名校
1 . 已知向量
,
,函数
.
(1)求函数
的解析式和图象的对称中心;
(2)若函数
的图象向左平移
个单位长度,得到函数
的图象,且关于x的方程
在
上有3个不同的解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a32e46a885a0e63daa9e6a9af718ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da2030c925bd33a207324870d575c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1659f0a03b6c37d87a0ff5e112ee3d2b.png)
(1)求函数
![](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/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d922c3e98888718eadbf5e253648f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23b25b89fc6cfa5e5497ad8c0be76ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
7日内更新
|
353次组卷
|
4卷引用:山西省临汾市名校联考2023-2024学年高一下学期5月质量检测数学试题
2 . 函数
在区间
上有两个零点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316898157440fb32f006cea97e7276e9.png)
_____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e10079e78e98160782b3a0debdc6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aed08076f1a35972d3e406d163f4226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316898157440fb32f006cea97e7276e9.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)若
的最小正周期为
,求
的值;
(2)将函数
的图象向下平移1个单位长度,得到函数
的图象,若函数
在区间
上没有最值,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60868fddd3c9b4a39f176fdcf89b2fde.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)将函数
![](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/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3736369e457d62b4878355726b91412e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
您最近一年使用:0次
4 . 对于分别定义在
,
上的函数
,
以及实数
,若任取
,存在
,使得
,则称函数
与
具有关系
.其中
称为
的像.
(1)若
,
;
,
,判断
与
是否具有关系
,并说明理由;
(2)若
,
;
,
,且
与
具有关系
,求
的像;
(3)若
,
;
,
,且
与
具有关系
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4413796ac3d5ca067bf70334101f5440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3ac1b540727626af78788a8e5f15de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce29c5d90d69a2601a0fb8d7a5ef10c7.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/9da4f4bf9fb72cabd7afc5a67f6ecf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a60d69900052abbd9d34706040fca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a0a57339e225e3ead79e05bb7212f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.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/9a033f4499f5216cd9f8b45d667e5260.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a60d69900052abbd9d34706040fca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec5d200b561e4be52ccaaebdc3105d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732eb83270ada2691daa4b8390d32416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.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/18302506ce6ae99c69000e690c7eb478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9255a62a04412025348c01beff3288bc.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a60d69900052abbd9d34706040fca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8fa4cd0822ad07ef0d2af24428ab9ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e490efb3bf51a37961a5cc53f725fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.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/d56d39424b5e536e241bfc07e37f299b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
5 . 定义非零向量
若函数解析式满足
,则称
为向量
的“
伴生函数”,向量
为函数
的“源向量”.
(1)已知向量
为函数
的“源向量”,若方程
在
上有且仅有四个不相等的实数根,求实数
的取值范围;
(2)已知点
满足
,向量
的“
伴生函数”
在
时取得最大值,当点
运动时,求
的取值范围;
(3)已知向量
的“
伴生函数”
在
时的取值为
.若在三角形
中,
,
,若点
为该三角形的外心,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefeca842285cfe6a09ee79a8d4108d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eeb34e5f4dbd027466a86df156fa7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72850427e83ff19a24305783e080b280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801d2cd298e1db6dc7bad6fc634988f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750b32f4a65ac47869454623571acaac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646ff4c9568c69355999bd80def2d8a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7325df3658628e64a870bd4670e10a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303da3900e7d236e218a004f1a1b7e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72850427e83ff19a24305783e080b280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0497ee4207717773f0154aaa594a6123.png)
(3)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a359f9aeb5add5377519c6f7650ae6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f196f6236188084f3b2c9f2b68c05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3e0f58ca588ad6103788815c053fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15167b49aad18e17a3b4e58ad6b61c13.png)
您最近一年使用:0次
2024-02-27更新
|
693次组卷
|
6卷引用:江苏省常州市北郊高级中学2023-2024学年高一下学期3月学情调研数学试卷
名校
6 . 已知函数
在区间
上有且仅有4条对称轴,则下面给出的结论中,正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c845de45921aa2aadbf03c1c1b228bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
A.![]() ![]() |
B.![]() |
C.![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
名校
7 . 已知
且
,则下列不等关系一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d2df1bee3c6d2d864fd8db2511bc76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d9e02722b5dca0a36f20b91136ca40a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-11-11更新
|
353次组卷
|
2卷引用:福建省三明市沙县区第一中学2023-2024学年高一上学期第三次月考数学试题
名校
解题方法
8 . 在一次研究性学习中,小华同学在用“五点法”画函数
在某一周期内的图像时,列表并填入的部分数据如下表:
(1)请利用上表中的数据,写出
的值,并求函数
的单调递减区间;
(2)将函数
的图像向右平移
个单位,再把所得图像上各点的横坐标缩小为原来的
,纵坐标不变,得到函数
的图像,若
在
上恒成立,求实数λ的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bcf12765642db141e404c077aea6eca.png)
x | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | 0 | ![]() | ![]() | ![]() | ![]() |
![]() | 1 | 0 | -1 | 0 | 1 |
![]() | ![]() | 0 | ![]() | 0 | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbd1d76aceb2efc0c1f3ab39b338060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e820f5bf097ea09e01c936a33f1911.png)
您最近一年使用:0次
2023-06-16更新
|
344次组卷
|
2卷引用:山东省威海市第一中学2023-2024学年高一下学期4月月考数学试题
名校
解题方法
9 . 对于函数
给出下列四个命题,其中正确命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db41ee1e9640fe9dfd43d651530711d.png)
A.该函数是以![]() |
B.当且仅当![]() ![]() |
C.该函数的图象关于直线![]() |
D.当且仅当![]() ![]() |
您最近一年使用:0次
2023-06-13更新
|
585次组卷
|
5卷引用:安徽省蚌埠市禹泽汉兴友谊联考2023-2024学年高一下学期4月月考数学试题
安徽省蚌埠市禹泽汉兴友谊联考2023-2024学年高一下学期4月月考数学试题江西省八校协作2023-2024学年高一下学期5月月考数学试题陕西省商洛市镇安中学2022-2023学年高一下学期期中数学试题第一章 三角函数 单元测试题(已下线)微考点3-1 新高考中三角函数的图像与性质应用中的九大核心考点-2
名校
解题方法
10 . 十字测天仪广泛应用于欧洲中世纪晚期的航海领域,主要用于测量太阳等星体的方位,便于船员确定位置.如图1所示,十字测天仪由杆AB和横档CD构成,并且E是CD的中点,横档与杆垂直并且可在杆上滑动.十字测天仪的使用方法如下:如图2,手持十字测天仪,使得眼睛可以从A点观察.滑动横档CD使得A,C在同一水平面上,并且眼睛恰好能观察到太阳,此时视线恰好经过点D,DE的影子恰好是AE.然后,通过测量AE的长度,可计算出视线和水平面的夹角
(称为太阳高度角),最后通过查阅地图来确定船员所在的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/f340736c-a23f-4b3e-a3ef-710244b4e922.png?resizew=359)
(1)若在某次测量中,横档
的长度为20,测得太阳高度角
,求影子AE的长;
(2)若在另一次测量中,
,横档
的长度为20,求太阳高度角的正弦值;
(3)在杆AB上有两点
,
满足
.当横档CD的中点E位于
时,记太阳高度角为
,其中
,
都是锐角.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5157b42da58d55daad27d98b2fec15ff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/f340736c-a23f-4b3e-a3ef-710244b4e922.png?resizew=359)
(1)若在某次测量中,横档
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b528818e98c5c2ddf301048b4228d2.png)
(2)若在另一次测量中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e847821c95966efc534f26fbe4f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)在杆AB上有两点
![](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/2059d1b10017e04aa35812c0354049b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafc046509e3ca71090d8a1de862efa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadb2357b7a648d3a69c7a84dbdffcc0.png)
您最近一年使用:0次
2023-04-26更新
|
1485次组卷
|
6卷引用:四川省德阳市德阳中学校2022-2023学年高一下学期5月月考数学试题