解题方法
1 . 在图甲所示的四边形
中,
,
,
,
,沿
将
进行翻折,使得
,得到如图乙所示的四棱锥
.四棱锥
的体积为
,
为边
上的动点(不与端点
,
重合).
(1)若
为
的中点,求证:
;
(2)设
,试问:是否存在实数
,使得锐二面角
的余弦值为
?若存在,求出实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b027ed57b9c6f24e27ec0ae282c76efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6956513649811bd1a2f8c3e4ca8793c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaed541a0f4ec6c8c7f22f37639796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795d1f8e68aee16240a4018dcbcb1e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f15a7b73234e611993abefa7d91c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d74ef32584586ec4857acd0a3f4fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/6337ec36-b13a-4219-bc3b-fad2819d2536.png?resizew=300)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0efbdc4cbc82cc55bed9905f81fbfc2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66cd314bbb958ce941210a4b84584f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1a4b8e6a3514ac93b69042d1f9553b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ee522b7fcdbbdd63bdf31419e1bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
2 . 平原上两根电线杆间的电线有相似的曲线形态,这些曲线在数学上称为悬链线.悬链线在工程上有广泛的应用.在恰当的坐标系中,这类曲线的函数表达式可以为
,其中a、b为非零实数
(1)利用单调性定义证明:当
时,
在
上单调递增;
(2)若
为奇函数,函数
,
,探究是否存在实数a,使
的最小值为
? 若存在,求出a的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49757d6d62b9c313b11aafd537475845.png)
(1)利用单调性定义证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48adb8a59b5c02fad5eada1b35171cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853ccd6cea4dd5f3491b10ca21828574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7b531ca02bb032e63ab7df9ee9e068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
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3 . 设抛物线
的焦点为
,从抛物线上点
出发的光线过点
后,从抛物线上的点
(异于原点
)反射,反射光线经过点
,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62af58509f7411cc0db452c36bdae2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356547c08d2cd7ba5a6aaf412266d7b7.png)
A.直线![]() ![]() |
B.![]() ![]() |
C.以![]() ![]() |
D.若直线![]() ![]() |
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2卷引用:广东省汕尾市2023-2024学年高二上学期1月期末教学质量监测数学试题
名校
4 . 如图,在
中,点D在线段
上,且
,E是
的中点,延长
交
于点H,点
为直线
上一动点(不含点A),且
(
).若
,且
,则
的面积的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc718b99fb52f53f988c91d8fc94dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734c5f0ab3f244ae2ce1ba7b618cb0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa72c594ebe33496fa7b9edf1db5c7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e85d9af8396f72458200570f08f03880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8a4d96d46fbb53d03eb5be87102fc2.png)
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5卷引用:广东省汕尾市2022-2023学年高二下学期期末数学试题
广东省汕尾市2022-2023学年高二下学期期末数学试题四川省2022-2023学年高一下学期“贡嘎杯”期末质量检测考试数学试题(已下线)第二节 平面向量基本定理及坐标表示 B素养提升卷湖南省邵阳市邵东市第三中学2024届高三上学期第二次月考数学试题(已下线)高一下学期期末复习填空题压轴题二十三大题型专练(1)-举一反三系列(人教A版2019必修第二册)
名校
解题方法
5 . 如图,已知直线
,
是
,
之间的一个定点,且点
到
,
的距离分别为1,2,
是直线
上的一个动点,作
,且使
与直线
交于点
.设
,
的面积为
.
的最小值;
(2)已知
,
,若对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027830fc47290062692964077ee481e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499d3ef329f85e59fd72dec6f453bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0496f7b645615d6cf59b8a7ec1fb6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0496f7b645615d6cf59b8a7ec1fb6e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4387e0bcdeae4ff80549beb1c5ef7ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcbe8b4bcd32e5a64ebfd873f8cbb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e1cfcf2f6f715c0e8384582947268c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2023-07-08更新
|
568次组卷
|
5卷引用:广东省汕尾市2022-2023学年高一下学期期末数学试题
广东省汕尾市2022-2023学年高一下学期期末数学试题 福建省莆田市第四中学2023-2024学年高一上学期期末联考数学试卷(已下线)专题05 三角函数5-2024年高一数学寒假作业单元合订本广东省广州市真光中学2023-2024学年高一下学期3月月考数学试题【人教A版(2019)】专题02三角函数(第二部分)-高一下学期名校期末好题汇编
解题方法
6 . 如图,在棱长均为2的平行六面体
中,
,点
,
,
分别是
,
,
的中点,
与平面
交于点
,下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/d884224a-7797-401d-8d93-40fb2446dc5a.png?resizew=185)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9c4adb05045cdd808a1ff7d6662d79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/d884224a-7797-401d-8d93-40fb2446dc5a.png?resizew=185)
A.![]() |
B.![]() |
C.直线![]() ![]() ![]() |
D.三棱锥![]() ![]() ![]() |
您最近一年使用:0次
名校
7 . 若
,
,
,则
、
、
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae9c985d77ee46accab4aae013bb821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b102b69dbeff939fef9d03b9e0ecc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0d927b8d3c01cb0a44e7a5ebcff3a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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|
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2卷引用:广东省汕尾市城区汕尾中学2023届高三下学期第一次月考(期末)数学试题
8 . 已知函数
,其中
为参数.
(1)讨论函数
的单调性;
(2)若函数
有两个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46723fcfe62759c3ab2c86b64d2698c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
.
(1)当
时,求不等式
的解集;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f012dc7a94b1aeb246ce7e0af772d612.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d122ecb0f6fa15aeb69fa57908f692b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5efbe27501ebed775a665de0ee88a7d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-10-13更新
|
591次组卷
|
2卷引用:广东省汕尾市城区汕尾中学2023届高三下学期第一次月考(期末)数学试题
名校
解题方法
10 . 某大学科研团队在如下图所示的长方形区域
内(包含边界)进行粒子撞击实验,科研人员在A、O两处同时释放甲、乙两颗粒子.甲粒子在A处按
方向做匀速直线运动,乙粒子在O处按
方向做匀速直线运动,两颗粒子碰撞之处记为点P,且粒子相互碰撞或触碰边界后爆炸消失.已知
长度为6分米,O为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/63a01095-e070-4050-a557-a210db24dc44.png?resizew=218)
(1)已知向量
与
的夹角为
,且
足够长.若两颗粒子成功发生碰撞,求两颗粒子运动路程之和的最大值;
(2)设向量
与向量
的夹角为
(
),向量
与向量
的夹角为
(
),甲粒子的运动速度是乙粒子运动速度的2倍.请问
的长度至少为多少分米,才能确保对任意的
,总可以通过调整甲粒子的释放角度
,使两颗粒子能成功发生碰撞?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888afd002858f23a84a8755a002bed7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/63a01095-e070-4050-a557-a210db24dc44.png?resizew=218)
(1)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888afd002858f23a84a8755a002bed7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888afd002858f23a84a8755a002bed7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7f004f23ec3f968d885cb111aac4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135466eb8ca64d002d0fad36176d1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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2022-07-07更新
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3卷引用:广东省汕尾市2021-2022学年高一下学期期末数学试题