名校
1 . 已知
内角
的对边分别为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd623ea765c80b3ba260e99f3504f481.png)
(1)求
的取值范围
(2)求
内切圆的半径的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd5b9bbd3d22bd2cef53dd4b9691257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd623ea765c80b3ba260e99f3504f481.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2fba30396c2d5cdd37433f34a70ef20.png)
(1)若函数
为偶函数,求
的值;
(2)当
时,(ⅰ)函数
,(ⅱ)若关于x的方程
有两个不同的实根
且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2fba30396c2d5cdd37433f34a70ef20.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d41244547838992c51263681a0ed2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8b79cbafa3dd8602fa3a103b5000d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4b360499547299003d8f5617f6c0ee.png)
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3 . 甲、乙两名乒乓球运动员进行一场比赛,采用7局4胜制(先胜4局者胜,比赛结束).已知每局比赛甲获胜的概率均为
,则甲以4比2获胜的概率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 如图,四棱锥
中,平面
平面
,
,
,
,
,
,
,
.设
中点为
,过点
的平面
同时垂直于平面
与平面
.
与平面
夹角的正弦值;
(2)求平面
截四棱锥
所得多边形的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e7cedc39297d66dbb177f2a1f6bee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c42bce098904b241986bb91c65ab33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d212c1709b8e72a055cf1b5381ef64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53df2a88f461611f7159d0f2f8ef60e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/421291381be28da4bd16560fd383b4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663f139d687116cba2d3badfbfb987cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b972027fef607dc50001a3895442a32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea03a10b5bbd8e745ecce6f3e598375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecfe1bf6f7bfe17f9bd28e97b0147f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383ec3453527947ed7a5960e9a8fbe0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c42bce098904b241986bb91c65ab33.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e7cedc39297d66dbb177f2a1f6bee2.png)
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解题方法
5 . 一个顶点为
,底面中心为
的圆锥体积为1,若正四棱锥
内接于该圆锥,平面
与该圆锥底面平行,
这4个点都在圆锥的侧面上,则正四棱锥
的体积的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 设
的内心为
,而且满足
,则
的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83664722706f3e4b272abf0cb7f523e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bcf5c0ccfc3f1a40c4430246edf4c8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 已知函数
,则关于
的方程
根的个数可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fecc39e5595d13318f6071ba4a56b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfde98d1334bbb9375d8df7130e379c.png)
A.0个 | B.1个 | C.2个 | D.3个 |
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8 . 常用放射性物质质量衰减一半所用的时间来描述其衰减情况,这个时间被称做半衰期,记为
(单位:天).铅制容器中有甲、乙两种放射性物质,其半衰期分别为
.开始记录时,这两种物质的质量相等,512天后测量发现乙的质量为甲的质量的
,则
满足的关系式为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5dd698ddbe275267809650dc551e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5dd698ddbe275267809650dc551e34.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 饮料瓶的主要成分是聚对苯二甲酸乙二醇酯,简称“PET”.随着垃圾分类和可持续理念的普及,饮料瓶作为可回收材料的“主力军”之一,得以高效回收,获得循环再生,对于可持续发展具有重要意义,上海某高中随机调查了该校某两个班(A班,B班)5月份每天产生饮料瓶的数目(单位:个),并按
分组,分别得到频率分布直方图如下:下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e676fe6ace0deae41bfa6b95e886f26.png)
A.![]() |
B.![]() ![]() |
C.已知该校共有学生1000人,则约有150人5月份产生饮料瓶数在![]() |
D.![]() |
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解题方法
10 . 已知
,
,则
在
上的投影向量为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f9df42552e714a5212708a04e160f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7205fd44617e416b38e5b0658d78ce96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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