1 . 已知集合
,对于
,
,定义
与
之间的距离为
.
(1)已知
,写出所有的
,使得
;
(2)已知
,若
,并且
,求
的最大值;
(3)设集合
中有
个元素,若
中任意两个元素间的距离的最小值为
,求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a1ddf7f51f115fa436aadb2de92b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e6a5b4c75edf2ee68f935b2e3fe12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1a7c3713945abc4eca8485945abf32.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/8ab4a9bfa50054c808dd8190305d0abd.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e25cf1d30f458593f08325f85f6e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c72cbaca91d8e578762c4f0b6750a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4aaf68eac26dd95e0eb726913dfc17b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003fbb029cdb6d5d7f93e29dca371f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e77ba8c90d21237670483bbcd8ac63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c332b53365518c5cf5361bf3cacd47b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a2681390214200443ae07c01a4abe.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11feb79d33ca429733a82c5d88393ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1071ac8657ef1c4e1ea7e0530196298d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d528f49ab8d7fd971c5bb8fa7f24d4.png)
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2 . “
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07bfacc3dc978aa313378533f9ec063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c21c6260bcade05f3a432841f449b5c.png)
A.必要不充分条件 | B.充分不必要条件 |
C.充要条件 | D.既不充分也不必要条件 |
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3 . 设正整数
,其中
,记
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e5e933cda0dcef211b65b0b4bba769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d570b3fbf37b821e65ab00054611d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092d08b0a38fd9bef76f7168ce1fc9dc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 已知非负实数
满足
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba96e16bcc3638214266c1b4b0ffc77.png)
A.![]() | B.2 | C.![]() | D.![]() |
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2024-06-09更新
|
1627次组卷
|
3卷引用:浙江省温州市十校联合体2023-2024学年高二下学期期中联考数学试题
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5 . 函数
在
的图象大致为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac8b73b18981f23aa275e5cce74242c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83b78bd48d655065a6e2023d86707be.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
444次组卷
|
2卷引用:浙江省丽水市五校高中发展共同体2023-2024学年高二下学期5月期中考试数学试题
6 . 已知
的最小正周期为
,
(1)求
的值;
(2)若
在
上恰有
个极值点和
个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6860740e5b0ae41e1f74ddf51a10656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff2c63586f5ca0a0bec4ec2a3883b51.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0883a142ae4d2002e32e355520c0d1a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2832f82fdeafa819c92ca5c1e74eb5ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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|
426次组卷
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2卷引用:浙江省温州市十校联合体2023-2024学年高二下学期期中联考数学试题
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解题方法
7 . 若集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9997af540e552afa4a49c57b606b0b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27c4583ff2664f25e115d1c6a7ea814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-06-07更新
|
172次组卷
|
3卷引用:河北省保定市部分学校2023-2024学年高二下学期5月期中考试数学试题
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8 . 三角函数公式在求值、化简、证明中起着非常重要的作用,如可以用含
的式子来表示
的任意三角数,如
,可见
也可以表示为只含
的表达式.以上推理过程体现了数学中的逻辑推理和数学运算等核心素养,同时也蕴含了转化和换元思想.
(1)试用以上素养和思想方法将
表示为只含
的代数式;
(2)已知
,利用以上结论求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267572d2dff2dc38cf9251b7f33a3e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4227d463b9a3c9c371e62176868476cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a080cab44a7d3605430d67b207f9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
(1)试用以上素养和思想方法将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5ff5a2e7663e6a21ccea3149a10113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44195745e40b014d886e28c21ccc316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7b915277169254e670ea51b693b9fc.png)
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9 . 已知
是锐角,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200daf028f09c3c7af4fb35fc97090e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c98694986a24b18bf1d042e0caeffa.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知函数
.若函数
对一切
均成立,则实数
的取值范围______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f207d545352a63e27d8b4dd729f04f66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a8a9f4f0d6590de86becb733bd1b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb005769d5478c56fc5a01d824167d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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