名校
1 . 已知椭圆
与双曲线
有相同的焦点
,其中F1为左焦点.点P为两曲线在第一象限的交点,e1、e2分别为曲线C1、C2的离心率,若△PF1F2是以PF1为底边的等腰三角形,则e2﹣e1的取值范围为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d101bd6b9e4d8bda938e85d2ddce2c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
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2020-07-26更新
|
747次组卷
|
5卷引用:2019年全国高中数学联赛福建省预赛
2 . 如图,在三棱锥P-ABC中,PA⊥平面ABC,
,PA=4.若三棱锥P-ABC的外接球的半径为
,则直线PC与平面ABC所成角的正切值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d46c17903078e0b38279353c5430d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://img.xkw.com/dksih/QBM/2020/5/11/2460509962600448/2460927605317632/STEM/0ac7595bc16242a08a6bda83902ed7b8.png?resizew=174)
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2020-05-12更新
|
399次组卷
|
3卷引用:2019年全国高中数学联赛福建省预赛
3 . 已知数列
的前
项和
满足
,
,且
.
(1)求数列
的通项公式;
(2)设
,
为数列
的前
项和,求使
成立的最小正整数
的值.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbe4d8a61d5d09e526ce573c1d02b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5572dd65d61abddd96dccb9e80e2892a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00db49ab3eb71571bb450052bafc00f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2019-01-28更新
|
925次组卷
|
7卷引用:2018年全国高中数学联赛福建省预赛
2018年全国高中数学联赛福建省预赛江西省宜丰中学、宜春一中、万载中学2021届高三3月联考数学(理)试题(已下线)2021年高考数学押题预测卷(新高考卷)01山西省运城中学校2022届高三冲刺模拟(一)数学(文)试题湖南省株洲市第二中学2021-2022学年高二下学期“同济大学”杯数理化联赛数学试题广东省高州中学2022-2023学年高二下学期期中数学试题(已下线)高二下学期期末押题卷01-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修)
4 . 若定义在
上的奇函数
的图像关于直线
对称,且当
时,
,则方程
在区间
内的所有实根之和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5c837522a811402efb9762210c5362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809d95382681197579c7f2d0386835cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f0f0ceb50ecec9476275fab9d15bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0167434c2c1a16e59e89d436ac0a1278.png)
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2013高三·福建·竞赛
5 . 将各项均为整数的数列
排成如图所示的三角形数阵(第
行有
个数,同一行中,下标小的数排在左边).
表示数阵中第
行第1列的数.
![](https://img.xkw.com/dksih/QBM/2018/12/13/2095791848275968/2096806503989248/STEM/04a91d1d2ed54f18ba345921c02c72be.png?resizew=256)
已知数列
为等比数列,且从第3行开始,各行均构成公差为
的等差数列,
,
,
.
(1)求数阵中第
行 第
列的数
(用
、
表示);
(2)求
的值;
(3)2013是否在该数阵中,说明理由.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/2018/12/13/2095791848275968/2096806503989248/STEM/04a91d1d2ed54f18ba345921c02c72be.png?resizew=256)
已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8175f8e14700a97c63722161b43f3ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74376770becdebc978f34a4929fef852.png)
(1)求数阵中第
![](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/a66c5f00b5b38a2d052354b5611970e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3946afb19ee05ad798d676320078b543.png)
(3)2013是否在该数阵中,说明理由.
您最近一年使用:0次
2013高三·福建·竞赛
名校
6 . 已知实数
、
满足
,且
.则
的最小值为___________ .
![](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/9654dfa192d3a84ed89aa06779967d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097ae8d30a20dd4aae75ae8945dbfb79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279d66cf6f2f8508d1a0325ba36874a6.png)
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2018-12-14更新
|
511次组卷
|
3卷引用:2013年全国高中数学联赛福建赛区预赛试题
7 . 在空间四边形 ABCD中,AB=2,BC=3,CD=4,DA=5.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ec06739ecc6a7bca769a960a5fd674.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ec06739ecc6a7bca769a960a5fd674.png)
您最近一年使用:0次
2018-12-10更新
|
164次组卷
|
2卷引用:2016年全国高中数学联赛福建赛区预赛
8 . 已知过点
、斜率为
的直线
与双曲线
:
交于
、
两点.
(1)求
的取值范围;
(2)若
为双曲线
的右焦点,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c477e5ade921ffa8377c4719319380ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c3900f10d369e55a409aafbe6f1db0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2018-12-06更新
|
256次组卷
|
3卷引用:2015年全国高中数学联赛福建赛区预赛试题
名校
9 . 在复平面内,复数
、
、
的对应点分别为
、
、
.若
,
,
,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8477bcc87b1401970171bf57b9ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c1fd680a5d355178273c6d6025eb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276bdeecec8e10c149c9653fa5f5facb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b43041d4c5a877739fc38e1529217ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a101fe79ea01a75a09a86f7d2ce224d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee281acc298c8c494d7e2d116822a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ddfb1a73da52b1916e118c27cf5aef.png)
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2018-12-06更新
|
163次组卷
|
2卷引用:2015年全国高中数学联赛福建赛区预赛试题
名校
10 . 甲、乙、丙三人用擂台赛形式进行训练.每局两人单打比赛,另一人当裁判.每一局的输方去当下一局的裁判,而由原来的裁判向胜者挑战.半天训练结束时,发现甲共打
局,乙共打
局,而丙共当裁判
局.那么整个比赛的第
局的输方
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1834490aacbee800ed5721312f4be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
A.必是甲 | B.必是乙 | C.必是丙 | D.不能确定 |
您最近一年使用:0次