名校
1 . 已知圆
,线段
的端点
的坐标是
,端点
在圆
上运动,且点
满足线段
,记
点的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
斜率为
的直线
与曲线
交于
,
两点,试探究:
①设
为坐标原点,若
,这样的直线
是否存在,若存在求出
;若不存在说明理由;
②求线段
的中点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41767cfe358450ef663200c7584ec024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1a6ce0b35896c8a1c687a4376e71f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560ab719df4b08d983743834d6d2bbc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d4d5ec4ecac0ed3f8b97665de2cb91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc878a5fd7b508cf817cbb65d3940547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63bdadca45fe8b843e36198736ccccdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac35b1e8a952aac4f4cdaaf02d868d04.png)
②求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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2021-12-09更新
|
1076次组卷
|
4卷引用:安徽省黄山市屯溪第一中学2021-2022学年高二上学期期中数学试题
名校
2 . 观察下列各式:
①
②
③
…探索以上式子的规律.
(1)第2021个式子是___________.
(2)试写出第n个等式,并证明第n个等式成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a0b193ae55b2e61567ff2fd45feab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8043e02f089d1ff72e2d14f950b768da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079ecc8973d0d46e39c5024832587a98.png)
…探索以上式子的规律.
(1)第2021个式子是___________.
(2)试写出第n个等式,并证明第n个等式成立.
您最近一年使用:0次
2021-09-03更新
|
86次组卷
|
2卷引用:安徽省黄山市屯溪第一中学2020-2021学年高二下学期期中文科数学试题
解题方法
3 . 一个棱长为2的正方体,用过同一顶点三条棱的中点平面截去各个顶点得到的一个新的几何体,对这个新的几何体说法错误的是( )
A.所有截面面积和为![]() | B.新几何体表面积为![]() |
C.新几何体表面积为![]() | D.新几何体的体积为![]() |
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2021-08-28更新
|
379次组卷
|
3卷引用:安徽省黄山市屯溪第一中学、中科大附中2020-2021学年高一下学期期中联考数学试题
安徽省黄山市屯溪第一中学、中科大附中2020-2021学年高一下学期期中联考数学试题(已下线)第08讲 简单几何体的表面积和体积(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)安徽省滁州市定远县育才学校2021-2022学年高一下学期5月月考数学试题
4 . 如图所示是《数列》一章的知识结构图,下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763481566658560/2777724324782080/STEM/25878dc40ea04df8b70238ece4c825bb.png?resizew=290)
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763481566658560/2777724324782080/STEM/25878dc40ea04df8b70238ece4c825bb.png?resizew=290)
A.“概念”与“分类”是从属关系; |
B.“等差数列”与“等比数列”是从属关系; |
C.“数列”与“等差数列”是从属关系; |
D.“数列”与“等差数列”是从属关系,但“数列”与“分类”不是从属关系. |
您最近一年使用:0次
名校
5 . 已知矩形
满足
,
,
是正三角形,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763481400066048/2778026887249920/STEM/481490f53c3640ebafab18c39e096d44.png?resizew=232)
(1)求证:
;
(2)设直线
过点
且
平面
,点
是直线
上的一个动点,且与点
位于平面
的同侧,记直线
与平面
所成的角为
,若
,求
的取值范围.
![](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/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763481400066048/2778026887249920/STEM/481490f53c3640ebafab18c39e096d44.png?resizew=232)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(2)设直线
![](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/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167eb605937f4390726d63ccf9d45002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
2021-08-03更新
|
169次组卷
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3卷引用:安徽省黄山市2020-2021学年高一下学期期末数学试题
6 . 在坐标平面内横纵坐标均为整数的点称为格点.现有一只蚂蚁从坐标平面的原点
出发,按如下线路沿顺时针方向爬过格点:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295492fc0519118488a5efabdf2afd7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cf6590154c8e47b658762dbc7f8dba.png)
,则蚂蚁在爬行过程中经过的第114个格点
的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295492fc0519118488a5efabdf2afd7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cf6590154c8e47b658762dbc7f8dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa7f738951fee6021e5b3a77160436d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7965779f786d8ca67f42800c566d0d83.png)
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763481566658560/2777724325150720/STEM/48c235567a6a436390587cc5f9ea101e.png?resizew=199)
您最近一年使用:0次
2021-08-02更新
|
165次组卷
|
2卷引用:安徽省黄山市2020-2021学年高二下学期期末文科数学试题
7 . 如图是高尔顿板的改造装置,当小球从
自由下落时,第一次与第二层中间的小木块碰撞,以
的概率向左或向右滚下,依次经过
次与小木块碰撞,小球最后进入槽口
处,则小球进入
处的概率为( )
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763481738346496/2776290518736896/STEM/5d7227b5-f75a-4605-8132-c8695be9c436.png?resizew=184)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763481738346496/2776290518736896/STEM/5d7227b5-f75a-4605-8132-c8695be9c436.png?resizew=184)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
8 . 随着老旧小区的改造,小区内的设施越来越完善,也有越来越多的居民用上了天然气.某然气公司为了制定天然气分档价格表,在全市随机抽取了200户居民,对其月均使用天然气的情况进行了调查,统计如下:
(1)求这200户居民的月均使用天然气的平均数
与标准差
的估计值(同一组中的数据用该组区间的中点值为代表)(结果精确到
);
(2)①已知全市居民的天然气月均使用量服从正态分布
,其中
分别取(1)中的
,
.现从全市居民任取一户,求该户天然气的月均使用量在区间
的概率;
②现从该市某小区任意抽取
户,记
表示这
户天然气的月均使用量在区间
的户数,求
的数学期望.
附:
,
,
,
月均用气量 | ![]() | ![]() | ![]() | ![]() | ![]() |
户数 | ![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87796ee30e6c5d5e6b6285b32abe10c.png)
(2)①已知全市居民的天然气月均使用量服从正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84c2c26cbb6b22a415fd0830401aeac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97dc0c4d9a68ca8ce797958f9084fd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0b175f394233f08ac25b70c0bab1db.png)
②现从该市某小区任意抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0b175f394233f08ac25b70c0bab1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affea1146bab950a7b978ad43cc62f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afa8e39e2e5bb0f5edf0ced8b99bb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ed6b426f34f2fb03066b495fbe8f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d3ae32667530b06edc80877d055e74.png)
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9 . (1)已知等差数列
中,首项
,公差
.求证:对任意正整数
,
,
,
都不成等差数列;
(2)已知
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b753c8ac2884e125fd3f3f4bfc56bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7e761be88728b3db50c2abd4377c12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06c4de60ad6a35764da233bd35c9a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192e541a4964ded591ba25ea3284827d.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a204c74f3b77e2ea203554481a54fed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa75bafd5db4c6b73126dacea72322d.png)
您最近一年使用:0次
10 . 在平面内,余弦定理给出了三角形的三条边与其中的一个角之间的关系.应用余弦定理,可以从已知的两边和夹角出发,计算三角形的第三边.我们把四面体与三角形作类比,并使四面体的面对应三角形的边,四面体各面的面积对应三角形各边的边长.而三角形两边的夹角,对应四面体两个面所成的二面角,这样可以得到“四面体的余弦定理”.现已知一个四面体
,
,
,二面角
,二面角
,二面角
为直二面角,则三角形
的面积为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1c768153258701b633e4198a5076bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a35d6900a9f7f3ea006d6fca13cc6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8136a77077c5ece74f4018185d7b70f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d778f77e525ac254b22ba54c4ba4d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07603856df484739f00c4f19905f3ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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