1 . 已知函数
,点
是函数
图象上不同的两个点,则
(
为坐标原点)的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a088ddc6d4f0738fe50aef7b4a6ebcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3fb867c7f875b17eeb5cd6f5600dc7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
名校
解题方法
2 . 已知定义在
上的函数
和
,
是
的导函数且定义域为
.若
为偶函数,
,
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.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/22add663bd26e87d972a10dc5fd9ada1.png)
![](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/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5109b54691be3a22f54de1dd4cca78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ffe7c17b3cf1e58045111629ccd446.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-11-26更新
|
568次组卷
|
3卷引用:山东省日照市2024届高三上学期期中校际联合考试数学试卷
名校
解题方法
3 . 下列命题为假命题的是( )
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
您最近一年使用:0次
2023-11-25更新
|
466次组卷
|
3卷引用:山东省青岛第三十九中学2023-2024学年高一上学期期中考试数学试卷
山东省青岛第三十九中学2023-2024学年高一上学期期中考试数学试卷(已下线)专题02 一元二次函数、方程和不等式1 -期末复习重难培优与单元检测(人教A版2019)上海市金山中学2023-2024学年高一下学期期末考试数学试卷
名校
解题方法
4 . 下列给出的各选项,正确的是( )
A.函数![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若函数![]() ![]() ![]() ![]() ![]() |
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解题方法
5 . 下列命题正确的是( )
A.函数![]() |
B.函数![]() |
C.“三角形是等腰三角形”是“三角形是等边三角形”的必要不充分条件 |
D.“有些三角形的外角至少有两个钝角”的否定是“所有三角形的外角至多有两个钝角” |
您最近一年使用:0次
6 . 已知命题
,
,则命题
是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243feae2a305f0e2f79deb30b137e42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1685ba4820f3aa0cb7ad1dcdb20dda5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc1bb9d53a27d484396ad74d6a26e0.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
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解题方法
7 . 已知
,
是椭圆
的左、右两个焦点,
为椭圆上一点,且
,则点
到
轴的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb4717d7fa6d522090c5e949f650bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093bec291d374725e9e4810847568a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.1 | B.2 | C.![]() | D.![]() |
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8 . “工艺折纸”是一种把纸张折成各种不同形状物品的艺术活动,在我国源远流长,某些折纸活动蕴含丰富的数学知识,例如:用一张圆形纸片,按如下步骤折纸(如图):
步骤1:设圆心是
,在圆内异于圆心处取一定点,记为
;
步骤2:把纸片折叠,使圆周正好通过点
(即折叠后图中的点
与点
重合);
步骤3:把纸片展开,并留下一道折痕,记折痕与
的交点为
;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕.
现取半径为4的圆形纸片,设点
到圆心
的距离为
,按上述方法折纸.以线段
的中点为原点,线段
所在直线为
轴建立平面直角坐标系
,记动点
的轨迹为曲线
.
(1)求
的方程;
(2)设轨迹
与
轴从左到右的交点为点
,
,点
为轨迹
上异于
,
,的动点,设
交直线
于点
,连结
交轨迹
于点
.直线
、
的斜率分别为
、
.
(i)求证:
为定值;
(ii)证明直线
经过
轴上的定点,并求出该定点的坐标.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/26/e6029915-10ec-40b2-b256-56e87680e481.png?resizew=147)
步骤1:设圆心是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
步骤2:把纸片折叠,使圆周正好通过点
![](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)
步骤3:把纸片展开,并留下一道折痕,记折痕与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
步骤4:不停重复步骤2和3,就能得到越来越多的折痕.
现取半径为4的圆形纸片,设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设轨迹
![](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/5963abe8f421bd99a2aaa94831a951e9.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/c5db41a1f31d6baee7c69990811edb9f.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f145b2ee281664660dea890bb24e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e29652da1247c6c90a5545b41327729.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d53a52aebd885294e323ee90c9b5382.png)
(ii)证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
9 . 已知抛物线
,焦点
,过点
作斜率互为相反数的两条直线分别交抛物线于
及
两点.则下列说法正确的是( )
![](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/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
A.拋物线的准线方程为![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.![]() |
您最近一年使用:0次
2023-11-25更新
|
599次组卷
|
3卷引用:山东省普高大联考2023-2024学年高二上学期11月期中联合质量测评数学试卷
解题方法
10 . 已知中心在原点,半焦距为4的椭圆
(
,
,
)被直线方程
截得的弦的中点横坐标为
,则椭圆的标准方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3997e2e743835239010fa32ee3e001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3777e8dd5c1a301c0eedd4cab5b2fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
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