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1 . 已知
,则这三个数的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9f240e910ccd1551938f51e76e7757.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7日内更新
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1665次组卷
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4卷引用:海南省部分学校2024届高三考前押题考试(三模)数学试题
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2 . 指数函数模型在生活生产中应用广泛,如在疾病控制与统计、物理学、生物学、人口预测等问题上都可以应用其进行解决.研究发现,某传染病传播累计感染人数
随时间
(单位:天)的变化规律近似有如下的函数关系:
,其中
为常数,
为初始感染人数.若前3天感染人数累计增加了
,则感染人数累计增加
需要的时间大约为( )(参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a96e95794da54dee50df12f0da1570c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18092f868ac7b7b1a50ae42fd4787aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84abbfb85a00f48b5db11eeb76b8d134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4781898416f29fc5127ac4cc44e08290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1213c2a26a77edc9d0615b9988474c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1525c56bbb8644c202d454a70c30db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51e1b38325d10bb7685a9b162ad8161.png)
A.10.5天 | B.9天 | C.8天 | D.6天 |
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3 . 把物体放在冷空气中冷却,如果物体原来的温度是
,空气的温度是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18c9583db613005922ec8d316ee94d3.png)
后物体的温度可由公式
求得,且把温度是
的物体放在
的空气中冷却
后,物体的温度是
,那么
的值约等于______ .(保留一位小数)(参考数据:
取1.099,
取0.693)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2456350210a7ed02daeb0010abc376a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18c9583db613005922ec8d316ee94d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f67e1147d0df6c52b45be0d2f8da090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962d6068a75a376f8487de79d4cbd80a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6cca692e47077db0c89675b1beb4847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c534228d6a812977052bc1afa5a95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cec183057249005d5f234c4bea5de7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866116aa168650d791609535627e3cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9df64fe88017dc4b4e97fbb6e276f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e24d42f61784c642e9eb1316afdd2ad.png)
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解题方法
4 . 艾宾浩斯遗忘曲线描述了人类大脑对新鲜事物遗忘的规律.基于此,某课题小组研究发现,在学习课程
后每经过一个星期,会遗忘掉所记忆内容的
.为使得所记忆的内容不低于原来的
,最多在
个星期之后对所学内容进行复习,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
__________ .(
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ee628efd6b2f7296c106dd5cbae42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d7abf02717d6e59d8a64a65a87c412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96209d77ac4893605e355c6597269492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8288e1d872c6b5872b84a32469ff9e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5114e1dbd4fc973e99293e1fdb3def.png)
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5 . 若函数
满足下列条件:在定义域内存在
,使得
成立,则称函数
具有性质
;反之,若
不存在,则称函数
不具有性质
.
(1)证明:函数
具有性质
,并求出相应的
;
(2)已知函数
具有性质
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110e5b2f8a412dc6528df8da2ed66cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc4e3775c850f1c1804f9eb7a70153a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7099e54df7bf582badbca0e1d3794b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
6 . 已知正实数
,
满足
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967d662a83942b23f2029bb73aa59372.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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7 . 求下列各式的值
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ae7fe2fd45f453cf60ebdf93e6302d.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ae7fe2fd45f453cf60ebdf93e6302d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ab037392bf5f09447e5c8f5e34080b.png)
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解题方法
8 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578bf56c33636a68f547abd5c954aea1.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efc0dd4a184c51caa3b4b6a7da09302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578bf56c33636a68f547abd5c954aea1.png)
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解题方法
9 . 已知
为
上的奇函数,且
,当
时,
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b568b2cee9ef2a32d2f27305a9104d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b402181e8e0ec843d3d7f441e35bd28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246de316aacce5e2a1b482840ff02f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769283338a97a882a7caa9438bccb2ac.png)
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解题方法
10 . 将边长为1的正六边形进行如下操作:第一次操作,在每条边上,以边长的
为长度作正六边形,保留新作的六个小正六边形,删除其余部分;第二次操作,将上一次操作剩余的正六边形进行第一次操作……以此方法继续下去,如图所示.若要使保留下来的所有小正六边形面积之和小于
,则至少需要操作的次数为( )(
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95efa0fc8533c54debe4c4952f04afd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5114e1dbd4fc973e99293e1fdb3def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab1cb23df1e01a5120207dbfb4ae6c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/2680182b-feed-41eb-8148-2064c40c78ab.png?resizew=406)
A.17 | B.18 | C.19 | D.20 |
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2023-09-19更新
|
348次组卷
|
2卷引用:海南省琼海市嘉积中学2023届高三三模数学试题