名校
解题方法
1 . 函数
,对任意的实数
,记
在
上的最大值为
,最小值为
,则函数
的值域为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d46eda990d5ae73ebca78a6d19576a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48222eea9755a7c7635578031a573bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0338b99cef985925abb9da31dc5dd2d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309bfced5fe755274e618762ead32061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7241f1687dfe4bd9178ae3263b102d6d.png)
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2 . 设
(
),
且为常数,若存在一公差大于0的等差数列
(
),使得
为一公比大于1的等比数列,请写出满足条件的一组
、
、
的值__________ .(答案不唯一,一组即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1d09671591397a292dee6069a64833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0e9d1ad9561d693958756ee8398218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ced7246280e4cb71987bee7cc17cb8.png)
![](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)
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2020-02-29更新
|
218次组卷
|
6卷引用:2012届上海市七宝中学高三模拟考试理科数学
名校
解题方法
3 . 已知椭圆
:
,过椭圆
上一点
作倾斜角互补的两条直线
、
,分别交椭圆
于
、
两点,则直线
的斜率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376789bd6a2786afd2500908f4b3bf8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0228042e28f9ba663dafe657e677cac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
4 . 对任意两个非零的平面向量
和
,定义
和
之间的新运算
:
.若非零的平面向量
,
满足:
和
都在集合
中,且
.设
与
的夹角
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b85ad4a60a2538f9083f863443331f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1124e9c95acf582c08b9bbd6eea2b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e142c5996d8e386bd8b41c0de8415d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1124e9c95acf582c08b9bbd6eea2b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e142c5996d8e386bd8b41c0de8415d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e16415b61722f9961e412386e6819f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c537a171757a1116720abfb87686dd27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0542b5dc0f350ee5cc737b4263cd4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25a063c932ad2cb75acd1daa1125864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04e934eea3fa45b89d740196a930021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0601dcb5cb79035066531c5dd18d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d34523a15d32633b459f7e803e4648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b85ad4a60a2538f9083f863443331f.png)
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2020-02-28更新
|
277次组卷
|
6卷引用:北京市北京大学附属中学2019-2020学年高三上学期月考(12月)数学试题
北京市北京大学附属中学2019-2020学年高三上学期月考(12月)数学试题2015-2016学年江苏省常州市溧阳市高一上学期期末数学试卷江苏省无锡市市北高级中学2022-2023学年高一下学期期中数学试题(已下线)第八章 平面向量(压轴题专练)-单元速记·巧练(沪教版2020必修第二册)(已下线)模块四 高一下期中重组篇(江苏)(已下线)专题4 考前优质试题精选练(4)(北师大版高一期中)
5 . 已知体积为
的正四棱锥
外接球的球心为
,其中
在四棱锥
内部.设球
的半径为
,球心
到底面
的距离为
.过
的中点
作球
的截面,则所得截面圆面积的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e155ff3b596343d686fcfb40c3f01edd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](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/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2212fc5ab7ac34a9008ddd345ad296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2019-03-27更新
|
813次组卷
|
5卷引用:【全国百强校】河北省衡水市第二中学2019届高三上学期期中考试理科数学试题
名校
6 . 如果函数
在
上存在
满足
,
,则称函数
是
上的“双中值函数”,已知函数
是
上“双中值函数”,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02197f63f00ee379100300eb7330375c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648301e87208ebdf66e87a3c455a4204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363b7bc6139d78757605177de6ee244b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86668178f0511e182bb64e6f6d02122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc7c54d6024d6dd5e31f661f0110821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ab580254da590daa0e387568951133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f51502fe21f5ed8b64af1c4c22cf33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2019-05-08更新
|
856次组卷
|
7卷引用:【全国百强校】四川省成都外国语学校2019届高三下学期3月月考试题 数学(文科)试题
2012·江西·一模
名校
解题方法
7 . 若直角坐标平面内
两点满足点
都在函数
的图像上,且点
关于原点对称,则称
是函数
一个“姊妹点对”(
与
可看作同一“姊妹点对”).已知
则
的“姊妹点对”有_______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41be4f4fbf21555f325caf280c392c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41be4f4fbf21555f325caf280c392c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7113de81db260e6666292f39b447b848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71cf61f127359e470386ce0def8b514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2020-03-19更新
|
330次组卷
|
11卷引用:2012届江西省重点中学高三第一次统考理科数学
(已下线)2012届江西省重点中学高三第一次统考理科数学(已下线)2015届甘肃省兰州第一中学高三12月月考数学试卷2017届广东省汕头市高三第一次模拟考试数学(文)试卷上海市天山中学2021届高三上学期开学考试数学试题(已下线)模块04 幂函数、指数函数和对数函数-2022年高考数学一轮复习小题多维练(上海专用)重庆实验外国语学校2022届高三上学期入学考试数学试题山西省晋中市祁县中学2021届高三(复习班)上学期9月月考数学(理)试题贵州省贵阳市乌当区2023届高三上学期期中质量监测数学(理)试题辽宁师范大学附属中学2018-2019学年高二下学期期末数学(理)试题广东省汕头市澄海中学2020-2021学年高二上学期期中数学试题广东省惠州市华罗庚中学2022-2023学年高二下学期3月月考数学试题
2018高三·全国·专题练习
名校
8 . 若点O和点F分别为椭圆
的中心和左焦点,点P为椭圆上的任一点,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdd1989149897babe496145a3812e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87550d73a945b26f977b5c47de6f1bc.png)
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2019-01-01更新
|
639次组卷
|
8卷引用:8-9-2 定点、定值、范围、最值问题(高效训练)-2019版导学教程一轮复习数学(人教版)
(已下线)8-9-2 定点、定值、范围、最值问题(高效训练)-2019版导学教程一轮复习数学(人教版)(已下线)考点52 圆锥曲线的综合问题-范围与最值问题(考点专练)-备战2021年新高考数学一轮复习考点微专题甘肃省兰州市城关区兰州第一中学2019-2020学年高二上学期期末数学(理)试题人教B版(2019) 选择性必修第一册 必杀技 第二章 平面解析几何 专题5 与圆锥曲线有关的取值范围(最值)问题、定点与定值问题黑龙江省大庆市铁人中学2020-2021学年高二上学期第一次月考数学试题山东省济南市商河县第一中学2020-2021学年第一学期高二数学期中试题福建省龙岩市上杭县第一中学2020-2021学年高二上学期数学期末复习试题甘肃省武威市天祝藏族自治县第一中学2022-2023学年高二上学期期末考试数学试题
名校
9 . 若函数
满足:对任意一个三角形,只要它的三边长
都在函数
的定义域内,就有函数值
也是某个三角形的三边长.则称函数
为保三角形函数,下面四个函数:①
;②
;③
;④
为保三角形函数的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699d32dbd2b31b313ae7154c9a072775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa624b10e67b044103128eeec67213ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641a8d86db7a96bd6ff25345ceb4cc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5d54d880c1903ee94379be6010e5ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b8e109a8fda1474ddae02822c01c1e.png)
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2018-08-30更新
|
570次组卷
|
2卷引用:四川省泸州市泸县第一中学2019-2020学年高三上学期期末考试数学(理)试题
名校
10 . 如图,在平面斜坐标系
中,
,斜坐标定义:如果
(其中
,
分别是
轴,
轴的单位向量),则
叫做
的斜坐标.
的斜坐标为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1ef9077cb0f9bad2490ac63b80ee6b.png)
__________ .
(2)在此坐标系内,已知
,动点
满足
,则
的轨迹方程是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce679ef7b3397eb5f150a12fda901cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0725eb3ba34ec2631d77a36385628059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8315ec34019d719771152be2252106e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf39ca3294f5520518dd4f1c0609876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9c5c7cffee04e1a5545ea43e6f0f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea4af84b44aa8c366c0d310b8be1e87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1ef9077cb0f9bad2490ac63b80ee6b.png)
(2)在此坐标系内,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99af23d024066c111f37d6d0bb78568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a3c7cab1a201ceed804482508809aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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