1 . 在四面体ABCD中,
,
,E,F,G分别是棱BC,AC,AD上的动点,且满足AB,CD均与面EFG平行,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def26b3c1c08356f8fa49c85fe19476b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7845382d527f8e73c2d1d1892ff4fa6.png)
A.直线AB与平面ACD所成的角的余弦值为![]() |
B.四面体ABCD被平面EFG所截得的截面周长为定值1 |
C.![]() ![]() |
D.四面体ABCD的内切球的表面积为![]() |
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2023-09-26更新
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3卷引用:安徽省皖东名校联盟体2024届高三上学期9月第二次质量检测数学试题
名校
解题方法
2 . 直观想象是数学六大核心素养之一,某位教师为了培养学生的直观想象能力,在课堂上提出了这样一个问题:现有10个直径为4的小球,全部放进棱长为a的正四面体盒子中,则a的最小值为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-09-26更新
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6卷引用:安徽省皖东名校联盟体2024届高三上学期9月第二次质量检测数学试题
安徽省皖东名校联盟体2024届高三上学期9月第二次质量检测数学试题四川省成都市2023-2024学年高二上学期九月调研考试(校级联考)数学试题(已下线)考点16 立体几何中的最值问题 2024届高考数学考点总动员【讲】(已下线)第11章 简单几何体(压轴必刷30题专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)吉林省白山市抚松县第一中学2023-2024学年高一下学期5月期中考试数学试题吉林省长春外国语学校2023-2024学年高一下学期5月期中考试数学试题
名校
3 . 若定义在
上的函数
满足:
的单调区间与
的单调区间完全相同,则称
为“二阶和谐函数”.
(1)求证:
是“二阶和谐函数”;
(2)若
是“二阶和谐函数”,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.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/16e56e3224d58e0cfd256493f3fc63df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a903745cd2cb536443d07579b606ece5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5491a30b301f7e0ce29db9e2c864b9bc.png)
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4 . 已知,在
中,
,
,D为线段
上一点,连接
,过点C作
,
,连接
,延长
到点E,连接
,使得
.
(1)如图1,若
,求
的长;
(2)如图2,点G是线段
上一点,连接
,过点G作
,过点D作
,交
于点H,求证:
;
(3)如图3,点M为
上一点,连接
,若
,
,请直接写出
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1a23f51a2ff0896988930f5209fc64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aebb5baea4ac1668b674a8634e15bcbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3a050023572923d07e5dfe7331d1d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/3/97c4562d-ecff-4562-8162-8990277527e8.png?resizew=587)
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1952b05bb629483a8217cf507f9309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
(2)如图2,点G是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4db1e6666de61eb94dd749fc95496d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfab24a9cb9315013b7e288ffe3eca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ca5432277c7163b99aabbccc254731.png)
(3)如图3,点M为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5fc7b695498b5f84bb41f0b3404e786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0277e5c10716e890877bf7daf1cbac93.png)
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5 . 如图,一次函数
的图象与x轴和y轴分别交于点B和点C,二次函数
的图象经过B,C两点,并与x轴交于点A.点
是线段
上一个动点(不与点O、B重合),过点M作x轴的垂线,分别与二次函数图象和直线
相交于点D和点E,连接
.
(1)求这个二次函数的解析式;
(2)①求
、
的值(用含m的代数式表示);
②当以C,D,E为顶点的三角形与
相似时,求m的值.
(3)点F是平面内一点,是否存在以C,D,E,F为顶点的四边形为菱形?若存在,请直接写出点M的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae652daf6059ff386f99bef2210518c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62769b7177ef4bc952dc1dd51d6b510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/3/fb45000a-be63-43b1-b1d3-77f73cd6044d.png?resizew=170)
(1)求这个二次函数的解析式;
(2)①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
②当以C,D,E为顶点的三角形与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)点F是平面内一点,是否存在以C,D,E,F为顶点的四边形为菱形?若存在,请直接写出点M的坐标;若不存在,请说明理由.
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2023-09-02更新
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2卷引用:安徽省六校教育研究会2022-2023学年高一上学期新生入学素质测试数学试题
6 . 已知抛物线C的标准方程为
,O为坐标原点,直线l为其准线,点A,B是C上的两个动点(不是原点O),线段
与x轴交于点M,连接
并延长交准线于点D,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
A.若点M为C的焦点,则直线![]() |
B.若点M为C的焦点,则线段![]() |
C.若![]() |
D.若![]() ![]() |
您最近一年使用:0次
7 . 已知抛物线
的焦点为
是抛物线上的两点,则下列说法中正确的是:( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a78559c9184218b6ca26670a268a23.png)
A.若线段![]() ![]() ![]() ![]() |
B.若线段![]() ![]() ![]() ![]() ![]() |
C.已知![]() ![]() ![]() ![]() ![]() ![]() |
D.抛物线上一动点![]() ![]() ![]() ![]() |
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名校
解题方法
8 . 古希腊数学家特埃特图斯(Theaetetus)利用如图所示的直角三角形来构造无理数. 已知
与
交于点
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194ff7014ac137d916bb11e430c837c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a1c30dd9f8080504a727abfb7fc567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-08-30更新
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1875次组卷
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7卷引用:安徽省A10联盟2024届高三上学期8月开学摸底考试数学试题
安徽省A10联盟2024届高三上学期8月开学摸底考试数学试题(已下线)第6章 平面向量初步-【优化数学】单元测试能力卷(人教B版2019)(已下线)专题11 平面向量小题全归类(练习)(已下线)专题01 平面向量压轴题(1)-【常考压轴题】重庆市涪陵第五中学校2023-2024学年高一下学期第一次月考数学试题河南省信阳市新县高级中学2024届高三考前第一次适应性考试数学试题重庆市部分学校2023-2024学年高一下学期5月月考数学试题
解题方法
9 . 已知以
为焦点的椭圆过
,记椭圆的另一个焦点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若直线
是曲线
的切线,且
与直线
和
分别交于点
,与
轴交于点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b3e7debe7a0950ae4367503d2929b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9c11cc36320090d0aaf0c621a63b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3b4416a186069ad6dbe9d9c1ed76e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfc8110ad2ae77111a45851aa0d5207.png)
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名校
解题方法
10 . 若函数
满足在定义域内的某个集合
上,对任意
,都有
是一个常数,则称
在
上具有
性质.
(1)设
是
上具有
性质的奇函数,求
的解析式;
(2)设
是在区间
上具有
性质的偶函数,若关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284756dd945e503ed2c497cf8219b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204cb82cb2f3ec6865eae88e3de8b809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e1f7e57c2217e251d4f62d54a29d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2023-07-25更新
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3卷引用:安徽省阜阳市2022-2023学年高一下学期期末教学质量统测数学试卷