名校
解题方法
1 . 已知椭圆的焦点分别是,
,点
在椭圆上,且
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4aafea08192eb812a06147bdb7e8dbd.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/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2024-06-14更新
|
143次组卷
|
2卷引用:2024届山东省德州市第一中学高三三模数学试题
2 . 已知
的其中两个顶点为
,点
为
的重心,边
,
上的两条中线的长度之和为
,记点
的轨迹为曲线
.
(1)求
的方程;
(2)过点
作斜率存在且不为0的直线
与
相交于
两点,过原点
且与直线
垂直的直线
与
相交于
两点,记四边形
的面积为S,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af2fdf1944afebb51cb6a5e6c74aadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3e029070ad0d2ce680d5336ed7150a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d3ae70ecef31f90e511eba69f99b0c.png)
您最近一年使用:0次
2024-04-24更新
|
1012次组卷
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5卷引用:山东省泰安市2024届高三下学期高考模拟((三模))数学试题
3 . 已知椭圆
的左、右焦点分别为
,
,离心率为
经过点
且倾斜角为
的直线l与椭圆交于A,B两点(其中点A在x轴上方),且
的周长为8.将平面
沿x轴向上折叠,使二面角
为直二面角,如图所示,折叠后A,B在新图形中对应点记为
,
.
时,
①求证:
;
②求平面
和平面
所成角的余弦值;
(2)是否存在
,使得折叠后
的周长为
?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f727d47ac94c374adb4fc3131dcca1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5465c4f86cbc6cc2c9ba7adbc2060b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e186ebc624ebacde9a03b96289f1ab.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b67dd99eb86dd623a222f37e558eaf.png)
②求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6e369cb5ba6c39478f101d5e48f855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d39836fc74c4129604e5c5962a942.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f727d47ac94c374adb4fc3131dcca1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704ed9f2e6dc0126720fc390ea193533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7163395f9aaa29be7f6b3106ba48b744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
4 . “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内容,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点,标记为
;
步骤2:把纸片折叠,使圆周正好通过点
;
步骤3:把纸片展开,并留下一道折痕;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕.
现对这些折痕所围成的图形进行建模研究.若取半径为6的圆形纸片,如图,设定点
到圆心
的距离为4,按上述方法折纸.以点
所在的直线为
轴,线段
中点为原点建立平面直角坐标系.
(1)若已研究出折痕所围成的图形即是折痕与线段
交点的轨迹,求折痕围成的椭圆的标准方程;
(2)记(1)问所得图形为曲线
,若过点
且不与
轴垂直的直线
与椭圆
交于
两点,在
轴的正半轴上是否存在定点
,使得直线
斜率之积为定值?若存在,求出该定点和定值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/9/67774f82-d758-48e1-bad3-0d10917493e7.png?resizew=289)
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)
步骤3:把纸片展开,并留下一道折痕;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕.
现对这些折痕所围成的图形进行建模研究.若取半径为6的圆形纸片,如图,设定点
![](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/b92dbe7d01d47d6c2db1396180caf76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(1)若已研究出折痕所围成的图形即是折痕与线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)记(1)问所得图形为曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451fc6e4248b63e70595f23842f06c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b312367cf51225ea3bfbee2103b0c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a887bfa3cac99e4bd33610515b722b.png)
您最近一年使用:0次
2023-07-07更新
|
694次组卷
|
13卷引用:山东省济南市历城第一中学2023届高考押题卷(二)数学试题
山东省济南市历城第一中学2023届高考押题卷(二)数学试题陕西省渭南市2023届高三下学期教学质量检测(Ⅰ)理科数学试题陕西省渭南市2023届高三下学期教学质量检测(Ⅰ)文科数学试题江西省南昌市第十中学2023届高三第一次模拟数学(文)试题江西省南昌市第十中学2023届年高三第一次模拟数学(理)试题四川省成都石室中学2024届高三零诊模拟考试理科数学试题四川省成都石室中学2024届高三零诊模拟考试文科数学试题四川省成都市玉林中学2022-2023学年高三下学期3月月考文科数学试题四川省成都市玉林中学2022-2023学年高三下学期3月月考理科数学试题河北省衡水中学2023届高三下学期五调数学试题(已下线)第八章 解析几何综合测试A(基础卷)黑龙江省哈尔滨市香坊区2024届高三上学期期末联考数学试题广东省深圳外国语学校(集团)龙华高中部2024届高三上学期第三次月考数学试题
名校
5 . 已知向量
、
不共线,夹角为
,且
,
,
,若
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29276b43a2950ed71f0f9629a35dfa74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404067afb19bd74f447a6c0c832af1da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23666d90f6a49c7215540f8bc883dc13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8055aa93044829d00202a737f05f6078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2b7c9eab4b1e202813309246457e22.png)
您最近一年使用:0次
2023-04-28更新
|
1162次组卷
|
3卷引用:山东省济宁市2023届高三二模拟数学试题
名校
解题方法
6 . “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内容,例如:用一张圆形纸片,按如下步骤折纸(如图)
,在圆内异于圆心处取一点,标记为
;
步骤2:把纸片折叠,使圆周正好通过点
;
步骤3:把纸片展开,并留下一道折痕;
步骤4:不断重复步骤2和3,就能得到越来越多的折痕.则这些折痕所围成的图形是一个椭圆.
现取半径为
的圆形纸片,定点
到圆心
的距离为
,按上述方法折纸.以向量
的方向为
轴正方向,线段
中点为原点建立平面直角坐标系.
(1)求折痕围成的椭圆
的标准方程;
(2)已知点
是圆
上任意一点,过点
做椭圆
的两条切线,切点分别是
,求
面积的最大值,并确定此时点
的坐标.
注:椭圆:
上任意一点
处的切线方程是:
.
![](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)
步骤3:把纸片展开,并留下一道折痕;
步骤4:不断重复步骤2和3,就能得到越来越多的折痕.则这些折痕所围成的图形是一个椭圆.
现取半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](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/b10e8abf8690e4b129466ddb918bcc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc78f89939084f4979069d2d5b45833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(1)求折痕围成的椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f285c23bbc61f073e174b411d4116d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
注:椭圆:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9656735f55e5de465e5667ba578d4e.png)
您最近一年使用:0次
2023-04-27更新
|
1219次组卷
|
10卷引用:山东省淄博市部分学校2023届高三下学期4月阶段性诊断考试数学试题
山东省淄博市部分学校2023届高三下学期4月阶段性诊断考试数学试题湖南省衡阳市第八中学2024届高三下学期高考适应性练习(一)数学试题(已下线)四川省巴中市2023届高三“一诊”考试数学(理)试题变式题16-20专题20平面解析几何(解答题)(已下线)第十章 导数与数学文化 微点3 导数与数学文化(三)湖南省张家界市慈利县第一中学2024届高三上学期第二次月考数学试题(已下线)微考点8-1 新高考新题型19题新定义题型精选(已下线)模块四 专题1 高考新题型专练(新定义专练)(人教A)(高二)广东省揭阳华侨高级中学2024届高三下学期第二次阶段(期中)考试数学试题湖南省岳阳市汨罗市第一中学2024届高三下学期5月期中数学试题
解题方法
7 . 已知
的两个顶点A,B的坐标分别为
,
,圆E是
的内切圆,在边AC,BC,AB上的切点分别为P,Q,R,
,动点C的轨迹为曲线G.
(1)求曲线G的方程;
(2)设直线l与曲线G交于M、N两点,点D在曲线G上,O是坐标原点
,判断四边形OMDN的面积是否为定值?若为定值,求出该定值;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa98b3f5fa18d38292170956357e0754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26d1b84ffffb01daebfd1a425fc16ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833951a2a0c59b170cc96c4e23fa8f71.png)
(1)求曲线G的方程;
(2)设直线l与曲线G交于M、N两点,点D在曲线G上,O是坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42813b07a70e6d132211d2b1c5877ca.png)
您最近一年使用:0次
8 . 已知圆
与圆
:
外切,同时与圆
:
内切.
(1)说明动点
的轨迹是何种曲线,并求其轨迹方程;
(2)设动点
的轨迹是曲线
,直线
:
与曲线
交于
,
两点,点
是线段
上任意一点(不包含端点),直线
过点
,且与曲线
交于
,
两点,若
为定值,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed65024898bb517e8cd6a2c663b836e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08f72e31d61847766a620b3d57c102c.png)
(1)说明动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36eaa4e819d4643ce02c8f3abf78b454.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0da1bdc4ccf70abdf0525bfb7e0e14c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2189887d9bc110b8a409df20ec4d827a.png)
您最近一年使用:0次
2022-04-04更新
|
1305次组卷
|
2卷引用:2022届山东省潍坊市高三下学期5月模拟数学试题(一)
名校
解题方法
9 . 已知椭圆
的焦距为2,点
在C上.
(1)求C的方程;
(2)若过动点P的两条直线
,
均与C相切,且
,
的斜率之积为-1,点
,问是否存在定点B,使得
?若存在,求出点B的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7167b1f25e38b061b3a234bf4d569a8.png)
(1)求C的方程;
(2)若过动点P的两条直线
![](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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4c1016bf87b416cff0f3fa79d3ef9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289542670b804bc81f924549035232f0.png)
您最近一年使用:0次
2022-03-04更新
|
2437次组卷
|
3卷引用:山东省潍坊市2022届高三一模统考(3月)数学试题