名校
解题方法
1 . 已知双曲线
的右焦点为F,c是双曲线C的半焦距,点A是圆
上一点,线段FA与双曲线C的右支交于点B.若
,则双曲线C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7893c7403a17f8ae296fb68fa7bbb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf571d61abf7a871224de2e4537f37f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f5ead4c208849a901eb56f1d054a21.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-06-08更新
|
876次组卷
|
3卷引用:北京市朝阳区2024届高三下学期质量检测二数学试题
解题方法
2 . 已知
是两个互相垂直的平面,
是两条直线,
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba83980a38c5e1fe4be841bc8a51d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/398fcd2493696aefeb0574d425e67022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90aaadafdc1b5187c6d3a045f44cda91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75350c0f16848247ec0602b0b9a55df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc457ba23645bb1fbaa297c5e565f978.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-06-03更新
|
1450次组卷
|
3卷引用:北京市朝阳区2024届高三下学期质量检测二数学试题
解题方法
3 . 已知函数
,存在最小值,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8c5670463879f58bf6ef159dbae062.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 北宋科学家沈括在《梦溪笔谈》中记载了“隙积术”,提出长方台形垛积的一般求和公式.如图,由大小相同的小球堆成的一个长方台形垛积的第一层有
个小球,第二层有
个小球,第三层有
个小球……依此类推,最底层有
个小球,共有
层,由“隙积术”可得 这 些 小 球 的 总 个 数 为
若由小球堆成的某个长方台形垛积共8层,小球总个数为240,则该垛积的第一层的小球个数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/9/08b5b114-291b-48fd-96e1-14b11208b7d0.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d993cf0a090de3b01f1dda52c6fdc9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b4f6054ca644083ecfa85ed1bb7592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b939f6c148a4e5fae83668aaa627836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023fc87942a6821ca78d8cae08917352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34cf59fcb503ce674a118159af9244c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/9/08b5b114-291b-48fd-96e1-14b11208b7d0.png?resizew=167)
A.1 | B.2 | C.3 | D.4 |
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解题方法
5 . 已知椭圆E的两个顶点分别为
,
,焦点在x轴上,且椭圆E过点
.
(1)求椭圆E的方程;
(2)设O为原点,不经过椭圆E的顶点的直线l与椭圆E交于两点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0c2c938daac9fd7de1a543fea4d534.png)
,直线BP与直线OC交于点H,点M与点Q关于原点对称.
(i)求点H的坐标(用
,
表示);
(ii)若A,H,M三点共线,求证:直线l经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108fb116d4b8df0b55280cc50aa378a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d208692e17b7d9df9886cffee6814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6d973205f1ee6c8ef7a728ed772017.png)
(1)求椭圆E的方程;
(2)设O为原点,不经过椭圆E的顶点的直线l与椭圆E交于两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0c2c938daac9fd7de1a543fea4d534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21e5e78dc87038431fa228f08c16ec4.png)
(i)求点H的坐标(用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
(ii)若A,H,M三点共线,求证:直线l经过定点.
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名校
6 . 已知函数
恰有两个零点,则实数
的取值范围是____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e626aba63d0e1b140650454b9afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
7 . 若函数
在区间
内为增函数,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e53c52ba6d187e4be564e7f1cd581b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f26f6cc6cf7d49eeffa37036436bc54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
8 . 已知函数
,关于
的性质,有以下四个推断:
①
的定义域是
;
②
的值域是
;
③
是奇函数;
④
是区间
上的增函数.
其中判断正确的选项是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aafb21bf0b3e9040907f773cf4e0610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf620d67c6625a449b5238d61b1c0e3.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d1805dc28d18576b8b49b98d8b438c.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e4586d136ad18160316ea6eed15e22.png)
其中判断正确的选项是
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名校
解题方法
9 . 袋中有大小相同、质量相等的3个白球和2个黑球,若每次抽取1个球,有放回地连续抽取3次,则恰有1次取到黑球的概率为________ ;取到黑球的个数
的数学期望是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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10 . 设
为正整数,集合
对于
,设集合
.
(1)若
,写出集合
;
(2)若
,且
满足
令
,求证:
;
(3)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb39983c5c3fc32d3f0a2c98f04cdb3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee7981aba05ee1d4945062913c8db8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08897069d8b3e4c9f42a768d7ae2d416.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40deecdcc73cfee7fe7624a813af16ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeff5c5f7214a5f9b920af89af5b3802.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee7981aba05ee1d4945062913c8db8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5c31ea128ff2a390979894f53486f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695e27822adf2901dd6f48a1a29e68d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764928f3bec8c40cbff944c0b36ffb57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18bf5b3e05fdd0bdb9597f5b9d2386cf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee7981aba05ee1d4945062913c8db8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53037f80f8cf5faf2f861a3859c3166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa4b0e70b5c191c6391263d905c52b0.png)
您最近一年使用:0次