1 . 计算下列各式的值
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81e051391798b29600c0a1be32f6ea5.png)
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81e051391798b29600c0a1be32f6ea5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abfda8667d3d36d27d520a445019a39.png)
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2 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bbdd8ed581148bde98b5dc7f7c1a642.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa3f4ad8ea3227becf739010ce5d022.png)
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解题方法
3 . 设集合
,函数
的定义域为集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0576ea320f8bc8ddd213d33a4c49e50d.png)
(1)当
时,求
;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860ebb6f76cd3cb9a265dfc233002a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed5f0146efea6acb76b154b4cd3ba71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0576ea320f8bc8ddd213d33a4c49e50d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b109e426e848c161a79366657ca264dc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdbbe46a98a8fdebfc46fcbc45dc88e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 为了衡量星星的明暗程度, 古希腊天文学家喜帕恰斯在公元前二世纪首先提出了星等这个概念.星等的数值越小, 星星就越亮; 星等的数值越大它的光就越暗.到了 1850 年, 由于光度计在天体光度测量的应用, 英国天文学家普森又提出了亮度的概念, 天体的明暗程度可以用星等或亮度来描述.两颗星的星等与亮度满足
, 其中星等为
的星的亮度为
.已知“心宿二”的星等是 1, “天津四”的星等是1.25 ,则“心宿二”的亮度大约是“天津四”的( )倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3a21d10a423e314de163a19e47d15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d45425834facf304acc3ee308ff5bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f25ea53a6a655955b0bc0f4fe709a1.png)
A.1 | B.![]() |
C.![]() | D.![]() |
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5 . (1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0386d5d23133f279a9de2d10424040c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8487cdb0d18da4d1b38eee6cbb064f18.png)
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名校
解题方法
6 . 求值:
(1)
;
(2)已知钝角
满足
,求
的值.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae309aa3f9e3320428b965f1cff9d1aa.png)
(2)已知钝角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469666b74526316d8a4c68f839f26d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5791764cda9345295d5d18dfa33799a.png)
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解题方法
7 . 函数
的定义域为
,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27bca6e7914c1f76eb81c096a6886d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2023-12-27更新
|
479次组卷
|
2卷引用:四川省宜宾天立高级中学2023-2024学年高一上学期11月月考数学试卷
名校
8 . 函数
(其中
且不等于1)的图象恒过定点__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477fcdb9b6368a224fbe0ee68955e0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
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解题方法
9 . 下列函数中,既是偶函数,又在区间
上单调递增的函数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
10 . 已知函数
的图象与
,且
的图象关于
对称,且
的图象过点
.
(1)求函数
的解析式;
(2)若
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4ca640296443f5119c6ae8f9ddba90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cd41dab0f2a8f84b0e9f1df4843fb.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e8ce93c53d0179da2fcd0376dcb2ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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