1 . 已知椭圆
的左、右焦点分别为
,
,过点
的动直线l交E于A,B两点,且点A在x轴上方,直线
与E交于另一点C,直线
与E于另一点D.
(1)求
的面积最大值;
(2)证明:直线CD过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff1455a4045eb93f482c0751840aea7.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
(2)证明:直线CD过定点.
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3卷引用:云南省昆明市第一中学2024届高三第十次考前适应性训练数学试卷
2 . 把分别写有1,2,3,4,5,6的六张卡片全部分给甲、乙、丙三个人,每人至少一张,若分得的卡片超过一张,则必须是连号,那么不同的分法种数为( )
A.60 | B.36 | C.30 | D.12 |
您最近一年使用:0次
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293次组卷
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3卷引用:云南省昆明市第一中学2024届高三第十次考前适应性训练数学试卷
云南省昆明市第一中学2024届高三第十次考前适应性训练数学试卷云南省昆明市第一中学2024届高三第十次考前适应性训练数学试卷(已下线)专题01 排列组合及其应用常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第二册)
3 . 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
4 . 南宋的数学家杨辉“善于把已知形状、大小的几何图形的求面积,体积的连续量问题转化为求离散变量的垛积问题”.在他的专著《详解九章算法·商功》中,杨辉将堆垛与相应立体图形作类比,推导出了三角垛、方垛、刍薨垛、刍童垛等的公式. 如图,“三角垛”的最上层有1个球,第二层有3个球,第三层有6个球……第
层球数比第
层球数多
,设各层球数构成一个数列
.
的通项公式;
(2)求
的最小值;
(3)若数列
满足
,对于
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](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/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba64e33de2e9b26c3ecd485a99df0bc.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538f7dd59772ba33a6fbb271893b1720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b947eaa62fc4796c9751afbd85f9681.png)
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名校
5 . 2023年,我国新能源汽车产销量占全球比重超过
,中国成为世界第一大汽车出口国. 某汽车城统计新能源汽车从某天开始连续的营业天数
与销售总量
(单位:辆),采集了一组共20对数据,并计算得到回归方程
,且这组数据中,连续的营业天数
的方差
,销售总量
的方差
.
(1)求样本相关系数
,并说明
与
的相关性;
(2)在这组数据中,若连续的营业天数
满足
,试推算销售总量
的平均数
.
附:经验回归方程
,其中
,
.
样本相关系数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a263874aa2031f847d06d6cef24aea.png)
![](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/ad1b1df9930aa20dc444b3dc184b92c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615bcf392209848e4c43c43caed7b2e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a27c01d07d13e9db124ead4efe0aba.png)
(1)求样本相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)在这组数据中,若连续的营业天数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7729593dd482cb71a2822520d6fda603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d80da4a6cb5f102be334006d875a7.png)
附:经验回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183200de4ff08be4eb636e8169c099a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
样本相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62e7e496bab282e2475829358054202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290486258731d1326003fbbe6d377c9e.png)
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解题方法
6 . 倾斜角为锐角的直线经过抛物线
的焦点
,且与
交于
,
两点,
为线段
的中点,
为
上一点,若
的最小值为8,则这条直线的斜率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d160544ddb1498b294c1798399e881d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/5ff21811ea84135ab28112ae687268f3.png)
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解题方法
7 . 抛掷一枚不均匀的硬币,正面向上的概率为
,反面向上的概率为
,记
次抛掷后得到偶数次正面向上的概率为
,则数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/e3f7fda69e2b32b9ced2239f915fa59b.png)
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2024-06-12更新
|
799次组卷
|
5卷引用:云南省昆明市第三中学2024届高三下学期高考考前检测数学试卷
云南省昆明市第三中学2024届高三下学期高考考前检测数学试卷河南省郑州市2024届高三第三次质量预测数学试题(已下线)第四套 艺体生新高考全真模拟 (三模重组卷)(已下线)第4套 新高考全真模拟卷(三模重组)河南省许昌市许昌高级中学2024届高三下学期三模数学试题
8 . 已知函数
的最小正周期大于
,若曲线
关于点
中心对称,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44bf3373b51f69ce7bbaa4c1d503012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3038a4b8c02b12b821fbd0fd69145900.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2024-06-11更新
|
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3卷引用:云南省昆明市2023-2024学年高三三模数学试题
名校
9 . 写出一个满足
,且
的复数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0729e26541fe5de75513a1730ed9acfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/017271a49fdbf0e9aec35c1edac8955f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
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2024-06-11更新
|
346次组卷
|
3卷引用:云南省昆明市第三中学2024届高三下学期高考考前检测数学试卷
10 . 如图,在三棱台
中,上、下底面是边长分别为2和4的正三角形,
平面
,设平面
平面
,点
分别在直线
和直线
上,且满足
,
.
平面
;
(2)若直线
和平面
所成角的正弦值为
,求该三棱台的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116aecda1a8df2a36a50941390a510a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd6f80993ce27b2619335e0d83bec57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5c7e9d7bfcf4ac0b430685e0d6d6cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72bf47c909082e035c91146b1293426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
您最近一年使用:0次