名校
1 . (1)计算:
;
(2)计算:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dbf5a21870b4404dd5b62913b35322b.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ba2036f7592aa0b13e5c857d4192e9.png)
您最近一年使用:0次
名校
2 . 心理学家根据高中生心理发展规律,对高中生的学习行为进行研究,发现学生学习的接受能力依赖于老师引入概念和描述问题所用的时间.上课开始时,学生的兴趣激增,中间有一段时间学生的兴趣保持理想状态,随后学生的注意力开始分散.分析结果和实验表明,用
表示学生掌握和接受概念的能力(
的值越大,表示接受能力越强),x表示提出和讲授概念的时间(单位:
),满足以下关系:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7db30acba367d7013dd04be8d1445e.png)
(1)上课多少分钟后,学生的接受能力最强?能维持多少分钟?
(2)有一道数学难题,需要54的接受能力及
的讲授时间,老师能否及时在学生处于所需接受能力的状态下讲授完成这道难题?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ce48eafd36547782174eb304d4a003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7db30acba367d7013dd04be8d1445e.png)
(1)上课多少分钟后,学生的接受能力最强?能维持多少分钟?
(2)有一道数学难题,需要54的接受能力及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1457a00c2b5977426358c8fcb8fcadf.png)
您最近一年使用:0次
2024-01-21更新
|
117次组卷
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2卷引用:吉林省四校2023-2024学年高一下学期期初联考数学试题
名校
解题方法
3 . 已知
是自然对数的底数,
.
(1)判断函数
在
上的单调性并证明;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c226088d7fca4e0b1497af964eb9327f.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d033362b3777e7abf16e6286495c10c.png)
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2024-01-14更新
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664次组卷
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5卷引用:吉林省长春吉大附中实验学校2023-2024学年高一上学期期末考试数学试题
名校
4 . 对于函数
,若
,则称实数
为函数
的不动点.设函数
,
.
(1)若
,求函数
的不动点;
(2)若函数
在区间
上存在两个不动点,求实数a的取值范围;
(3)若对任意的
,不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d468b616235df122370cf58f03bb678f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f5900e71882dbcd2e4f8e723c54df82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e845964df4b271bd7b4cf99ede79be.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e354f44c5841806fdc363073abdd052.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad3e87122fa7a9d6388712acf2fb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b4ae37353927beb9f1f763fccb71f3.png)
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2024-01-13更新
|
780次组卷
|
3卷引用:吉林省长春市东北师范大学附属中学2023-2024年高一上学期期末考试数学试题
名校
5 . 已知函数
,且
.
(1)设
,若对任意
,总存在
,使
成立,求实数t的取值范围;
(2)函数
的图象与函数
的图象关于直线
对称,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b95ca61627cda16d509ffa29cb9646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308e1e751853f5eb489240ce33ed36b5.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b324aceadfd941605fa757a5ea014c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef85b287d0fc9611ac7ba4bade11d864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d402c79f35ebafa3ac4a35e7263d4ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6154e00013d9dee84c0e941f676ea9.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e56709c76b5ae87d528fb5240e7617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9ae051b39abb83cf7960a07db2b200.png)
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解题方法
6 . 已知
.
(1)化简
;
(2)若
是第三象限角,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268af8e2ffdb4fbd924a480e95078ec9.png)
(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc362bbfbef33b22b68108364cd2a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e8b1ad8282c6176fcff6c5a70aceedb.png)
您最近一年使用:0次
2024-01-13更新
|
1125次组卷
|
4卷引用:吉林省长春市东北师范大学附属中学2023-2024年高一上学期期末考试数学试题
吉林省长春市东北师范大学附属中学2023-2024年高一上学期期末考试数学试题安徽省马鞍山市劲松学校2023-2024学年高一下学期开学考试数学试题(已下线)1.4-1.5 正余弦函数的图象和性质(1)-同步精品课堂(北师大版2019必修第二册)广西百色市平果市铝城中学2023-2024学年高一下学期4月月考测试数学试卷
7 . 已知函数
(其中
,
,
)的部分图象如图所示,将函数
的图象向右平移
个单位长度,得到函数
的图象.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/27/23caaec8-958d-4c9b-bf6b-e6f51465ae64.png?resizew=136)
(1)求
与
的解析式;
(2)令
,求
在区间
内的所有实数解的和.
![](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/c2ec7dc63956169362373e179ce6f67c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/27/23caaec8-958d-4c9b-bf6b-e6f51465ae64.png?resizew=136)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870a586e90a7bb79dc44f9451dee19ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8c4e6035e36bfd8609e81147a047d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e05f651acdda29d79ccd63843f80e1.png)
您最近一年使用:0次
8 . 已知函数
.
(1)求函数
的最小正周期及单调递增区间;
(2)将函数
的图象上所有点向上平移
个单位得到曲线
,再将
上的各点纵坐标变为原来的
倍(横坐标不变),得到函数
的图象.若
,
,不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1219915edf37830423a6a8c691f8ef.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89eea593c79973e97f6f3cdf621cdfc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a2b71d4dc6f6aa3f8fa66f8da8c4db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a739bc599aac5fe2fb61ab308bab65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27245adffcbca647109308b498ed2193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
9 . 茶,是中华民族的举国之饮,它发乎神农,闻于鲁周公,兴于唐朝,盛在宋代,如今已成了风靡世界的三大无酒精饮料(茶叶、咖啡和可可)之一,并将成为
世纪的饮料大王.中国茶文化博大精深,茶水的口感与茶叶类型和水的温度有关.把物体放在冷空气中冷却,如果物体原来的温度是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635ccd929471d564cc9d2d96266b34d1.png)
,空气温度是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddcd21e3f7e1e6da96d70ba17e6282a.png)
,那么
后物体的温度
(单位:
)可由公式
求得,其中
是一个随着物体与空气的接触情况而定的常数.现有某种刚泡好的普洱茶,茶水温度是
,放在室温
的环境中自然冷却,
分钟后茶水的温度是
.
(1)求
的值;
(2)经验表明,当室温为
摄氏度时,该种普洱茶用
的水泡制,自然冷却至
时饮用,可以产生最佳口感,那么,刚泡好的茶水在室温为
时自然冷却大约需要放置多长时间才能达到最佳饮用口感?(结果精确到
)
(附:参考值
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1834490aacbee800ed5721312f4be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635ccd929471d564cc9d2d96266b34d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa088a4729226b696c536845791d4c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddcd21e3f7e1e6da96d70ba17e6282a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa088a4729226b696c536845791d4c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cec183057249005d5f234c4bea5de7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53954abebf92060badd0116b5f4f0b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa088a4729226b696c536845791d4c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6513b926b52e478960d85926dcc6b1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd146454ed5eb20c1c1bdec42827892c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77761480d4b99092be634491809b3685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e044325ad7fdaef36758daa8b9fe4456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e94d90c5ea993e7f453e273e54cb2ff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)经验表明,当室温为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e594a134277c5a9fed7f0077a1833a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae25989c7e577c70d1c6fadc06a3235d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd58b3de052f2818ccf283fe0bae15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e594a134277c5a9fed7f0077a1833a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b591a4e2f06db96fa295ce99f67af7e.png)
(附:参考值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2266816738946471c28ffa04ff10c91c.png)
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2024-01-12更新
|
281次组卷
|
2卷引用:吉林省吉林市普通高中2023-2024学年高一上学期期末调研测试数学试题
10 . 在平面直角坐标系
中,已知锐角
的终边与单位圆的交点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
.
(1)求
;
(2)在①
, ②
,③
这三个条件中任选一个条件补充在下面(把序号填在答题卡对应位置的横线上)并解答问题.
问题:已知
, ,求
.
(注:如果选择多个条件分别解答,按第一个解答计分.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3cab31b0dc223c40b05f7d4d2b0199d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269a796239ef54e6ee3b848c1a0bd15f.png)
(2)在①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f584f913b804131ad1a7c6b67e14cb03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ef83936add3c767d5c59f787a00075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2194eafede73216a419a0b5cbc1da126.png)
问题:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef94560b7d4755c9229c0b39230a6bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db796b223b35e52aa7b4114da8072f5.png)
(注:如果选择多个条件分别解答,按第一个解答计分.)
您最近一年使用:0次
2024-01-12更新
|
249次组卷
|
3卷引用:吉林省吉林市普通高中2023-2024学年高一上学期期末调研测试数学试题