解题方法
1 . 已知函数
,
.定义
,设
,
,
为常数.
(1)当
时,判断函数
的奇偶性;
(2)定义区间
的长度为
.若
的解集为
,问是否存在
,使得
的全部区间长度之和等于6,若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df18da1ecd1a83afc4544ee71f00c56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92fd3003a50fc4b754f134fe799b12a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726263a79bec039dd073ff799e52eca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647a44d40e8b50a9c308541bbe646dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
(2)定义区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701fce58a3087d253fd4fa948030eb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ed2fb4a6389a9994694ba9aa5e6422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2 . 已知三棱锥
中,
平面
,
,
,
为
中点,
为
中点,
在
上,
.二面角
的平面角大小为
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f3956f008cc29ca4bae44a087d5427.png)
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc63b945d37ff1fc7c4df312c3c23fd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b17ba2410af31808093fc780fd2438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f3956f008cc29ca4bae44a087d5427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
解题方法
3 . 已知函数
,其中
.
(1)若
,求实数
的取值范围;
(2)证明:函数
存在唯一零点;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5faf097501529bae12117c6a9576f840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ce5820ca9e8f9b6398c2462d1396a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36825543013336c9df727bc51ff62c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921882a3b6a472935b3e9c7f5dcebddc.png)
您最近一年使用:0次
名校
4 . 如图,在四棱锥
中,平面
平面PAD,
,
,
,
,
,E是PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/75999df6-7b26-4bc9-b456-9eece69fa814.png?resizew=168)
(1)求证:
;
(2)若点M在线段PC上,异面直线BM和CE所成角的余弦值为
,求面MAB与面PCD夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7ae4091a3a2767fde8e9f5a604c1a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646d135e77c1ea69390d9e937f88b85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/75999df6-7b26-4bc9-b456-9eece69fa814.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371853a703a8dafa6f8e942f46cb8706.png)
(2)若点M在线段PC上,异面直线BM和CE所成角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
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2022-12-27更新
|
2197次组卷
|
7卷引用:山东省莱西市第一中学2022-2023学年高二学业水平检测(二) 数学试题
名校
解题方法
5 . 已知抛物线
的焦点与椭圆
的右焦点重合,直线
与圆
相切.
(1)求椭圆
的方程;
(2)设不过原点的直线
与椭圆
相交于不同的两点A,B,M为线段AB的中点,O为坐标原点,射线OM与椭圆
相交于点P,且O点在以AB为直径的圆上,记
,
的面积分别为
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4856428c4f87eada4e504fce8cc91d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d2aff5570bd20fb94f9320551bd32c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed3bd5e9ec4e61d5c888ff5aa0d276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)设不过原点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323eb2e41f461ac655012a986d5a27bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3877c5dd48bc7311f79a38de74a6cab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2022-12-27更新
|
701次组卷
|
3卷引用:山东省莱西市第一中学2022-2023学年高二学业水平检测(二) 数学试题
解题方法
6 . 设函数
.
(1)当a=8时,求f(x)在区间[3,5]上的值域;
(2)若
,使f(xi)=g(t),求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ff62b5e6f86670b8078ed40b6123c8.png)
(1)当a=8时,求f(x)在区间[3,5]上的值域;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381fd346d669684d551bf040ccb84386.png)
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7 . 已知函数
,
.
(1)若函数
在
上是减函数,求实数
的取值范围;
(2)设
,若函数
有三个不同的零点,求实数
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab790987b551636f09f83bfde6ae4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b081b1439dd4a3f6dafec805b6785700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc783f102bc48d296dd51878da1455a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
8 . 已知函数
.
(1)写出
的定义域并判断
的奇偶性;
(2)证明:
在
是单调递减;
(3)讨论
的实数根的情况.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1865e72c14aebf1a170c6ad1667ee0.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
(3)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beaf743093c9bafdfb1e0ef87b7c2984.png)
您最近一年使用:0次
2022-06-27更新
|
942次组卷
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3卷引用:2022年湖南省学业水平考试高二数学试题
名校
9 . 设函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若函数
在区间
上存在唯一零点,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b97c4a1f84476a09f78e61c0a08ed0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
您最近一年使用:0次
2022-04-26更新
|
678次组卷
|
2卷引用:江苏省南京市金陵中学2022届高三学业水平选择性模拟考前最后一卷数学试题
名校
解题方法
10 . 规定抽球试验规则如下:盒子中初始装有白球和红球各一个,每次有放回的任取一个,连续取两次,将以上过程记为一轮.如果每一轮取到的两个球都是白球,则记该轮为成功,否则记为失败.在抽取过程中,如果某一轮成功,则停止;否则,在盒子中再放入一个红球,然后接着进行下一轮抽球,如此不断继续下去,直至成功.
(1)某人进行该抽球试验时,最多进行三轮,即使第三轮不成功,也停止抽球,记其进行抽球试验的轮次数为随机变量
,求
的分布列和数学期望;
(2)为验证抽球试验成功的概率不超过
,有1000名数学爱好者独立的进行该抽球试验,记
表示成功时抽球试验的轮次数,
表示对应的人数,部分统计数据如下:
求
关于
的回归方程
,并预测成功的总人数(精确到1);
(3)证明:
.
附:经验回归方程系数:
,
;
参考数据:
,
,
(其中
,
).
(1)某人进行该抽球试验时,最多进行三轮,即使第三轮不成功,也停止抽球,记其进行抽球试验的轮次数为随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)为验证抽球试验成功的概率不超过
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
1 | 2 | 3 | 4 | 5 | |
232 | 98 | 60 | 40 | 20 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5d2b05c1bb3d089b0b44ee0f1309b.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d915be3110988ff6c69b27001e2aea38.png)
附:经验回归方程系数:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb95d42bac326c177d3d11f981d5511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebff20f21ae41fd8d1f1e3145895842.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34cadc0d82392089138ecd9c71006f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e22c63f3a796ae8d1cfa9e2769b26be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9141a6d3fd0084de0bfa9136e826865a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9dd2642b6808b94f8f09d6726ef3e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0593a949e9ca8680f71bad6725806bd.png)
您最近一年使用:0次
2022-04-08更新
|
6868次组卷
|
16卷引用:江苏省南京市金陵中学2022届高三学业水平选择性模拟考前最后一卷数学试题
江苏省南京市金陵中学2022届高三学业水平选择性模拟考前最后一卷数学试题山东省青岛市2022届三下学期一模数学试题重庆市缙云教育联盟2022届高三第二次诊断性检测数学试题湖北省襄阳市第五中学2022届高三下学期适应性考试(三)数学试题(已下线)秘籍11 统计与概率-备战2022年高考数学抢分秘籍(全国通用)(已下线)2022年高考考前20天终极冲刺攻略(三)【数学】(新高考地区专用)(6月4日)(已下线)2022年高考考前20天终极冲刺攻略(四)【理科数学】(6月2日)江苏省无锡市天一中学2021-2022学年高二强化班下学期期中数学试题(已下线)第01讲 线性回归分析-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第二册)(已下线)8.6 分布列与其他知识综合运用(精讲)(已下线)专题17 概率与统计的创新题型(已下线)专题26 概率综合问题(分布列)(解答题)(理科)-1广东省东莞外国语学校2024届高三上学期第一次月考数学试题广东省七校联合体2024届高三上学期开学第一次联考(8月)数学试题专题16回归分析(已下线)专题05 成对数据的统计分析压轴题(1)