名校
解题方法
1 . 在如图所示的多面体中,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe21d51a66caafa14054a41c9a37d1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836b56dbc08431a5b102a49dade806c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4b8eb77297ee04a78626433a90b58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b812363d7a76cc17df075a874d851ee3.png)
上求作点
使
平面
请写出作法并说明理由;
(2)求三棱锥
的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe21d51a66caafa14054a41c9a37d1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836b56dbc08431a5b102a49dade806c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4b8eb77297ee04a78626433a90b58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b812363d7a76cc17df075a874d851ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8fbc229c957487495bb8cda1d4cfd8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f79db7c270b6ff9fb0a538ee201cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed46dc5ff6947bffc737c001fd1f11a.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f178906e90bafd73e0ef9f89814855d5.png)
您最近一年使用:0次
名校
2 . 如图,四棱锥
中,底面
是边长为2的正方形,
,
,且
,
为
的中点.
平面
;
(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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0063f3f48e49f2970ec7f097567cef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
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3 . 对于数集
,其中
,
,定义向量集
,若对任意
,存在
,使得
,则称X具有性质P.
(1)设
,请写出向量集Y并判断X是否具有性质P(不需要证明).
(2)若
,且集合
具有性质P,求x的值;
(3)若X具有性质P,且
,q为常数且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7a53ccddc5210a37f12e3ab6e99df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3fe482c5e20abfc9f89c876f653ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966888395e433b9c2a30138e7fb59cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122d308af408739c2717376e932122d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c6bb4424eb1e5ab02b8ac83fd6ad10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8de3dabcc3150fd539ac97718ba10c5.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66317f3834697e2b5642906bb751eb25.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7511e6ce72a5232820b7007f976be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864dd49f786346bc320deace92f949b0.png)
(3)若X具有性质P,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2f5028bb9e126607ef62b402300c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57313119f26fc9ba177f6ce7b57ab4f3.png)
您最近一年使用:0次
2024-04-23更新
|
312次组卷
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2卷引用:湖南省慈利县第一中学2023-2024学年高一下学期期中考试数学试题
名校
4 .
为正实数,已知函数
.
(1)若
时,求函数
的极值.
(2)若函数
有且仅有2个零点,求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0908b6d9cb47896ae0cc155df3b8635.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
5 . 袋中有大小相同,质地均匀的3个白球,5个黑球,从中任取2个球,设取到白球的个数为
.
(1)求随机变量
的分布列;
(2)求随机变量
的数学期望和方差.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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2024-04-10更新
|
1055次组卷
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3卷引用:湖南省张家界市民族中学2023-2024学年高二下学期第一次月考数学试题
湖南省张家界市民族中学2023-2024学年高二下学期第一次月考数学试题(已下线)7.4 二项分布与超几何分布(8大题型)精讲-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第三册)河北省石家庄十二中2023-2024学年高二下学期期中数学试题
名校
6 . 如图,在四棱锥
中,底面
是矩形,侧棱
底面
,
,
是
的中点,作
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/9085b855-0673-40a2-9357-dfd1535a8f2f.png?resizew=153)
(1)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef6e4af238e058322913fdc783900d7.png)
(2)求二面角
的正弦值.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb886ce5fa68b1bafeed307589576348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4a6a1e70241d600bc6c104313eac61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/9085b855-0673-40a2-9357-dfd1535a8f2f.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef6e4af238e058322913fdc783900d7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8424bdcf257367472c217c92d559f39f.png)
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2024-03-29更新
|
1110次组卷
|
3卷引用:湖南省张家界市慈利县第一中学2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
7 . 据统计,2024年元旦假期,哈尔滨市累计接待游客304.79万人次,实现旅游总收入59.14亿元,游客接待量与旅游总收入达到历史峰值.现对某一时间段冰雪大世界的部分游客做问卷调查,其中
的游客计划只游览冰雪大世界,另外
的游客计划既游览冰雪大世界又参观群力音乐公园大雪人.每位游客若只游览冰雪大世界,则得到1份文旅纪念品;若既游览冰雪大世界又参观群力音乐公园大雪人,则获得2份文旅纪念品.假设每位来冰雪大世界景区游览的游客与是否参观群力音乐公园大雪人是相互独立的,用频率估计概率.
(1)从冰雪大世界的游客中随机抽取3人,记这3人获得文旅纪念品的总个数为
,求
的分布列及数学期望;
(2)记
个游客得到文旅纪念品的总个数恰为
个的概率为
,求
的前
项和
;
(3)从冰雪大世界的游客中随机抽取100人,这些游客得到纪念品的总个数恰为
个的概率为
,当
取最大值时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b140062c06ce287ca862555287e3d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c88e52743f3dedd4e60569cb958fe.png)
(1)从冰雪大世界的游客中随机抽取3人,记这3人获得文旅纪念品的总个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.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)
(3)从冰雪大世界的游客中随机抽取100人,这些游客得到纪念品的总个数恰为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2024-03-29更新
|
2449次组卷
|
7卷引用:湖南省张家界市慈利县第一中学2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
8 .
中,
为
边的中点,
.
的面积为
,且
,求
的值;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32104791e7ef79623fe410e4f4a18bec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32e2f2d7147cf1699fbfdef9cf4af74.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3acf551f38311eccdcc325c0d283473.png)
您最近一年使用:0次
2024-03-24更新
|
2245次组卷
|
7卷引用:湖南省慈利县第一中学2023-2024学年高一下学期期中考试数学试题
湖南省慈利县第一中学2023-2024学年高一下学期期中考试数学试题陕西省宝鸡市2024届高三下学期高考模拟检测(二)数学(理科)试题(已下线)6.4.3.2?正弦定理15种常考题型归类(2)-高频考点通关与解题策略(人教A版2019必修第二册)江苏省扬州市新华中学2023-2024学年高一下学期4月期中考试数学试题(已下线)3.5 解三角形的应用(高考真题素材之十年高考)广东省广州市第六十五中学2023-2024学年高一下学期期中考试数学试卷(已下线)第九章:解三角形章末重点题型复习--同步精品课堂(人教B版2019必修第四册)
名校
解题方法
9 . 如图,在
中,已知
边上的中点为
,点
是边
上的动点(不含端点),
相交于点
.
;
(2)当点
为
中点时,求:
的余弦值;
(3)当
取得最小值时,设
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bafeb3a419c78eea6d9fda05581cde3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e4d7503a7d57ba242ad4e05c7006a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45a8a837c11c07073da3ff751d70278.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340f84b11637ee42eaeeec250d0f0c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90940b82d29c6a781a368bcda5577756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-03-12更新
|
795次组卷
|
2卷引用:湖南省慈利县第一中学2023-2024学年高一下学期第一次月考数学试题
名校
解题方法
10 . 已知函数
为奇函数.
(1)求
的值;
(2)判断函数
的单调性,并加以证明;
(3)若对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faab0e945072325e609f617aa6a4fee.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62114be1b4855205182a630dc2e1065e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-03-12更新
|
538次组卷
|
3卷引用:湖南省慈利县第一中学2023-2024学年高一下学期第一次月考数学试题