2005高三·天津·竞赛
1 . 已知二次函数
满足
,且
对一切实数
恒成立.那么,函数
的解析式为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a431537df789febf4bc45e3dc23cefaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db33c85fcb3076ba3da3b4ac5677575a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2 . 如图(a),已知正方体八个顶点分别赋值为
,
,
,
,
,
,
,
,然后,将与每个顶点相邻的正方体的三个顶点所赋值的算术平均值
,
,
,
,
,
,
,
放在另一个正方体的相应顶点处,如图(b).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/43b481e4-ac1e-462e-8552-5381db39297b.png?resizew=260)
若
,
,
,
,
,
,
,
,则
的值为______ .
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276509f01529d982ab21e479a4619268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444967c743802e9da4571cf68c3aad6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b66779784b6e6377429c6efd1c0c1b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9489d4a6d1af0f194ae6b76aa2dddf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104d13a3453c8730d00c3192df071895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a81d40071c627bb2d5f4ca6242a0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2be1199becdf7d29b3c69f6893eb11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a7e63081c9165bf8004baf863d8136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdadf5794e1c3709cc641309e1d20a53.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/43b481e4-ac1e-462e-8552-5381db39297b.png?resizew=260)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb08424861b202a34be7983f741214a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019eb94a6a2b38308811470d860e1a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a95aa173fcea62b59350555f7d097b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346441065912bc61b277cf21198b5bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80bb6845d79938c65ce2d7b4a2b8c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5f1cfa28daec426fd042e5e5106a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4825db18aaa741352361d54bab86b03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca41e8c40d8619786f761e2ecec5a56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d0f1bff3c31c592d555f2300563de2.png)
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2005高三·天津·竞赛
3 . 如图,菱形
的边长为1,
.若
是
延长线上任意一点,
交
于点
,则向量
与
的夹角的大小为______ 度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/c332154e-95dc-481e-b20a-39020e6ca32b.png?resizew=210)
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4 . 在数列
中,已知
,
.若
为数列
的前
项和,那么,
的值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b5040af13ac6c22fbad4baeafb8c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba0b2c75953e41ec3d778989cb11343.png)
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2005高三·天津·竞赛
5 . 已知函数
是定义在
上的减函数,且对于
,
恒成立.则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbfd40765e7c214147d889bb35368d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2736db1cf9cc5472c2a2f8aac60e83b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2005高三·天津·竞赛
6 . 已知定点
.若动点
在抛物线
上,且点
在
轴上的射影为点
,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c3b664ef08cc518de3627319bf2993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04d44a23f9e18a768757bedc013d518.png)
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7 . 将
、
、
、
、
五种不同的文件放入一排编号依次为1,2,3,4,5,6,7的七个抽屉内,每个抽屉至多放一种文件.若文件
、
必须放入相邻的抽屉内,文件
、
也必须放入相邻的抽屉内,则文件放入抽屉内的满足条件的所有不同的方法有种.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
A.60 | B.120 | C.240 | D.480 |
您最近一年使用:0次
2005高三·天津·竞赛
8 . 如图,已知正方体
中,
、
分别是
、
的中点.则平面
与平面
所成二面角的平面角的正弦值为.
![](https://img.xkw.com/dksih/QBM/2018/12/14/2096468374495232/2097489469980672/STEM/14761db1282e48f8b5ce3c2c8409b494.png?resizew=169)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207b39b8f34b488e65d68339af6dc131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6faa87ffe5df16520e92446b3bd42f.png)
![](https://img.xkw.com/dksih/QBM/2018/12/14/2096468374495232/2097489469980672/STEM/14761db1282e48f8b5ce3c2c8409b494.png?resizew=169)
A.![]() | B.![]() | C.![]() | D.1 |
您最近一年使用:0次
9 . 设由正整数有序数对
组成如下数列:
,
,
,
,
,
,
,
,
,
,…,按
的值由小到大的顺序排列,当
的值相等时,按
的值由小到大的顺序排列.则有序数对
(
、
均为正整数)在该数列中的位置是.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e88ebfb5c0d6cce558b515be06404d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86022205a7487439dd8d0897cd3bf19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0481d24e2af1e0cd348732b9444d1dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69abe959988e4c8c0739f5857ccfb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3654254401fc902c3cb4912969f21f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ce2830528c2ea6b5d4df0c77644e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.第![]() | B.第![]() |
C.第![]() | D.第![]() |
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2005高三·天津·竞赛
名校
10 . 已知
是定义在
上的不恒为0的函数.如果对于任意的
、
都满足
,则函数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6aa5b51b3ff1469ee7a334543b6616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.是奇函数 | B.是偶函数 |
C.既是奇函数又是偶函数 | D.既不是奇函数也不是偶函数 |
您最近一年使用:0次
2018-12-15更新
|
148次组卷
|
3卷引用:2005年全国高中数学联赛天津赛区初赛试题
(已下线)2005年全国高中数学联赛天津赛区初赛试题第二届高一试题(决赛)-“枫叶新希望杯”全国数学大赛真题解析(高中版)上海市上海外国语大学附属外国语学校2015-2016学年高一上学期期末数学试题