1 . 已知椭圆
的上顶点
与左顶点
的距离为
,离心率为
,
为
轴上一点.
(1)求椭圆方程;
(2)连接
交椭圆于点
,过
点作
轴的垂线,交椭圆另一个点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a0b452fd57bbdc105589e871baa009.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/db98d5309e420e7c638deca07a5b3e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964e47d91c761d9a8caf29cd83f891e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求椭圆方程;
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4673ef63a8d89687b96ee09887ac3daa.png)
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解题方法
2 . 一只小虫在正八面体的表面上爬行,每秒从某一个顶点等可能地爬往4个相邻的顶点之一,则小虫在第八秒爬回初始位置的概率为________
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解题方法
3 . 已知点
,过点P的直线l与x轴、y轴的正半轴分别交于A,B两点,O点为坐标原点,则
的周长的最小值为___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2719ce8a1c0aaa60da102db5712d63e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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4 . 校乒乓球锦标赛共有
位运动员参加.第一轮,运动员们随机配对,共有
场比赛,胜者进入第二轮,负者淘汰.第二轮在同样的过程中产生
名胜者.如此下去,直到第n轮决出总冠军,实际上,在运动员之间有一个不为比赛组织者所知的水平排序,在这个排序中
最好,
次之, …,
最差,假设任意两场比赛的结果相互独立,不存在平局,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363e6156a9f7c1ca23b02e1a6ec63b6a.png)
当
与
比赛时,
获胜的概率为p,其中
,求最后一轮比赛在水平最高的两名运动员
与
之间进行的概率为_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cc8f06c961b64b15a90b99f7adc604.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/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363e6156a9f7c1ca23b02e1a6ec63b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05250abe6da85eb0b555948d7dbaf317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6ba141730fd5aae78ada1a8eb17d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa1c1fc581f356ba5cf85f56fc21801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
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5 .
是
次多项式,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e8936c9fe1e81726455908657a29fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da20e4b3a366685c00621e504a6c6b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
6 . 求所有的
,使
对
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e93438d2a1d82963d4e81fd74cab18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
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7 .
,求所有的
,使得
中有无穷多项为正整数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad039ab9ca99b3d62b798884e8988b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629507dcfdeb6866da428c4f45e2b21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
8 .
是从
中随机抽取3个不同的数排列出的最大的三位数,
是从
中随机抽取3个不同的数排列出的最大的三位数.求
的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9faa718b750cd0be91d5d9b76f948de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c804bc27c6d7423946410c8a98db66bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae370cd09065372355be1ba7b78e6423.png)
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9 . 数列
满足
.前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc625e19e7ca2b9d097f67a3d472e47.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4f3c8c19eea149d50f4ab21eb3288e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc625e19e7ca2b9d097f67a3d472e47.png)
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2024-04-13更新
|
205次组卷
|
2卷引用:第九届高一试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
10 . 定义运算“
”满足:
为从向量
按逆时针方向到向量
的夹角
,向量
垂直于
所确定的平面,当
时,其垂直平面的方向向上;当
时,其垂直平面的方向向下,下列说法一定正确的有__________ .(填序号)
①
;②
;③
;④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872c64b1cc0dd66a0d4f4bb437d6d50b.png)
;⑤当
时,
;⑥
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad8d792188dba9a934ff4e034e6eedd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3dfb49ad8bb91cc8a7488ff6f2b48d.png)
![](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/2624a5cff11216693d7ecc7a8661c945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18020f8f5d3ec9988d05d367b9858fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c82ef71de70fda2db4b882e57bacbb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef7b23414e09377caa0d7fe2e6a5dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932413ffae6ac40f704ef9606bdc06a8.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a5dd9c18ec68a4e1af7a86abb44d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14f57826c118e5772513c03354d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17be5a6799ad26c91a8fd58448a3ce03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872c64b1cc0dd66a0d4f4bb437d6d50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea925583bb5b08798bf5c0f9f43aad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b958a367fa2f08b6202a5a6ebf5e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d94b1db1042e2b0dbe7efb3a6e33190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb176d7f8f34762a45717df116878ed.png)
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