1 . 已知函数
的图象过原点.
(1)求
的值及
的最小正周期;
(2)若函数
在区间
上单调递增,求正数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e21a4f2ac5a067bed55933ff8f8fd1be.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424843950ee17f6f18b5c181c1f6ee34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
解题方法
2 . 已知椭圆
的左顶点为
,上顶点为
,原点
到直线
的距离为
,
的面积为
.
(1)求椭圆
的方程;
(2)过点
的直线
与椭圆
交于不同的两点
,过点
作
轴的垂线分别与直线
交于点
.判断点
是否为线段
的中点,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d033187cbcb305e6df0ba622f0cd3e4.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f40d5459e1385ab7d829ea96ca0b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.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/cea77ba313fcc751481ac1ca214df3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
您最近一年使用:0次
3 . 已知函数
,
为偶函数,且当
时,
,记函数
,给出下列四个结论:
①当
时,
在区间
上单调递增;
②当
时,
是偶函数;
③当
时,
有3个零点;
④当
时,对任意
,都有
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda5ab0495110870938c761638ae6ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed62208af6047cd1374c6db9d21e8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a3bc841b0c96fada3e4f8ca5f1396f.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c787b3ae93138bac7485c406d29f94b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5069fb2cd95b9595065b4294e308322.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd2215e5cdeb3f6b0b7929a4a05ba65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c787b3ae93138bac7485c406d29f94b1.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a915c1a8a9304aeb307d130faaeb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c787b3ae93138bac7485c406d29f94b1.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6163bf8b74410bfb93919ec5130795ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078f88a148727f0bba99fde30d056d03.png)
其中所有正确结论的序号是
您最近一年使用:0次
解题方法
4 . 将函数
的图象向左平移
个单位长度,得到函数
的图象.若函数
的图象关于y轴对称,则
的一个取值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19d6fa3789aed1a7750709cbcfabae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4145ac17697bc0f91225af690eeeff0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
您最近一年使用:0次
解题方法
5 . 已知双曲线
的一条渐近线过点
,则其离心率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879a4007beef22e009248112d664f7c2.png)
您最近一年使用:0次
6 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77eb9decfc641e3d4b82b5c07de0fa24.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-25更新
|
408次组卷
|
2卷引用:北京市朝阳区2023-2024学年高一上学期期末质量检测数学试题
7 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879779123641388c50bc027caecfe331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-25更新
|
309次组卷
|
3卷引用:北京市朝阳区2023-2024学年高一上学期期末质量检测数学试题
8 . 已知等差数列
的公差为
,
为其前
项和,且
成等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b1b845916a4b6a18cdfbcd308d09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
您最近一年使用:0次
解题方法
9 . 设函数
,当
时,
的最大值为______ ;若
无最大值,则实数
的一个取值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf067013acfc1b55f2e146951148b6d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
10 . 设函数
,且
.
(1)求
的值;
(2)再从条件①、条件②、条件③这三个条件中选择一个作为已知,使函数
存在,求
的值及
的零点.
条件①:
是奇函数;
条件②:
图象的两条相邻对称轴之间的距离是
;
条件③:
在区间
上单调递增,在区间
上单调递减.
注:如果选择的条件不符合要求,第(2)问得
分;如果选择多个符合要求的条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0ad0086eb9edf9cc9742d9ce1e1ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61c9a7ed0961f8977a21dab37aab396.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)再从条件①、条件②、条件③这三个条件中选择一个作为已知,使函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a37ed7d5bf043795fd8d9ba77092b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daad6de6e7d7b4032989c2cfd29300f1.png)
注:如果选择的条件不符合要求,第(2)问得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
您最近一年使用:0次