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1 . 已知抛物线
的焦点为
,其准线与
轴的交点为
,过点
的直线
与抛物线
交于
,
两点(
点位于
点右方).若
为
的角平分线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24d4627c643c5aeee873c6e1e626aa.png)
__________ ;直线
的斜率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4fb72e39d79b7a0cd892fa5fa34bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed24d7acba0b3a7ebf4d520296424a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24d4627c643c5aeee873c6e1e626aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2 . 已知函数
图象的一个对称中心为
,且
在
上单调递增,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629ab2b9cf61f4b02419beb7754767a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b212e0d4339cbd3d236a807547ebf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed440b9f974492068a68203e5029f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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解题方法
3 . 已知实数
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4edfef181ed229ed1a3bb2295be7db9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 已知随机事件
满足
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55693a57bf5575d696bb0aad4b5113f5.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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5 . 已知方程
的两个复数根分别为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f397b1e5a55fd4688c479c97c16f45c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
6 . 已知双曲线
的左焦点为
,过坐标原点
的直线与双曲线
交于
两点,且点
在第一象限,满足
.若点
在双曲线
上,且
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ed44d86cace7852eaa810b6a554bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babfc8ea7a7cbfbd9c1f8f61bf19a36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 在三棱锥
中,
,且
平面
,过点
作截面分别交
于点
,且二面角
的平面角为
,则所得截面
的面积最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f62607ef069f2b522be8ea768bfef08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8604bb5b9230053450634f041292cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f8c417f5c19cc076dc6baeb0c173a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
A.![]() | B.![]() | C.![]() | D.1 |
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8 . 统计学中通常认为服从于正态分布
的随机变量
只取
中的值,简称为
原则.假设某厂有一条包装食盐的生产线,正常情况下食盐质量服从正态分布
(单位:
),某天生产线上的质检员随机抽取了一包食盐,称得其质量小于
,他立即判断生产线出现了异常,要求停产检修.由此可以得到
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4214e4a8a854826199a992771c60c1ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45d81fb351bc6c693fb0a114152b2d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed11f4400d756bc0fccf2338799532a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3960d67499df76159982657fe3a1cbca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdd622e240604c1e93d8d488207eb6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
A.2 | B.4 | C.6 | D.8 |
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9 . 阅读材料一:“装错信封问题”是由数学家约翰·伯努利(Johann Bernoulli,1667~1748)的儿子丹尼尔·伯努利提出来的,大意如下:一个人写了
封不同的信及相应的
个不同的信封,他把这
封信都装错了信封,问都装错信封的这一情况有多少种?后来瑞士数学家欧拉(Leonhard Euler,1707~1783)给出了解答:记都装错
封信的情况为
种,可以用全排列
减去有装正确的情况种数,结合容斥原理可得公式:
,其中
.
阅读材料二:英国数学家泰勒发现的泰勒公式有如下特殊形式:当
在
处
阶可导,则有:
,注
表示
的
阶导数,该公式也称麦克劳林公式.阅读以上材料后请完成以下问题:
(1)求出
的值;
(2)估算
的大小(保留小数点后2位),并给出用
和
表示
的估计公式;
(3)求证:
,其中
.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4e8502106802f1485c3b0f28f2664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8412f5256b2b370e421c07f18cc732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4403d632f9a81e52c6cd135c6834bc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
阅读材料二:英国数学家泰勒发现的泰勒公式有如下特殊形式:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce152ca98ac7e21237e00667f005b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35993bd1db970330494665d925c0be7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395c6efaa63dcd4ee513323d51c6a7eb.png)
(2)估算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2598975ac1edb754817eada15b9a473e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4e8502106802f1485c3b0f28f2664.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca08ded0d1136421f0a81517f5c2fc9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
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10 . 我国南宋著名数学家秦九韶(约1202~1261)独立发现了与海伦公式等价的由三角形三边求面积的公式,他把这种称为“三斜求积”的方法写在他的著作《数书九章》中.具体的求法是:“以小斜幂并大斜幂减中斜幂,余半之,自乘于上.以小斜幂乘大斜幂减上,余四约之,为实一为从隅,开平方得积.”如果把以上这段文字写成公式,就是
.现将一根长为
的木条,截成三段构成一个三角形,若其中有一段的长度为
,则该三角形面积的最大值为( )
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3e9552a31d2e2c9ce90150650f9a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd6f4250ca6b1b9bce234a01f00d44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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