1 . 定义函数
,其中
表示不小于
的最小整数,如
,
.当
时,函数
的值域为
,记集合
中元素的个数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab342d472fe409e73bee1be8a61774d3.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90455c0d197e72cce9591f005739447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f344fd588492f8bcbb5f55b2946ea735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddffa0c43a184cd7a2b43a645f46ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6da80ad94ab5ac73d5f69c2131a495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08dbc86aa7e43ee1d538ebd7d997fc01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab342d472fe409e73bee1be8a61774d3.png)
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2021-09-20更新
|
374次组卷
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6卷引用:2015届湖北省黄冈中学高三上学期期中考试理科数学试卷
名校
2 . 在正方形
中,边长
,
的中点为
,现将
沿对角线
翻折(如图),则在翻折的过程中.下列说法正确的是______ .(填正确命题的序号)
![](https://img.xkw.com/dksih/QBM/2020/1/9/2373284223197184/2373910197141504/STEM/3d34b3eb289f4fad9954143a7410becf.png?resizew=302)
①直线
与直线
所成的角为
(
,
不重合时);
②三棱锥
体积的最大值为
;
③三棱锥
外接球的表面积为
;
④点
运动形成的轨迹为椭圆的一部分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c505c02c59313fe0108392a5bf5127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2020/1/9/2373284223197184/2373910197141504/STEM/3d34b3eb289f4fad9954143a7410becf.png?resizew=302)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41ffdaecfb3c73d403179e5745c71a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c9298da3cd8b9db58692e0173f3fd3.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4986217611fc5eefe70fd217a9d5726a.png)
④点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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3 . 定义“等积数列”,在一个数列中,如果每一项与它的后一项的积都为同一个常数,那么这个数列叫做等积数列,这个常数叫做该数列的公积.已知数列
是等积数列且
,公积为10,那么这个数列前41项和
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ec134c205df40f98165c809006fa77.png)
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4 . 已知函数
两个零点差的绝对值为
,若
为质数,
为正整数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1cc71dfc9f9bc46fa170abc968e1deb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8e6ee7ce1ce50718a3e302ebb0f167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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5 . 对于定义在R上的函数
,如果存在实数a,使得
对任意实数
恒成立,则称
为关于a的“
函数”.已知定义在R上的函数
是关于0和1的“
函数”,且当
时,
的取值范围为
,则当
时,
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd025247fb7a6a5ae2b323a7e79c4af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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6 . 对于曲线C所在平面上的定点
,若存在以点
为顶点的角
,使得
对于曲线C上的任意两个不同的点A,B恒成立,则称角
为曲线C相对于点
的“界角”,并称其中最小的“界角”为曲线C相对于点
的“确界角”.曲线
相对于坐标原点
的“确界角”的大小是 _________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c157bfa880fbf4d8592108127cd98f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a382f5752485e05daadecbc39f271b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2019-12-03更新
|
527次组卷
|
4卷引用:上海市上海师范大学附属中学2018-2019学年高三下学期质量检测数学试题
上海市上海师范大学附属中学2018-2019学年高三下学期质量检测数学试题(已下线)课时37 双曲线-2022年高考数学一轮复习小题多维练(上海专用)上海市复兴高级中学2017-2018学年高二上学期期末数学试题上海市川沙中学2022-2023学年高二下学期开学考试数学试题
名校
7 . 定义满足不等式|x
A|<B(A∈R,B>0)的实数x的集合叫做A的B 邻域.若a+b
t(t为正常数)的a+b邻域是一个关于原点对称的区间,则a2+b2的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
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2019-12-01更新
|
354次组卷
|
7卷引用:上海市三林中学2021届高三上学期期中数学试题
名校
8 . 对于函数y=f(x),若存在x0,使f(x0)+f(﹣x0)=0,则称点(x0,f(x0))是曲线f(x)的“优美点”•已知f(x)
若曲线f(x)存在“优美点”,则实数k的取值范围为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b79893efd80c5aed962dab5d1408bf.png)
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9 . 《九章算术》中的“两鼠穿墙题”是我国数学的古典名题:“今有垣厚若干尺,两鼠对穿,大鼠日一尺,小鼠也日一尺,大鼠日自倍,小鼠日自半,问何日相逢,各穿几何?”题意是:“有两只老鼠从墙的两边打洞穿墙,大老鼠第一天进一尺,以后每天加倍;小老鼠第一天也进一尺,以后每天减半.”如果一墙厚10尺,请问两只老鼠最少在第________ 天相遇.
您最近一年使用:0次
2019-11-21更新
|
255次组卷
|
3卷引用:四川省成都市新都区2019-2020学年高三诊断测试文科数学试题
名校
10 . 已知二次函数
(
),若存在
,满足
,则称
为函数
的一个“近似整零点”,若
有四个不同的“近似整零点”,则
的取值范围是________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8afc28970bb2f3052658650f72f541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d54293010aa7ba44e4a6c44cef88e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b503fb6eb2fb077966b15e4ad9cfc9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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