名校
1 . 对于无穷数列
,“若存在
,必有
”,则称数列
具有
性质.
(1)若数列
满足
,判断数列
是否具有
性质?是否具有
性质?
(2)对于无穷数列
,设
,求证:若数列
具有
性质,则
必为有限集;
(3)已知
是各项均为正整数的数列,且
既具有
性质,又具有
性质,是否存在正整数
,
,使得
,
,
,…,
,…成等差数列.若存在,请加以证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3cb1321c970c49c9f6a5635ac23d6a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99699ac8106034f647e4f460b3bf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa8264eb8eea3025a152318df8720b1.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e836ef3b31693dcaf25b414277e8ae8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8f894492a8126f5f133dec4cd68833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c414a10d73f453fc1109e5b2243d2369.png)
(2)对于无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926b0a2429ebf269f7e9368ac0306956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e691589e9aafddefcbb613c7030f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470297de40027847c5c73fc5d1719c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0699adb388000a87241d6b113e733cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969293569368540b9517380795cb571b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfaf6fb5cd9a53f7adc324976735b9a.png)
您最近一年使用:0次
2019-06-18更新
|
1787次组卷
|
5卷引用:专题06 数列
(已下线)专题06 数列江西省吉安市第一中学2024届高三“九省联考”考后适应性测试数学试题(一)广东省湛江市雷州市第二中学2023-2024学年高二下学期开学考试数学试题(已下线)新题型01 新高考新结构二十一大考点汇总-32019年上海市普陀区高三高考三模数学试题
名校
2 . 如图,一个几何体是由半径和高均为2的圆柱
和三棱锥
组合而成,圆柱的轴截面为
,点A,B,C在圆O的圆周上,
平面
,
,
,
.
;
(2)求平面
与平面
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4739afd7311501e948aa4e1e5c1cb17.png)
您最近一年使用:0次
2024-03-25更新
|
950次组卷
|
2卷引用:河北省正定中学2024届高三三轮复习模拟试题数学(二)
解题方法
3 . 椭圆
的离心率为
分别为椭圆的右顶点和上顶点,
为坐标原点,已知
面积为3.
(1)求椭圆
的标准方程;
(2)过点
作直线
交椭圆
于P,Q两点,过点
向
轴引垂线交MN于点B,点C为点P关于点B的对称点,求证:C,Q,M三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5894e8358f5d868a0e8547f8133b967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066ea7c8dac31105aadedad5f34d93fa.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ceec39aaaccbeaac9a4a5bdbb0f0e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
4 . 已知椭圆C:
(
),F是其右焦点,点
在椭圆上,且PF⊥x轴,O为原点.
(1)求椭圆C的方程;
(2)若M,N是椭圆C上的两点,且△OMN的面积为
,求证:直线OM与ON的斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a818c7b7f571f7173feb9b73424d5ffe.png)
(1)求椭圆C的方程;
(2)若M,N是椭圆C上的两点,且△OMN的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次
名校
解题方法
5 . 如图所示,在等腰直角
中,
,点
、
分别为
,
的中点,将
沿
翻折到
位置.
;
(2)若
,求平面DEF与平面DEC夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc0ff6ac76f024f57a606db5cda137e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3cd6a7b1a8edf3a190c4bf09fca6bcf.png)
您最近一年使用:0次
2024-06-14更新
|
142次组卷
|
2卷引用:河北省邯郸市部分示范性高中2024届高三下学期三模数学试题
6 . 对于任意给定的四个实数
,
,
,
,我们定义方阵
,方阵
对应的行列式记为
,且
,方阵
与任意方阵
的乘法运算定义如下:
,其中方阵
,且
.设
,
,
.
(1)证明:
.
(2)若方阵
,
满足
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e76d1d8e50dda4d50229a8a20c57e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc29ee719feeedfbc8c529cf11348abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e11a5b70e1e2e685d1783a4707872e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ec97af19b15cd584710a3faf30c716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f44b167b4e75af29a18637f71f3ebfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b39fcc210ec89dbc7d684a70a34542c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d17ebf9f595cdb9dab841dec703b512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a4ed514630bd37fab9765b3fb5f2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709d09c76c222f156df31a1bba5f2ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e4a35eca00ea2f4580d62515d54d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95035eeae686e910be45f08093e406c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e7d309cb178b71c6e56f5b7f610413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109b4ece615b08a89a7f69d436f448b0.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb109c49695bce8c5b5cf4fad95772.png)
(2)若方阵
![](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/2221c60bc15c59fa1b3ac74a23b57cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa9bfe3bf3e3b7265da3c49d31f1bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35536fb98d8b24cead230c8df95fd9d3.png)
您最近一年使用:0次
2024-06-13更新
|
166次组卷
|
3卷引用:2024届河北省保定市九县一中三模联考数学试题
名校
解题方法
7 . 已知数列
的首项是3,且满足
.
(1)求证:
是等比数列;
(2)求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb59c9f271200ad4757c483fc54631f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b5f4672f6f64c96601cecacbdc073c.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2024-02-14更新
|
641次组卷
|
3卷引用:河北省保定市2023-2024学年高二上学期期末调研数学试题
河北省保定市2023-2024学年高二上学期期末调研数学试题广东省佛山市南海区南海中学2023-2024学年高二下学期第一次阶段考试数学试卷(已下线)专题03等比数列及其前n项和6种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
名校
8 . 如图,在三棱台
中,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/13/c8d56a2f-4382-453b-ade3-645ecbaf736b.png?resizew=161)
(1)求证:
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744c13d7a552602487e83ad827cf8e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/13/c8d56a2f-4382-453b-ade3-645ecbaf736b.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7852669d7f32cdad2880e22aaf1d5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
您最近一年使用:0次
2024-06-12更新
|
650次组卷
|
3卷引用:河北省唐山市2024届普通高等学校招生统一考试第二次模拟演练数学试题
名校
解题方法
9 . 如图,在四棱锥
中,
平面
,四边形
是矩形,
,点
是
的中点,点
分别是线段
上的点,且
.
;
(2)求平面
与平面
夹角的余弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d709ed19bfa7843cb3b1f3a77b7f9df1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1dd85bba0144a46b824273c585de9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47891397990336f55f96bd66d367758b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d32ac3ac558207fc0e81462c7e2fdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637d4c2a9cedf650ac75ee7ec6f8033c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d4248d9672aa3436ea1d9f1e267edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e106f4233be16e98f2c1bf9f1635622.png)
您最近一年使用:0次
2024-02-11更新
|
118次组卷
|
2卷引用:河北省石家庄市赵县河北赵县中学、高邑县第一中学、无极中学2023-2024学年高二下学期4月月考考试检测数学试题
名校
10 . 如图,在四棱锥
中,底面
是菱形,
分别为
的中点,且
.
.
(2)若
,求平面
与平面
夹角的余弦值.
![](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/bd8ecf52dec6e2ddcb6853947827a0a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea77ba313fcc751481ac1ca214df3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8a1ea8fca7c80a86dbe4d85cf9707d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f523d89b2aa3d1e97628c7c670eac13a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa13ea01adb56b09930c077223a97522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbbe7f48676298f2ee0cb1901992eaf.png)
您最近一年使用:0次
2024-06-08更新
|
789次组卷
|
2卷引用:河北省保定市2024届高三下学期第二次模拟考试数学试题