名校
1 . 函数
的部分图象如图所示.
(1)求函数
的解析式;
(2)将函数
的图象先向右平移
个单位,再将所有点的横坐标缩短为原来的
(纵坐标不变),得到函数
的图象,求
在
上的最大值和最小值;
(3)若关于
的方程
在
上有两个不等实根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0ef9d537e1849ed448318247dce9f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/11/2b62466c-d1d8-4547-bab4-48cac19e5e61.png?resizew=150)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80586bb4383ef1d08ae68d093de3c68.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b97537de8e5111a3fd21a175577e504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80586bb4383ef1d08ae68d093de3c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3卷引用:广东省深圳市福田区红岭中学2023-2024学年高一下学期第一次月考数学试卷
广东省深圳市福田区红岭中学2023-2024学年高一下学期第一次月考数学试卷广东省华南师范大学附属中学2024届高三下学期模拟测试(一)数学试题(已下线)专题02 三角函数的图象与性质常考题型归类-期末考点大串讲(人教B版2019必修第三册)
2 . 现需要设计一个仓库,由上、下两部分组成,上部的形状是正四棱锥
,下部的形状是正四棱柱
(如图所示),并要求正四棱柱的高
是正四棱锥的高
的4倍.
,
,则仓库的容积是多少?
(2)若正四棱锥的侧棱长为
,
,则正四棱锥
的侧面积是多少?
(3)若正四棱锥的侧棱长为
,当
为多少时,下部的正四棱柱侧面积最大,最大面积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724625d4f91f0e48712d6d143a6389b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fb50c66cd2de786b39cb442ec54a16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49caee3119b29a99e62cbe419fb261fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67c2eb45b423807aa39632e0d25fbfe.png)
(2)若正四棱锥的侧棱长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e17ee14bd91bfff409c06fd434f6745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67c2eb45b423807aa39632e0d25fbfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724625d4f91f0e48712d6d143a6389b7.png)
(3)若正四棱锥的侧棱长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e17ee14bd91bfff409c06fd434f6745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fb50c66cd2de786b39cb442ec54a16.png)
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名校
解题方法
3 . 如图,二面角
等于
,
是棱
上两点,
分别在半平面
内,
,
, 且
则
的长等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9f6f75005ab8e946e7195afaf44c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504b434a5d06fa23809a709fa42da886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf464ac1bfdd9bb59f9ab4d55ad2667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c638fb895acd987140d0ca6bef097499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0a2d7d40a6c0bf1fddb802db381689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cef00fc08e3ca1da8f78d7a742ee75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.4 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 中国有悠久的金石文化,印信是金石文化的代表之一.印信的形状多为长方体、正方体或圆柱体,但南北朝时期的官员独孤信的印信形状是半正多面体,如图1.半正多面体是由两种或两种以上的正多边形围成的多面体.如图2,某半正多面体的表面由18个全等的正方形和8个全等的正三角形构成,该半正多面体的所有顶点都在同一个棱长为
的正方体的表面上.
(2)求该半正多面体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2b42b76abb6aca31dabaaf2456825d.png)
(2)求该半正多面体的体积.
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5 . 窗花是贴在窗户上的剪纸,是中国古老的传统民间艺术之一,图1是一个正八边形窗花隔断,图2是从该窗花图中抽象出的几何图形的示意图.已知正八边形
内角和为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
______ ;若正八边形
的边长为2,P是正八边形八条边上的动点,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a1e8072b2126e33aa203db4635211a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2535c0d4662a3a92cabbd44dcdd6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83b9f01e806bf74042ba41b26423022.png)
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6 . 如图,某大型厂区有三个值班室
,值班室
在值班室
的正北方向3千米处,值班室
在值班室
的正东方向4千米处,仓库
在
边上且满足
.
到值班室
的距离;
(2)保安甲沿
从值班室
出发行前往值班室
,保安乙沿
从值班室
出发行前往值班室
,甲乙同时出发,甲的速度为
,乙的速度为
.若甲乙两人通过对讲机联系,对讲机在厂区内的最大通话距离不大于3千米,请问有多长时间两人不能通话?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942a9a6bde4a5b9803b68b1e9065de62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)保安甲沿
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/3b1dfb863105600ca271cd6a597187ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15bca4fc0b0fc4f8e492d8c1fe449c9b.png)
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解题方法
7 . 已知函数
的一段图象如下图所示:
的解析式.
(2)将函数
的图象上所有点保持纵坐标不变,把图象上所有点的横坐标伸长到原来的4倍,再把图象上所有点向右平移
个单位,得到
的图象.则当
时,求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0ef9d537e1849ed448318247dce9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4deb7ec68a4e56ccfef8995de3ae3b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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解题方法
8 .
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b047198608ca5d68846ee83fd1a0e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
9 . 对任意两个非零向量
,定义新运算:
.
(1)若向量
,求
的值;
(2)若非零向量
满足
,且
,求
的取值范围;
(3)已知非零向量
满足
,向量
的夹角
,且
和
都是集合
中的元素,求
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662917aedec92809a13618093c8e0c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c8fcfe76ebcc117a04aff784c708cf8.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f35da65fbee7dc112ad98c897a21e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5bb7c28c450198e14a6003c8429ea4a.png)
(2)若非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82a102684873f9dfde748535cdc6b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd48a034a37514095fd2b435640230a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd873a8e0052ca540c08b6cf84408822.png)
(3)已知非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9fd92a255799ab6b864600fabd5831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5141e1f11fe9486d1769d0a9b1f340fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5bb7c28c450198e14a6003c8429ea4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd873a8e0052ca540c08b6cf84408822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8a50d960d91796ec129aa16c0fc550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5bb7c28c450198e14a6003c8429ea4a.png)
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解题方法
10 . 如图,在六面体
中,
,四边形
是平行四边形,
.
平面
.
(2)若G是棱
的中点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dced11455b3e31a9090915f80a046fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3ae72e7e4d456f262d498b2a2f4473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d782bc4aad7cf35baa3de7b8ea73e41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若G是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee06116d96046169b42ecf458401020.png)
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