名校
解题方法
1 . 已知函数
.
(1)若
是
上的单调函数,求
的取值范围;
(2)当
时,求
在
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ec8903aef8c996b74479d753ee625e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7300838ad476bc1c75c1cca1fc9880cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
您最近一年使用:0次
2024-06-16更新
|
174次组卷
|
2卷引用:上海市上海中学东校2023-2024学年高二下学期5月月考数学试卷
2 . 如图,在直四棱柱
中,底面
为正方形,
为棱
的中点,
.
的体积.
(2)在
上是否存在一点
,使得平面
平面
.如果存在,请说明
点位置并证明.如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8da7fd8e46e7db2d692486c252274cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ee3afb7e2c8943673449a1b136faf0.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb08e0d3c956a81a029e6353fc4adb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-05-09更新
|
2234次组卷
|
7卷引用:上海市育才中学2023-2024学年高三下学期5月质量调研考试数学试题
上海市育才中学2023-2024学年高三下学期5月质量调研考试数学试题山东省潍坊市部分学校2023-2024学年高一下学期第二次月考数学试题陕西省咸阳市武功县普集高级中学2023-2024学年高一下学期5月期中数学试题(已下线)11.3.3 平面与平面平行-【帮课堂】(人教B版2019必修第四册)(已下线)专题06 立体几何初步解答题热点题型-《期末真题分类汇编》(江苏专用)(已下线)专题01 高一下期末真题精选(2)-期末考点大串讲(人教A版2019必修第二册)四川省遂宁市射洪中学校2024届高三高考考前热身数学(文)试题
名校
解题方法
3 . 已知椭圆
的短轴长为2,离心率为
.
(1)求
的方程;
(2)直线
与
交于
两点,与
轴交于点
,与
轴交于点
,且
.
(ⅰ)当
时,求
的值;
(ⅱ)当
时,求点
到
的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154ff2f73c51da6abb81b4bf8ed0d368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77befd29297b4311a188381b6de618e.png)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d544f5a3293299a221d37729f3d637c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2183add7abab73f3c3b79ccf4349ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2838530a3a6a8e814e4c17ce0f042a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-04-19更新
|
1208次组卷
|
4卷引用:上海市复旦中学2023-2024学年高二下学期5月月考数学试卷
4 . 已知
,集合
其中
.
(1)求
中最小的元素;
(2)设
,
,且
,求
的值;
(3)记
,
,若集合
中的元素个数为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b0d89736a10c53998013df4a354396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8165d6243c2ce6dac87a9bcc2be577ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b76979d0a46e9b56e2f7f3e44c48423.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8e702da77e0bd37abdd29d9b12992e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6b5d77069ced356d738aea8e3efb63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e56e0fa5fb1fc2a2dbd0a152812a1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d103dda0bac3393c7544c4d0c8a37e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1ebce51879137ab48c506e9cdb0187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045c531b9582478b5f0ea99c7ccf686c.png)
您最近一年使用:0次
2024-04-18更新
|
1772次组卷
|
4卷引用:上海市育才中学2023-2024学年高三下学期5月质量调研考试数学试题
上海市育才中学2023-2024学年高三下学期5月质量调研考试数学试题浙江省绍兴市2024届高三下学期4月适应性考试数学试卷(已下线)数学(九省新高考新结构卷03)(已下线)压轴题05数列压轴题15题型汇总-3
解题方法
5 . (1)已知角
终边上一点
,求
的值;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bcc512ec11bf8f6e0f42977dec712c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f301ebc700ef54766c031c2cd34ea7d5.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e06037941c1d94820db105c95f350ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd1c8b02aca62526f312c027740420a.png)
您最近一年使用:0次
解题方法
6 . 已知
.
(1)求
的值;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5233e507a859511bba01cd0c518d9f67.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12985501466d636d234ee4cdea749df8.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad23bcc6b917fb9c1c3c9fde2ecc9bcc.png)
您最近一年使用:0次
名校
解题方法
7 . 在临港滴水湖畔拟建造一个四边形的露营基地,如图ABCD所示.为考虑露营客人娱乐休闲的需求,在四边形ABCD区域中,将三角形ABD区域设立成花卉观赏区,三角形BCD区域设立成烧烤区,边AB、BC、CD、DA修建观赏步道,边BD修建隔离防护栏,其中
米,
米,
.
米,求烧烤区的面积?
(2)如果烧烤区是一个占地面积为9600平方米的钝角三角形,那么需要修建多长的隔离防护栏?(精确到0.1米)
(3)考虑到烧烤区的安全性,在规划四边形ABCD区域时,首先保证烧烤区的占地面积最大时,再使得花卉观赏区的面积尽可能大,则应如何设计观赏步道?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2dcf2debb4c733c88061662bd22a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e7cdc183f6e2f163aa1e4caeb485e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c3a1f1a37e69b2dc06bf0affd58f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbabd6229d1bbd4736b776b2e111318.png)
(2)如果烧烤区是一个占地面积为9600平方米的钝角三角形,那么需要修建多长的隔离防护栏?(精确到0.1米)
(3)考虑到烧烤区的安全性,在规划四边形ABCD区域时,首先保证烧烤区的占地面积最大时,再使得花卉观赏区的面积尽可能大,则应如何设计观赏步道?
您最近一年使用:0次
2024-03-25更新
|
718次组卷
|
5卷引用:上海市闵行第三中学2023-2024学年高一下学期3月月考数学试题
上海市闵行第三中学2023-2024学年高一下学期3月月考数学试题山东省泰安市泰山国际学校2023-2024学年高一下学期3月月考数学试题湖南省常德市第一中学2023-2024学年高一下学期第一次月考数学试题(已下线)高一下学期期中考试--重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)9.2 正弦定理与余弦定理的应用-【帮课堂】(人教B版2019必修第四册)
8 . 已知椭圆
的左、右焦点分别是
,其离心率
,过
且垂直于
轴的直线被椭圆
截得的线段长为1.
(1)求椭圆
的方程;
(2)点
是椭圆
上除长轴端点外的任一点,过点
作斜率为
的直线
,使得
与椭圆
有且只有一个公共点,设直线
的斜率分别为
,若
,证明:
为定值,并求出这个定值;
(3)点
是椭圆
上除长轴端点外的任一点,设
的角平分线
交椭圆
的长轴于点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323227dd8a7a31c078eac609b9acf472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587662afaaecad25c6f5f9e5e7ff28b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fe8d1be8a033e33fcc111cdbcf7b04.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62769b7177ef4bc952dc1dd51d6b510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-03-25更新
|
621次组卷
|
2卷引用:上海市浦东新区上海实验学校2024届高三下学期2月测验数学试卷
9 . 已知O为坐标原点,点W为
:
和
的公共点,
,
与直线
相切,记动点M的轨迹为C.
(1)求C的方程;
(2)若
,直线
与C交于点A,B,直线
与C交于点
,
,点A,
在第一象限,记直线
与
的交点为G,直线
与
的交点为H,线段AB的中点为E.
①证明:G,E,H三点共线;
②若
,过点H作
的平行线,分别交线段
,
于点
,
,求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129252fedd811438b120240cd9aa5d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed919c5b87f48f117bcddee8783f6f06.png)
(1)求C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f537c893dfe2661ba4273cf218c72d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb633c0e8698fc28359c61d4518088b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182a54447325faa238a34a1595538620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12daf5fea89631b84f896939c503d88a.png)
①证明:G,E,H三点共线;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86239f4474ba8806e3afc4755900a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e01c77ea8aec0f14e3e6c37ed374cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2a46ea6ecc0a8efd8cd05770830106.png)
您最近一年使用:0次
2024-03-15更新
|
1665次组卷
|
5卷引用:上海市实验学校2023-2024学年高二下学期4月月考数学试卷
名校
解题方法
10 . 已知
.
(1)若
,求
中含
项的系数;
(2)若
,求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d97a7a452c4f3726822576afc5a42a0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a94d42b3ea947a019c87f75466e421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e06f5fe6e701f1bceaaca31071b564b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42104b9d059d10510570ca30eef57b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21091b4494c2d6963059f9ce879b6981.png)
您最近一年使用:0次
2024-03-14更新
|
905次组卷
|
5卷引用:上海市进才中学2023-2024学年高二下学期3月月考数学试题