名校
解题方法
1 . 为迎接2024新春佳节,某地4S店特推出盲盒抽奖营销活动中,店家将从一批汽车模型中随机抽取50个装入盲盒用于抽奖,已知抽出的50个汽车模型的外观和内饰的颜色分布如下表所示.
(1)从这50个模型中随机取1个,用
表示事件“取出的模型外观为红色”,用
表示事件“取出的模型内饰为米色”,求
和
,并判断事件
与
是否相互独立;
(2)活动规定:在一次抽奖中,每人可以一次性拿2个盲盒.对其中的模型给出以下假设:假设1:拿到的2个模型会出现3种结果,即外观和内饰均为同色、外观和内饰都异色以及仅外观或仅内饰同色.假设2:按结果的可能性大小,概率越小奖项越高.假设3:该抽奖活动的奖金额为一等奖30000元、二等奖2000元、三等奖1000元.请你分析奖项对应的结果,设
为奖金额,写出
的分布列并求出
的期望(精确到元)
红色外观 | 蓝色外观 | |
棕色内饰 | 20 | 10 |
米色内饰 | 15 | 5 |
![](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/108ab49f370919e730e3567070deee65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9faccaa71316eb97aaf56af15365425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)活动规定:在一次抽奖中,每人可以一次性拿2个盲盒.对其中的模型给出以下假设:假设1:拿到的2个模型会出现3种结果,即外观和内饰均为同色、外观和内饰都异色以及仅外观或仅内饰同色.假设2:按结果的可能性大小,概率越小奖项越高.假设3:该抽奖活动的奖金额为一等奖30000元、二等奖2000元、三等奖1000元.请你分析奖项对应的结果,设
![](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/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
2024-06-16更新
|
145次组卷
|
2卷引用:安徽省六安第一中学2024届高三下学期三模数学试题
名校
2 . 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)
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2024-06-12更新
|
650次组卷
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3卷引用:安徽省安庆市第一中学2024届高三下学期6月第四次模拟(热身考试)数学试卷
名校
3 . 已知函数
.
(1)若过点
可作曲线
两条切线,求
的取值范围;
(2)若
有两个不同极值点
.
①求
的取值范围;
②当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30e674c62fd9e25645b3984827759a6.png)
(1)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e868d1326bf73ac658885d4936bbe04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7913a814e2c4ba5e643af885b6ff0efb.png)
您最近一年使用:0次
2024-06-11更新
|
616次组卷
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4卷引用:安徽省六安第一中学2024届高三下学期质量检测(三 )数学试卷
名校
4 . 如图,在四棱锥
中,底面
是正方形,
底面
,
.
为
中点,求证:
平面
;
(2)求平面
与平面
的夹角.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd3bd9c2db8c9f3cb8c6c7d7cbf5465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
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2024-06-04更新
|
1748次组卷
|
4卷引用:安徽省江淮十校2024届高三第三次联考数学试题
安徽省江淮十校2024届高三第三次联考数学试题黑龙江省牡丹江市第三高级中学2024届高三下学期高考前适应性演练数学试卷海南省部分学校2024届新高考二卷押题卷(三)数学试题(已下线)6.4 空间向量与立体几何(高考真题素材之十年高考)2
名校
解题方法
5 . 如图,在三棱锥
中,
分别为棱
的中点.
平面
;
(2)若点
到底面
的距离等于
,且
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd33c6c97ae75127cf9ade58627c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0bb8127547d4978311d81d93244e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448cbac9a1ef3de7538a6b30cdc39582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea58ce272b1b4b8a256e6f1f39b3964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3976d08e5f9e24e76ce9579c06a8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4183602e71ff9a3fae892145082eaf.png)
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2024-06-02更新
|
686次组卷
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2卷引用:安徽省皖豫名校联盟&安徽卓越县中联盟2024届高三联考5月三模数学试题
名校
6 . 如图,四棱锥
中,四边形
是菱形,
,
是正三角形,
是
的重心,点
满足
.
平面
;
(2)若
,求直线
与平面
所成角的正弦值.
![](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/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566a4158b0fb4670a68c61cf12c1bad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a779876cdfb2c489ad0eaed0f73e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38711ce72877e0c4b4523f6f9b5a2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
您最近一年使用:0次
名校
解题方法
7 . 若正实数数列
满足
,则称
是一个对数凸数列;若实数列
满足
,则称
是一个凸数列.已知
是一个对数凸数列,
.
(1)证明:
;
(2)若
,证明:
;
(3)若
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c162242a938a5a12decf95e793a38bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb56942a7c324e61bf64f45182aac6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010baf415f792018ad9abd752e37b983.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7de869d778679e553d65c8feee7a0b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fae07f950aea5270e6b48fe2cedaaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e44bb3c3c56c02ae33d480b556fece.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e32b345649f33632c83903c6014dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac648580405ecaa29e91d45738a08af7.png)
您最近一年使用:0次
解题方法
8 . 如图,在四棱锥
中,
为等边三角形,底面
是矩形,平面
平面
分别为线段
的中点,点
在线段
上(不包括端点).
,求证:点
四点共面;
(2)若
,是否存在点
,使得
与平面
所成角的正弦值为
,若存在,求出
,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e78042a384255038de485fd7bc0839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1995c33caa487cf6d5410218590f129b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa364dffb98a94fb8285c2cdb9ad14b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4e54e5f68aba2836820c09e3847cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512efef36576084492bf3b06131fbdcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58da37b3d1dbd2fee75089d5ba28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e108d5c61e85e0741ec2c484fc5768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8df877496fdae8f20414130174368.png)
您最近一年使用:0次
2024-05-16更新
|
502次组卷
|
2卷引用:安徽省皖南八校2024届高三4月第三次联考数学试卷
9 . 如图,在四面体
中,
,
,
两两垂直,
,
是线段
的中点,
是线段
的中点,点
在线段
上,且
.
平面
;
(2)若点
在平面
内,且
平面
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0f630195bcf6c3ca8f4fdeff43b082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e3c9755dbd39fb01de614840d230f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cf187bc2ede965870b90757b495f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c5ef850e256c98ca4f033999e61311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c015d99f2677951bdcd0447240ef93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
解题方法
10 . 如果X,Y是两个离散型随机变量,
的所有可能取值为:
,则称
为
在
事件下的条件期望.已知甲每次投篮的命中率均为
,其中
,设随机变量
是甲第一次命中时的投篮次数,随机变量
是甲第二次命中时的投篮次数.
(1)若
,求
;
(2)已知
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6a5dc4ce8f36f14dae312835cff836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a71f2ff30791e8b210727912600096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25b322e9f1f8a3aedd48a01e0af8290.png)
(2)已知
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