1 . 在直角坐标平面
上的一列点
简记为
若由
构成的数列
满足
其中
为方向与
轴正方向相同的单位向量,则称
为
点列.有下列说法
①
为
点列;
②若
为
点列,且点
在点
的右上方.任取其中连续三点
则
可以为锐角三角形;
③若
为
点列,正整数若
,满足
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa8c70ae987108297f3db5928a2e26d.png)
④若
为
点列,正整数若
,满足
则
.
其中,正确说法的个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c730f8788ed12d109a19f1b30fb28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23862d3f6fe4e871cc3e4cd1836213a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e64e2b95d4c62288288965cf4db053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039271f3111b0e21bc1282fcc22cf016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98e297d9913e4cf3f02e9784a88a3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cdb00326a922074494892c166aeefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23862d3f6fe4e871cc3e4cd1836213a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8f1d479672c63860821c026c7ae47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23862d3f6fe4e871cc3e4cd1836213a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d812c7378eb14cd328ca0feb6cfa8072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97750a40688f592447e36349df63e8d6.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23862d3f6fe4e871cc3e4cd1836213a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc529610992db25f9e2c718eeeb14a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1576d1aa7d0455db3ec684ed1f37448c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa8c70ae987108297f3db5928a2e26d.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23862d3f6fe4e871cc3e4cd1836213a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc529610992db25f9e2c718eeeb14a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1576d1aa7d0455db3ec684ed1f37448c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4006e8af4f30377d1621184d6f13abd7.png)
其中,正确说法的个数为
A.1 | B.2 | C.3 | D.4 |
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8-9高二下·辽宁锦州·期末
2 . 在等差数列
中,有
,其中
分别是
的前
项和,用类比推理的方法,在等比数列
中,有________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0242e98ae52be08247a7cd2bafd806d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057ff2c35d2bbe68dcb65f5786b631f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f361cfa414b52679ba2b700d809b090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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3 . (1)已知椭圆方程为,点
.
i.若关于原点对称的两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbcc503afffd7e2190ed12abeb2a86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f452b29a3b541cd3a594bba6d1da6798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ddcd7f6faa338d8ac8e983b14459e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cbbacf4c53d29e898fd0ea3ee11863.png)
ii.若关于原点对称的两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a9b60f96cfcaa4882efe55f9122cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8e11b37d7ca2b1adaee4d8039b4d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d518174b43b680ca4e67b79df8843c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445c0c682f357da974c8a08f23ee3c18.png)
(2)根据上题结论探究:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2352fd3ab9597b8256a41675bc0404bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210c3e9f39ff560a1c6e4a9242fe5195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a9e95e14ed90d4d7ce0d75530947f8.png)
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4 . “现代五项”是由现代奥林匹克之父顾拜旦先生创立的运动项目,包含射击、击剑、游泳、马术和越野跑五项运动.已知甲、乙、丙共三人参加“现代五项”.规定每一项运动的前三名得分都分别为
,
,
(
且
),选手最终得分为各项得分之和.已知甲最终得22分,乙和丙最终各得9分,且乙的马术比赛获得了第一名,则游泳比赛的第三名是
![](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/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17b39cf99251d5f357317f531acf25a.png)
A.甲 | B.乙 | C.丙 | D.乙和丙都有可能 |
您最近一年使用:0次
名校
5 . 对于
维向量
,若对任意
均有
或
,则称
为
维
向量. 对于两个
维
向量
定义
.
(1)若
, 求
的值;
(2)现有一个
维
向量序列:
若
且满足:
,求证:该序列中不存在
维
向量
.
(3) 现有一个
维
向量序列:
若
且满足:
,若存在正整数
使得
为
维
向量序列中的项,求出所有的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d5161d0f48af5d683e6437e7263a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475426b747f4fb1632ab89616983f44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca64ef9e0c3dd14e99d113dbbe973ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4988a9309359e790f4750d640a615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c267471981116d4f1efafbdb5d8a307a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5881e8018da8862a8d6ce6d8ad0961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
(2)现有一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e81fd1ebe96bd830c057f5f9c2c871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069e0779f6f4c055d2b1ae8819856aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164e87e68a2189679fd71b910611abf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deea0d65e8bba231c24029c419d8623e.png)
(3) 现有一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e81fd1ebe96bd830c057f5f9c2c871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea0a314158f7ddb302b29c03a7b4446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fb7a0db2d0ed0c3b60c989ec52da1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4d9051450515a74d33bbb0aa92be19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2017-05-04更新
|
609次组卷
|
5卷引用:北京市东城区2017届高三二模理科数学试题
北京市东城区2017届高三二模理科数学试题北京市东城区2017届高三5月综合练习(二模)数学理试题北京市东城区2017届高三5月综合练习(二模)理数试题(已下线)卷02-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(北京专用)(已下线)北京市第四中学2023~2024学年高二上学期期中考试数学试题
6 . 椭圆
和椭圆
满足椭圆
,则称这两个椭圆相似,m称为其相似比.
(1)求经过点
,且与椭圆
相似的椭圆方程;
(2)设过原点的一条射线L分别与(1)中的两个椭圆交于A、B两点(其中点A在线段OB上),求
的最大值和最小值;
(3)对于真命题“过原点的一条射线分别与相似比为2的两个椭圆
和
交于A、B两点,P为线段AB上的一点,若
,
,
成等比数列,则点P的轨迹方程为
”.请用推广或类比的方法提出类似的一个真命题,不必证明.
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/b3b73588d6cd4823a6e1c06f53147407.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/73372f3c5cfe466abc4520b26ed76dbf.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/a961d2de2ddc42e6aa4733e9a6636f56.png)
(1)求经过点
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/12788e7320994894adfe84744182992a.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/a790da9c33a44bbdb5285b8c4df042ba.png)
(2)设过原点的一条射线L分别与(1)中的两个椭圆交于A、B两点(其中点A在线段OB上),求
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/a4b91864c2734508a88f600f08b6c2dc.png)
(3)对于真命题“过原点的一条射线分别与相似比为2的两个椭圆
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/fa6874c499664391bc5222501cb07b28.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/987856df02554329adbe98554156ad34.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/ec42272bc6a74c68ac2e96223724377e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/074ca952fc974848b27e53a92d30ab8c.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/762442ca1bb74216bc321bf5891e5337.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572679131873280/1572679137910784/STEM/5e1ab4aeac03426a9feb1ad2532862c3.png)
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7 . 设点C在线段AB上(端点除外),若C分AB的比
,则得分点C的坐标公式
,对于函数
图像上任意两点
,
,线段AB必在弧线AB上方.由图象中的点C在点C′(点C′在函数y=x2图像上)正上方,有不等式
成立.对于函数
的图象上任意两点
,
,类比上述不等式可以得到的不等式是(正确的)_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb03c91ca1c1c21d2e05c10d1fa49ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06a5be9fb7373a61a069ef3ef273745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aff7c364fc3f38b604188fbfa454372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad3fe9cb465aad3ae07973aa3965e06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ad572eb25682267ca6f62f04c37fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f291843464c84768914bc95d5d4ec8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926313a88e506ac53561de6681f10ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1542c68be243615165b7f9411a555d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/11/6848ef24-62b7-4d47-8706-17e16b8324ff.png?resizew=288)
您最近一年使用:0次
8 . 如图所示是一个有
层
的六边形点阵,它的中心是一个点,算作第1层,第2层每边有2个点,第3层每边有3个点,…,第
层每边有
个点,则这个点阵共有_________ 个点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4232c633dc8ee1dfecee64c5917045a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/2018/5/3/1937478189146112/1938614139789312/STEM/6f0612f5995642b8b3fac54675074279.png?resizew=133)
您最近一年使用:0次
2018-05-05更新
|
639次组卷
|
4卷引用:2010年广东湛江市第二中学高二下学期期末考试数学卷
(已下线)2010年广东湛江市第二中学高二下学期期末考试数学卷【全国百强校】安徽省屯溪第一中学2017-2018学年高二下学期期中考试数学(文)试题宁夏六盘山高级中学2019-2020学年高二上学期期中考试数学(文)试题新疆皮山县高级中学2019-2020学年高二下学期期末考试数学(理)试题
9 . 当
时,有如下表达式:
两边同时积分得:
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826633728/STEM/4dd0dbc86a734c078f63f9b2e038c037.png?resizew=309)
从而得到如下等式:
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826633728/STEM/628391d6099a4522a465b95c20d50791.png?resizew=329)
请根据以上材料所蕴含的数学思想方法,计算:
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826633728/STEM/f0fa8ffff2e0482b8b120d084ad0ff76.png?resizew=344)
___________
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826633728/STEM/f471a4e6b4a84f8d97248b471a69075a.png?resizew=71)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826633728/STEM/3a4633d7e6b6493fa11882028c19602f.png?resizew=177)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826633728/STEM/4dd0dbc86a734c078f63f9b2e038c037.png?resizew=309)
从而得到如下等式:
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826633728/STEM/628391d6099a4522a465b95c20d50791.png?resizew=329)
请根据以上材料所蕴含的数学思想方法,计算:
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826633728/STEM/f0fa8ffff2e0482b8b120d084ad0ff76.png?resizew=344)
您最近一年使用:0次
10-11高三上·浙江绍兴·阶段练习
名校
10 . 计算
,可以采用以下方法:
构造等式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9b00bba9b11fba5a137412e9886f2d.png)
,两边对x求导,
得
,
在上式中令
,得
.类比上述计算方法,计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a705beb8c304f43ace696f2a7aa814.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11c07e61cdd45d468ae7dc896b9728ce.png)
构造等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9b00bba9b11fba5a137412e9886f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7addd583c589844f72ab47d68001d1d4.png)
得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d83287631ccdf6099a87830ae559e43.png)
在上式中令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2642d6aca84e463b2d2d5dc71e5f351c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a705beb8c304f43ace696f2a7aa814.png)
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2016-11-30更新
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