1 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,证明:在
上
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d99210d95cea8aad823d04ada1032.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4f133cb14a3a1f0266da8cb55025ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32af76ca980c959bcde29df3a08aec3.png)
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2024-02-12更新
|
384次组卷
|
2卷引用:内蒙古包头市2024届高三上学期期末教学质量检测数学(理)试题
解题方法
2 . 已知
为锐角三角形,
,
,
,是角
,
,
分别所对的边,若
;且
,则
面积的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.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/af30a92eda72d7b4daf2dc17c0c078af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2024-01-29更新
|
780次组卷
|
5卷引用:内蒙古包头市2024届高三上学期期末教学质量检测数学(理)试题
内蒙古包头市2024届高三上学期期末教学质量检测数学(理)试题内蒙古自治区锡林郭勒盟2023-2024学年高三上学期1月期末教学质量检测理科数学试题内蒙古自治区锡林郭勒盟2023-2024学年高三上学期1月期末教学质量检测文科数学试题(已下线)考点13 正弦定理及应用 --2024届高考数学考点总动员【练】(已下线)第一次月考填空题压轴题十四大题型专练-举一反三系列
名校
解题方法
3 . 在平面直角坐标系
中,已知抛物线
和点
.点
在
上,且
.
(1)求
的方程;
(2)若过点
作两条直线
与
,
与
相交于
,
两点,
与
相交于
,
两点,线段
和
中点的连线的斜率为
,直线
,
,
,
的斜率分别为
,
,
,
,证明:
,且
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1ca392fe837b53eca8582b9879a4bd.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/bd813a0d9662cd3b96d99e12b34ec234.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.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/2e9b0f5f44abbc6544a2f672b025b013.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/3f6f17bc385bafb37e8f964e5eb99cd0.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3307e11f7e6896e32aa510bbed949ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5daf9b772660af2af01d8cb179f32ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03a47a07c3d0348b0ad4b27963f9134.png)
您最近一年使用:0次
2024-01-29更新
|
2100次组卷
|
8卷引用:内蒙古包头市2024届高三上学期期末教学质量检测数学(理)试题
内蒙古包头市2024届高三上学期期末教学质量检测数学(理)试题内蒙古自治区锡林郭勒盟2023-2024学年高三上学期1月期末教学质量检测理科数学试题江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(一)湖南省常德市临澧县第一中学2023-2024学年高三第七次阶段性考试数学试题(已下线)2024年高考数学二轮复习测试卷(新题型,江苏专用)(已下线)专题07 双曲线与抛物线(分层练)(五大题型+12道精选真题)(已下线)黄金卷04(2024新题型)(已下线)题型24 5类圆锥曲线大题综合解题技巧
名校
解题方法
4 . 德国著名数学家狄利克雷在数学领域成就显著,以其命名的函数
被称为狄利克雷函数,其中
为实数集,
为有理数集,则以下关于狄利克雷函数
的结论中,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350887fb5cda6f0048c0ec4053f1eca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e680c82535270feea54ec5cc81fcc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.函数 ![]() |
B.函数 ![]() ![]() |
C.对于任意的 ![]() ![]() |
D.在 ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-10更新
|
432次组卷
|
6卷引用:内蒙古自治区包头市2023-2024学年高一上学期期末数学试题
5 . 已知点
,
,动点
满足直线
与
的斜率之积为
,记
的轨迹为曲线
.
(1)求
的方程,并说明
是什么曲线;
(2)过坐标原点的直线交
于
,
两点,点
在第一象限,
轴,垂足为
,连结
并延长交
于点
.证明:直线
与
的斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b4c07fce745f6b839493640489f381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c92e835e6811cdf63caf16ed19af9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过坐标原点的直线交
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602f64f0c8a0fa105d583d698d0af3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
您最近一年使用:0次
名校
6 . 已知函数
.
(1)若
存在极值,求
的取值范围;
(2)当
,且
时,证明:函数
有且仅有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a970882dcc8b8f54905841c10e6e3a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffd1f6bd3686a07efa4086a02b96a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556eac935a69ae56fb1d63bee5a1e5dc.png)
您最近一年使用:0次
2023-02-21更新
|
777次组卷
|
3卷引用:内蒙古包头市2022-2023学年高三上学期期末教学质量检测文科数学试题
名校
解题方法
7 . 9年来,某地区第
年的第三产业生产总值
(单位:百万元)统计图如下图所示.根据该图提供的信息解决下列问题.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/26/86c59d1c-c8e0-4006-bb80-3cacb08d1b95.png?resizew=186)
(1)求这9个生产总值中超过其平均值的概率;
(2)由统计图可看出,从第6年开始,该地区第三产业生产总值呈直线上升趋势,试从第6年开始用线性回归模型预测该地区第11年的第三产业生产总值.
(附:对于一组数据
,
,
,其回归直线
的斜率和截距的最小二乘法估计分别为:
,
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/26/86c59d1c-c8e0-4006-bb80-3cacb08d1b95.png?resizew=186)
(1)求这9个生产总值中超过其平均值的概率;
(2)由统计图可看出,从第6年开始,该地区第三产业生产总值呈直线上升趋势,试从第6年开始用线性回归模型预测该地区第11年的第三产业生产总值.
(附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7b73af3dc8b4f5cbf01551ce6f78fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9d4f56dc2eb55aaebcb5dcc125eaf72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92abae836b8026511113ad8c3ea23028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526e9468a69101c351c5bf382c835c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f4d3ab5f8ec8405fe32fd181ce32.png)
您最近一年使用:0次
2023-02-21更新
|
723次组卷
|
3卷引用:内蒙古包头市2022-2023学年高三上学期期末教学质量检测文科数学试题
8 . 如图,直四棱柱
的底面是平行四边形,
,
,
,
,
,
分别是
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/11/7662c5ac-f390-46d0-a11e-ff1a752f0bf5.png?resizew=139)
(1)证明:
平面
;
(2)求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/11/7662c5ac-f390-46d0-a11e-ff1a752f0bf5.png?resizew=139)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82050fbb5d6b10fb9a0c658cce34f83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
9 . 已知点
,
,动点
满足直线
与
的斜率之积为
,记
的轨迹为曲线
.
(1)求
的方程,并说明
是什么曲线;
(2)过坐标原点的直线交C于A,B两点,点A在第一象限,
轴,垂足为
,连接
并延长交
于点
.
(i)证明:直线
与
的斜率之积为定值;
(ii)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b4c07fce745f6b839493640489f381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c92e835e6811cdf63caf16ed19af9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过坐标原点的直线交C于A,B两点,点A在第一象限,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602f64f0c8a0fa105d583d698d0af3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(i)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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解题方法
10 . 已知抛物线
,斜率为
的直线
与
的交点为E,F,与
轴的交点为
.若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab27bcb94ea22d0f21e0280984cd335c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a21ed0ad8eec28554536a4b20279465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a25ce1c865429c97c0d5313cf8269be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
A.5 | B.4 | C.3 | D.2 |
您最近一年使用:0次
2023-02-06更新
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317次组卷
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3卷引用:内蒙古自治区包头市2022-2023学年高三上学期期末数学理科试题
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