名校
1 . 设椭圆
与双曲线
有相同的焦距,它们的离心率分别为
,
,椭圆
的焦点为
,
,
,
在第一象限的交点为P,若点P在直线
上,且
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8210484dd6815b5bebc7b22f1389cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82b84d8369b8792d0296638dd0fbe43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f9bdc6d9f09e14b037ea7d3ee1f623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a708c976cfe1b2741cb79d078db8e453.png)
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名校
2 . 设直线
,圆
,则l与圆C( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e792f29004485835fb9641ed6fd77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd8592184be802e00f50389a4dc11a5.png)
A.相交 | B.相切 | C.相离 | D.以上都有可能 |
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3 . 在平面直角坐标系xOy中,设向量
.
(1)若
,求
的值;
(2)设
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c37fc79619507a7ea309a14794555a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8a4f93274f06ba1fa756163ef082c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152f33e0c3380e2ddb3f35781a5b5314.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7228ccc4fffb86489a02f0588d3761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1040ac7b05cd9f524a7ce965abffc04a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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名校
4 . 设向量
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
_____ ,
和
所成角为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66896c6d926d0bdc2d4f4e212d09681f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef84d275246c94cd7d9c983231210fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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5卷引用:山东省菏泽第一中学八一路校区2023-2024学年高三下学期三月份月考数学试题
山东省菏泽第一中学八一路校区2023-2024学年高三下学期三月份月考数学试题云南、广西、贵州2024届“3+3+3”高考备考诊断性联考(二)数学试卷云南、广西、贵州2024届“3+3+3”高考备考诊断性联考(二)数学试卷(已下线)信息必刷卷03(北京专用)(已下线)云南、广西、贵州2024届“3+3+3”高考备考诊断性联考(二)数学试题变式题11-15
名校
5 . 襄阳市某中学一研究性学习小组为了了解襄阳市民每年旅游消费支出费用
单位:千元
,寒假期间对游览某签约景区的
名襄阳市游客进行随机问卷调查,并把数据整理成如下表所示的频数分布表:
(1)从样本中随机抽取两位市民的旅游支出数据,求两人旅游支出均不低于
元的概率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若襄阳市民的旅游支出费用
近似服从正态分布
,
近似为样本平均数
同一组中的数据用该组区间的中间值代表
,
近似为样本标准差
,并已求得
,利用所得正态分布模型解决以下问题:
(i)假定襄阳市常住人口为
万人,试估计襄阳市有多少市民每年旅游费用支出在
元以上![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(ii)若在襄阳市随机抽取
位市民,设其中旅游费用在
元以上的人数为
,求随机变量
的分布列和均值.
附:若
∽
,则
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366d02f85d55ee1188ed6e19c0ce0b91.png)
组别
| ||||||||
频数 |
(1)从样本中随机抽取两位市民的旅游支出数据,求两人旅游支出均不低于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc713f9d979d29032d793ab900b8ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若襄阳市民的旅游支出费用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cb0962026eb79ff8f21f8955c4f00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7d41fa0555ccaa304c772c5382d58d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01441912ed554944a2a3f3af1ebfa64d.png)
(i)假定襄阳市常住人口为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0aac1830ede61d27561e5e93ccdc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d577f49387c9dc2a98358eacec4e4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(ii)若在襄阳市随机抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdc02a6b594c968910c282133d5b189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
附:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cb0962026eb79ff8f21f8955c4f00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100b933ed7a1ee750b90affd31fa4488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3ea69266c57d1fc638cf8475c5734e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889f9fa6316a541a96bc9af0906df2fc.png)
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名校
6 . 已知
,
之间的一组数据:
若
与
满足回归方程
,则此曲线必过点__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8aca16ad7b2e7c21bb5555a12578831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5d658174f8bccba30e268305c8bdd1.png)
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名校
7 . 球类运动对学生的身心发展非常重要
现某高中为提高学生的身体素质,特开设了“乒乓球”,“排球”,“羽毛球”,“篮球”,“足球”五门选修课程,要求该校每位学生每学年至多选
门,高一到高三三学年必须将五门选修课程选完,每门课程限选修一学年,一学年只上学期选择一次,则每位学生的不同的选修方式有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 定义:对于定义在区间
上的函数,若存在实数
,使得函数在区间
上单调递增(递减),在区间
上单调递减(递增),则称这个函数为单峰函数且称
为最优点.已知定义在区间
上的函数
是以
为最优点的单峰函数,在区间
上选取关于区间的中心
对称的两个试验点
,称使得
较小的试验点
为好点(若相同,就任选其一),另一个称为差点.容易发现,最优点
与好点在差点的同一侧.我们以差点为分界点,把区间
分成两部分,并称好点所在的部分为存优区间,设存优区间为
,再对区间
重复以上操作,可以找到新的存优区间
,同理可依次找到存优区间
,满足
,可使存优区间长度逐步减小.为了方便找到最优点(或者接近最优点),从第二次操作起,将前一次操作中的好点作为本次操作的一个试验点,若每次操作后得到的存优区间长度与操作前区间的长度的比值为同一个常数
,则称这样的操作是“优美的”,得到的每一个存优区间都称为优美存优区间,
称为优美存优区间常数.对区间
进行
次“优美的”操作,最后得到优美存优区间
,令
,我们可任取区间
内的一个实数作为最优点
的近似值,称之为
在区间
上精度为
的“合规近似值”,记作
.已知函数
,函数
.
(1)求证:函数
是单峰函数;
(2)已知
为函数
的最优点,
为函数
的最优点.
(i)求证:
;
(ii)求证:
.
注:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb94dc04ff686b4e3023ff3f3f0ebb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819123c00dd8547948fd6a142d23eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a62461b16d4a05da2cfdd0c9b79a9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f89a8b5cf6996a6455375e405bfb9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef130ac86847aa71b7dcbb631b60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976f8d8750bfaf95aac23678f0bd926a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976f8d8750bfaf95aac23678f0bd926a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbba4740e36449b5c76eedd40519cbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fc0013f0aabb967d8efa25d0e90849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3449936da13a15ad19bf5c113c04a2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f556fdf351f94bfb3d7ed2ded23fda93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34acf1ac6dfe5e76b611e465464344c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f556fdf351f94bfb3d7ed2ded23fda93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d8e0a088b964419617c5bae4b033bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2acec765e99a3ac8d612a1ad0727c762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efec0433e7bdec251e52323372a5f0b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5d19be359b21225331a07e6cf98d41.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538004bbc472e5dbf323325a596a7cf6.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9c33cd26d7faec943ffca1fcb449db.png)
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a5efb1aa1c4e3f8017ffa6e5025d73.png)
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名校
解题方法
9 . 如图,在平面直角坐标系
中有一个点阵,点阵中所有点的集合为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9163ebe812708ee5337d62298c2e3363.png)
,从集合
中任取两个不同的点,用随机变量
表示它们之间的距离.
时,求
的分布列.
(2)对给定的正整数
.
(i)求随机变量
的所有可能取值的个数;(用含有
的式子表示)
(ii)求概率
.(用含有
的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9163ebe812708ee5337d62298c2e3363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85de57c45c6c4fab766b3f79845a1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)对给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1270caa3ba39ed6da3e04ae0cf32ba9e.png)
(i)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(ii)求概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee83048ccebcc5c77d91d5d5222dcf1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2卷引用:山东省菏泽市第一中学南京路校区2024届高三下学期4月月考数学试题
名校
10 . 如图,在直三棱柱
中,点
是
的中点,
.
平面
;
(2)若
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1b049abfab17512ac0683cb4d39d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445fa5620db75293f7795f79ef5d6a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
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4卷引用:山东省菏泽市第一中学南京路校区2024届高三下学期4月月考数学试题
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