11-12高三上·福建·阶段练习
1 . 已知函数:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e18f72df2acd6f3e19fe6260617595f.png)
(1)讨论函数
的单调性;
(2)若函数
的图像在点
处的切线的倾斜角为
,问:
在什么范围取值时,函数
在区间
上总存在极值?
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e18f72df2acd6f3e19fe6260617595f.png)
(1)讨论函数
![](https://img.xkw.com/dksih/QBM/2011/12/14/1570612347838464/1570612353523712/STEM/d0fce710afa245ffa4e5129cecb215a8.png?resizew=34)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150e8e4ca6aa729a72a6a17c36b8ebfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18507a11438684e4f6836a8e6021c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be3ad3dd6803d92df6ff8a80cd35095.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3434c372ecb36a447efb19744ab410.png)
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9-10高三下·北京东城·期中
2 . (
已知椭圆
,以原点为圆心,椭圆的短半轴为半径的圆与直线
相切.
(1)求椭圆C的方程;
(2)设
轴对称的任意两个不同的点,连结
交椭圆![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/4415d940d8904a9689cda1d42e7522a6.png)
于另一点
,证明:直线
与x轴相交于定点
;
(3)在(2)的条件下,过点
的直线与椭圆
交于
、
两点,求
的取值
范围.
已知椭圆
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/d317303a9cba459a8167a1bae5ebcd04.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/e66f218312e34cc9afd1768e36ef0ae1.png)
(1)求椭圆C的方程;
(2)设
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/54b2eef1aeff4bc685e7c0cc2d4fafa4.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/ff50b06d875243aa9c5fec5e4b82948c.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/4415d940d8904a9689cda1d42e7522a6.png)
于另一点
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/caf7547391e64ab4ba1a6b0f1d170ed3.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/a906fb03e42b4188abba78dc1072ff0d.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/eea432741420472ebfb45fae7d8c381d.png)
(3)在(2)的条件下,过点
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/eea432741420472ebfb45fae7d8c381d.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/4415d940d8904a9689cda1d42e7522a6.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/dfc1063fb8cd470a9d120b2c915ec9c7.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/b2d5c16639af4707b7212c764bd13816.png)
![](https://img.xkw.com/dksih/QBM/2011/3/8/1570028693577728/1570028699033600/STEM/ffebbda395f049cfb4fe73a8d4323ad6.png)
范围.
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2010·湖北黄冈·二模
3 . (注意:在试题卷上作答无效)
如图,直角△BCD所在的平面垂直于正△ABC所在的平面,PA⊥平面ABC,
,E为DB的中点.
(Ⅰ)证明:AE⊥BC;
(Ⅱ)若点
是线段
上的动点,设平面
与平面
所成的平面角大小为
,当
在
内取值时,求直线PF与平面DBC所成的角的范围.
如图,直角△BCD所在的平面垂直于正△ABC所在的平面,PA⊥平面ABC,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd0a1e0b93cedf080012ca1419908fc.png)
(Ⅰ)证明:AE⊥BC;
![](https://img.xkw.com/dksih/QBM/2010/8/10/1569811319152640/1569811324067840/STEM/b9ff58d5-ba9c-4608-9338-d5521d5bc79c.png?resizew=171)
(Ⅱ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5542d8ba7c5d294f64bd63ec4f43f4d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de694144e7993d8a34e6c5d98664d031.png)
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名校
4 . 符号
表示不大于x的最大整数(
),例如:
,
,
.
(1)已知方程
的解集为M,方程
的解集为N,直接写出集合M、N;
(2)在(1)的条件下,设集合
,是否存在实数k使得
且
,若存在,请求出实数k的范围;若不存在,请说明理由;
(3)设函数
(
),方程
的两个实根为
和
,且满足
.若函数
在
时的函数值记为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ae4ee70c548e841fd7ceeac3250b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a6c086cd67c729ec094c21c0d45a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c15f3d64ba357a69efe1d0c36c0d94.png)
(1)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583b10b1050c1de417cf05733d9943f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f70582a9395aec59113e8747b7f8a5.png)
(2)在(1)的条件下,设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8515650079724b6b297689ad2e13cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1744aae300e6de013e882a9ab565d5ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8965c92d1248c68efdc1dcecea46c90c.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16faec6a9498f6d89494a565fd4ab2fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55cc8e31f2dd9f776d4483b8c917a1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985354e11259c93e6cd249d87091ebe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d8742c296a7949b598114a34c51f69.png)
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名校
解题方法
5 . 已知二次函数
,关于
的不等式
的解集为
,其中
为非零常数,设
.
(1)求
的值;
(2)
如何取值时,函数
存在极值点,并求出极值点.
(3)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3289d2e4520c5b872e814959bc3bed4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed0999d8e7611707d763ca4614ad8f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88ea43f1e36cc084b861b7f5ea0c12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e357538192b0086515ca082025dad9b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93b4456ee6a913deb88a86347c1f033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ae93af9569df6f519c4fe2dad87228.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d05263c941d9ae09cab4e459b40e9a9.png)
您最近一年使用:0次
20-21高二·全国·单元测试
解题方法
6 . 已知二次函数
,关于
的不等式
的解集为
,其中
为非零常数,设
.
(1)求
的值;
(2)
如何取值时,函数
存在极值点,并求出极值点.
(3)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3289d2e4520c5b872e814959bc3bed4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08bbe508332272fd1769bb2b87de3805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987ee644169ad93379283ae715d8ebf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbd77a292834deca9109cfeae8d00e9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6944a8bd2626880b18de6424a4400c60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e965748980da1f255beabd63032e56.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff88dfd467a01b177854545de17534a.png)
您最近一年使用:0次
7 . 已知二次函数
,关于
的不等式
的解集为
,(
),设
.
(1)求
的值;
(2)
R
如何取值时,函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc6c0fd1a3e2428542dbefb518280e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3c39d7e70f6291e47adb6367c5f31f.png)
存在极值点,并求出极值点;
(3)若
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
,求证:
N
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb145e4d81c71721c0dcabd187431b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d1d10e3278c5523d0b7344e6b128ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db50808197f81f61da6de81c0d4abe22.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572051425050624/1572051431342080/STEM/16d1e6bbc6554282b575bfc1e1c12d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d977fb6d13ca2e62dbdc66e31e4ff5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d8e18d9660c3aeecf78020dc54c075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc6c0fd1a3e2428542dbefb518280e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3c39d7e70f6291e47adb6367c5f31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fa30b8a0cf03566e59f39cb394d8a1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0019efd932db51afcfa2c4f6b160ec3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72106152f5d2d9a120c5709ccba49902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81a57cae6fe8a6542f2b56ff5e0c9b2.png)
您最近一年使用:0次
2016-12-03更新
|
266次组卷
|
2卷引用:2015届陕西省西安交大附中高三上学期期中考试理科数学试卷
8 . 设
.
(1)当
时,用函数单调性的定义证明:函数
在区间
上是严格增函数.
(2)①根据a的不同取值,讨论函数
在区间
上零点的个数;
②若函数
在区间
(k为正整数)上恰有7个零点,求k的最小值及此时a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14696ba10834f2d6b8891bf80abd0c79.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301605e86e5a5e61a65c91cd3dd8b77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)①根据a的不同取值,讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d6a66a015ddd2a8076f35ed191927.png)
②若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7f465e11dcb6a1cf9b4cf111f7b249.png)
您最近一年使用:0次
解题方法
9 . 已知函数
,
,
.
(1)若函数
在
上单调递增,求
的取值范围;
(2)若关于
的方程
有两个实根
,
(i)求
的范围;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4784338464ebd7b72876659bcb2df179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020d756192f4dc7939f3b73891ced2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c34a0d539a1a149edfd5b6c2e3dfb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1ed1edfb1823ff324796448f20bd690.png)
您最近一年使用:0次
名校
10 . 设
,函数
.
(1)若
,求证:函数
为奇函数;
(2)若
,判断并证明函数
的单调性;
(3)若
,函数
在区间
上的取值范围是
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5029bd373d0a619fd342eeb67a03dd2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711e45f600c091e6830c0b70cd012ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1897096c9888358bf2b8322f66b8ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
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2024-01-26更新
|
354次组卷
|
2卷引用:河南省信阳市信阳高级中学2023-2024学年高一上学期12月月考数学试题