1 . 黎曼函数(Riemann function)在高等数学中有着广泛应用,其一种定义为:
时,
,若数列
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27b29af44657073c9966ac5529db772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53f0964519bd9a2d6b2a95a52f23397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
2 . 已知椭圆
:
的离心率为
,斜率为
的直线
与
轴交于点
,
与
交于
,
两点,
是
关于
轴的对称点.当
与原点
重合时,
面积为
.
(1)求
的方程;
(2)当
异于
点时,记直线
与
轴交于点
,求
周长的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8059a935a2325a9e7abbcbf56aa167f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a6b832d2922f5c5fea6a1143250f70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.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/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
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3 . 已知数列
的前n项和为
,且满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234605545a58197b26d52799abbb17b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fbdd2e3efbef1ff014df55b242eced.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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今日更新
|
423次组卷
|
3卷引用:河北省张家口市2024届高三下学期第三次模拟考试数学试卷
名校
4 . 射影几何学中,中心投影是指光从一点向四周散射而形成的投影,如图,光从
点出发,平面内四个点
经过中心投影之后的投影点分别为
.对于四个有序点
,若
,
,定义比值
叫做这四个有序点的交比,记作
.
时,称
为调和点列,若
,求
的值;
(2)①证明:
;
②已知
,点
为线段
的中点,
,
,求
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fc2a215a63f1846cdc94cc0260d4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcda6a2a013e61f30eac744d57ab86fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9440bcb5362e00e5a6b4af27940b3007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a881d00bcb6fcdc1029c55898c464d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1c84057882768f20a01365c81b6760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e839a2f596ac7266b6ff41a35c4a94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274f162e5e5a9d358342ddbe2b6c1519.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73966616bd0b56416b4089a6dc884347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5ed371ae0038e0d5d2717418869b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70bcf4326b5da2c4cf1caf567b55d1a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb0c703f6effcbcf1770569971b3cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34da8e5ecc3d124fd1455c8a18bd45a.png)
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解题方法
5 . 为了选拔雏鹰计划的预备人员,某地区教育局对高一年级新生进行了测试(测试分为初试和复试).现共有400名学生参加初试,且所有学生的初试成绩
近似服从正态分布
,根据以往入选同学的初试和复试成绩走势,本届复试作出如下规定:①初试成绩高于91分者免于复试,直接确定为雏鹰计划的预备人员;②初试成绩高于80分且不超过91分的学生有资格参加复试,下图为从以往入围雏鹰计划预备人员的所有同学中随机抽取的20名同学的的初试和复试成绩.
(2)复试试题由两道数学题和两道物理题构成,已知数学题的难度系数为0.5(可以理解为进入复试的学生答对每道数学题目的概率是0.5),物理题目的难度系数均为
,能否答对这些题目相互独立,每个考生需答完四个题目,至少答出其中三个即通过复试并确定为雏鹰计划的预备人员,如果本次确定为雏鹰计划的预备人员数目不能超过33人,请确定物理试题的难度系数
的取值范围.
附:若随机变量
服从正态分布
,则
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0210a70d3664db67006ecd0cbc88e864.png)
(2)复试试题由两道数学题和两道物理题构成,已知数学题的难度系数为0.5(可以理解为进入复试的学生答对每道数学题目的概率是0.5),物理题目的难度系数均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfc26b8bdcd1fd3781c4593217c725e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04398619f7b3251b93fb34cc14930f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14360db70f4872cf5b47f12090fc211b.png)
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解题方法
6 . 已知函数
.
(1)求函数
的最值;
(2)若
,设曲线
与
轴正半轴的交点为
,该曲线在点
处的切线方程为
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd14ea273c21800c00132219688c61c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c28eea59d06bd471fb15d2111014817.png)
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解题方法
7 . 如图所示,在棱长为2正方体
中,
分别为
的中点,
为侧面
内的动点(不包含边界),且
//平面
,
是三角形
内一动点(包含边界),且直线
与直线
的夹角等于直线
与直线
的夹角,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c427d77e282b60f0d65cd332a281b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03a049b1a67f3bfd2f11b3521a141cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59375dfae3a8ec264204cfe78caac97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9104c2027ce95a663dfd92d68835a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
A.存在点![]() ![]() |
B.点![]() ![]() |
C.三棱锥![]() ![]() |
D.过点![]() ![]() ![]() ![]() ![]() |
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8 . 已知函数
,若存在
使得
,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd2c7b8627bd16e0fc05cfff8ae880d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6440574a832dc3d79d8172b07bc5fc6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知函数
,若
,则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571bdbe6e09cf983787cb70c4b811d64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6cc553a81e66a1b15d457aa39a72917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 函数
的函数值表示不超过
的最大整数,例如,
.下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1550a97c21c1d71c9e95dde569668be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2ae14cdf62d0a69dda9a58d1ea9640.png)
A.函数![]() ![]() |
B.若![]() ![]() |
C.![]() |
D.所有满足![]() ![]() ![]() |
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