名校
1 . 帕德近似是利用分式有理函数逼近任意函数的一种方法,定义分式函数
为
的
阶帕德逼近,其分子是m次多项式,分母是n次多项式,且满足
,
,
,…,
时,
为
在
处的帕德逼近.
(1)求函数
在
处的
阶帕德逼近
;
(2)已知函数
.
①讨论
的单调性;
②若
有3个不同零点
,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbfee67d1c1cb26b67ef0fe3169e6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd909ba3e40f03e2f58a4eed2e05f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcb8c6a69df1a0deaba265e204d5f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047a8c1ed551fccee1c1848746c5f282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72029562177dfc99a171c9013eb90227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4573475f70860a3d99b92a329d0d07f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b1868d9850b7103e1326eb001dfbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58de4362237a2a719cde7c9049903da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adc63ce466d20e93f7d09d8b0bf9076.png)
①讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fc0ce080b8ad8b63ba63259c680b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e03829b4bbd1148c7f479ca409d436.png)
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2 . 如图,矩形
中,
,
,
分别是矩形四条边的中点,设
,
,设直线
与
的交点
在曲线
上.
的方程;
(2)直线
与曲线
交于
,
两点,点
在第一象限,点
在第四象限,且满足直线
与直线
的斜率之积为
,若点
为曲线
的左顶点,且满足
,直线
与
交于
,直线
与
交于
.
①证明:
为定值;
②是否存在常数
,使得四边形
的面积是
面积的
倍?若存在求出
,若不存在说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e39fda3cda5ddc03b085413f2030aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f17edac849a0691e52146021e05d83e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56966d92b71ae6ec41ccb88667f5db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e17a42c1b3c7c8f38e1cb877365b5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2871d7f054a9313823d6885fd69f071a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba28c45f78fb7643ec9781a800271cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7ebdc16bd34f6daddd1a988ab2ac68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69837fef2bc60f34cdee393543af5fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c07b101a1a118c7558a9e59b13c95c.png)
②是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbae7bfee1523506ffb27f8adce8554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d90f8e1d845107aa138d5b6376e54f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
3 . 如图,四面体
的每条棱长都等于2,
分别是棱
的中点,
分别为面
,面
,面
的重心.
面
;
(2)求平面
与平面
的夹角的余弦值;
(3)保持点
位置不变,在
内(包括边界)拖动点
,使直线
与平面
平行,求点
轨迹长度;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ae3327287e5093b663e96e8f9dcbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5262192e49cf903ee094457dbc250f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9bc3fdf89de0b8e725961f8ddc096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e388bba4de84bc9d6919cb6aa9b72447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0f9bc9123d19a09babe8609cf12327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6684d8fe0d6da7564247e47b948e3997.png)
(3)保持点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a373959bb9026f8a09845c0b828bf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0f9bc9123d19a09babe8609cf12327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
名校
解题方法
4 . 材料一:英国数学家贝叶斯
在概率论研究方面成就显著,创立了贝叶斯统计理论,对于统计决策函数、统计推断等做出了重要贡献.贝叶斯公式就是他的重大发现,它用来描述两个条件概率之间的关系.该公式为:设
是一组两两互斥的事件,
,且
,
,则对任意的事件
,有
,
.
材料二:马尔科夫链是概率统计中的一个重要模型,也是机器学习和人工智能的基石,在强化学习、自然语言处理、金融领域、天气预测等方面都有着极其广泛的应用.其数学定义为:假设我们的序列状态是
,
,那么
时刻的状态的条件概率仅依赖前一状态
,即
.
请根据以上材料,回答下列问题.
(1)已知德国电车市场中,有
的车电池性能很好.
公司出口的电动汽车,在德国汽车市场中占比
,其中有
的汽车电池性能很好.现有一名顾客在德国购买一辆电动汽车,已知他购买的汽车不是
公司的,求该汽车电池性能很好的概率;(结果精确到0.001![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(2)为迅速抢占市场,
公司计划进行电动汽车推广活动.活动规则如下:有11个排成一行的格子,编号从左至右为
,有一个小球在格子中运动,每次小球有
的概率向左移动一格;有
的概率向右移动一格,规定小球移动到编号为0或者10的格子时,小球不再移动,一轮游戏结束.若小球最终停在10号格子,则赢得6百欧元的购车代金券;若小球最终停留在0号格子,则客户获得一个纪念品.记
为以下事件发生的概率:小球开始位于第
个格子,且最终停留在第10个格子.一名顾客在一次游戏中,小球开始位于第5个格子,求他获得代金券的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e742ff4e5752d6e031f6430284ebf7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252bab154aa5bdc9b4bce4c0d43aaf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b495bde2a91e4a81db5a23b0691d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16d0f702177ab62d9e520728fd18136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91f85fc4d2f3894351dd2c4d4f5c975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1f6165ced7d66fcfbf399fc660a5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67de0630a8794aaf2015025f561fcce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91f85fc4d2f3894351dd2c4d4f5c975.png)
材料二:马尔科夫链是概率统计中的一个重要模型,也是机器学习和人工智能的基石,在强化学习、自然语言处理、金融领域、天气预测等方面都有着极其广泛的应用.其数学定义为:假设我们的序列状态是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42ce25b52b6c094880eca189edb205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b49fdb5924134bfc54266f0fee35ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb150b73ea7c87972a0b57510a99472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb7b7d1f7f2afc71dda3740f6cc6b9f.png)
请根据以上材料,回答下列问题.
(1)已知德国电车市场中,有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28555fa2f3a09261cb4e0305d390145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b971b2c43a814d35dfe0c1be4c45d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c88e52743f3dedd4e60569cb958fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(2)为迅速抢占市场,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da684da6a14c603a81085cb37005564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c709117ab1d3ef620883a732aed68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
您最近一年使用:0次
2024-06-11更新
|
768次组卷
|
3卷引用:云南省2024届高三学期”3_3_3“高考备考诊断性联考卷(二)数学试题
名校
5 . 已知总体分为2层,通过分层随机抽样,各层抽取的样本量、样本平均数和样本方差分别为:
,
,
;
,
,
.记总样本的平均数为
,样本方差为
.
(1)试证明:
;
(2)在对某高中1500名高三年级学生的身高的调查中,采用按学生性别比例分配的分层随机抽样抽取100人,已知这1500名高三年级学生中男生有900人,且抽取的样本中男生的平均数和方差分别为170cm和12,女生的平均数和方差分别为160cm和38.试用(1)证明的公式估计高三年级全体学生身高的方差.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c44826e58f11a58d3a6c233fc5df2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbc29b47b83fdc5368770b7b1acb439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215b1424b299b737554386b090af8316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb525270c748eddaaecc4a549cca250e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1295cbd36fdc55a55b549aa2dd5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02931526ba46098639424f341794bd45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
(1)试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06119159922742550d148c6fb8ddfb02.png)
(2)在对某高中1500名高三年级学生的身高的调查中,采用按学生性别比例分配的分层随机抽样抽取100人,已知这1500名高三年级学生中男生有900人,且抽取的样本中男生的平均数和方差分别为170cm和12,女生的平均数和方差分别为160cm和38.试用(1)证明的公式估计高三年级全体学生身高的方差.
您最近一年使用:0次
6 . 甲、乙两位同学组成学习小组进行项目式互助学习,在共同完成某个内容的互助学习后,甲、乙都参加了若干次测试,现从甲的测试成绩里随机抽取了7次成绩,从乙的测试成绩里随机抽取了9次成绩,数据如下:
甲:93 95 81 72 80 82 92
乙:85 82 77 80 94 86 92 84 85
经计算得出甲、乙两人的测试成绩的平均数均为85.
(1)求甲乙两位同学测试成绩的方差;
(2)为检验两组数据的差异性是否显著,可以计算统计量
,其中
个数据的方差为
,
个数据的方差为
,且
.若
,则认为两组数据有显著性差异,否则不能认为两组数据有显著性差异.若
的临界值采用下表中的数据:
例如:
对应的临界值
为5.41.请根据以上资料判断甲、乙两位同学进行项目式互助学习的效果是否有显著性差异.
甲:93 95 81 72 80 82 92
乙:85 82 77 80 94 86 92 84 85
经计算得出甲、乙两人的测试成绩的平均数均为85.
(1)求甲乙两位同学测试成绩的方差;
(2)为检验两组数据的差异性是否显著,可以计算统计量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f680865f78af4c4b3e927069b2643b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c44826e58f11a58d3a6c233fc5df2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473a8d7ae72ff82688775ab85b8d1e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215b1424b299b737554386b090af8316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15360590950bc97c61346f179078181b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69b19ad60939d9fbc395fdf93ac6ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6571b42f1d75eb0ed502b3432d27d8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b519e5794ef9932b64715619adf860db.png)
![]() | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
1 | 161 | 200 | 216 | 225 | 230 | 234 | 237 | 239 |
2 | 18.5 | 19.0 | 19.2 | 19.2 | 19.3 | 19.3 | 19.4 | 19.4 |
3 | 10.1 | 9.55 | 9.28 | 9.12 | 9.01 | 8.94 | 8.89 | 8.85 |
4 | 7.71 | 6.94 | 6.59 | 6.39 | 6.26 | 6.16 | 6.09 | 6.04 |
5 | 6.61 | 5.79 | 5.41 | 6.19 | 5.05 | 4.95 | 4.88 | 4.82 |
6 | 5.99 | 5.14 | 4.76 | 4.53 | 4.39 | 4.28 | 4.21 | 4.15 |
7 | 5.59 | 4.74 | 4.35 | 4.12 | 3.97 | 3.87 | 3.79 | 3.73 |
8 | 5.32 | 4.46 | 4.07 | 3.84 | 3.69 | 3.58 | 3.50 | 3.44 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bc22afe474c5f065cb32b172bd2b4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b519e5794ef9932b64715619adf860db.png)
您最近一年使用:0次
解题方法
7 . 椭圆
的左、右焦点分别为
,点
在椭圆
上运动(与左、右顶点不重合),已知
的内切圆圆心为
,延长
交
轴于点
.
(1)当点
运动到椭圆
的上顶点时,求
;
(2)当点
在椭圆
上运动时,
为定值,求
内切圆圆心
的轨迹方程;
(3)点
关于
轴对称的点为
,直线
与
相交于点
,已知点
的轨迹为
,过点
的直线
与曲线
交于
两点,试说明:是否存在直线
,使得点
为线段
的中点,若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
(1)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5090bb83d608ab7adfce6b0396b19a.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5090bb83d608ab7adfce6b0396b19a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8ad9e94d07405a6be585f81a0d623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbdbe9a17a23c44cec8c7475c4dc1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b953cbf0af04882e009f09051bbaef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
解题方法
8 . 4月23日是联合国教科文组织确定的“世界读书日”.某高校为了了解全体师生阅读时间的分配情况,对全校师生进行抽样问卷调查日平均阅读时间(单位:小时),得到样本数据,并绘制如图所示的频率分布直方图.
的值;
(2)根据频率分布直方图估算全校师生日平均阅读时间
;(每组数据用该组的区间中点值作代表)
(3)将(2)所得到的日平均阅读时间
保留为整数,并根据频率分布直方图估算师生日平均阅读时间的方差
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)根据频率分布直方图估算全校师生日平均阅读时间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2675ddd069a5b22f57b933e44065b5.png)
(3)将(2)所得到的日平均阅读时间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2675ddd069a5b22f57b933e44065b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742d3e642d52e01899f66df411100838.png)
您最近一年使用:0次
解题方法
9 . 已知曲线
由半圆
和半椭圆
组成,点
在半椭圆上,
,
.
的值;
(2)
在曲线
上,若
(
是原点).
(ⅰ)求
的取值范围;
(ⅱ)如图,点
在半圆上时,将
轴左侧半圆沿
轴折起,使点
到
,使点
到
,且满足
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264440f5af29bbdd38635ab6e5d31851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1dda09e3eb7a46e07422742d46f4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb898663f98b8400a897913b4d3102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67761f75cee6201ec2b2dbf40db77c0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb40dae2b0f4048d3fabff25e6cbe443.png)
(ⅱ)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b1ba4307cfde9b424d468bfcdf6c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81154c32dcbe56cb5c392b9388ca4475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22285c8766c10ccaaddd6ad47d20f9f1.png)
您最近一年使用:0次
10 . 已知椭圆
的离心率为
,中心是坐标原点
,焦点在
轴上,右焦点为F,A、B分别是
的上、下顶点.
的短半轴长是圆
的半径,点
是圆
上的动点,且点
不在
轴上,延长BM与
交于点
的取值范围为
.
(1)求椭圆
、圆
的方程;
(2)当直线BM经过点
时,求
的面积;
(3)记直线AM、AN的斜率分别为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a113b91a6ed3ebf040ccba0de6c5b82a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1156a8b29780810bd472f6d9e11b0e39.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)当直线BM经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620e762afe722cc547553805ec8e2ce.png)
(3)记直线AM、AN的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f35d98c6705b2eb7fe4864e1efe11ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a3f348a942d468f0d77c0dfbb41d87.png)
您最近一年使用:0次