名校
解题方法
1 . 对于各数互不相等的正数数组
(
是不小于2的正整数),如果在
时有
,则称
与
是该数组的一个“逆序”,一个数组中所有“逆序”的个数称为此数组的“逆序数”.例如,数组
中有逆序“2,1”,“4,3”,“4,1”,“3,1”,其“逆序数”等于4.若各数互不相等的正数数组
的“逆序数”是2,则
的“逆序数”是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d7e260d4df410310ea3e4541eefbb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4610754dff007c541aa4887d8705329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8149ae00fb94a16b872a4d1ee311fea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10d9894335fb59c22f8f5d6a0f67c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faee37d6362a556db87dab0e55c6bb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd02ed53ee86e28402f8558c5120f573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d2077503a0451f242ef6bc8f7d05b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b218fe968da4e0a9dc51348c4a7094f0.png)
A.13 | B.24 | C.15 | D.25 |
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2 . 若曲线
在点
处的切线与直线
垂直,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e769eb0d5d8cc6549a024d955460a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0adc4374ff1eb661165544bf6a385696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d8808a43dcf049e19e9c2fd4af0f87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.1 | B.![]() | C.2 | D.![]() |
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3 . 将三颗骰子各掷一次,记事件
“三个点数都不同”,
“至少出现一个6点”,则条件概率
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af61ac71ade09d3b07b7232065163346.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知实数
满足
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde3da412c997c926ae842ddc107cf35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095354f5d4e5dc28402af7b089ebb2f9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知曲线
,过点
作该曲线的5条弦,这些弦的长度构成一个递增的等差数列,则该数列公差的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df58ee3360883170516d2a75629c8162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a6b0736b4972224e50d2cef4654b07.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 已知函数对任意
存在,有如下4个命题,
在
上为严格增函数,
在
上为增函数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ab455e7f86b11acb175fe17c7f2a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90751d580fa088c50259c6fa174b5158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89853a84b96c3f8f49c4b89de2327fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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7 . 设
是双曲线
上一点,
分别是双曲线左右两个焦点,若
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311f4e2e5bdfbb147f32a6421c80a8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d478d9b6b08fb5b27f6a9442a2d443e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fa27f8db6167d4802a510371077bb5.png)
A.1 | B.17 | C.1或17 | D.5或13 |
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8 . 已知向量
,
,若
,
,则
的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393cd7132b6de2f08899bdebfdc2839f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a391513a7fa5b0be3e4f8709f94948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c22fc9f7e478d49b9abfc4bd813902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
A.![]() | B.3或![]() | C.![]() | D.1 |
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9 . 已知抛物线方程
,过点
的直线与抛物线只有一个交点,这样的直线有( )条
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
A.0 | B.1 | C.2 | D.3 |
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解题方法
10 . 从某个角度观察篮球(如图1)可以得到一个对称的平面图形(如图2),篮球的外轮廓为圆
,将篮球的表面粘合线视为坐标轴和双曲线,若坐标轴和双曲线与圆
的交点将圆的周长
等分,且
,则该双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d363b57e9e494641bb3c2a8048becd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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