名校
1 . 已知空间向量
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6a0c8f851443a3cf3f0845e1dc35ce.png)
A.![]() |
B.![]() ![]() ![]() |
C.若向量![]() ![]() ![]() |
D.向量![]() ![]() |
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2024-03-03更新
|
327次组卷
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2卷引用:甘肃省兰州市第二中学2023-2024学年高二下学期期中考试数学试卷
名校
2 . 已知函数
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cad89a93eb64a1042897ffd26938ae7.png)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.若方程![]() ![]() |
D.设![]() ![]() ![]() ![]() |
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2024-02-28更新
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1649次组卷
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6卷引用:甘肃省兰州第一中学2023-2024学年高二下学期3月月考数学试题
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3 . 已知函数
及其导函数
的定义域均为
,且
,
的图象关于点
对称,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afae8a24472c2ad833ea7aa89cd35e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.![]() |
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2024-02-23更新
|
1083次组卷
|
4卷引用:甘肃省兰州市第二中学2023-2024学年高二下学期期中考试数学试卷
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解题方法
4 . 已知向量
,则点A到直线
的距离为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c9e69b7d07118b514174f391f1a58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
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2024-02-23更新
|
223次组卷
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2卷引用:甘肃省兰州市第二中学志果班2023-2024学年高二下学期期中考试数学试题
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5 . 抛物线
的焦点为
,其准线与双曲线
相交于
两点,若
为等边三角形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c315e4d8bc93ca6f4c991ebe7df0a1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
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解题方法
6 . 已知经过点
的直线l的一个法向量为
,则直线l的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48befa5d90fafd8bfdb6c90fd241ebfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
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解题方法
7 . 已知直线
和直线
.
(1)试判断
,
能否平行,若平行,请求出两平行线之间的距离;
(2)若原点到
距离最大,求此时的直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b677a6b73f24cc267b15a3a66c88a565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872d370ba75dbd8515552207c713810b.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)若原点到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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解题方法
8 . 已知各项均为正数的数列
前
项和为
,且
,
.
(1)求数列
的通项公式;
(2)令
,数列
的前
项和为
.
(i)求
;
(ii)是否存在整数
,使得不等式
恒成立?若存在,求出所有
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1621660898279a626e21ceee67e96a3f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(ii)是否存在整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba428b8196729443880a5064ddfaba06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d085f77f4952b2c96927c93e5b80fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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9 . 在数列
中,
,
,则数列
的前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0511e5743d242ec106c1f68fc1061b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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解题方法
10 . 在平面直角坐标系
中,圆
与圆
内切,且与圆
外切,记动圆M的圆心的轨迹记为曲线C.直线
与曲线C相交于P,Q两点.
(1)求曲线C的方程;
(2)若
是一个与m无关的定值,求此时k的值及△OPQ的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a9e1eb4c3226489d1344321b10b7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5debc075b89bf00c374b0f86264e719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753c1a07e8f377085956b249e434495a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f44c9010af5e7b8c487b125dd053d35.png)
(1)求曲线C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f6c5fd93aed88bec58002a20ea2e90.png)
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