1 . 某学校数学实践小组为该校一块长方形空地设计种树方案,在坐标纸上设计如下:第
棵树种在点
处,其中
,当
时,
,[
]表示不大于x的最大整数,按此设计方案,第3株树种植点的坐标为___________ ;第2025棵树种植点的坐标为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a9ea0c17c1c1576541f981a202701b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e93eb05e988d2fd48fac631e479b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7437284d09b06a4e911be5feaf83dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2024-05-11更新
|
216次组卷
|
2卷引用:山东省潍坊市2023-2024学年高二下学期期中质量监测数学试题
名校
解题方法
2 . 假设视网膜为一个平面,光在空气中不折射,眼球的成像原理为小孔成像. 思考如下成像原理: 如图,地面内有圆
,其圆心在线段
上,且与线段
交于不与
重合的点
,
地面,且
,
点为人眼所在处,视网膜平面与直线
垂直. 过
点作平面
平行于视网膜平面. 科学家已经证明,这种情况下圆
上任意一点到
点的直线与平面
交点的轨迹(令为曲线
)为椭圆或圆,且由于小孔成像,曲线
与圆
在视网膜平面上的影像是相似的,则当视网膜平面上的圆
的影像为圆时,圆
的半径
为____________ . 当圆
的半径
满足
时,视网膜平面上的圆
的影像的离心率的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d33c8575602cb3480ba3825dece9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dc6893e52bbca0d011ac46845334d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
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2024-05-09更新
|
94次组卷
|
2卷引用:四川省成都市实验外国语学校2023-2024学年高二上学期期末能力测评数学试题
名校
3 .
,若
有且只有两个零点,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3674866b157f3e7912b53c9cb3e8cee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151a63686f67da8d0534026099971755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 已知定义在上的函数
满足
,且
,则下列说法正确的是
①是奇函数 ②
③ ④
时,
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名校
解题方法
5 . 已知数列
满足
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd21f4cb498101d26b4aaa2e1a6addc.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d01cb54a947465f5640b6c422a049e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd21f4cb498101d26b4aaa2e1a6addc.png)
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2024-03-29更新
|
361次组卷
|
2卷引用:浙江省杭州学军中学紫金港校区2023-2024学年高二上学期期末数学试题
名校
解题方法
6 . 如图所示,已知椭圆
的左右焦点分别为
,点
在
上,点
在
轴上,
,则
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b0dadb875cccce870b69409a476606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68f65429501ec4986bef9cce8dff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ade9ff1a02f622b86b36ffadfbfaae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/13/d4d339ca-022c-40ed-a36d-740d028ccdd3.png?resizew=170)
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2024-03-27更新
|
786次组卷
|
3卷引用:山东省青岛市即墨区2023-2024学年高二上学期1月教学质量检测数学试题
解题方法
7 . 如果
是离散型随机变量,则
在
事件下的期望满足
其中
是
所有可能取值的集合.已知某独立重复试验的成功概率为
,进行
次试验,求第
次试验恰好是第二次成功的条件下,第一次成功的试验次数
的数学期望是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0010cb466163db1349fc1040f6b439.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/97ad71223cc853bc21bf203e7a5321f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385f040f4037e9934620d6971da08131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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解题方法
8 . 已知正项数列
的前n项和
满足
(n为正整数),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
_________ ;记
,若函数
的值域为
,则实数k的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b395a99c51ee3d33279d0650c245593e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2a0686fb74ed14df00e0efefc354d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfc381be76b874a795d81bb6c085116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
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2024高三下·全国·专题练习
9 . 关于曲线
有以下五个结论:
①当
时,曲线C表示圆心为
,半径为
的圆;
②当
,
时,过点
向曲线C作切线,切点为A,B,则直线AB的方程为
;
③当
,
时,过点
向曲线C作切线,则切线方程为
;
④当
时,曲线C表示圆心在直线
上的圆系,且这些圆的公切线方程为
或
;
⑤当
,
时,直线
与曲线C表示的圆相离.
以上正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983416abb2a19329feee784025961f1a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484121f8076509e579f91dd919e4632a.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4681073487d89441a8db549f4187dda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e729c58c343ef3cebb8bd720278c26ed.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d694b4de9f0bef15f2917a4ed214e01c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9891da64b7a4a2f83f2af4d4c313246e.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e8c8fd6d9c4ed8cf35504db1918b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a10732055a4228ab2b1a0f1bb16b67.png)
⑤当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1578a4b2d61c2b65532f5dcb25003.png)
以上正确结论的序号为
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解题方法
10 . 已知
,
是双曲线C:
的左右焦点,过
作双曲线C的一条渐近线的垂线,垂足为N,直线
与双曲线C交于点
,且
均在第一象限,若
,则双曲线C的离心率是________ .
![](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/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbdbe9a17a23c44cec8c7475c4dc1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef02d2d4013d3d82a7eea017f17bca93.png)
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