1 . 已知
.
(1)当
时,若
的展开式中第3项与第8项的二项式系数相等,求展开式中
的系数;
(2)设
.
①求
的系数(用
表示):
②求
(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1312efa155c4cace3f23aee7dcfd2f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbcd23a8020d731bd512bb8df45ea594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800f03de80068a1172beac3a2c75587.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c945ee7b5ea6e316f36eccf33687be4.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba6e27a50b212256655e53fe4d19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-04-29更新
|
304次组卷
|
2卷引用:江苏省淮安市洪泽中学,金湖中学,清河中学,清浦中学等学校2023-2024学年高二下学期5月月考数学试题
2 . 已知双曲线
的离心率为
,实轴长为
.两条不同直线
与双曲线
分别交于A,B两点和C,D两点,两条直线的斜率分别为
.
(1)求双曲线
的方程;
(2)若直线l1过右焦点,求线段AB长度的最小值;
(3)若两条不同直线
都过点
且演足
分别为线段AB,CD的中点,求证直线MN过定点,并求出该定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线l1过右焦点,求线段AB长度的最小值;
(3)若两条不同直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797c488729678e74e0825c2e92b544b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2808e15e69d26104ef0662bffb7edfd.png)
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2024-04-09更新
|
274次组卷
|
2卷引用:江苏省淮阴中学2023-2024学年高二下学期级阶段测试(一)数学试卷
名校
3 . 以
为钝角的
中,
.
(1)若
,且
,
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942a42bbc5abc30793245ed2965f4a56.png)
(2)若
,当角
最大时,求
的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bd069b35ea935375e93da13b91b6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d18d62f2b8c06e20eb31d2007ae66cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b751e33ead651932d2145090888e7b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942a42bbc5abc30793245ed2965f4a56.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0958c17b0d01520cbfe4528f16b45bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
4 . 已知函数
.
(1)讨论函数
的单调区间;
(2)当
时,函数
有两个零点
,求
的取值范围:
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/784548dbfa097ef19fd7a4e68739e478.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e189dbc979fad6bf8ca03ac1388cbac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc93e6c831bd03403d423b88746e733.png)
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2024-04-01更新
|
344次组卷
|
3卷引用:江苏省淮阴中学2023-2024学年高二下学期级阶段测试(一)数学试卷
名校
解题方法
5 . 对于集合
和常数
,定义:
为集合A相对的
的“余弦方差”.
(1)若集合
,求集合A相对
的“余弦方差”;
(2)若集合
,是否存在
,使得相对任何常数
的“余弦方差”是一个与
无关的定值?若存在,求出
的值:若不存在,则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8368b2cc0b5ea5bcde2e386e49f57641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c399e314ea3779046c8f1aa2e5555c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcd000ab235793dc4ec905c36dd2f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71b7dc3ec4bc675166b126e56c083cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82100419449370da67bf679e9dc44814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
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2024-03-31更新
|
241次组卷
|
2卷引用:江苏省淮阴中学2023-2024学年高一下学期3月阶段性考试数学试题
名校
6 . 在
中,点
是
内一点,
,过点
的直线
交直线
分别于
两点,且
,已知
为非零实数.试求
的值.
(2)若
,且
,设
,试将
表示成关于
的函数,并求其最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc4fc0635e1651eb2d8caad240b859b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9cc092cab61924df0048df59637a720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2272838844227e6874f863f61e2f134b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb183aab96cdb1e25caabda59fb8fbb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39346db456e8935d6d95a14b1d50ccde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661f3c446093390a3be8fe5993c549c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c9d96d2dc0082bb375c3b0e7214bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d81674538e4af9b8d4946f48d940011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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2024·全国·模拟预测
解题方法
7 . 已知椭圆
的离心率为
分别为
的左、右焦点,
为上顶点,且
的内切圆半径为
.
(1)求
的方程;
(2)
是
上位于直线
异侧的两点,且
,证明:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02904676fe59cd21f036b222273b8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e01955f8c8fe2f0041b35d8d602a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734adc7103826fe972f836233544a19c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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8 . 已知函数(
为自然常数),
为实数.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
9 . 已知函数
.
(1)讨论
的单调性;
(2)设
为两个不相等的实数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871bbc0c88332bb2de90f33024da19c2.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530a664e40a51a906ac10e44ff360807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ada0ecff751d0cda00141ef7b598570.png)
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2023-12-15更新
|
515次组卷
|
2卷引用:江苏省淮安、南通部分学校2023-2024学年高三上学期11月期中监测数学试题
10 . 在平面直角坐标系
中,已知圆
的方程为
,且圆
与
轴交于
,
两点(
在
的左侧),若直线
:
(
)与圆
相交于
,
两点.
(1)若
,求实数
的值;
(2)设直线
与直线
交于点
,记直线
,直线
,直线
的斜率分别为
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81338417602aa3f61f2f62a63fb1184a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.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)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296e72680e0f6ed1f35ac4687f3b5f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.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/7d9c8ddf61e690eee503c015d4afdf9b.png)
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