名校
解题方法
1 . 奉节脐橙,是重庆市奉节县特产,中国地理标志产品.奉节脐橙的栽培技术始于汉代,历史悠久,产区位于三峡库区,所产脐橙肉质细嫩化渣,酸甜适度,汁多爽口,余味清香,深受广大群众的喜爱.某果园从一批(个数很多)成熟的脐橙中随机抽取了100个,按质量(单位:
)将它们分类如下:质量在
的为二级果,质量在
的为一级果,质量在
的为特级果,个数分别为30个,40个,30个.
(1)从这100个脐橙中任取2个,求2个果都为一级果的概率;
(2)按照比例分配的分层随机抽样,在样本中从二级果,一级果,特级果中抽取10个脐橙进行检测,再从10个脐橙中抽取3个脐橙作进一步检测,这3个脐橙中特级果的个数为X,求X的分布列和数学期望;
(3)若这批脐橙的质量都在
内,用样本估计总体,从该批脐橙中任取4个,求4个脐橙中二级果的个数Y的期望与方差.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d927be31040b0782b6c0e30b6f58a72a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1ea8729e96da57d1f100f7dace530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec0cd1bc3f31bd6a7c1deba52e758d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0401f03ca946cde6d9a4b3b93aa677a3.png)
(1)从这100个脐橙中任取2个,求2个果都为一级果的概率;
(2)按照比例分配的分层随机抽样,在样本中从二级果,一级果,特级果中抽取10个脐橙进行检测,再从10个脐橙中抽取3个脐橙作进一步检测,这3个脐橙中特级果的个数为X,求X的分布列和数学期望;
(3)若这批脐橙的质量都在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de03721de71e08d5bfca59c03a652547.png)
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2 . 已知甲箱中有2个白球和4个红球,乙箱中有4个白球和2个红球.质点从原点出发,每次等可能的向左或向右移动一个单位,记事件
“质点移动6次,最终在2的位置”.
发生的概率;
(2)若事件
发生,从甲箱中取一球,否则从乙箱中取一球.求取出的球是红球的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2024-05-11更新
|
783次组卷
|
3卷引用:重庆市永川北山中学校2024届高三下学期高考预测卷(最后一套)数学试题
重庆市永川北山中学校2024届高三下学期高考预测卷(最后一套)数学试题四川省南充市第九中学2023-2024学年高二下学期5月月考数学试卷(已下线)第七章:随机变量及其分布章末重点题型复习-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)
名校
解题方法
3 . 已知
的内角
所对的边分别为
,设向量
,
.且
.
(1)求角
;
(2)若
,在
内部取一点
(不含边界),使得
,
,四边形
的面积为
,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93505d79c7e48ebeb3931edfb3a9565d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/622eef0a3bbb2369215570aafa1ecb81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242b0af4f33851007b2052508dd3790e.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe7a93172d308a58200e3c722fe1072.png)
![](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/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b547d886c528fa2c63016c217b8fb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b35151087982fc1d27b804ccccb9a1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
的内角
,
,
的对边分别为
,
,
.若
.
;
(2)若
,求
的值;
(3)如图所示,若
,
三等分
,
,
在线段
上(
靠近
),已知
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](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/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/96d04c0e55999fcfd1e98aa992f48d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f019d881499c2c91512b410b6c57754.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6812acd3c8f7daec0c65fc9bc4591e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd00662d7395918fac8794d85ee13a5.png)
(3)如图所示,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae894373e6b6862d5ec3c772f9fc8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94031fdc9a4f96d9ec780ba985bb13f.png)
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名校
解题方法
5 . 某公园湖心有一浮动观景亭
,湖边一点
到观景亭
的一座桥长为
米.现公园打算升级改造,在湖边选取两个点
,
,新建两座桥梁
,
,且
.
为
中点,且
米,求两座桥梁长度之和
的值;
(2)若
,已知玻璃桥的建设成本为2千元/米,普通桥的建设成本为1千元/米,若
用玻璃桥,
用普通桥梁,不考虑其他费用支出,请你帮公园规划部计算一下,建设这两座桥梁总预算成本的最大值(单位:千元)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e4123975f257306440158659634c4a.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/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da16fe2e1ce327bcc7a83495338e735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c54afdd80b4bd65bf2571da9d852a5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173572e631b7f87f8673d2cd57c7b818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
您最近一年使用:0次
名校
解题方法
6 .
的内角
的对边分别为
,已知
.
(1)求角
;
(2)若
,
的周长为
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc98ebe9ea4f030abe13aab644e41f1f.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82986ab38a4ae58593191ccae2a44f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac988c3805bb84dd0a10fde30be2538.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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7 . 陶瓷历史已逾千年,始于春秋,兴于辽金,盛于明清.目前某省有53家陶瓷企业,某陶瓷厂准备烧制甲、乙、丙三件不同的工艺品,制作过程必须先后经过两次烧制,当第一次烧制合格后才可进入第二次烧制,两次烧制过程相互独立.根据该厂现有的技术水平,经过第一次烧制后,甲、乙、丙三件产品合格的概率依次为
,
,
,经过第二次烧制后,甲、乙、丙三件产品合格概率依次为
,
,
.
(1)求第一次烧制后恰有一件产品合格的概率;
(2)经过前后两次烧制后,如果陶瓷合格则可以上市销售,每件陶器可获利100元;如果陶器不能合格,则每件陶器亏损80元,求这3件陶器最终盈亏
的分布列和数学期望.
(3)
,
,
三位学徒跟师傅学习制作某种陶器,经过一段时间的学习后,他们各自能制作成功该陶器的概率分别为
,
,
,且
,现需要他们三人制作一件该陶器,每次只有一个人制作且每个人只制作一次,如果有一个人制作失败则换下一个人重新制作,若陶器制作成功则结束.按
,
,
的顺序制作陶器,若
,
,求制作陶器人数
的数学期望的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357821e0e5595eaf3028df63d47b2c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6c7567972273b4ba733b47bf9d5408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5a1a2ee471c67aa5264c0991d05421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
(1)求第一次烧制后恰有一件产品合格的概率;
(2)经过前后两次烧制后,如果陶瓷合格则可以上市销售,每件陶器可获利100元;如果陶器不能合格,则每件陶器亏损80元,求这3件陶器最终盈亏
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
(3)
![](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/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b21b872313f7d8c5b606981f954a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd6038d8cca23b957fc71004b9d48a2.png)
![](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/3f9aa31c4d7191c45670557d4625b233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1050285b32bf3850376ba59a052ffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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8 . 已知
,其中
,
,
,
,
.且
展开式中仅有第5项的二项式系数最大.
(1)求
的值;
(2)求
(用数值作答);
(3)若
,求二项式的值被7除的余数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52be4494727bc959442eb4abebd06e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a5d7258973bf6c6afab73fcc1e8263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac13369db3a6cd9c7f4b923e334d0c0d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fe8fecffe2d718a9a346173e5f7e6e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103cea2c82157fff071c63913c09a350.png)
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名校
解题方法
9 . 在直三棱柱
中,点D,E分别为棱AB,
的中点,点F在棱
上.
平面CDE,并证明;
(2)若多面体
的体积为直三棱柱体积的
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4b704ed06bd72367cc20c54bce7969.png)
(2)若多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7aafc0421a1e01de7bde49a6291ed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16d09692f7b0fb5633964437202d21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4313f14d9304509745287e0250e17c.png)
您最近一年使用:0次
名校
解题方法
10 . 已知向量
,
,
.
(1)求向量
与
的夹角
的大小;
(2)若向量
,
(
),当
取得最小值时,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e59d5bbd80ec0a39484a30d546fc6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3881ae6f5a0b20955d54a65212035547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd89778ba4ca371b5a791f710d8d2e9.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8bbd4a1ca9a630cf84552ef61f5f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df7be311e725bcfb4989c975ec74e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc10c8559d983c5098c351ce034c594e.png)
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3卷引用:重庆市育才中学校2023-2024学年高一下学期阶段测试数学试题