解题方法
1 . 下列说法正确的是( )
A.若圆心角为![]() ![]() ![]() |
B.已知向量![]() ![]() ![]() ![]() ![]() |
C.向量![]() ![]() ![]() ![]() |
D.已知扇形的周长是4,当扇形面积最大时,则扇形的圆心角的弧度数是2 |
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2 . 下列说法正确的是( )
A.不等式![]() ![]() |
B.函数![]() ![]() |
C.已知![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
名校
解题方法
3 . 已知曲线
,点
,
是曲线
上任意两个不同点,若
,则称
,
两点心有灵犀,若
,
始终心有灵犀,则
的最小值
的正切值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b773ce76a64bf854edf0fd972a28049e.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762a9015473e9ec9b21eccc15224ff72.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04992fc293d05964e8b6b373549cd013.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b773ce76a64bf854edf0fd972a28049e.png)
您最近一年使用:0次
2023-04-17更新
|
989次组卷
|
6卷引用:江西省丰城中学2023-2024学年高二创新班上学期开学考试数学试题
名校
解题方法
4 . 某公园有一块矩形空地ABCD,其中
,
百米,
百米.为迎接“五一”观光游,欲从边界AD上的中点P处开始修建观赏小径PM,PN,MN,其中M,N分别在边界AB,CD上,小径PM与PN相互垂直,区域PMA和区域PND内种植绣球花,区域PMN内种植玫瑰花,区域BMNC内种植杜鹃花.设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/7fcfc667-9835-427e-a85d-20ccdfb81366.png?resizew=159)
(1)设种植绣球花的区域的面积为S,试将S表示为关于
的函数,并求其取值范围;
(2)为了节省建造成本,公园负责人要求观赏小径的长度之和(即
的周长l)最小.试分析当
为何值时,
的周长l最小,并求出其最小值,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff04d6bd71917563cbd1f967d50465cc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/7fcfc667-9835-427e-a85d-20ccdfb81366.png?resizew=159)
(1)设种植绣球花的区域的面积为S,试将S表示为关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)为了节省建造成本,公园负责人要求观赏小径的长度之和(即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
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2023-04-15更新
|
634次组卷
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3卷引用:江西省全南中学2022-2023学年高一下学期期中数学试题
5 . 若函数
满足
,且
,
,则称
为“
型
函数”.
(1)判断函数
是否为“
型
函数”,并说明理由;
(2)已知
为定义域为
的奇函数,当
时,
,函数
为“
型
函数”,当
时,
,若函数
在
上的零点个数为9,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4507b17a17ff47358e4cd01a48025522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79aee38af513b812038e5d9eb0c67c6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd89ae03df9499a37df8893edc0329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bcf5c39cd6005441157b4a871279af7.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa951a727b38bb328957cbe4813e171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d3be86b97b440b5a3559340c485a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4056900c3e5389df60f2f875e873dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ec330cc887a2230871d2e7c6592387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-04-14更新
|
973次组卷
|
5卷引用:江西省全南中学2022-2023学年高一下学期期中数学试题
6 . 如图所示,在等腰梯形
中,
,现将梯形
依次绕着
各点顺时针翻转,则在第一次绕着点
翻转的过程中,对角线
扫过的平面区域面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/e748e22a-cc92-41c8-b835-8383704dd89f.png?resizew=231)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304d140bf689c07b057d922648da3dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28855a0db693584aabac1df99dfade3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/e748e22a-cc92-41c8-b835-8383704dd89f.png?resizew=231)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 某病毒在一天内的活跃度
与时间
(
,单位:
)近似满足关系式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a3289a3372a8af0ca66c718e8d4b00.png)
,其图象如图所示.已知
时,该病毒对人类不具有传染性,则该病毒在一天内对人类不具有传染性的时长大约为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/11/8efb91f5-c659-4d88-a35a-dd136b199004.png?resizew=213)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238dccfbd5e8c3031f2f86088739ece1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933311c0c090e1138e4dd388b7adf8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a3289a3372a8af0ca66c718e8d4b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede2c277b6a8f9ae7d19f5e0ad1a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2ee0d57439903e73ead0d43887bde8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/11/8efb91f5-c659-4d88-a35a-dd136b199004.png?resizew=213)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-10更新
|
291次组卷
|
3卷引用:江西省上饶市民校考试联盟2022-2023学年高一下学期阶段测试(四)数学试题
8 . 已知函数
的最小正周期
,
,且
在
处取得最大值.现有下列四个结论:①
;②
的最小值为
;③若函数
在
上存在零点,则
的最小值为
;④函数
在
上一定存在零点.其中结论正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114eef9b222c5481d2e53e4efd77d067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c3998d58abf7be810d3fc31e0fae52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e3129378e15392b3d3078bbc0147f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3204d98fd0532edb9a010693b835716b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b9889e0cbe3df77335191563ca41b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7163395f9aaa29be7f6b3106ba48b744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f985e053aa34c664db8457ada68d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/490dab77e2976fd4ae7535cb0ff54ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1e89691838b95288ece44d97e445a6.png)
A.1 | B.2 | C.3 | D.4 |
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解题方法
9 . 毕达哥拉斯树,也叫“勾股树”,是由毕达哥拉斯根据勾股定理画出来的一个可以无限重复的树形图形(如图1).现由毕达哥拉斯树部分图形作出图2,
为锐角三角形,面积为
,以
的三边为边长的正方形中心分别为
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03460f2cf6f0048679447ea1e564e23a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75193c2de6968a93cf0bffc2f77f807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afddba5bee9c050f44b9ddb25572e3e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/11/1b95ae21-f2ca-4946-bf6e-a45c57adfd89.png?resizew=393)
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2023·江西·二模
10 . 研究某点轨迹时,数学上常用向量来表示一个点.例如:M是车轮边缘的一点,初始态在原点,车轮半径为r,轮子沿着x轴滚动,M点的轨迹
即为摆线
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/69603ab5-65af-44a5-9dbb-1939222d5bc4.png?resizew=340)
(1)若以车轮旋转角度为参数,请写出M轨迹的参数方程
(2)若坐标原点处固定一半径为r的轨道,现在让车轮沿着该轨道转一圈,M初始态在
点,试写出M轨迹的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/69603ab5-65af-44a5-9dbb-1939222d5bc4.png?resizew=340)
(1)若以车轮旋转角度为参数,请写出M轨迹的参数方程
(2)若坐标原点处固定一半径为r的轨道,现在让车轮沿着该轨道转一圈,M初始态在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411a2b535a9a2fd094c4f19c2698b60b.png)
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