名校
1 . 若
,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0317d5211e6afbf1ae502088b3ce1cf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e0c3af84eafcb39a83b492f8d18230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8ff8d7850a95a592a3a4f20197ccd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4080c30a53fc86de61f349ca766510.png)
A.![]() | B.![]() | C.![]() | D.1 |
您最近一年使用:0次
2024-04-08更新
|
1159次组卷
|
3卷引用:天津市第四十七中学2023-2024学年高二下学期第二次阶段性检测(6月)数学试题
解题方法
2 . 设数列
、
的前n项和分别为
、
,若
,
,
,则下列4个结论中,正确结论的个数是______ 个.
①
;
②
;
③无论实数m取何值,直线
恒过定点
;
④椭圆
的两个焦点分别为点
、
,点P为椭圆上的任意一点,则
的周长与
的值相同.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe98dae6e275a3b14a20ee5cabc77165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3a8343b8b6ff765681e7b93e6c28f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a70e556387e31472b493faa331f0ce.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8569915a8c010b9ee6ace39ca9fc925a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9dd66e01a5b86179f63085fa2da761.png)
③无论实数m取何值,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8327e623be36ea9b1831530e36398d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b10c99659501287b44db33253e3ddcc.png)
④椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd56e68f760f146bb4de048a58357df.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0fcf02ab751cc3910a0bc0872ac2a7.png)
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解题方法
3 . “数学在晚旁,月也在晚旁.”是时候为《晚旁》写一句诗、做一枚徽标了.“晩旁”徽标是借两个圆设计而成,其状如月(如图1).已知
,其中
.如图
为圆
与
的交点,若弦
将圆
分为长度之比为
的两段弧,则组成“月亮”的两段弧长之比为__________ .(请写出长度较小的弧与长度较长的弧的长度之比,即该比值小于1.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109a4a3c69477302a8dd701a2b408662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4689e7492d26d4f77a0c74d4444550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d65e051e943ab28fa57aee2fb57994.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/bfce779f-2379-4245-9f8f-528b91428588.png?resizew=267)
您最近一年使用:0次
2023-12-03更新
|
380次组卷
|
3卷引用:天津市南开中学2023-2024学年高二上学期第二次学情调查数学试卷
名校
4 . 下面命题中正确的有__________ .
①直线
的斜率为
;
②直线
与
垂直的充要条件是斜率满足
;
③截距相等的直线都可以用方程
表示;
④
若
,则四点P,A,B,C必共面;
⑤
为直角三角形的充要条件是
;
⑥若
为空间的一个基底,则
,
,
构成空间的另一基底;
⑦在空间中,直线
的方向向量
,平面
的一个法向量
,若
,则
.
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b6e44dd054b54f89e7c237eb1428da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f7cb8e59593788135eeb7db4aaa5d4.png)
②直线
![](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/8d4cc51d393a94365f7008de5eae8879.png)
③截距相等的直线都可以用方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/087af7a99d3e752994c8081970f5050d.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02afb6613b182e45f56cd05e5fe838c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457721171986ec01cca634ae94f04a6f.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a2d2b2b666b03344637a73e05f5226.png)
⑥若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5401d7f4a297c8b097e74bdebaaa8570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed492f7b29166ba5c1f0023b05a439c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e3921e92ab4a807bfb6e793240d879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf598b46aeef4c44c259a101a9e29e2.png)
⑦在空间中,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb0cf2f475d1997eeadb34a641867b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff259ba50b735db32427fc0ebfbdfdaf.png)
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解题方法
5 . 已知点
,
,
为坐标原点.若
关于直线
的对称点为
,延长
到
,且
.已知直线
经过点
,则直线
的倾斜角为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a682ceca64f8b53216746fb76f3e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5137f9ddb2ae0ccdf33aeef59735cd5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb99c9a026be17b229037e6343976f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023高三·全国·专题练习
名校
解题方法
6 . 下列命题不正确的是( )
①空间中任意三个不共面的向量都可以作为基底.
②直线的方向向量是唯一确定的.
③若直线a的方向向量和平面α的法向量平行,则a
α.
④在空间直角坐标系中,在Oyz平面上的点的坐标一定是(0,b,c).
⑤若
,则
是钝角.
①空间中任意三个不共面的向量都可以作为基底.
②直线的方向向量是唯一确定的.
③若直线a的方向向量和平面α的法向量平行,则a
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
④在空间直角坐标系中,在Oyz平面上的点的坐标一定是(0,b,c).
⑤若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084305253490e6587aba68e67dcb7323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7be4359335d6e4f961bf1913d47b904.png)
A.①③④ | B.②③⑤ | C.③④⑤ | D.①②④ |
您最近一年使用:0次
2023-09-22更新
|
550次组卷
|
3卷引用:天津市嘉诚中学2023-2024学年高二上学期阶段测试二数学试卷
天津市嘉诚中学2023-2024学年高二上学期阶段测试二数学试卷湖北省襄阳市第一中学2023-2024学年高二上学期10月月考数学试题(已下线)第七章 立体几何与空间向量 第五节 空间向量与线、面位置关系 讲
7 . 已知正项等比数列
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624105bed7b063236a82a7429d576a21.png)
(1)求数列
的通项公式;
(2)已知
,①求数列
的前
项和
;
②
恒成立,求实数
的范围.
(3)
求前
项和
.
(4)请同学们只分析通项公式,确定求和方法即可,无需求和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624105bed7b063236a82a7429d576a21.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0bd4db81c4af12bd201c2f43d7881c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c18b8b5eb45abf5c2039894f999804a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d50ec0ce0f0d2120e13e1eb8a882e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
(4)请同学们只分析通项公式,确定求和方法即可,无需求和.
通项公式 | 求和方法 |
![]() | ① |
![]() | ② |
![]() | ③ |
您最近一年使用:0次
解题方法
8 . 随着中国羽毛球队第13次捧起苏迪曼杯,2023年世界羽毛球混合团体锦标赛在5月21日落下帷幕.国家羽毛球队在面对东道主和卫冕冠军的双重压力下,多次面临困境,一度濒临绝境但最终都战胜了对手,站上了冠军领奖台,展现了队员们强大的心理素质和永不放弃、顽强,拼搏的中国精神,队员们圆梦经历也告诉我们:人生中会遇到很多逆境,只要逆境中坚定信心,永不放弃,一切皆有可能,就会有奇迹发生.精彩的苏迪曼杯羽毛球比赛激发了某校同学们参加,羽毛球活动的热情,甲、乙两位同学相约打一场羽毛球比赛,若采用五局三胜制,无论哪一方先胜三局则比赛结束,假设在每局比赛中,甲获胜的概率为
,乙获胜的概率为
,各局比赛结果相互独立.
(1)求甲以
的比分获胜的概率;
(2)设
表示比赛结束时进行的总局数,求
的分布列及数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)求甲以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84783b6ba0f36789519816101a437f46.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
解题方法
9 . 在某次世界乒乓球锦标赛的团体比赛中,中国队将对阵韩国队.比赛实行5局3胜制.根据以往战绩,中国队在每一局中获胜的概率都是
.
(1)求中国队以
的比分获胜的概率;
(2)求中国队在先失1局的前提下获胜的概率;
(3)假设全场比赛的局数为随机变量
,在韩国队先胜第一局的前提下,求
的分布列和数学期望
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
(1)求中国队以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef414095084c4c5eb3be5b73e719b44.png)
(2)求中国队在先失1局的前提下获胜的概率;
(3)假设全场比赛的局数为随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
您最近一年使用:0次
2023-06-19更新
|
813次组卷
|
2卷引用:天津市河西区2022-2023学年高二下学期期中数学试题
10 . 有5人承担
,
,
,
,
五种不同的工作,每人承担一种,且每种工作都有人承担.若这5人中的甲不能承担
种工作,则这5人承担工作的所有不同的方法种数为( )
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.24 | B.60 | C.96 | D.120 |
您最近一年使用:0次
2023-04-24更新
|
882次组卷
|
2卷引用:天津市部分区2022-2023学年高二下学期期中数学试题