解题方法
1 . 已知椭圆
的离心率为
,短轴长为
.
(1)求椭圆
的方程;
(2)设
为坐标原点,过点
分别作直线
,直线
与椭圆相切于第三象限内的点
,直线
交椭圆
于
两点.若
,判断直线
与直线
的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b391091ceb8521e5fd369d7cbb8c9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/30fa0cf31a13c1fe5ae56acddc7aaeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307bd991211ec79b47a4be52933bb8e7.png)
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2 . 下列函数中,在区间
上为减函数的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 已知集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188791535098a44dcdea38cd18d79ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e33cac3ae96733190b786adc9e8d9e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 对于曲线
,给出下列三个命题:
①关于坐标原点对称;
②曲线
上任意一点到坐标原点的距离不小于2;
③曲线
与曲线
有四个交点.
其中正确的命题个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf7f9e7937189b2185feffcbedfa438.png)
①关于坐标原点对称;
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
③曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c6cd83f8662fe04dd9aec7e1304d1c.png)
其中正确的命题个数是( )
A.0 | B.1 | C.2 | D.3 |
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5 . 直线
与圆
相交于
两点,则线段
的长度可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494ee92717842238d9678ddc152e27cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.5 | B.7 | C.9 | D.14 |
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名校
6 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)求
在区间
上的最大值与最小值;
(3)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678e56777ef9fddc36eb79ada94abb89.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d08d05d268209edc64ea895209edd235.png)
您最近一年使用:0次
2024-03-28更新
|
1927次组卷
|
2卷引用:北京市石景山区2024届高三下学期3月统一练习数学试卷
解题方法
7 . 已知函数
的部分图象如图所示,则
的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f9e0d2ee27c0edf4ee241649fc36ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8320e05871f5dfbaa1aa9887191a6d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/9a79f2a2-fe97-44df-9098-c4fb06c63662.png?resizew=105)
A.![]() | B.1 | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-28更新
|
1070次组卷
|
3卷引用:北京市石景山区2024届高三下学期3月统一练习数学试卷
8 . 等差数列
的首项为1,公差不为0.若
成等比数列,则
的前5项和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e018deab6a5ae6fb4d47b8e197df4df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() | B.![]() | C.5 | D.25 |
您最近一年使用:0次
2024-03-28更新
|
1166次组卷
|
2卷引用:北京市石景山区2024届高三下学期3月统一练习数学试卷
解题方法
9 . 在锐角
中,角
的对边分别为
,且
.
(1)求角
的大小;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b3f73a9385a5673b73d713b182e524.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b6c22c5ef4daca2f13848ebbc752fe.png)
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解题方法
10 . 已知向量
满足
,
与
的夹角为
,则当实数
变化时,
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fa8ea29001bb1f0c1e5157aff2fca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fdd453a7bf9249f37924848b85727d.png)
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