e473e304e218637b06ec9b5.png)
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2024-03-27更新
|
938次组卷
|
6卷引用:北京市第五十五中学2023-2024学年高二下学期3月调研数学试卷
名校
3 . 设函数
,曲线
在点
处的切线斜率为1.
(1)求a的值;
(2)设函数
,求
的单调区间;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3277c191ed96a1761d30412786a3f83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(1)求a的值;
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7a75bcd70f6b1a6d02dbb92e964e1b.png)
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2024-03-10更新
|
2606次组卷
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8卷引用:北京市丰台区第二中学2023-2024学年高二下学期3月月考数学试题
北京市丰台区第二中学2023-2024学年高二下学期3月月考数学试题广东省揭阳市普宁市勤建学校2023-2024学年高二下学期第一次月考数学试题北京市平谷区2023-2024学年高三下学期质量监控(零模)数学试卷北京市平谷区2024届高三下学期质量监控(零模)数学试卷四川省仁寿实验中学2023-2024学年高二下学期4月期中考试数学试题(已下线)第8题 导数一般大题(高三二轮每日一题)(已下线)2024年高考数学全真模拟卷07(新题型地区专用)甘肃省民乐县第一中学2023-2024学年高三下学期5月第一次模拟考试数学试卷
名校
4 . 已知函数
.
(1)若曲线
在点
处的切线与直线
垂直,求
的值;
(2)讨论函数
的单调性;
(3)设
,当
时,函数
的图象在函数
的图象的下方,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a3bfbecf59825b416de300aec0f14a.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04eed461026f69fe9ab2c5dc12af8ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd10968900343aaaa158451018166fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c12b64c84b3bef41942a5a4f2409799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-01-25更新
|
855次组卷
|
3卷引用:北京市第八十中学2023-2024学年高二下学期3月阶段测评数学试题
名校
解题方法
5 . 如图,四棱锥
中,
是以
为斜边的等腰直角三角形,且面
面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/962c9964-06e6-4592-b687-2d641ac95bc2.png?resizew=202)
(1)求二面角
所成角的余弦值;
(2)设
是
的中点,判断点
是否在平面
内,并证明结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97af544ff15da3c70835cdb34079bf88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/962c9964-06e6-4592-b687-2d641ac95bc2.png?resizew=202)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9f1e2b86f4eca37c72011d3dffb0c9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
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2024-01-22更新
|
564次组卷
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2卷引用:北京市八一学校2023-2024学年高二上学期12月月考数学试卷
名校
解题方法
6 . 已知椭圆
(
)的长轴长是短轴长的2倍.
(1)求椭圆的离心率
;
(2)直线
过点
且与椭圆有唯一公共点
,
为坐标原点,当
的面积最大时,求椭圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
(1)求椭圆的离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c41b2f7ca11db3aaea46c69286adbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2023-12-20更新
|
396次组卷
|
4卷引用:北京市陈经纶中学2023-2024学年高二上学期12月月考数学试题
7 . 已知椭圆
:
的右焦点为F(1,0),短轴长为2.直线
过点F且不平行于坐标轴,
与
有两个交点A,B,线段
的中点为M.
(1)求椭圆
的方程;
(2)证明:直线
的斜率与
的斜率的乘积为定值;
(3)延长线段
与椭圆
交于点P,若四边形
为平行四边形,求此时直线
的斜率.
![](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/0f85fca60a11e1af2bf50138d0e3fe62.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)延长线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-12-08更新
|
1270次组卷
|
4卷引用:北京市第一六一中学2023-2024学年高二上学期12月阶段练习数学试题
名校
解题方法
8 . 已知椭圆
的焦点是
,
,且
,离心率为
.
(1)求椭圆C的方程;
(2)若椭圆C与直线
交于M,N两点,且
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2644e9f73e5871db934fdafc431d675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆C的方程;
(2)若椭圆C与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8662e599a613100e4e42115bee71a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-12-08更新
|
1413次组卷
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6卷引用:北京市第一六一中学2023-2024学年高二上学期12月阶段练习数学试题
北京市第一六一中学2023-2024学年高二上学期12月阶段练习数学试题上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题内蒙古通辽市科左中旗民族职专·实验高中2023-2024学年高二上学期期末数学试题(已下线)专题27 直线与椭圆的位置关系及椭圆的弦长问题、面积问题(期末大题1)2023-2024学年高二数学上学期期末题型秒杀技巧及专项练习(人教A版2019)甘肃省兰州市第五十八中学2023-2024学年高二上学期期末数学试题(已下线)高二上学期期末考点大通关真题精选100题(3)
名校
9 . 已知直线
与圆
交于
两点,点
在圆
上运动.
(1)当
时,求
;
(2)已知点
,求
的中点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844c8c7c4846a18ad97648824ab3e617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8785046420bdd426bbd7a26041ff214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cef568cfe2fc12a4dec11533ada274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2023-11-13更新
|
892次组卷
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7卷引用:北京市丰台区怡海中学2023-2024学年高二上学期12月月考数学试题
名校
10 . 已知
中,
.
(1)求
;
(2)求
;
(3)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4cf92c0b58f63c2132c798e08d51ed.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7a71b30063e929dfcb71ae1693149e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2023-10-25更新
|
479次组卷
|
9卷引用:北京市延庆区第五中学2023-2024学年高二上学期10月阶段测试数学试题
北京市延庆区第五中学2023-2024学年高二上学期10月阶段测试数学试题北京市延庆区2022-2023学年高一下学期期末数学试题内蒙古科左中旗民族职专实验高中普高2023-2024学年高三第一次月考数学(文)试题广东省深圳市福田区外国语高级中学2023-2024学年高二上学期期中数学试题天津外国语大学附属河北外国语中学2023-2024学年高一下学期第一次月考数学试题(已下线)专题04 正余弦定理4种常考题型归类-《期末真题分类汇编》(北京专用)【北京专用】专题09解三角形(第二部分)-高一下学期名校期末好题汇编新疆维吾尔自治区巴音郭楞州博湖县奇石中学2024届高三上学期期中数学试题(已下线)专题06正余弦定理期末9种常考题型归类-《期末真题分类汇编》(人教B版2019必修第四册)