名校
解题方法
1 . 设
、
,且
、
,若定义在区间
上的函数
是奇函数,则
的值可以是______ .(写出一个值即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc91d92eb161e54def20b039d2089201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab0dcfadc782654c0e25b54e0fdbe4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a530496cae4bfc2af021fb8014427b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
.
(1)用五点法作出
在一个周期内的图象,并写出
的值域,最小正周期,对称轴方程(只需写出答案即可);
(2)将
的图象向左平移一个
单位得到函数
的图象,求
的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cffd6ce2d8bb0714c90bf559381e852.png)
(1)用五点法作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
3 . 写出函数
的值域、单调递增区间、对称轴方程、对称点坐标(只需写出答案即可),并用五点法作出该函数在一个周期内的图像.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4754e6673e7806500b926192004c0c1a.png)
您最近一年使用:0次
4 . 已知函数
,其中
、
、
、
均为实数,且
,
,
,写出满足
,
,
,
的一个函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3c988d875438535244ee2b092a779b.png)
________ (写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7362670cbc15810c5470f348e0c18c5d.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/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.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/61be752f425c2dfd536e30ad22a3808c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6855784817151468771f29c0fc38fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1905a264af365bcc660da927ee93c280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91e401aa4c557085d25e04d92e813bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2dec9053c9d6608fa34b48afc23d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3c988d875438535244ee2b092a779b.png)
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5 . 已知有限集
,如果A中的元素
满足
,就称A为“复活集”.给出下列结论:①集合
是“复活集”;②若
,
,且
是“复活集”,则
;③若
,
,则
不可能是“复活集”;④若
,则“复活集”A有且只有一个,且
.其中正确的命题个数是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efec56223466e12376205f8c3ddf3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1d004bb7d6018cd15e7a20caf1fa33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed53a09e3678584a1e4545d9697675a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ad2c82dc3ecba5db7b19291697a43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc6288dca7b6191642b11db9dfb2577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1318c477abcb233b6fcdec5e6a8845ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd2995bc6100a2ba0ff45d28dea41b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca9bfce116c67e7f4afdfb54fa84b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1318c477abcb233b6fcdec5e6a8845ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61e241c6c220b3b4705a8c1a465d7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2021-12-01更新
|
252次组卷
|
2卷引用:上海市闵行区六校联考2023-2024学年高一上学期期中数学试题
2014·山东日照·一模
名校
6 . 已知有限集
. 如果
中元素
满足
,就称
为“复活集”,给出下列结论:
①集合
是“复活集”;
②若
,且
是“复活集”,则
;
③若
,则
不可能是“复活集”;
④若
,则“复活集”
有且只有一个,且
.
其中正确的结论是____________ .(填上你认为所有正确的结论序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd07fd90f9d998db8d2600ba0f2b42c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ca68be77aea221cd8efc1a293aebbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5deeed8d5eefca600669724369678a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ad2c82dc3ecba5db7b19291697a43d.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c38216ac0eb2bcaa85fd8c61901f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ed17b083fe22b6f302ee13b7d181d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd2995bc6100a2ba0ff45d28dea41b9.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb0cfdd23ce5234d0a14b0055baab3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ed17b083fe22b6f302ee13b7d181d9.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238d69b84446b56240d2a8ea5de04837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
其中正确的结论是
您最近一年使用:0次
2020-01-07更新
|
275次组卷
|
6卷引用:上海市行知中学2019-2020学年高一上学期10月月考数学试题
上海市行知中学2019-2020学年高一上学期10月月考数学试题上海市交大附中2017-2018学年高一上学期第一次月考数学试题上海市上海交通大学附属中学2017-2018学年高一上学期10月月考数学试题上海市晋元高级中学2017-2018学年高一上学期期中数学试题(已下线)2014届山东省日照市高三5月统一质量检测考试理科数学试卷(已下线)2015届河南省顶级名校高三入学定位考试理科数学试卷
23-24高一上·上海·期中
名校
7 . 对于正整数
,定义
.对于任意的
,称
为
的第
个分量,称
是
的一个“协同子集”.如果
同时满足:①
的元素个数不少于
;②对于任何
、
、
,存在
,使得
、
、
的第
个分量都是
.
(1)对于
,若
是
的一个恰好含有四个元素的“协同子集”,且其中两个元素是
和
,直接写出另外两个元素;
(2)证明:若
是
的一个“协同子集”,则
的元素个数不超过
;
(3)证明:若
是
的一个“协同子集”,且
的元素个数恰好是
,则存在唯一的
,使得
中所有元素的第
个分量都是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d3dc6cad699aa2713482c9f4306802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6aa5d5b774230400311326853ed898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a86c79fb771a07a413c755e4295b160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01433c50807a7878f60c05f43c3fa652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9154d05e636d76f2726e226a5ef3d7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b01af54049b27ca6e8159518b7b18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968b3f41b9a2f481de4b9d95547c5423.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e1f6f6f70deeead9aa004fe0697323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
您最近一年使用:0次
名校
解题方法
8 . 在解决问题:“证明数集
没有最小数”时可用反证法证明:
假设
是
中的最小数,则存在
,
可得:
,与假设中“a是A中的最小数”矛盾,
所以数集
没有最小数.
那么对于问题:“证明数集![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148c4902eb8e6a73046dedab761e3abf.png)
,并且
没有最大数”,也可以用反证法证明:我们可以假设
是
中的最大数,则存在
,且
,其中
的一个值可以是__________ (用
、
表示),由此可知,与假设
是
中的最大数矛盾.所以数集
没有最大数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79950aacd93566f38d8e16021d2eb23b.png)
假设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc7dff3ffdad01a473cc8bdb236f2d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2710435ef4f66f24a0f4b67d7e83f0e.png)
可得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54bfb810e811cb3d9482e2ec0d8db742.png)
所以数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79950aacd93566f38d8e16021d2eb23b.png)
那么对于问题:“证明数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148c4902eb8e6a73046dedab761e3abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb45566dd4ac7dd3524acdb890c29bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f313d192b9d871f1e543f8ac1209b0a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad6060180ef1fa5784a087be85d1f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a25178d007036b7fbde4ab793c98c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfc6ee6f3b4da7817d30e1b9dc36d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff1301d5d66379471b648952aea6310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e93d8fb77f5bd2c0fc690752dfd771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad6060180ef1fa5784a087be85d1f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
您最近一年使用:0次
2022-10-26更新
|
178次组卷
|
2卷引用:上海市进才中学2022-2023学年高一上学期10月月考数学试题
名校
9 . 若函数
是偶函数,则
的一个值可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3eb0eb8c262efdf2f8beefaabc972e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
A.0 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-11-20更新
|
924次组卷
|
3卷引用:上海市建平中学2019-2020学年高三上学期期中数学试题
名校
解题方法
10 . 为宣传2023年上海马拉松,某校现要设计如图的一张矩形宣传海报,该海报含有形状、大小相等的左中右三个矩形栏目,这三栏的面积之和为
,四周空白的宽度均为
,栏与栏之间的中缝空白的宽度为
.
(1)设其中一个栏目
的宽
为
,试把整个矩形海报的面积
表示成
的代数式,并求出
的最小值;
(2)如果要求整个矩形海报的面积不超过
,并且
的长度不超过
的一半,求
长度的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf9324ec099c85f586a93dbe1ccbd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb26c5cdef6f16f4b39cd091041b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a9eed64d225267a58cd001db67e2a3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/7ac9ec2a-9304-40a4-a8eb-2070306f7596.png?resizew=144)
(1)设其中一个栏目
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)如果要求整个矩形海报的面积不超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3ac41d1166c53e015acbc1e13a512a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次