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1 . 如图,某公园内有一块边长为2个单位的正方形区域
市民健身用地,为提高安全性,拟在点A处安装一个可转动的大型探照灯,其照射角
始终为
(其中
,
分别在边
,
上),则
的取值范围______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5604d3e156df3e7ccca0ccec9c9d45.png)
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5卷引用:江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题
江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题安徽省合肥市第一中学2023-2024学年高一下学期5月期中联考数学试题(已下线)专题03 高一下期末考前必刷卷01(基础卷)-期末考点大串讲(人教A版2019必修第二册)(已下线)专题2 以平面向量数量积为背景的最值与范围问题【讲】(高一期末压轴专项)(已下线)专题03 平面向量的数量积常考题型归类-期末考点大串讲(人教B版2019必修第三册)
2 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8ee93f7771f73f0303642db5783b21.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1854fd8bf76e74f6414fc8c9a77a0216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8ee93f7771f73f0303642db5783b21.png)
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3 . 函数
满足
,
,
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a580cb582c782207eea3e1387cc627.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0f201ef91b07563cb830f20fc5cea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32447060a910faf370a7715ecf4c97e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a35707dd2ed993f63bccfa59dba978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b894b7836b2dd6c45d8224de34d2cda6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a580cb582c782207eea3e1387cc627.png)
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4 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800873ce02ed63eda88ea3976d1a17e3.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f346995b45341dad7e7c8edfbcac6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800873ce02ed63eda88ea3976d1a17e3.png)
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5 . 已知函数
,则不等式
的解集为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c210ade9ec72d8184a8ad001e44281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0fdf83014454a5ef251bd80cd1653d.png)
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2卷引用:山东师范大学附属中学2024届高三下学期考前适应性测试数学试题
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6 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe37f4368957fc9acd074d6634923fa.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2970a6edd396d10826a92b71c9d3fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe37f4368957fc9acd074d6634923fa.png)
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2卷引用:江苏省南通市如皋中学2024届高三下学期高考适应性考试(三)(3.5模)数学试题
7 . 欧拉函数
的函数值等于所有不超过正整数
,且与
互质的正整数的个数(公约数只有1的两个正整数称为互质整数),例如:
,
,则数列
的前
项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad13428d2891b2bccd870f2a8061f77d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8113f70737283a31ba1c5af62a8118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d53e72365953a1fb223b7255cc43e6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc96280ed7f6538a23bb7d3fec82a331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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8 . 已知函数
满足
,函数
,若
与
的图象恰有2024个交点,其坐标分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53fc1e454b8ebe551922002d655c7b4.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05058811ee2ad1aa2679606000e4ca4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbbde55680888f02d88785efa6d8dc2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea43f2947378deae97c0c073fc20fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53fc1e454b8ebe551922002d655c7b4.png)
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9 . 在数字
和
中,更大的数字是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172370f9adae2e388a4a777ad92ca18f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/013407782cf6bdec227a4e6ad8c9dba7.png)
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10 . 已知
且
,
,
,则
的大小关系为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/170829bcc0d2df7abf4043cf2f553963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75427eed2236464950247d0aee8f8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3359babceedece9218c216e3324523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba0f50c94fbd7f5b2a5388b34161c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
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