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1 . 用篱笆在一块靠墙的空地围一个面积为
的等腰梯形菜园,如图所示,用墙的一部分做下底
,用篱笆做两腰及上底,且腰与墙成
,当等腰梯形的腰长为多少时,所用篱笆的长度最小?并求出所用篱笆长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8fbf64cd29a08ae703e9fa2035f3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
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解题方法
2 . 已知函数
则下列说法中,正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b657a78e815866a767d39a3c8b9247cc.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若方程![]() ![]() |
D.若方程![]() ![]() |
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3 . 下列命题中,是真命题的有( )
A.集合![]() ![]() |
B.若![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.![]() |
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4 . 已知圆
(
为坐标原点),圆
的圆心为点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8365d7c7c74eed93f5b9461ce31870f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.圆![]() ![]() ![]() |
B.![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.圆![]() ![]() ![]() ![]() ![]() |
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5 . 2023年中秋国庆放假期间,某同学对西昌市的空气质量进行了检测(AQI是表示空气质量的指数,AQI指数值越小,表明空气质量越好),检测数据如图( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/74d36cf7-c1e6-4a07-a435-da60cf29c841.png?resizew=296)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/74d36cf7-c1e6-4a07-a435-da60cf29c841.png?resizew=296)
A.这8天的AQI指数值的中位数为18.5 |
B.从10月2日到6日,空气质量越来越好 |
C.这8天的AQI指数值的平均值为19.375 |
D.这8天的AQI指数值的第75百分位数是21 |
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解题方法
6 . 在空间直角坐标系
中,平面
的一个法向量
,设
,
,
,则下列说法一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a834024400d0730af3e640ca4d5f54b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a02615b56fc93b8513bb1f90ad496f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9e56551e3aa3385d21d8a82bbec79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37906cac34ab721e14debf49606ec14c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ac5c1599f2cd82ff678e5ff34e0ef5.png)
A.直线![]() ![]() |
B.直线![]() ![]() |
C.直线![]() ![]() ![]() |
D.A,B,C三点在![]() |
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7 . 石室中学“跳蚤市场”活动即将开启,学生们在该活动中的商品所卖款项将用来支持慈善事业.为了在这次活动中最大限度地筹集资金,某班进行了前期调查.若商品进货价每件10元,当售卖价格(每件x元)在
时,本次活动售出的件数
,若想在本次活动中筹集的资金最多,则售卖价格每件应定为______ 元.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1941663f777bbbfa24cd72470636d3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23584d8ebc47c497bd5156e13de922f4.png)
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8 . 如图,弓形
中,弦
,
为
的中点,且
到
的距离为
,则
所在的圆的半径为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176385d91d5e29324fce4a932eff6a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/7b00d91c-7dfa-4ad3-8437-cef4f73c7b0b.png?resizew=171)
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解题方法
9 . 已知圆
和点
.
(1)过点
向圆
引切线,求切线的方程;
(2)点
是圆
上任意一点,
在线段
的延长线上,且点
是线段
的中点,求
点运动的轨迹
的方程;
(3)设圆
与
轴交于
两点,线段
上的点
上满足
,若
直线
,且直线
与(2)中曲线
交于
两点,满足
.试探究是否存在这样的直线
,若存在,请说明理由并写出直线
的斜率,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8c4afeb6cf6e4eac6c1044ecb12a2f.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d567bdeba9b8e17d0911f594e141eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03c5e1e4e2669563b22dcf05bfb9b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(3)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00579944399da601ec0a3f6b9adaaefc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53cc2d788ad5a5dc288b4237e45b89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d510eda8af3e2964bdc97c8d2be8ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
10 . 圆
称为椭圆
的蒙日圆.已知椭圆
:
的离心率为
,
的蒙日圆方程为
.
(1)求
的方程;
(2)若
为
的左焦点,过
上的一点
作
的切线
,
与
的蒙日圆交于
,
两点,过
作直线
与
交于
,
两点,且
,证明:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833bf16f0161259e9d973dbdd5c6b18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49137970108f50350a3211aa0281faaf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095c036b49c3327baaa2c3c7f746134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb43ee1cddcc3e1773260a7ac1dc3fea.png)
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2023-12-16更新
|
272次组卷
|
5卷引用:四川省部分名校2023-2024学年高二上学期期中联合质量检测数学试题