名校
解题方法
1 . 定义在
的函数
满足:任意
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9511b59df7b31567a59574d21d4fd8de.png)
A.![]() |
B.![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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名校
2 . 任意一个复数z的代数形式都可写成复数三角形式,即
,其中i为虚数单位,
,
.棣莫弗定理由法国数学家棣莫弗(1667~1754)创立.设两个复数用三角函数形式表示为:
,
,则:
.如果令
,则能导出复数乘方公式:
.请用以上知识解决以下问题.
(1)试将
写成三角形式;
(2)试应用复数乘方公式推导三倍角公式:
;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1266e4d6e189cbd788785b44eb4491d6.png)
(3)记
,由棣莫弗定理得
,从而得
,复数
,我们称其为1在复数域内的三次方根. 若
为64在复数域内的6次方根.求
取值构成的集合,其中
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1810abd6348f8d3863be355fdce70c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fea9021362c5e232929a37a05225cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f687593cb4ecef31667bf2320fdfe000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45eef4221f949bbea8498b39ac1c136a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c825b7acba8f9997d38806be7b3b87eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5137aa9fb53b43fd558b2f1c26b0951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed43030ca376eb5e3331d75f103fc762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c6bdabdb3bfa767e0cb2f73eec6270.png)
(1)试将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb232df15bbcb2addccf8d5e7adc4d1f.png)
(2)试应用复数乘方公式推导三倍角公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a47bdf9c678020d1d50082f7bb208557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1266e4d6e189cbd788785b44eb4491d6.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0c30155ec5bc576f72e97afc42abaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2443c796f97e4b9b209a207abb3bf1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3eabab9c270c5390e9930a1376e6906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c88c2ca3f32231770665622da3ba4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930009e5e260660214817c4eaae0c712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75cd58d17916b906defc4d6817514272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b70cd6a9f071d3a89f3c1c65b609b2.png)
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3 . 已知椭圆C的标准方程为
,梯形
的顶点在椭圆上.
(1)已知梯形
的两腰
,且两个底边
和
与坐标轴平行或在坐标轴上.若梯形一底边
,高为
,求梯形
的面积;
(2)若梯形
的两底
和
与坐标轴不平行且不在坐标轴上,判断该梯形是否可以为等腰梯形?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)已知梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d2530e7023b2345c651e8f53629ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若梯形
![](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/9e52a8f07834cbbbe4224962672fbbb2.png)
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2卷引用:海南省2022-2023学年高二下学期学业水平期中考试数学试题
4 . 已知椭圆
的焦距为2,两个焦点与短轴一个顶点构成等边三角形.
(1)求椭圆
的标准方程;
(2)设
,过点
的两条直线
和
分别交椭圆
于点
和点
(
和
.不重合),直线
和
的斜率分别为
和
.若
,判断
是否为定值,若是,求出该值;若否,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9195fe550aabe5aefb626892f4483ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c6fa2ef2d5a1be4c7c2bd3be4b4366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
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名校
解题方法
5 . 设为原点,
为双曲线
的两个焦点,点
在
上且满足
,
,则该双曲线的渐近线方程为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
6 . 已知函数
,若
,则a,b,c的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558595e25f5ad4a2581cd9e1bcb67abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ef508a4d22bfe22f6af7d1463c9e7f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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5卷引用:海南省部分学校2024届高三下学期高考考前押题(二)数学试题
海南省部分学校2024届高三下学期高考考前押题(二)数学试题山西省2024届高三下学期适应性考试二数学试题(已下线)【人教A版(2019)】高二下学期期末模拟测试B卷江西省宜春市丰城中学2023-2024学年高一下学期第三次段考(5月月考)数学试题(已下线)函数-综合测试卷A卷
名校
解题方法
7 . 设函数
,
.
(1)求
在
上的最值;
(2)若函数
图象恰与函数
图象相切,求实数
的值;
(3)若函数
有两个极值点
,
,设点
,
,证明:
、
两点连线的斜率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603589540f7897790f99a8d75fd725f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5602d1637fb9dab9ef09ae6030b4ed7d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10bb9a8107bd9c4f083578f473b9a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a3f0d7706dd7b38b770656f6937776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210304b08abfee9be4e4d3b01e323a66.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/b387bb66f74a73d9f08c79e77a4df771.png)
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8 . 已知函数
满足
,
,当
时,
,则函数
在
内的零点个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31acd41fe30b9063846f76788d66f5c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27720c167f429e80705dff7b8eeb23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937d22e3eb1cfbeb93c774eab78a243b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd62e93e4c04b37e0dafdad19cbb02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20512e20a5caf6488599b2c5ea017d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9ee0ee7f51cfe25a00eda7b361372c.png)
A.3 | B.4 | C.5 | D.6 |
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|
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5卷引用:海南省部分学校2024届新高考二卷押题卷(三)数学试题
海南省部分学校2024届新高考二卷押题卷(三)数学试题湖南省部分学校2024届高三下学期一起考大联考模拟(二)数学试题河南省焦作市博爱县第一中学2024届高三三模数学试题(已下线)专题6 函数的零点问题【讲】(压轴题大全)(已下线)压轴题01集合新定义、函数与导数13题型汇总-2
9 . 已知数列
的各项均为正整数,记集合
的元素个数为
.
(1)若
为1,2,3,6,写出集合
,并求
的值;
(2)若
为1,3,a,b,且
,求
和集合
;
(3)若
是递增数列,且项数为
,证明:“
”的充要条件是“
为等比数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c540d73bfd5449a65bd3938606a734e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9721608a6a8893ab6ed39687ea3c5cc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9721608a6a8893ab6ed39687ea3c5cc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e068e11427f0179d2233862d835b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87ced0211b3e32adbaae957c084973e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
10 . 在四面体
中,
都是边长为6的正三角形,棱
与平面
所成角的余弦值为
,球
与该四面体各棱都相切,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031183520b32eebfbc60b7c0109ad48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.四面体![]() |
B.四面体![]() ![]() |
C.球![]() ![]() |
D.球![]() ![]() ![]() |
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