1 . 已知函数
.
(1)若曲线
在
处的切线与
轴垂直,求
的极值.
(2)若
在
只有一个零点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2f49cb8095d79914f4c1a8f75dfd75.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 如图,在四棱锥
中,底面
是边长为2的正方形,
平面
,
,
是
中点,
是
中点.
平面
;
(2)若
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb26a48f8374885250345659418585c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5a4dfcf4c24a8ecb210cc4c53db221.png)
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3 . 记
为等差数列
的前
项和,已知
,
.
(1)求
的通项公式;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9651204c54475c2e8cda8d0a6eeba177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5032706dd285c22e149c675da465d9ac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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今日更新
|
687次组卷
|
2卷引用:陕西省西安市第一中学2023-2024学年高三下学期高考考前模拟考试理科数学试题
名校
解题方法
4 . 已知函数
.
(1)当
时,证明:
.
(2)若函数
,试问:函数
是否存在极小值?若存在,求出极小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101e3891ef8ae75f240e6081b9d0dc81.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b12f2ff24c52fded1dfd0f0b6940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f88baa414c8b4a16a46234b7b1d874d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d85caf6029742b5c99994233f76e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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名校
解题方法
5 . 在
中,角
,
,
所对的边分别为
,
,
,已知
,
,
.
(1)求
的值;
(2)求
的值;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f317b022b06f638d7a5d08c8cdf43a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5204b80258bb8536bd73d0221e2e3243.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dcfa3e340b3976832d450dd4ae7e7a7.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afaae441de0ffcd471bd58b16cd3fbd0.png)
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名校
解题方法
6 . 宜昌市是长江三峡起始地,素有“三峡门户”、“川鄂咽喉”之称.为了合理配置旅游资源,管理部门对首次来宜昌旅游的游客进行了问卷调查,据统计,其中
的人计划只参观三峡大坝,另外
的人计划既参观三峡大坝又游览三峡人家.每位游客若只参观三峡大坝,则记1分;若既参观三峡大坝又游览三峡人家,则记2分.假设每位首次来宜昌旅游的游客计划是否游览三峡人家相互独立,视频率为概率.
(1)从游客中随机抽取2人,记这2人的合计得分为
,求
的分布列和数学期望;
(2)从游客中随机抽取
人
,记这
人的合计得分恰为
分的概率为
,求
;
(3)从游客中随机抽取若干人,记这些人的合计得分恰为
分的概率为
,随着抽取人数的无限增加,
是否趋近于某个常数?若是,求出这个常数;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
(1)从游客中随机抽取2人,记这2人的合计得分为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)从游客中随机抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ee630a60a614286996835ddb63bb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8040a226539b2c3c6ad15a0d71880fa.png)
(3)从游客中随机抽取若干人,记这些人的合计得分恰为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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7 . 跑步是人们日常生活中常见的一种锻炼方式,其可以提高人体呼吸系统和心血管系统机能,抑制人体癌细胞生长和繁殖.为了解人们是否喜欢跑步,某调查机构在一小区随机抽取了40人进行调查,统计结果如下表.
(1)根据以上数据,判断能否有95%的把握认为人们对跑步的喜欢情况与性别有关?
(2)该小区居民张先生每天跑步或开车上班,据以往经验,张先生跑步上班准时到公司的概率为
,张先生跑步上班迟到的概率为
.对于下周(周一~周五)上班方式张先生作出如下安排:周一跑步上班,从周二开始,若前一天准时到公司,当天就继续跑步上班,否则,当天就开车上班,且因公司安排,周五开车去公司(无论周四是否准时到达公司).设从周一开始到张先生第一次开车去上班前跑步上班的天数为
,求
的概率分布及数学期望
.
附:
,其中
.
喜欢 | 不喜欢 | 合计 | |
男 | 12 | 8 | 20 |
女 | 10 | 10 | 20 |
合计 | 22 | 18 | 40 |
(2)该小区居民张先生每天跑步或开车上班,据以往经验,张先生跑步上班准时到公司的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187714e660234f0b72f2b47d3ea685a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.100 | 0.050 | 0.025 | 0.010 | 0.001 | |
2.706 | 3.841 | 5.024 | 6.635 | 10.828 |
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名校
8 . 如图,在直四棱柱
中,
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
平面
;
(2)求
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96486f5fd1670d138c22b9480635d24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2095691cd6e3e50722061cbc0bb648.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2095691cd6e3e50722061cbc0bb648.png)
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9 . 已知数列
的首项
且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27abc0ddb1696ba33720fe25cb57fb75.png)
(1)证明:
是等比数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8268477a9da05189133a427668aa4c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27abc0ddb1696ba33720fe25cb57fb75.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5816ff5a1585c9b748b13f5b8bd0b6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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昨日更新
|
299次组卷
|
2卷引用:宁夏回族自治区银川一中2024届高三第三次模拟考试理科数学试题
名校
10 . 为了回馈长期以来的顾客群体,某健身房在五周年庆活动期间设计出了一种游戏活动,顾客需投掷一枚骰子三次,若三次投掷的数字都是奇数,则该顾客获得该健身房的免费团操券5张,且有2次终极抽奖机会(2次抽奖结果互不影响);若三次投掷的数字之和是6,12或18,则该顾客获得该健身房的免费团操券5张,且有1次终极抽奖机会;其余情况顾客均获得该健身房的免费团操券3张,不具有终极抽奖机会.已知每次在终极抽奖活动中的奖品和对应的概率如下表所示.
(1)已知某顾客有两次终极抽奖机会,求该顾客获得一个健身背包和一盒蛋白粉的概率;
(2)求一位参加游戏活动的顾客获得蛋白粉的概率.
奖品 | 一个健身背包 | 一盒蛋白粉 |
概率 | ![]() | ![]() |
(2)求一位参加游戏活动的顾客获得蛋白粉的概率.
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