1 . 已知a为实数,且对任意k∈[-1,1]当x∈(0,6]时,6lnx+x2-8x+a≤kx恒成立,则a的最大值是_____ .
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2 . 异面直线
、
分别在平面
、
内,若
,则直线
必定是( )
![](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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b707f5ee4fbb2e637c65fbc6d8ed03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.分别与![]() ![]() | B.与![]() ![]() |
C.至少与![]() ![]() | D.至多与![]() ![]() |
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2020-02-05更新
|
614次组卷
|
7卷引用:1989年四川省高中数学联合竞赛试题
3 . 对任意正整数
,定义
为使得
是
的倍数的最小正整数
.关于下列三个命题:
①若
为奇质数,则
;
②对任意正整数
,都有
;
③对任意正整数
,都有
.
其中所有真命题的序号为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f378b8bfaacc38d98321122c1ed7c927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42753ada77daee9f575ad735e05462c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626674c321964b32bb6d31f8d712a1d3.png)
②对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fec80a250e8f692c8322aa4e2773235.png)
③对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a0cff970343dbc4fdf533643c42db6.png)
其中所有真命题的序号为( ).
A.①② | B.①③ | C.②③ | D.①②③ |
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4 . 设
分别是椭圆
的左、右焦点,
为该椭圆上一点,满足
.若
的面积为2,则
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f9bdc6d9f09e14b037ea7d3ee1f623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9df1061c3ba5151ba2f7359acaf356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
A.1 | B.![]() | C.![]() | D.2 |
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5 . 设多项式
除以
的商式为
,余式
,其中
为实数,则
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a22390e38a79e7638b722704272c8de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81843351cfa63bb76c9f39aa96434283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b2373399a8dcbcfaa270d31e5e7bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83c14cf5a64502e8345f6a84012ba0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
A.0 | B.1 | C.2 | D.3 |
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6 . 设
分别是等差数列
与
的前
项和,对任意正整数
,都有
若
为质数,则正整数
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80cfa0dd330a316deb2c576da63a0c51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915c2d93e74539d834b2680daa45de12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3984de10a443d8a9a9575fec057bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.2 | B.3 | C.5 | D.7 |
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7 . 函数
的最大值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32640b470a14c95f11b5facc3e142403.png)
A.![]() | B.1 | C.![]() | D.![]() |
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8 . 设动点
到点
的距离与到直线
的距离之比为2,则
的轨迹方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14436636ec6a7aec09cb63cecf6e970d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 若一圆台的上底周长为4,下底周长为9,平行于底的截面周长是上、下底周长的比例中项,则这个截面分圆台的高所成的两段的比为______ .
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10 . 已知:
.求证:
(1)若
,且
,则 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8f6bf5c2f04c84550957271c5cb115.png)
(2)当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17e3231e8d07e6f17cca273949d2bbc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f364bd19eda02fa19a278441b2aa401b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8f6bf5c2f04c84550957271c5cb115.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eadd42e1f5910bcf2080d46d60db4f91.png)
您最近一年使用:0次