1 . 如图
,在长度为
的线段
上取两个点
、
,使得
,以
为边在线段
的上方做一个正方形,然后擦掉
,就得到图形
;对图形
中的最上方的线段
作同样的操作,得到图形
;依次类推,我们就得到以下的一系列图形设图
,图
,图
,图
,各图中的线段长度和为
,数列
的前
项和为
,则( )
![](https://img.xkw.com/dksih/QBM/2023/5/22/3243090716803072/3243998592204800/STEM/2415332591ae4d05be4aeb530e11615e.png?resizew=349)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/d95e81fcd744d8ffb168275315b36bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c842efb73bb5b4d8dd028dba6f5d0c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](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://img.xkw.com/dksih/QBM/2023/5/22/3243090716803072/3243998592204800/STEM/2415332591ae4d05be4aeb530e11615e.png?resizew=349)
A.数列![]() | B.![]() |
C.存在正数![]() ![]() | D.![]() |
您最近一年使用:0次
2022·全国·模拟预测
解题方法
2 . 已知正三棱锥
的底面
的面积为
,体积为
,球
,
分别是三棱锥
的外接球与内切球,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
A.球![]() ![]() |
B.二面角![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.在三棱锥![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
3 . 已知
,函数
,其中
…为自然对数的底数.
(1)证明:函数
在
上有唯一零点;
(2)记
为函数
在
上的零点,证明:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3adb9acead48e36b705874dc96979f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597de8046b5baecf54be4b0516de67ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89e13ea43300cc01379c96614d8e9cc.png)
您最近一年使用:0次
2021-10-12更新
|
557次组卷
|
3卷引用:湖北省武汉市部分重点中学2021-2022学年高二下学期期末联考数学试题
名校
4 . 如图1,在边长为2的正方形
中,
,
,
分别为
,
,
的中点,沿
、
及
把这个正方形折成一个四面体,使得
、
、
三点重合于
,得到四面体
(如图2).下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/7ce26cb7-5ea8-445f-a356-5c8f0b0150d2.png?resizew=318)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.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/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922dae27e2bef111979574e15de3a4cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/7ce26cb7-5ea8-445f-a356-5c8f0b0150d2.png?resizew=318)
A.四面体![]() ![]() |
B.顶点![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.过点![]() ![]() ![]() |
您最近一年使用:0次
2021-07-09更新
|
2151次组卷
|
5卷引用:湖北省武汉市蔡甸区汉阳一中2021-2022学年高二上学期9月月考数学试题
湖北省武汉市蔡甸区汉阳一中2021-2022学年高二上学期9月月考数学试题(已下线)第一章 空间向量与立体几何单元检测(能力挑战卷)-【一堂好课】2021-2022学年高二数学上学期同步精品课堂(人教A版2019选择性必修第一册)广东省广州市广州大学附属中学2021-2022学年高二上学期9月入学考试数学试题湖南省邵阳市第二中学2021-2022学年高二下学期入学考试数学试题湖南省长沙市长郡中学2020-2021学年高一下学期期末数学试题
名校
解题方法
5 . 如图,二面角
的大小为
,
,
分别在平面
,
内,
,
,
,
,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/df2cc5cb-0485-4a0d-8f62-01e3bd32213b.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ce3f859c6b9a0cfc98bdf5b3d0f395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ededa0e19291b5b7eb9884af5bdeb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cec3803e3e4da37bd4ec4ebdc3cfa94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bab9b67eabe74756b8cd7344515135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b56ed991a28fe7c6efac4dbca46b66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee28f91a63a0af514725b2792927494e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/df2cc5cb-0485-4a0d-8f62-01e3bd32213b.png?resizew=167)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-11-04更新
|
1895次组卷
|
8卷引用:湖北省武汉市育才中学2019-2020学年高二上学期第二次段考理科数学试题
湖北省武汉市育才中学2019-2020学年高二上学期第二次段考理科数学试题安徽省六安市第一中学2020-2021学年高二下学期开学考试数学(理)试题(已下线)专题04 空间向量与立体几何的压轴题(二)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)浙江省台州市书生中学2021-2022学年高二上学期10月月考数学试题河南省焦作市温县第一高级中学2021-2022学年高二上学期10月月考数学(文)试题浙江省杭州学军中学紫金港校区2021-2022学年高二上学期期中数学试题浙江省台州市玉环市玉城中学2022-2023学年高二上学期第一次月考数学试题山东省泰安新泰市第一中学(弘文部)2023-2024学年高二上学期第一次大单元自主测试数学试题
6 . 已知正三棱锥侧面与底面所成二面角的余弦值为
,则此三棱锥的高h与其内切球半径r之比是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
A.5 | B.6 | C.7 | D.8 |
您最近一年使用:0次
2020-05-28更新
|
321次组卷
|
2卷引用:湖北省九校教研协作体2022-2023学年高二上学期9月联考数学试题
名校
7 . 有一大批产品,其验收方案如下,先做第一次检验:从中任取8件,经检验都为优质品时接受这批产品,若优质品数小于6件则拒收;否则做第二次检验,其做法是从产品中再另任取3件,逐一检验,若检测过程中检测出非优质品就要终止检验且拒收这批产品,否则继续产品检测,且仅当这3件产品都为优质品时接受这批产品.若产品的优质品率为0.9.且各件产品是否为优质品相互独立.
(1)记
为第一次检验的8件产品中优质品的件数,求
的期望与方差;
(2)求这批产品被接受的概率;
(3)若第一次检测费用固定为1000元,第二次检测费用为每件产品100元,记
为整个产品检验过程中的总费用,求
的分布列.
(附:
,
,
,
,
)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)求这批产品被接受的概率;
(3)若第一次检测费用固定为1000元,第二次检测费用为每件产品100元,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
(附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62f65d65c83f18eac8539ee787e6c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640513792121f58176c100b81237615f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503054b701bcbde512e1c341c9d88f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289198673260a570941a2a74d2c0f7c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cd2dca19ed5263086782bf8490dad9.png)
您最近一年使用:0次
2020-01-30更新
|
273次组卷
|
2卷引用:湖北省黄冈市2019-2020学年高二上学期期末数学试题
20-21高一上·湖北荆州·期末
名校
8 . 若复数
满足
,则
在复平面内对应点的轨迹方程是__________ (结果要求化简)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aab89d89529fa6c56beea82de7d7a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
您最近一年使用:0次
名校
解题方法
9 . 将一枚质地均匀的硬币连掷三次,设事件
:恰有1次正面向上;事件
:恰有2次正面向上,则
( )
![](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/9a1b07ee565865ba17b1be0b91450ec8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-03-16更新
|
168次组卷
|
2卷引用:湖北省重点高中(孝感一中、应城一中、安陆一中等六校)协作体2018-2019学年高二上学期期末联考数学(文)试题
10 . 一个结晶体的形状为平行六面体,以同一个顶点为端点的三条棱长均为6,且它们彼此的夹角均为
,则以这个顶点为端点的晶体的对角线长为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
您最近一年使用:0次
2019-12-12更新
|
450次组卷
|
3卷引用:湖北省襄阳市四校2019-2020学年高二上学期期中数学试题