1 . 已知复数
使得
为纯虚数,
,
,则
的最小值是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be94c746ea0cb4834e5295672e229a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77138483e183730dc3d94cdf96370f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed55697f8a3975926f807581d28c0bf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ddfb1a73da52b1916e118c27cf5aef.png)
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2 . 设f(x)是定义在(0,+∞)上的单调函数,对任意x>0有f(x)>
,则f(8)=_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c09443f0875afbb6c95a116e56a17f.png)
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3 . 数列{an}满足
.
(1)证明:数列{an}是正整数数列;
(2)是否存在m∈Z+,使得2109|am,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48158643c10dee10828f2a143f2c8d5.png)
(1)证明:数列{an}是正整数数列;
(2)是否存在m∈Z+,使得2109|am,并说明理由.
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4 . 已知△ABC为椭圆
的内接三角形,且AB过点P(1,0),则△ABC的面积的最大值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6205da5e1d2730ee0b3de8bca3e29f5e.png)
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5 . 已知正四面体可容纳10个半径为1的小球则正四面体棱长的最小值为_______ .
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6 . 设A为三元集合(三个不同实数组成的集合),集合B={x+y|x,y∈A,x≠y},若
,则集合A=_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981ad92b2b40fcbaaf00f0f09c96a1d6.png)
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7 . 函数
的最小值为m,最大值为M,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303cfb9f2d99ba4c0601487341506d5f.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2537b9f694a6a1d43167f53022acaf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303cfb9f2d99ba4c0601487341506d5f.png)
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8 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac535eb7cc47b42d7db3b803f76a00e.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac535eb7cc47b42d7db3b803f76a00e.png)
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9 . 已知向量
满足
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a019c35a09b9fcb44a885e9e8be09b5.png)
,若
为
的夹角,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38dd8aad9cfb5e1fe2a45d80923f1571.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae951e0bb5a2a406f1572fc1e4964265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d0692ba6c44c6087233b88c19bdba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a019c35a09b9fcb44a885e9e8be09b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbba9a992583ff1d781549a9065028e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ddc6cbc0819cacb4116db926b2e6ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38dd8aad9cfb5e1fe2a45d80923f1571.png)
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名校
10 . 设函数
(a≠0)满足
,
,
,求当
时
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd0587f5d6a3b5db9e4a93e0dbc0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b501b3d9f1ed6143799e34b45e54742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46006273eb4b084e8fbb46020fb908b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad150b78dc4b86bdcc650d7de2a5209a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac571d2a4938fc8d60b02d72c202fe39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd713a9809d5df1de33c6f11b81eca7.png)
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2018-12-16更新
|
410次组卷
|
3卷引用:2018数学竞赛(重庆赛区)预赛试题