1 . 对于函数
的图象与性质,有下面四个结论:①函数
的最小正周期为
;②
在
上是增函数;③若
,则
;④若
,则
.则其中所有正确结论的编号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b4b153fcbcfb5b624b1d93c39b20b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f99068d04739b7e411a43be1c9c81a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dec9f116e6735b0f14242e86d0e559a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf0426749202e2c3c3a745e10fcc7d6.png)
A.①③ | B.②③ | C.①④ | D.②④ |
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2 . 已知圆锥的侧面展开图是一个半径为5,弧长为
的扇形,则此圆锥的侧面积和体积分别是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80f16c3278cd252725625dcf253cda.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210bd436958916bc2a848c46365af767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765b4dea4f6db129680d2f7658d5d171.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 计算
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a452c78a5b7a3bc2ba494f743cf91f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知函数
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482e0a1b00857f35812dfe21a70bf2b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f86903aa550324f11d3b1e7b075e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.8 | B.7 | C.2 | D.0.5 |
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6 . 函数
的零点是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f84d2ed801146c57ebaa79978d112f.png)
A.2 | B.![]() | C.-2 | D.2或-1 |
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7 . 样本数据
的第80百分位数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95c7361e1a05c6de4bdbeea4fc040ba.png)
A.4 | B.6 | C.7 | D.8 |
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8 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86388ea17f8dcc25a79582fe7276c643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1336d38741aab2255a35c26612bbd7cc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 如图,某人沿围墙
修建一个直角梯形花坛
,设直角边
米,
米,若
米,问当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
______ 米时,直角梯形花坛
的面积最大.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2633a6f46b0847158eebb05c743561aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9e9e100705a796f2d3c3855d61c721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b482495ca023cb1ca3476eea0e2b593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/05aaff19-b357-40b3-b171-d46eea818d0d.png?resizew=160)
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解题方法
10 . 一个袋子中有大小和质地相同的3个球,其中有2个黑色球(标号为1和2),一个白色球(标号为3),从袋中有放回地依次随机摸出2个球.设事件
“第一次摸到白色球”,事件
“两次摸到的球颜色不同”.
(1)用集合的形式写出试验的样本空间,并求
;
(2)求
,并说明事件
与
是否相互独立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
(1)用集合的形式写出试验的样本空间,并求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84455d653ff40b53e4418531efd20991.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aecbf1c6626bbb1c3a4e0952db8a25e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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