1 . 设
为整数,
为实数.证明:存在整数
,使得对于任意实数
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abefc7e7354cd2d17283c16c494ea879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5040ce82e687fd1a6f48442f36975523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821ce7a655e8b5fecb99e04313c700b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f97bc1796c160ab600db7d85287ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e137ac7b96922341e43887e7f5fed30.png)
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2 . 如图,在钝角
中,
为钝角.设
的外角平分线与
过B和过C的高线分别交于点E,F,点M在线段EC上使得
,点N在线段BF上,使得
.证明:E,F,M,N四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854f480c60b88b546cb15d3b5622e212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21fa3492cd1ac2b3f9278d3fe4cd4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21fa3492cd1ac2b3f9278d3fe4cd4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854f480c60b88b546cb15d3b5622e212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd09bf3d43769b015a0a8d5b34cdefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37595daefab7761a896f29f785d253d1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/bc6bb557-dd54-4bd6-8e9a-982625129d7d.png?resizew=217)
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3 . 设平面向量
,
,
满足
,
,
,
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5196f84fd2a77d7ee14328cc26ab1ea.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524594bf0942ed86f56fc1eee120a81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c559d3aa4e5178683a408e5b7e7cbdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5397753affa9833ade8daaba7748e3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bb9e1b4f7ba936949195aa99d6159a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75cbb7c27eb8a2af305aa60c5fa2acb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f0e123349c41a4804013241a518860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5196f84fd2a77d7ee14328cc26ab1ea.png)
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2022-10-19更新
|
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3卷引用:2022年7月浙江省高中数学联赛全真模拟六校联考试题
4 . 设
为整数,数列
定义为
,
,且对任意
都有
.试求所有的
,使得这个数列的每一项都是完全平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7bf0d4b73924e85ee5be8d6b170ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18aa1cccf2f341a7886ca7a22d63513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01fc0bf43fa7dcffcf1daebc1b0830c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97bccd30b914efbdf1bcedfb60d63b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5575ee73675d9fb24280bb3d8d33361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0b397225aafbf5906a2b928c8f2947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
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解题方法
5 . 若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8807d7a6387cd566aa94f0e1732f4676.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1babd909eada9008e6474b28fb28921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffe6e4b89baac0ee6ce15bddc7de263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8807d7a6387cd566aa94f0e1732f4676.png)
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2022-10-11更新
|
781次组卷
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5卷引用:2022年7月浙江省高中数学联赛全真模拟六校联考试题
2022年7月浙江省高中数学联赛全真模拟六校联考试题(已下线)第5章 三角函数(基础、典型、易错、压轴)分类专项训练(1)上海市奉贤区致远高级中学2023届高三上学期10月月考数学试题广东省深圳市罗湖外国语学校2023届高三上学期10月月考数学试题山西省晋城一中教育集团南岭爱物学校2022-2023学年高二上学期第三次月考数学试题
名校
解题方法
6 . 如图,OPQ是半径为2,
的扇形,C是弧PQ上的点,ABCD是扇形的内接矩形,设
,若
,四边形ABCD面积S取得最大值,则
的值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a42094fcc37954384a12a626ab5440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b710be34d39a3058bad08e397849e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f8783429be686df75afcd56e847dfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
![](https://img.xkw.com/dksih/QBM/2023/2/15/3175050697228288/3179764983521280/STEM/9de0199207b1475aa448293eba86fab0.png?resizew=262)
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2023-02-21更新
|
1298次组卷
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6卷引用:浙江省杭州学军中学西溪校区2020-2021学年高一下学期3月计算大赛数学试题
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7 . 已知复数
(其中
为虚数单位),
的共轭复数为
,则下列说法错误 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05264b1e869c59a33a5cf07454b7c18f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 设函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb1b4adc744507c0f6a08bbb170386.png)
A.若![]() ![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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2022-09-21更新
|
718次组卷
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3卷引用:2022年浙江省温州市摇篮杯高一数学竞赛试题
名校
9 . 设
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6ba7e7517081568b9c102a0c32f257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ab2b427e8c38a8d89c4cc9523ee6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1058df8f5e0b85f5ac758ed1b0886e2a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知
,
,则
是
的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fff76a82efd3cb49b3bc016ebb876e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244f3f01fbc161563b7979494b5e7e9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
A.充分不必要条件 | B.必要不充分条件 | C.充要条件 | D.既不充分也不必要条件 |
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2022-09-19更新
|
692次组卷
|
2卷引用:2022年浙江省温州市摇篮杯高一数学竞赛试题