1 . 设二次函数
与x轴有交点.若对一切
,有
,且
.求
、
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb6885a889969e7c1c1a9ee8d07c800d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1253159e63fa46a919e34b1b081cc9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d8d9c616912e2e0cead02b7f9496e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
2010高一·河南·竞赛
2 . (必修3)袋中装有6个形状、大小完全相同的球,其中黑球2个、白球2个、红球2个.规定取出一个黑球记0分,取出一个白球记1分,取出一个红球记2分;在抽取这些球的时候,谁也无法看到球的颜色,首先由甲取出3个球,并不再将它们放回原袋中,然后由乙取出剩余的3个球.规定取出球的总积分多者获胜.
(1)求甲、乙成平局的概率;
(2)如果可以选择先后取球的顺序,你会先取还是后取,为什么?
(1)求甲、乙成平局的概率;
(2)如果可以选择先后取球的顺序,你会先取还是后取,为什么?
您最近一年使用:0次
2018-12-25更新
|
155次组卷
|
3卷引用:2010年全国高中数学联赛河南省预赛(高一)试题
2010高一·河南·竞赛
3 . 已知向量
,
,又函数
是以
为最小正周期的周期函数,若函数
的最大值为
,则是否存在实数
,使得函数
的图像能由函数
的图像经过平移得到?若能,求出实数
并写一个平移向量
;若不能,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ae81d1f5cf668ca1c1c8cb1c9ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102c0641eb7f46462004b2ee39444b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbee0519d7ab138a2a5b46f501b0ca47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b70dc4ebe8677bd7ebe2fc378012ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2010高一·河南·竞赛
4 . 如图,在
中,已知
,
,
,
为内角平分线,以
为弦作一个圆与
相切,且与
、
分别交与点
、
.求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d649afbddd907f0dfec1420f02f82fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f186ea827f7becafd1ac4955e22c6812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/9224249e-f2b3-4b3d-b1f1-4e83c0734354.png?resizew=149)
您最近一年使用:0次
2009高三·山东·竞赛
5 . 如图,平面
平面
,线段
分别交平面
、
于点
、
.过点
的另一直线分别交平面
、
于点
、
,过点
的另一直线分别交平面
、
于点
、
.已知
.求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/741dc880ae307477262f4b07edee682f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668e9dfdea9e83e02c29408ca959a2c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f9215613b7b05217ed77268c238391.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/6e8e21d9-8698-4541-8ce4-72ed31bd7ece.png?resizew=137)
您最近一年使用:0次
2007高一·河南·竞赛
6 . 在数列
中,
.
⑴若集合
,
,求
;
(2)求所有的实数θ,使得数列
的每一项都是负数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ac72b2288292f132441f2b707b36c3.png)
⑴若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52a85883e466d7537b17e776bbd1150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53ce306dd6b6cba3eb9755f45a41627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
(2)求所有的实数θ,使得数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2007高一·河南·竞赛
7 . 定义在
上的奇函数
满足
,且当
,
,时,有
.
(1)证明:
是
上的增函数;
(2)证明:当
时,
;
(3)若
对所有的
,
恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821632252680978d2619aacec310e64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bc2eeaca8a8ce4bcce2bff011a11bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b84952d33957e5b90d8cd3b3bcc127.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08829c3ec099f3427ede9062d19a78c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51035f9b1a84d36570e1eefa1386a6a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb2922de7222b364f096db55a57e926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
您最近一年使用:0次
8 . 已知数列
的前n项和
.
(1)求数列
的通项公式;
(2)设
为数列
的前n项和,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b899f861183a1c5edbe4604f7c2940ec.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3669d0785ebc3fad3809a9d2aaeb7b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2007高一·河南·竞赛
9 . 如图,直线l过线段AB的端点A且垂直于AB,E、F为l上的任意两点,且EB丄BF,O为AB的中点,过E作EP∥AB,联结FO并延长交EP于点P,联结PB并延长到点D.求证:FB平分∠ABD.
![](https://img.xkw.com/dksih/QBM/2018/12/19/2100023638065152/2102234164936704/STEM/68811bb5-18da-437c-9065-40156f74dba5.png?resizew=164)
您最近一年使用:0次
10 . 设
,
:把平面上任意一点
映射为函数
.
(1)证明:不存在两个不同的点对应于同一个函数;
(2)证明:当
时,
,
为常数;
(3)设
时,
,
,在映射
的作用下,
作为像,求其原像,并说明它是什么图像?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daae0ebb960d1651cc03a9cbdf9125a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ad344885d99bab0ee5f54b8aa21f82.png)
(1)证明:不存在两个不同的点对应于同一个函数;
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a7f178193d9efda0253eb3774ec9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b948a136c7e490687edc37a1c29027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a7f178193d9efda0253eb3774ec9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5e8684efcfe6f9a4a7db33a6fd3f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995ec593baa4ef50b6d87c78380953d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
您最近一年使用:0次