名校
1 . 设向量集合
.若对于任意
、
以及任意
,都有
,则称集合S是“凸集”.现有四个命题:
①集合
是“凸集”;
②集合
是“凸集”;
③若集合
、
都是“凸集”,则
也是“凸集”;
④若集合
、
都是“凸集”,且交集非空,则
也是“凸集”.
其中,所有正确命题的序号是________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a8aa6b0a40a2ef451c9f6c263662d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c1870a8601323a0fefb2f90c669f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304c5050fdb05bd5ccdf8bdfc00e8108.png)
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275e06e147f70046e6c91b1cac72bfc.png)
②集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f32c01a67d79efc9fb98afc8bd2fb8.png)
③若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2646f41226f24960a6186dc7860ef45.png)
④若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76d26b78e63683dfacf10d3da6d74d.png)
其中,所有正确命题的序号是
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解题方法
2 . 曲线
在
处的切线倾斜角是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99635a019eef1dfce9e8126e431884cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 下列四个函数中,最小正周期为
,且为偶函数的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 已知函数
,
,若存在
,使得
,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a81ee8cda11afd2b4fd02ff2991126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/382ceccc09426f99e4cc949f88bbca36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c98f678d5c72b75ccb5f246915a6e4.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6363449f064b8aeeaa11ae6e096cb25e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1896acf9e1e52cad1c541a9d70505be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c98f678d5c72b75ccb5f246915a6e4.png)
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6 . 已知函数
在
上有最小值没有最大值,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f674a5ec6f21c7e333180f68a3cb3938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8ec0ccdb6db6fbaeb1172e281ec22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知函数
的部分图象如图所示,其中
,
,则以下五个说法正确的个数为( )
的最小正周期是
;
②函数
在
上单调递减;
③函数
的图象关于直线
对称;
④将函数
的图象向右平移
个单位长度后关于
轴对称;
⑤当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f9e0d2ee27c0edf4ee241649fc36ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c00f4bd37ae98cdff46774abaf3bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ff45c7869a6164bc3b570922957333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8f382b249d0afd2e124a5b3b075a62.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae820410b02ed0c6bffd689ee42a139.png)
④将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf9c2a14f31481ee2c32e0434157a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
⑤当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f320dbae77f07865013a0191470406d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e50ddb0e054a89ef9c0bc04ae325cf.png)
A.0 | B.1 | C.2 | D.3 |
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2024·全国·模拟预测
解题方法
8 . 若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e979b6bca0a87a94ced7e3687fad0401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e7cd4e866f7e0e38c51a799b087ace.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024·全国·模拟预测
9 . 已知函数
,对于任意的
,
,
都恒成立,且函数
在
上单调递增,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d25ffc739618adc609f7fd95cfeadf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3ea053a64e8640bd9e8403948af4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb0ede35f35f89f28515cc081b93db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de26c33c5ab86fbd2ffdec6de7e56d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.3 | B.9 | C.3或9 | D.![]() |
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10 . 函数
的单调递增区间为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc815d8cc759cf2a1f083b42112fdc27.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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