名校
解题方法
1 . 已知
,且满足
.
(1)求
的值;
(2)若角
的终边与角
的终边关于y轴对称,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fcc0606aa9ce75269c63af6be62f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c0853d16a34fc8b9776ff1a1f29dea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7aee715ac87a76f7a00996af77481ed.png)
(2)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be4e1a0e7c86ad340d097044203cc8df.png)
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2 . 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
,当
与
比赛时,
获胜的概率为p,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a998c92f966aae015d3e1e37c967e7b5.png)
(1)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.
(2)证明:
,
为总冠军的概率大于
为总冠军的概率.
![](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/519321dbfc38d9b89948762478f71d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9454ddb2d570f884b15bd3ddf2a4545d.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/a998c92f966aae015d3e1e37c967e7b5.png)
(1)求最后一轮比赛在水平最高的两名运动员
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae64cb0b1c5e4f556e0ee0ca54fa9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5654866bd68198db845fb43c6b4c858.png)
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名校
3 . 已知函数
是偶函数
(1)求a的值;
(2)若函数
的图像与函数
的图像没有交点,求实数b的取值范围;
(3)若函数
,
是否存在实数k使得
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c4c1150e58f5fc9b9ad5d4b04f07fb.png)
(1)求a的值;
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0d06245241dc3d1d673af1f5990e5f.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6968b2a782093a022764cda7b3c8a497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7758c571ee31edfbd528ada5c822c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
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解题方法
4 .
为正实数,满足
,求
的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19cb3b888b46a0c5e62ccbb09bd77ba.png)
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解题方法
5 . 双五棱锥是由两个侧面均为边长为1的正三角形的五棱锥上下拼接而成的,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/17/7b4e1fa0-9c3c-43ca-b5b3-188c8bc7d378.jpg?resizew=133)
(1)求双五棱锥的内切球半径;
(2)求分别位于拼接面(正五边形)两侧的相邻的两个正三角形构成的二面角的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/17/7b4e1fa0-9c3c-43ca-b5b3-188c8bc7d378.jpg?resizew=133)
(1)求双五棱锥的内切球半径;
(2)求分别位于拼接面(正五边形)两侧的相邻的两个正三角形构成的二面角的余弦值.
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解题方法
6 . 如图,已知三棱柱
,
平面
.D,E分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/03e0cf8e-497b-4d52-a9f4-08f68e020eed.png?resizew=177)
(1)证明:
平面
;
(2)设
与平面
所成角的大小是
,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc117eb1a2d0ea7123b2ca898547546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310e5cf87aa443ca7f0ff80aba6dddc4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/03e0cf8e-497b-4d52-a9f4-08f68e020eed.png?resizew=177)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a8670759c61d785b9a336885df700b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2cf0e95fdf1fd8a5b01d3dfd905e08.png)
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解题方法
7 . 在四面体
中,
为
中点,
为
外接球的球心,
.
(1)证明:
;
(2)若
,求四面体
体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0398ca118304f21b6fc3c36ecf8bf2f4.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab17db0e6518d617247e17afd313a6a2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578b12f739ef7fc54c65b8435b3c16aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af286347445bc77ba5dc6efb5fcc5b8f.png)
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解题方法
8 . 设
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5083da35f1c479de1ce005364043da3.png)
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b958dc0b71559463006d1d5894d12c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5083da35f1c479de1ce005364043da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e3fdecd7a072eac3619a2b5082e63a.png)
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9 . 在正方形ABCD所在的平面内找一点P,使得
,
,
,
均为等腰三角形,求P的个数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8fe4026f1a0745ab9aa9fe64f0e482.png)
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10 . 从1,2,⋯,2024中任取两数
(可以相同),则
个位为
的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff03c70269c31117bef45eb47e618e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
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