1 . 计算:
(1)
+
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf25a1c2309a9481f9a6a11dd01696f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce41c4328b168868eb82ab52744bedb9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c09388ea35449352e5630d72d89317b.png)
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名校
2 . 正安县是中国白茶之乡.在饮用中发现,茶水的口感与水的温度有关.经实验表明,用100℃的水泡制,待茶水温度降至60℃时,饮用口感最佳.某实验小组为探究室温下刚泡好的茶水达到最佳饮用口感的放置时间,每隔
测量一次茶水温度,得到茶水温度随时间变化的数据如下表:
设茶水温度从100℃经过
后温度变为
℃,现给出以下三种函数模型:
①
;
②
;
③
.
(1)从上述三种函数模型中选出最符合上述实验的函数模型,并根据前3组数据求出该解析式;
(2)根据(1)中所求函数模型,求刚泡好的白茶达到最佳饮用口感的放置时间(精确到
);
(3)考虑到茶水温度降至室温就不能再降的事实,求进行实验时的室温约为多少.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17166d730bec1b4ee345727b42265ff.png)
时间![]() | 0 | 1 | 2 | 3 | 4 | 5 |
水温![]() | 100 | 91 | 82.9 | 78.37 | 72.53 | 67.27 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd5573e0e86c2f23dae923c5cfae82f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e945ac2dcd67fe03b19fca9b236e4e4.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f168594ec0e581bf703844922a0471.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba599953a087d32131caf6e653efeb3b.png)
(1)从上述三种函数模型中选出最符合上述实验的函数模型,并根据前3组数据求出该解析式;
(2)根据(1)中所求函数模型,求刚泡好的白茶达到最佳饮用口感的放置时间(精确到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c4d12b3a705daab723ab243b6cc88.png)
(3)考虑到茶水温度降至室温就不能再降的事实,求进行实验时的室温约为多少.(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c8a5c70da098ad8d3ef6284886140b.png)
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2024-02-21更新
|
280次组卷
|
3卷引用:贵州省遵义市2023-2024学年高一上学期1月期末质量监测数学试题
3 . 人们通常以分贝(符号是
)为单位来表示声音强度的等级,其中
是人们能听到的等级最低的声音.一般地,如果强度为
的声音对应的等级为
,则有:
(
为常数).已知人正常说话时声音约为
,嘈杂的马路声音等级约为
,而
的声音强度是
的声音强度的1000倍.
(1)求函数
的解析式;
(2)若某种喷气式飞机起飞时,声音约为
,计算该种喷气式飞机起飞时的声音强度是人正常说话时声音强度的多少倍?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca586d4c35ce52dec4b545cf13ee0721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238014c690f09b7c14f7619953f20369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23fdfc8592db67def8fd867f6b6de62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94e4c67f5015c8cb3232cee339739bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d80cd188c2b87c5e167842708098e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59922fee37241fde49e4ac70677b24a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59922fee37241fde49e4ac70677b24a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d80cd188c2b87c5e167842708098e3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若某种喷气式飞机起飞时,声音约为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b94c117d2daf2e5b14a1819da6d08e.png)
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解题方法
4 . (1)计算
.
(2)某工厂生产一种溶液,按市场要求杂质含量不得超过
,而这种溶液最初的杂质含量为
,现进行过滤,已知每过滤一次杂质含量减少
,求使产品达到市场要求的过滤的最少次数(参考数据:
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c606ca9e345453d1ea7739ecdf66491b.png)
(2)某工厂生产一种溶液,按市场要求杂质含量不得超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe619bd93756ad8656ba0d02c4fddca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b971b2c43a814d35dfe0c1be4c45d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc146f4d7196cfb8fe3cd04575f5dcee.png)
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5 . (1)已知
,求
的值;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbe7ea044718fb7c2c7774f89bc5d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ba4f4450d63609ad3665858d35d82e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb38a67c53abe51ec2929d4431ac99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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6 . 计算下列各式:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162cd68ee3617c4a7bed52bc76babb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00510e32ac1e140c2a5f2cb790f638a2.png)
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7 . (1)计算:
;
(2)已知
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca1849af6d57186c20eb831943851d1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbe7ea044718fb7c2c7774f89bc5d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0666cbe081eb4ae1c2e4fd96b1cdc37.png)
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解题方法
8 . 已知函数
.
(1)是否存在实数
,使得函数
为奇函数,若存在求出
的值,若不存在,说明理由;
(2)若
为正整数,当
时,
,求
的最小值.
(参考值:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd99e63f2eb72c912613c350d99156b.png)
(1)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34220e24228a108a51006463af44ca22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(参考值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae7a9d0428c1de519213c1f0e2b89c1.png)
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解题方法
9 . 解下列关于x的不等式:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe8634aad7ad15b2caf75b492419591.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db391adaa9a348b74be575fe65538f8.png)
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10 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0cc5f125edd24c1d9a6d7fbcadbc74.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafa6ed6fa88f7841d640d90d46360a5.png)
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2023-12-23更新
|
182次组卷
|
2卷引用:贵州省2023-2024学年高一上学期12月月考数学试题