2012·河北·三模
1 . 若关于
的方程组
有实数解,则实数
满足
![](https://img.xkw.com/dksih/QBM/2013/6/3/1571238655975424/1571238661439488/STEM/0a6a31bff587472ab2513ad7ba90d3cc.png)
![](https://img.xkw.com/dksih/QBM/2013/6/3/1571238655975424/1571238661439488/STEM/326a16666f5549dab82c29860f6061f4.png)
![](https://img.xkw.com/dksih/QBM/2013/6/3/1571238655975424/1571238661439488/STEM/073e56a05b5542aca75c1495d43bbfe4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
2 . 若方程
的任意一组解(
)都满足不等式
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd18ab170f2f52856d3ef5ff51ec1787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d84a86bcc06a73a04db1b9d7363525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2017-08-17更新
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2卷引用:吉林省松原市实验高级中学等三校2016届高三下学期联合模拟考试理数试题
名校
解题方法
3 . 已知O为坐标原点,
,对于函数
,称向量
为函数
的伴随向量,同时称函数
为向量
的伴随函数.已知函数
,
(1)求
的伴随向量
,并求
.
(2)关于x的方程
在
内恒有两个不相等实数解,求实数
的取值范围.
(3)将函数
图象上每一点纵坐标不变,横坐标变为原来的2倍,再把整个图象向左平移
个单位长度得到函数
的图象,已知
,
,在函数
的图象上是否存在一点P,使得
,若存在,求出点P坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15749886728078478e1eb8129f55b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66655b7a6825b124ce596197bf2aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad690f43eb62e063ff394a77a0a44c1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941cefcb5869a853010bbe90aa11e0c5.png)
(2)关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba1f65bfa485c0fa5cf314adb28158f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34249e9efcd74ff7bdd383797a1d5972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f985137ecc361cf8d07e61e68729f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b354aefbabbc26c70388d76919dad557.png)
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2022-05-02更新
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165次组卷
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2卷引用:北京市中关村中学2021-2022学年高一下学期期中考试数学试题
4 . 某同学解答一道解析几何题:“已知直线l:
与x轴的交点为A,圆O:
经过点A.
(Ⅰ)求r的值;
(Ⅱ)若点B为圆O上一点,且直线AB垂直于直线l,求
.”
该同学解答过程如下:
解答:(Ⅰ)令
,即
,解得
,所以点A的坐标为
.
因为圆O:
经过点A,所以
.
(Ⅱ)因为
.所以直线AB的斜率为
.
所以直线AB的方程为
,即
.
代入
消去y整理得
,
解得
,
.当
时,
.所以点B的坐标为
.
所以
.
指出上述解答过程中的错误之处,并写出正确的解答过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b5062be5cf27ae8089ad0c25d1b7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1410414ebd007a6aebfb75240e2b458f.png)
(Ⅰ)求r的值;
(Ⅱ)若点B为圆O上一点,且直线AB垂直于直线l,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
该同学解答过程如下:
解答:(Ⅰ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7c0975761c23d6a82e3c26e8f03711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
因为圆O:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1410414ebd007a6aebfb75240e2b458f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8176754726d2194c890e80df1a1f1c3a.png)
(Ⅱ)因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae781496bb5bc79b67abced9aa3cd0c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
所以直线AB的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c9b54fd6a486dbbfb0b0b2aeedb92d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d58aabf178e41b21e3982b4e53e4d0.png)
代入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05648259e81bf85d96734d2d91019cdf.png)
解得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de10eb4cf291d00db3bb92596143afa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab932c81ada9989e0abacfe60c92e0e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab932c81ada9989e0abacfe60c92e0e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2341715e53f3d2a0da19ec0be038fa2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872ab7da892ac55e006b48b4660594b7.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791554b9ac1af79855d8c526c77c42ec.png)
指出上述解答过程中的错误之处,并写出正确的解答过程.
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2019-10-22更新
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2卷引用:2019年北京市第二次普通高中学业水平合格性考试数学试题