1 . “杨辉三角”是中国古代数学文化的瑰宝之一,最早出现在南宋数学家杨辉于1261年所著的《详解九章算法》一书中.“杨辉三角”揭示了二项式系数在三角形数表中的一种几何排列规律(如图所示),则“杨辉三角”中第30行中第12个数与第13个数之比为__________ .
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2 . 函数
在
上的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37afa854716507fca59b6210f79ed59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97ab84192e12bb292bc9fbd0b29fbee.png)
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3 . 三个车间生产同样的零件,其中1号车间生产的占
号车间生产的占
号车间生产的占
.已知1号车间,2号车间,3号车间生产的零件分别有
和
不合格.现有一批由1号车间,2号车间,3号车间生产的零件,从中随机地抽取一个零件,则取到的是不合格零件的概率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e3dc9421f8f1c26ae116c0ac3b2bd7.png)
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4 . 已知等差数列
的前
项和为
,若
,
,
成等差数列,
,
,
成等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
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5 . 在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等比数列.若
为1阶等比数列,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_________ ;若数列
是2阶等比数列,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6016be828be0c8e87f425f3b9437ba1.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
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6 . 已知某食品厂生产的一款袋装食品的质量
(单位:
)服从正态分布
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcde38205c0695488450dd091221a3ba.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3960d67499df76159982657fe3a1cbca.png)
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7 . 平面几何中有定理:若点
为锐角
的外心,直线
,
,
分别与锐角
外接圆交于另外一点
,
,
,则
,若锐角
的外接圆方程为
,且该圆与
轴的交点分别为
,
,则六边形
的面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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8 . 第三次人工智能浪潮滚滚而来,以ChatGPT发布为里程碑,开辟了人机自然交流的新纪元.ChatGPT所用到的数学知识并非都是遥不可及的高深理论,概率就被广泛应用于ChatGPT中,某学习小组设计了如下问题进行研究:甲和乙两个箱子中各装有5个大小相同的小球,其中甲箱中有3个红球、2个白球,乙箱中有4个红球、1个白球.掷一枚质地均匀的骰子,如果点数小于等于4,从甲箱子中随机抽出1个球;如果点数大于等于5,从乙箱子中随机抽出1个球,若抽到的是红球,则它是来自乙箱的概率是______________ .
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9 . 如图,在四面体
中,
与
均是边长为
的等边三角形,二面角
的大小为
,则此四面体的外接球表面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
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2024-06-08更新
|
727次组卷
|
2卷引用:广西柳州市第一中学2023-2024学年高二下学期阶段性期中考试数学试题
解题方法
10 . 已知点M在直线
上,点P在圆
上,过点M引圆C的两条切线,切点分别为A,B,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea0ebea8c46d415c3ee394f201b3865d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf403ffe0ea3647c53782ea0dd5618f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
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