1 . “垛积术”(隙积术)是由北宋科学家沈括在《梦溪笔谈》中首创,南宋数学家杨辉、元代数学家朱世杰丰富和发展的一类数列求和方法,有茭草垛、方垛、刍童垛、三角垛等等.某仓库中部分货物堆放成如图所示的“茭草垛”:自上而下,第一层1件,以后每一层比上一层多1件,最后一层是
件.已知第一层货物单价1万元,从第二层起,货物的单价是上一层单价的
,第
层的货物的价格为______ ,若这堆货物总价是
万元,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357821e0e5595eaf3028df63d47b2c58.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/7b57261d-a961-452f-bedc-60539b6a87e4.png?resizew=106)
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2020-02-05更新
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1073次组卷
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4卷引用:江苏省苏州市昆山市周市高级中学2021-2022学年高三上学期暑期网课自主学习测试数学试题
江苏省苏州市昆山市周市高级中学2021-2022学年高三上学期暑期网课自主学习测试数学试题(已下线)2021年全国新高考Ⅰ卷数学试题变式题13-17题江苏省常州高级中学2023届高三上学期1月月考数学试题辽宁省葫芦岛市2019-2020学年高二上学期期末数学试题
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2 . 已知两定点
,
位于动直线
的同侧,集合
点
到直线
的距离之和等于
,
.则集合
中的所有点组成的图形面积是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd3f69d1431599c1a52eb520042bbad.png)
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3 . 我国南宋数学家秦九韶撰写的名著《数书九章》第五卷提出了“三斜求积术”,即已知三角形三边长,求三角形面积的公式.设三角形的三条边长分别为a,b,c,则三角形的面积S可由公式
求得,其中p为三角形周长的一半,这个公式也被称为“海伦—秦九韶”公式,现有一个三角形的边长满足
,
,则三角形面积的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684c13a2cea962fb204256ca433a4d58.png)
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2020-01-29更新
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392次组卷
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3卷引用:2020届辽宁省大连市高三双基测试数学(文)试题
4 . 在中国古代数学著作《就长算术》中,鳖臑(biēnào)是指四个面都是直角三角形的四面体.如图,在直角
中,
为斜边
上的高,
,
,现将
沿
翻折
,使得四面体
为一个鳖臑,则直线
与平面
所成角的余弦值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
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2020-01-23更新
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614次组卷
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3卷引用:2020年1月浙江省杭州市余杭区部分学校学考高三数学试题
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5 . 给定函数y=f(x),设集合A={x|y=f(x)},B={y|y=f(x)}.若对于∀x∈A,∃y∈B,使得x+y=0成立,则称函数f(x)具有性质P.给出下列三个函数:①
;②
;③y=lgx.其中,具有性质P的函数的序号是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996a92bcfc7fb20171fa1768d5ffddb2.png)
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2020-01-19更新
|
1018次组卷
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7卷引用:北京市第十四中学2021届高三上学期期中考试数学试题
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解题方法
6 . 设函数
与
是定义在同一区间
上的两个函数,若对任意的
,都有
,则称
与
在
上是“
度和谐函数”,
称为“
度密切区间”.设函数
与
在
上是“
度和谐函数”,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2020-04-20更新
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345次组卷
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5卷引用:安徽省六安中学2020-2021学年高三上学期第三次月考数学(理)试题
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7 . 在学习导数和微积分时,应用到了“极限”的概念,极限分为函数极限和数列极限,其中数列极限的概念为:对数列
,若存在常数
,对于任意
,总存在正整数
,使得当
时,
成立,那么称
是数列
的极限,已知数列
满足:
,
,
,由以上信息可得
的极限![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
__________ ,且
时,
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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8 . 设函数
,
,
,
,
,记
,
.则
,
,
大小关系是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04e15196ce905f578e53b845242ee30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425c67c8c78ed8a09410355fe08ee85f.png)
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9 . 在平面直角坐标系
中,已知圆
:
与
轴交于
、
(点
在点
的左侧),圆
的弦
过点
,分别过
、
作圆
的切线,交点为
,则线段
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2020-03-05更新
|
335次组卷
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2卷引用:2020届江苏省淮阴中学、姜堰中学高三12月阶段性测试数学试题
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10 . 等差数列
中,
,
,给出下列命题:①
,②
,③
是各项中最大的项,④
是
中最大的值,⑤
为递增数列.其中正确命题的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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