名校
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1 . 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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2 . 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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3 . 已知f(x)是定义在R上的奇函数,
且对任意
均有
则 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9eacff7f456194640de6801dc94799a.png)
_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a2ffb7236b18cec72e965944a2ed75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6f37ea158078072f8bd7771119d077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa07570d61c2b610b8e5bbf93d944047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9eacff7f456194640de6801dc94799a.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 . 设
.在
的方格表的每个小方格中填入区间
中的一个实数.设第i行的总和为
,第i列的总和为
.求
的最大值______ (答案用含a的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f98da45d4de19a962cfa1d186e2755a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ace7d64e7ff100db25a07330654d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af908bca1b10f5de7e2d8979989c806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352c5c9b17f090e53bcdfd9e05c7e5fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a71c7129333f890292aa75bc1d080a7.png)
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解题方法
6 . 设集合
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1336d38741aab2255a35c26612bbd7cc.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572da1779063e50817003fdf378f5452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48df188a1720f0b293a350eb2f6e05c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1336d38741aab2255a35c26612bbd7cc.png)
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2024-04-15更新
|
340次组卷
|
2卷引用:贵州省贵阳市北京师范大学贵阳附属中学2023-2024学年高二下学期3月第一届“圆周率”杯竞赛数学试题
7 . 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)
8 . 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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9 . 已知O,A,B,C四点均在半径为
的球S的表面上,并且满足
,
平面
,
,则三棱锥
的体积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0bac81568b8624599b4b9b39fbae2f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886c25cbaff27a9c4cf52dacec0eac4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa3a310c1f8a5af35dc3328d874e18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2166bb9a23c7ed545791eb6b5d66858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
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10 . 从由正数组成的集合A中随机地选出一个数
的概率为
,则在下面给出的四个集合中:①
;②
;③
;④
.
能当成集合A的为______ (填上符合要求的所有序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5d56dd753b6e01de12da6168e86cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a96775b72021e81351f88745cd9abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2e24d0f06625ed7fb1ecbd5bcd2348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1980f8c04858721acfdbc8bd1e2368df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47ef75dd4e477266b40de5136b14f89.png)
能当成集合A的为
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