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1 . 下列说法正确的是( )
A.“![]() ![]() |
B.“幂函数![]() ![]() ![]() |
C.命题![]() ![]() ![]() |
D.已知一扇形的圆心角![]() ![]() ![]() |
您最近一年使用:0次
2024-03-24更新
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437次组卷
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2卷引用:重庆市青木关中学校2023-2024学年高一上学期期末考试数学试题
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解题方法
2 . 若
满足以下条件:①
;②
的图象关于
对称;③对于不相等的两个正实数
,有
成立,则
的解析式可能为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c38a21483a2dc328d2e0b1d1b62599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdefd43c07f5f2fe560a5dd6848c9d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
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3 . 已知双曲线
的渐近线为
,双曲线
与双曲线C的渐近线相同,过双曲线
的右顶点的直线与
,在第一、四象限围成三角形面积的最小值为8.
(1)求双曲线
的方程;
(2)点P是双曲线
上任意一点,过点P作
依次与双曲线C和
交于A,B两点,再过点P作
依次与双曲线C和
交于E,F两点,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017262e45089093f70001cae2c60257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(2)点P是双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca086092226075eb257f10f674eed9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49ac3a8f9f4f495cbc7629eb7c855b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2868ec4ce76288fe9b77247f4f467f6.png)
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4 . 在经济学中,常用Logistic回归模型来分析还款信度评价问题.某银行统计得到如下Logistic模型:
其中x是客户年收入(单位:万元),
是按时还款概率的预测值,如果某人年收入是10万元,那么他按时还款概率的预测值大约为( )(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f5952b3c9667025b65a60efd43fe0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826308511448f7b791edf4199c690768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be46cbc56dee6fa2257bc9225d9cb6e.png)
A.0.35 | B.0.46 | C.0.57 | D.0.68 |
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解题方法
5 . 长时间的实践表明,冲泡绿茶用
开水最为合适,饮用时茶水温度在
至
之间口感最佳.已知环境温度为
,物体温度为
吋,经过
分钟后物体温度
满足
,其中
为常数.某实验小组通过数据收集,计算得常数
,假设近期室内温度均为
.
(1)以
开水冲泡绿茶,经过8分钟后茶水温度约为多少?
(2)早上张老师到办公室上班,先用
开水泡好一杯绿茶,然后去教室看早自习,再回到办公室准备喝茶,请帮张老师计算一下他泡的茶水能保持最佳口感的时长.
(注意:本题结果都保留两位小数,参考数据
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13708f01d71b3172e2508af0d620572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7158d8fec00479a56aa0333f550a92d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627d1038ec568d0540e3258528b2533f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635ccd929471d564cc9d2d96266b34d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4a380f8b1ccd6f70a1e1ecf8c98d61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cb3767bf1cc7b8ffd5ab9099a19269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ccac4181d8a1fe89f03c89ca7c42fe.png)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13708f01d71b3172e2508af0d620572.png)
(2)早上张老师到办公室上班,先用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13708f01d71b3172e2508af0d620572.png)
(注意:本题结果都保留两位小数,参考数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a458f4716b7fb99418d762909eecab11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59004c5916a745f186e0bd66aa3bca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d333e0ad053f9ef9fe12dc6e0d4cf.png)
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解题方法
6 . 已知函数
的定义域为
,
,满足
,
,令
,设当
时,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea944fa5b7030c92f0d06e7e15c1c135.png)
(1)计算
,并证明
在
上单调递增;
(2)对任意的
,
,总存在
,使得
成立,求t的取值范围?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f21febe8749e5e598124c2f6bb4025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c137b664f5c1b3368a55c3e7adb1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5409f79d5899f4822deaf275df1739c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea944fa5b7030c92f0d06e7e15c1c135.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006dd721f6e19ee105cf6e3a10b69c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a47fb2689296e12a46e6a9b65e74ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e805e0506d37973afc0664ae0a6af0.png)
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2024-01-25更新
|
374次组卷
|
2卷引用:重庆市渝中区巴蜀中学校2023-2024学年高一上学期1月期末数学试题
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7 . 小红学了高一年级《基本不等式》后,高兴地告诉她正读高三的哥哥小东说:“哥哥,我知道你以前说的“基本不等式”是怎么回事了,我还可以对它扩充呢”.然后小红在草稿本上工工整整地写下了“若
,
,则
”.小东微笑着说:“恭喜你获得了新知,加油!等你上高三了还可以往这个不等式里面补充内容,看我写一个.”然后小东就把刚才小红写的内容改成了:“若
,
,
,则
”.小东看着小红崇拜的眼睛,又补充说:“虽然你现在还不能完全证明它,但是你可以用‘若
,
,
,则
’作为条件来证明另一个结论:‘若
,则
’”.
(1)请完成小东所说结论的证明,即用“若
,
,
,则
”作为条件,证明结论“若
,则
”成立;
(2)请用(1)中的结论解决问题:已知函数
有两个不同的零点
,证明
;
(3)小红成功完成(2)中的证明后,翻开哥哥小东的高三资料发现这样一道题:若函数
有两个不同的零点
,证明
.她兴奋地对哥哥说:“我发现这个题在本质上跟(2)中的题目是一模一样的!”.请问你认同小红的说法吗?写出你的观点并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d473e7e88342bd8cf463d2f0d644e536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bf4dc2e9fea34fa1ba06d8df94b1ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc807f76d58df49f083de0c4a21eff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e7ce5311b94977b94dc25a7a30b678.png)
(1)请完成小东所说结论的证明,即用“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc807f76d58df49f083de0c4a21eff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e7ce5311b94977b94dc25a7a30b678.png)
(2)请用(1)中的结论解决问题:已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d34a824ee29777ed157f992027d9b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
(3)小红成功完成(2)中的证明后,翻开哥哥小东的高三资料发现这样一道题:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74da4b06c434c46d5a8958ad77f2592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4900c67f4b57fa430c4bd863f8e896.png)
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8 . 下列说法不正确的有( )
A.点![]() ![]() ![]() |
B.经过点![]() ![]() |
C.过双曲线![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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2024-01-22更新
|
330次组卷
|
2卷引用:重庆市西南大学附属中学校2023-2024学年高二上学期期末考试数学试题
解题方法
9 . 1837年,狄利克雷提出了函数的现代定义,即如果变量
与变量
相关,使得根据某个规则,每个
值都对应唯一一个
值,那么
就是关于自变量
的函数.并举出了个著名的函数-狄利克雷函数:
,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07eec4f873e724716282f677c596fa5a.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
10 . 下列说法正确的是( )
A.函数![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.已知函数![]() ![]() ![]() |
您最近一年使用:0次
2024-01-20更新
|
556次组卷
|
2卷引用:重庆市第一中学校2023-2024学年高一上学期期末考试数学试题