名校
1 . 某重点中学为了扩大校园绿化面积,规划沿着围墙(足够长)边画出一块面积100平方米的矩形区域
修建花圃,规定
的每条边长不超过20米,如图所示,要求矩形区域
用来种花,且点
四点共线,阴影部分为1米宽的种树区域,设
米,种花区域
的面积为
平方米,则
的最大值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df06c8b3aed8f5b0c093026aeae1ff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72612b8c71c18355fc97f22f8b3f6f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c4dce884147e801b50675b9c0714e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c4dce884147e801b50675b9c0714e5.png)
![](https://img.xkw.com/dksih/QBM/2022/10/18/3090215116849152/3090317719814144/STEM/a8191cdc4e1c4a88859a7f6bd7c48e8d.png?resizew=207)
您最近一年使用:0次
2022-10-18更新
|
183次组卷
|
2卷引用:浙江省杭州四中下沙校区2023-2024学年高一上学期期中数学试题
名校
解题方法
2 . 已知定义在R上的奇函数
,当
时
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/f48cde33-ece2-4db8-9f1a-b9704a806607.png?resizew=269)
(1)求函数
的表达式;
(2)请画出函数
的图像;并写出函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a709fac76762ce4503bbed9644f91649.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/f48cde33-ece2-4db8-9f1a-b9704a806607.png?resizew=269)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)请画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2022-11-28更新
|
361次组卷
|
21卷引用:浙江省金华市曙光学校2020-2021学年高一上学期期中数学试题
浙江省金华市曙光学校2020-2021学年高一上学期期中数学试题新疆实验中学2019-2020学年高一上学期期中数学试题广东省深圳市盐田高级中学2020~2021学年高一上学期期中数学试题山东省临沂市兰山区、罗庄区2021-2022学年高一上学期中考试数学试题河北省石家庄十五中2021-2022学年高一上学期期中数学试题陕西省西安市周至县第四中学2022-2023学年高一上学期期中数学试题山东省济宁市泗水县2022-2023学年高一上学期期中考试数学试题山东省聊城颐中外国语学校2022-2023学年高一上学期期中考试数学试题福建省厦门市新店中学2023-2024学年高一上学期期中考试数学试题广东省揭阳市普宁市勤建学校2023-2024学年高一上学期第二次调研数学试题湖南省邵阳市新邵县第三中学2023-2024学年高一上学期期中数学试题四川省金堂县金堂中学2019-2020学年上学期高一数学必修1第一次月考试题甘肃省天水市甘谷一中2019-2020学年高一上学期第一次月考数学试题内蒙古乌兰察布市集宁一中(西校区)2019-2020学年高一上学期期末数学(文)试题内蒙古乌兰察布市集宁一中(西校区)2019-2020学年高一上学期期末数学(理)试题2019-2020学年高一上学期期末复习1月第02期(考点03)-《新题速递·数学》四川省宜宾市第四中学2020-2021学年高一上学期第一次月考数学试题云南省大姚县第一中学2019-2020学年高一上学期期末数学试题新疆石河子第二中学2021-2022学年高一上学期第二次月考数学试题山东省青岛市部分中学2022-2023学年高一上学期12月月考数学试题河北省保定市唐县第一中学2022-2023学年高一上学期12月月考数学试题
3 . 已知函数
,
且
的解集为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/1fddab14-26eb-47ff-89ee-c5ed12575ba1.png?resizew=173)
(1)求a,b的值;
(2)用
表示
,
中的较大者,记为
,请画出
的图像,并求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b56fbfec39c7fdaba45a751e647928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4343355685d9f682200f13e9d50755dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af13a4237d12fef312b3d6e30b72ab54.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/1fddab14-26eb-47ff-89ee-c5ed12575ba1.png?resizew=173)
(1)求a,b的值;
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859cd3de4d6d485df050b0f5321d6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c065dc2782f5e5a662df2ea357b9c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859cd3de4d6d485df050b0f5321d6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859cd3de4d6d485df050b0f5321d6c6.png)
您最近一年使用:0次
4 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/06bf6dae-32c7-4d4c-a7f8-8083589b48d4.png?resizew=258)
(1)用分段函数的形式表示该函数,并在所给的坐标系中画出该函数的图象;
(2)写出该函数的值域、单调区间(不要求证明);
(3)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5487f615f60ea4af926cafd404190c90.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/06bf6dae-32c7-4d4c-a7f8-8083589b48d4.png?resizew=258)
(1)用分段函数的形式表示该函数,并在所给的坐标系中画出该函数的图象;
(2)写出该函数的值域、单调区间(不要求证明);
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdaffa9c15517afe6d7ba6488f88f67.png)
您最近一年使用:0次
5 . 已知四棱锥
的底面
是平行四边形、侧棱
平面
,点
在棱
上, 且
, 点N是在棱
上的动点 (不为端点).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/59285671-7446-4479-8c98-11e189f4d6e3.png?resizew=169)
(1)若N是棱
中点, 完成:
(i)画出
的重心G(在图中作出虚线),并指出点G与线段
的关系;
(ii) 求证:
平面
;
(2)若四边形
是正方形, 且
, 当点
在何处时, 直线
与平面
所成角的正弦值取得最大值, 并求出最大值.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85ce5e111acf7162b8e1b5a3f6b220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/59285671-7446-4479-8c98-11e189f4d6e3.png?resizew=169)
(1)若N是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(i)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
(ii) 求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2304c541406034dd83040e9a7887ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
您最近一年使用:0次
名校
6 . 已知函数
是定义在
上的偶函数,且当
时,
,现已画出函数
在
轴左侧的图象,如图所示,请根据图象.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/552e1125-50b7-444e-a5f9-ec9821c5f406.png?resizew=223)
(1)补充完整图象并写出函数
的增区间;
(2)写出函数
的解析式;
(3)若函数
,求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becd598a11b876d858728161a7a09705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/552e1125-50b7-444e-a5f9-ec9821c5f406.png?resizew=223)
(1)补充完整图象并写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb7f04a0d543ab3f626b6fff5d2305f7.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb7f04a0d543ab3f626b6fff5d2305f7.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a3e8f8d4cd047c61800c3babeeddc54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2022-04-16更新
|
722次组卷
|
6卷引用:浙江省衢州市乐成寄宿中学2022-2023学年高一上学期期中数学试题
名校
解题方法
7 . 设函数
,
(1)证明
是偶函数;
(2)画出这个函数的图像;
(3)指出函数
的单调区间,并说明在各个单调区间上
是增函数还是减函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b273dab294a02d82d412f920b876267.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)画出这个函数的图像;
(3)指出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2022-09-21更新
|
557次组卷
|
3卷引用:浙江省之江中学2022-2023学年高一上学期期中数学试题
名校
解题方法
8 . 求范围和图象:
(1)
的函数图象先向左平移
个单位, 然后横坐标变为原来的
,得到
的图象,求
在
上的取值范围.
(2)如图所示, 请用“五点法”列表,并画出函数
一个周期的图象.
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/69418aa885c148baad8dd40f0ed7084e.png?resizew=297)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f457df0f9d14437a7f0443bb297e6ee8.png)
(2)如图所示, 请用“五点法”列表,并画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c3d302e263382a01339fa43fece182.png)
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/69418aa885c148baad8dd40f0ed7084e.png?resizew=297)
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/c7574a95-f8a7-44e7-a7fd-3fb3a5f67026.png?resizew=376)
您最近一年使用:0次
2022-03-16更新
|
758次组卷
|
3卷引用:浙江省杭州第二中学2021-2022学年高一上学期期中数学试题
9 . 已知函数
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/9/2867880225972224/2892841369731072/STEM/b832d09c-605d-48a4-a271-ee5e7b9e79a8.png?resizew=155)
![](https://img.xkw.com/dksih/QBM/2022/1/9/2867880225972224/2892841369731072/STEM/f77cd0ce-27c1-4666-b20e-4ebaf31e5633.png?resizew=154)
(1)在图1中画出函数
,
的图象;
(2)定义:
,用
表示
,
中的较小者,记为
,请分别用图象法和解析式法表示函数
.(注:图象法请在图2中表示,本题中的单位长度请自己定义且标明)
(3)写出函数
的单调区间和函数的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4cf498ba2567f964247137477d0ea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab35b554b72ea94c27c6bea4600554f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://img.xkw.com/dksih/QBM/2022/1/9/2867880225972224/2892841369731072/STEM/b832d09c-605d-48a4-a271-ee5e7b9e79a8.png?resizew=155)
![](https://img.xkw.com/dksih/QBM/2022/1/9/2867880225972224/2892841369731072/STEM/f77cd0ce-27c1-4666-b20e-4ebaf31e5633.png?resizew=154)
(1)在图1中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
(2)定义:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c780149aef1bd77162e85f7f8906a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355aff360b365e8ac73f8cf0943c8031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7f5414a3f7ae588b5d9daabe8c0e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355aff360b365e8ac73f8cf0943c8031.png)
(3)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355aff360b365e8ac73f8cf0943c8031.png)
您最近一年使用:0次
解题方法
10 . 对于任意的实数a,b,
表示a,b中较小的那个数,即
.已知函数
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e5344989-c5f8-41ff-a400-016fb32711b1.png?resizew=284)
(1)在同一直角坐标系中画出
,
的图象;
(2)设
,
,写出函数
的解析式并求出
最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6a571b150fe6d3e7239e0cbe19886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f58d2f5fddd5b0356e58da89c6b353d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d0e90719b4157a266e317246889b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96f623802cd414e590247155ad0d62b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e5344989-c5f8-41ff-a400-016fb32711b1.png?resizew=284)
(1)在同一直角坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c90d8022d215c7bc6ef22caba97e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
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