解题方法
1 . 已知函数
.
(1)求
的极值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcea74d330997ee9c92a223c0335851.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ef77c5ca443b038dd5be9edd4e05f6.png)
您最近一年使用:0次
7日内更新
|
1858次组卷
|
3卷引用:2024届山东省威海市高考二模数学试题
名校
2 . 如图,在四棱锥
中,平面
⊥平面
,
为等边三角形,
,
,
,
,M为
的中点.
⊥平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e18836bc7fee22f8f813a6f525d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77dd36d86b0f066b437e5ffec67110ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f35614aff055b98b76ca262f64e629d.png)
您最近一年使用:0次
2024-06-05更新
|
1392次组卷
|
5卷引用:2024届山东省威海市高考二模数学试题
2024届山东省威海市高考二模数学试题(已下线)第五套 艺体生新高考全真模拟 (二模重组卷)(已下线)湖南省益阳市2024届高三下学期5月适应性考试数学试题广东省江门市鹤山市第一中学2023-2024学年高二下学期第二阶段考试(5月)数学试题江苏省海门中学2023-2024学年高二下学期5月学情调研数学试卷
3 . 在直角坐标系xOy中,已知曲线C:
过点
,且与x轴的两个交点为A,B,
.
(1)求C的方程;
(2)已知直线l与C相切.
(i)若l与直线
的交点为M,证明:
;
(ii)若l与过原点O的直线相交于点P,且l与直线OP所成角的大小为45°,求点P的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3666050060fb25232784bb8ed3545ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
(1)求C的方程;
(2)已知直线l与C相切.
(i)若l与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4563a428e0d34788fca58fb099bc0191.png)
(ii)若l与过原点O的直线相交于点P,且l与直线OP所成角的大小为45°,求点P的轨迹方程.
您最近一年使用:0次
4 . 设
,y是不超过x的最大整数,且记
,当
时,
的位数记为
例如:
,
,
.
(1)当
时,记由函数
的图象,直线
,
以及x轴围成的平面图形的面积为
,求
,
及
;
(2)是否存在正数M,对
,
,若存在,请确定一个M的值,若不存在,请说明理由;
(3)当
,
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9322dd8f56b5f8d2c667fdf0d4a9f9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b7f26fe1977bda9de200debe99f020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888f3535e96d599e0840c74f44e90293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2fd68df194a8b9f184abb07ada0877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290d361e6c11b7c934a53d866a73522.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290e62b6c28d766f6a64fc6557667db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c9cfd43ce24a0d820f0044d9c837db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae72830ccc2633ada579cf63fd6932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831ed34d8c6d99fdd0b94688ef03bfcb.png)
(2)是否存在正数M,对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c21606ef2837d3a77d25e0c6473731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf968fe2653e0b497d78907096467d9.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b95079ade5ac98fc651fafc489761f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49fd568e4f8120ace4d486adc764f55.png)
您最近一年使用:0次
解题方法
5 . 市场供应的某种商品中,甲厂产品占60%,乙厂产品占40%,甲厂产品达到优秀等级的概率为90%,乙厂产品达到优秀等级的概率为65%.现有某质检部门对该商品进行质量检测.
(1)若质检部门在该市场中随机抽取1件该商品进行检测,求抽到的产品达到优秀等级的概率;
(2)若质检部门在该市场中随机抽取4件该商品进行检测,设抽到的产品中能达到优秀等级的件数为X,求X的分布列和数学期望.
(1)若质检部门在该市场中随机抽取1件该商品进行检测,求抽到的产品达到优秀等级的概率;
(2)若质检部门在该市场中随机抽取4件该商品进行检测,设抽到的产品中能达到优秀等级的件数为X,求X的分布列和数学期望.
您最近一年使用:0次
名校
解题方法
6 . 平面内给定三个向量
,
,
.
(1)求满足
的实数m,n.
(2)若
满足
,且
,求
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29b6b7f33003606c66bb6511fa8b0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14dfa17632f933e0468b8a7864259517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7bc8d458d57e3721c6c30cb6570adc.png)
(1)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4a5e281f06621bd090489d10da41e6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b76118bdca6c463cfb19b66f30281c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a51215462c6f53f5fc33ab50b43a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f2d7a4a788a8de4246248d1c297a3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b76118bdca6c463cfb19b66f30281c4.png)
您最近一年使用:0次
2024-05-12更新
|
348次组卷
|
2卷引用:山东省威海市第一中学2023-2024学年高一下学期4月月考数学试题
名校
解题方法
7 . 如图1所示,在△ABC中,点D在线段BC上,满足
,G是线段AB上的点,且满足
,线段CG与线段AD交于点O.
,求实数t;
(2)如图2所示,过点O的直线与边AB,AC分别交于点E,F,设
,
(
,
);求
的最大值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dc95aa3f1f159dbf4c61239a8df7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffe1c7041b1b338246d456672db377b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40afbc01f47b02602acee4b39c1fbc91.png)
(2)如图2所示,过点O的直线与边AB,AC分别交于点E,F,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cb96903ddcfe069075ef87760ff6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e12eb1c1546ff4ae9878ffa87136c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c98c0ec4c99989333faa478a946985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adebff9fb726cd58eda1ef994890901.png)
您最近一年使用:0次
名校
解题方法
8 . 已知
,且
是第三象限角,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaad097d72229aa0de42e1fe0206ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef70f4a784bc212bd2cc7b55ce86482.png)
您最近一年使用:0次
名校
9 . 如图是函数
(
,
,
)的部分图像,M,N是它与x轴的两个不同交点,D是M,N之间的最高点且横坐标为
,点
是线段DM的中点.
的解析式;
(2)若
时,函数
的最小值为
,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fcd3cea5f5e2fe943490dcb65d74c73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af87a22a39bd12c4734b0bdf1596b42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5389b197345ddd861b9eda4dc9e1fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c02143be07f7f980c4a2a3bb37b87e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f322f4d15d76b0b5e69e7bf1b43b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
您最近一年使用:0次
解题方法
10 . 已知
的展开式中的第二项和第三项的系数相等.
(1)求
的值;
(2)求展开式中所有二项式系数的和,并求出二项式系数最大的项;
(3)求展开式中所有的有理项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/250c63451843d520f22a181218371990.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求展开式中所有二项式系数的和,并求出二项式系数最大的项;
(3)求展开式中所有的有理项.
您最近一年使用:0次