名校
解题方法
1 . 已知直线l过点
,且在横坐标轴与纵坐标轴上的截距的绝对值相等的直线方程可以是___________ (写出一种即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
您最近一年使用:0次
2021-11-05更新
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345次组卷
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3卷引用:北京市首都师范大学附属中学2021-2022学年高二上学期期中数学试题
名校
解题方法
2 . 在直线l上任取不同的两点A,B,称
为直线l的方向向量与直线l的方向向量垂直的非零向量称为l的法向量,在平面直角坐标系中,已知直线
是函数
的图象,直线
是函数
的图象.
(1)求直线
和直线
所夹成的锐角的余弦值;
(2)已知直线
平分直线
与直线
所夹成的锐角,求直线
的一个方向向量的坐标;
(3)已知点
,A是
与y轴的交点,
是
的法向量.求
在
上的投影向量的坐标(求出一个即可),并求点P到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c30fd97fafb3779aa4f4660f41e2939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549bc1c85c955e6511fff0a81b6adc39.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d658b3385c5aa6be7e66f636648af14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f654198c1e01d97f1378b35d7c68ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
解题方法
3 . 已知直线
经过点
倾斜角
的余弦值为
.
(1)求直线
的方程;
(2)判断直线
与圆C:____________的位置关系;如果相交,记交点为
,
,求经过
,
两点的圆的面积的最小值;如果相离,过直线
上的点
作圆
的切线,切点为
,求
长的最小值.
现给出两个条件:①
;②
,从中选出一个条件填在横线上,写出一种方案即可.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bcc512ec11bf8f6e0f42977dec712c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
现给出两个条件:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc2a82f9871e32bd2d5871bf159cadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8644d2fa86c82386e1d234f59e54ca90.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在平行四边形
中,已知点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9528f9b8db429b42ad8a1924b72c9bd3.png)
![](https://img.xkw.com/dksih/QBM/2021/11/24/2858207179153408/2859808809033728/STEM/fda9917a-bf6a-489d-8523-af30bd7f9e58.png?resizew=238)
(1)求
所在直线的方程
(2)过点
作
于点
,求线段
的长度
(3)设线段
的中点为
,则点
的坐标为 (注:不要求推理过程,直接写坐标即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9528f9b8db429b42ad8a1924b72c9bd3.png)
![](https://img.xkw.com/dksih/QBM/2021/11/24/2858207179153408/2859808809033728/STEM/fda9917a-bf6a-489d-8523-af30bd7f9e58.png?resizew=238)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2021高二·江苏·专题练习
解题方法
5 . 已知
为正方形ABCD的中心
B,C,D逆时针排列
,AB边所在直线方程为
.
(1)求对角线AC,BD所在直线的方程;
(2)已知
是一个定点,
是x轴上一个动点,过点M作直线MN,满足MN与MQ斜率之和为零,且直线MN与正方形ABCD有公共点.
①求出直线MN分别过正方形各顶点时,M点的坐标;
②写出实数t的最大值与最小值
不需要过程,直接写出答案即可
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39faeffdcfb1341246236e8b89a1f018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b125b6b68ee26087d01a08b4dd6a1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a841ee7676cd49834c376dee1c07d6.png)
(1)求对角线AC,BD所在直线的方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aa8babf848f921fcdc0ef9c6a4b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a4e7a7d38d0cdcabc25b8b5821539b.png)
①求出直线MN分别过正方形各顶点时,M点的坐标;
②写出实数t的最大值与最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
您最近一年使用:0次
名校
6 . 在下列四个命题中:
①若向量
所在的直线为异面直线,则向量
一定不共面;
②向量
,若
与
的夹角为钝角,则实数m的取值范围为
;
③直线
的一个方向向量为
;
④若存在不全为0的实数
使得
,则
共面.
其中正确命题的个数是( )
①若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ccba3b87a8a48ac3dd5f72d00bdb1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ccba3b87a8a48ac3dd5f72d00bdb1a.png)
②向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7631b13b6101c95be2ee66610d9ca8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cae012863d0c18ee1535449b751e8b.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f6e613ffa032e7e893daa1970d3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703b2bfea50e6309f81e3a0a64c0900a.png)
④若存在不全为0的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf0c71b8e2cf6437cf1e3c12ddcef50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96022a881e03e32d3483d997c3f170c6.png)
其中正确命题的个数是( )
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
2021-12-29更新
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1009次组卷
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3卷引用:山东省2021-2022学年高二12月“山东学情”联考数学试题