名校
1 . (1)若
,求
的值;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac64f5c3f43d15d6abd192a44e3050cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be943adec1e5cccb4be3e7266a8ebc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20dd33d45da16d7ba00341cfe26cf9c.png)
您最近一年使用:0次
2023-12-24更新
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371次组卷
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2卷引用:安徽省阜阳市第三中学2023-2024学年高一上学期二调(12月)数学试题
2 . 如图,在直三棱柱
中,
,
为棱
的中点,
,二面角
的大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/23/06a66602-3044-4524-9529-59d823918a91.png?resizew=209)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e4a2df58a236c20df5df0d29a466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0685676650662a1f1a7dc762792979b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e32f701757a5bf0c41cc3a7745fdd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/23/06a66602-3044-4524-9529-59d823918a91.png?resizew=209)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd597851c0db4e4de4769e10e09383b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0e7e39306c02ab9c0d606dbca6685e.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0e7e39306c02ab9c0d606dbca6685e.png)
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解题方法
3 . 在正方体中
,已知
为
中点,如图所示.
(1)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b18b18114885976dd212328d335068d.png)
(2)求异面直线
与
夹角大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/25/81480e32-6aad-423c-aab1-48013257c5b2.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a4b438e2e6687c7cd55ea08bbaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b18b18114885976dd212328d335068d.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
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解题方法
4 . 已知圆
的圆心为
(
且
),
,圆
与
轴、
轴分别交于
,
两点(与坐标原点
不重合),且线段
为圆
的一条直径.
(1)求证:
的面积为定值;
(2)若直线
经过圆
的圆心,求圆
的方程;
(3)在(2)的条件下,设
是直线
上的一个动点,过点
作圆
的切线
,
,切点为
,
,求线段
长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3b5fe7ff4823684bcbd303eb74833a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045cf6c42c53f44921c55a01fc4cdd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803a617fb53e67edbc2955cb629c329b.png)
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解题方法
5 . 已知直线
.
(1)若直线l不经过第二象限,求k的取值范围.
(2)若直线l与x轴、y轴正半轴分别交于A、B两点,当△AOB的面积为
时(O为坐标原点),求此时相应的直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a003a68edc192692dcfee9d2e203b8.png)
(1)若直线l不经过第二象限,求k的取值范围.
(2)若直线l与x轴、y轴正半轴分别交于A、B两点,当△AOB的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0874f019492261eb175bdcc08c189d.png)
您最近一年使用:0次
名校
6 . 已知空间中三点
,
,
.设
,
.
(1)求
;
(2)若
与
互相垂直,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469780cd5a58a130d6edc45e0aee052b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbafeecf9ef82b8fa2802b8fe31b8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fb52b52abfc937fd9d0dd186ed83f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21841338587f28e2b8adbc39897a145b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04d418c27621284f0b1f68587178adc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb6118172f384a565afcdfd84e9cdb0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5420712af80f88249f4a45cd0f3abbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d5d06c8ba359e2f95bd6abbeb9d696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2023-12-20更新
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327次组卷
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3卷引用:安徽省皖豫名校联盟2023-2024学年高二(上)期中考试数学试卷
解题方法
7 . 已知圆
经过
,
两点.
(1)求圆
的半径;
(2)判断圆
(
且
)与圆
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693f2138ceb7dee28e012142fcbfccb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc878a5fd7b508cf817cbb65d3940547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf8f5d8be251bf2848d6d10aa0340f9.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)判断圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458f692e00f30df65348237049473bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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名校
8 . 一艘运送化工原料的船只在江面上发生故障导致化学品泄漏,发现时已有
的水面被污染,且污染面积以每小时
的速度扩大,经测算,水面被污染造成的直接经济损失约为每平方米300元.有关部门在发现的同时立即安排清污船清理被污染的水面,该部门需要支付一次性租金为每条清污船1600元,劳务费和耗材费合计为每条清污船每小时200元.若安排
条清污船清理水面,假设每条清污船每小时可以清理
的水面,需要
小时完成污染水面的清理(污染面积减小到
).
(1)写出
关于
的函数表达式;
(2)应安排多少条清污船清理水面才能使总损失最小?(总损失
水面被污染造成的直接经济损失+清污工作的各项支出)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1f5e7f88875edb2d6419cd21c3dbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa3cc81e3e4058ea7a5bdfd87007059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63f5aef91bfa0404a356b683c517d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca0ce86fc55c819be84f6a6e36fd2de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ae952b3be241402fee4c9c9bebff3d.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)应安排多少条清污船清理水面才能使总损失最小?(总损失
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
您最近一年使用:0次
2023-12-20更新
|
161次组卷
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2卷引用:安徽省皖豫名校联盟&安徽卓越县中联盟2023-2024学年高一上学期期中联考数学试题
名校
解题方法
9 . 如图,在正方体
中,E,F,G分别是
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/98ffef06-8ff5-41b2-aadf-df77276cbb80.png?resizew=157)
(1)证明:
.
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/98ffef06-8ff5-41b2-aadf-df77276cbb80.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f838933ac032270e24d15265461a89bd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab8375daa062d56ac9dcd77eebcf9f4.png)
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2023-12-18更新
|
141次组卷
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4卷引用:安徽省六安市舒城县晓天中学2023-2024学年高二上学期期中数学试题
安徽省六安市舒城县晓天中学2023-2024学年高二上学期期中数学试题(已下线)专题02 空间向量与空间角、空间距离【考题猜想】-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)云南省昭通市一中教研联盟2023-2024学年高二上学期期末质量检测数学试题(C卷)(已下线)6.3 空间向量的应用 (4)
名校
10 . (1)已知函数
满足
为奇函数,函数
为偶函数,求
的解析式;
(2)已知函数
满足
,判断
在
上的单调性并用定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70fe16a463dbd772c5b0d39165a30046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773f9cc964ea8df2a9cb14f5e87376c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aae3650a4036147a4d7c7bde2d10e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
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2023-12-15更新
|
203次组卷
|
2卷引用:安徽省皖豫名校联盟&安徽卓越县中联盟2023-2024学年高一上学期期中联考数学试题