解题方法
1 . 定义在
上的连续可导函数
的导函数为
,
满足
,且
为奇函数.当
时,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad1257d33c2d8c1304f0554e72a6fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e60ec6a333922ae57061844bba82cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5370f944ace7b95c5429418124766a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b713218cab6d29c142634efb005efbfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce6ccd64f57fe8ab250aa45d3376d92.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 已知双曲线
的左、右焦点分别为
、
,过
作直线
,使得它双曲线的一条渐近线垂直且垂足为点
,
与双曲线的右支交于点
,若线段
的垂直平分线恰好过
的右焦点
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
3 . “绿水青山就是金山银山”理念已经成为全党全社会的共识和行动,工业废水中的某稀有金属对环境有污染,甲企业经过数年攻关,成功开发出了针对该金属的“废水微循环处理利用技术”,废水每通过一次该技术处理,可回收20%的金属.若当废水中该金属含量低于最原始的5%时,至少需要循环使用该技术的次数为( )(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef98775e12ea3852135792e34526a519.png)
A.12 | B.13 | C.14 | D.15 |
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2023-04-30更新
|
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|
3卷引用:四川省攀枝花市2023届高三第三次统一考试理科数学试题
四川省攀枝花市2023届高三第三次统一考试理科数学试题(已下线)第二章 函数的概念与性质 第六节 指数式、对数式的运算(讲)宁夏回族自治区银川市宁夏育才中学2023-2024学年高一上学期第二次月考数学试题
4 . 已知
为锐角,
,角
的终边上有一点
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bc052a11cf1a01445992672dde2836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b729f3bcad3527fd911eb71de25a64f9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 设集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9beff64c596e583f35035e6b6883338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc7cac84161162bd4bffd8028025932d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1336d38741aab2255a35c26612bbd7cc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-04-30更新
|
1036次组卷
|
4卷引用:四川省攀枝花市2023届高三第三次统一考试理科数学试题
四川省攀枝花市2023届高三第三次统一考试理科数学试题(已下线)湖南省新高考教学教研联盟2023届高三下学期4月第二次联考数学试题变式题1-5(已下线)2023年新课标全国Ⅰ卷数学真题变式题1-5河北省邯郸市鸡泽县第一中学2024届高三上学期第二次月考数学试题
解题方法
6 . 已知函数
.
(1)解不等式
;
(2)设函数
的最小值为c,正实数a,b满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d85ab9b6287f810bfb1443ba4a98065.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b25f064496c350525916aa7ad80bb0f.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4e94d78949138071e0c9994de12c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7696cf6cd983f29d8834c6df01c5fb27.png)
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2023-04-30更新
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3卷引用:四川省攀枝花市2023届高三第三次统一考试文科数学试题
解题方法
7 . 在平面直角坐标系
中,曲线
的参数方程为
(t为参数),曲线
,以坐标原点O为极点,x轴的非负半轴为极轴建立极坐标系.
(1)求
,
的极坐标方程;
(2)若射线
分别与曲线
,
相交于A,B两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59dc051dc44914c66b4e8a4d1b72093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23c01c2dcfe916f69ba00ee47c801bf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44670943f3d1ba89787b7cd2060d87ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e673424448e33a6fb69b195118360c.png)
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2023-04-30更新
|
763次组卷
|
3卷引用:四川省攀枝花市2023届高三第三次统一考试文科数学试题
名校
解题方法
8 . 已知函数
在
处的切线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51abd816a2ea3492513fa1a9fc4ebce6.png)
.
(1)求实数a,b的值;
(2)当
时,
恒成立,求正整数m的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c3f016897d3a48b9284ee25be6b864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51abd816a2ea3492513fa1a9fc4ebce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b92db837661bd16bd1b01f88f91f89.png)
(1)求实数a,b的值;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503a002dd51f5338c4bc0e15fb201c3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9c62f562f3dd05b5ceaeddb6395bfc.png)
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628次组卷
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2卷引用:四川省攀枝花市2023届高三第三次统一考试文科数学试题
9 . 已知椭圆
的焦点坐标为
和
,且椭圆经过点
.
(1)求椭圆
的标准方程;
(2)椭圆
的上、下顶点分别为点
和
,动点
在圆
上,动点
在椭圆
上,直线
、
的斜率分别为
、
,且
.证明:
、
、
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813f9a2814013e2407b5b1c216159359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748902ce5e3dc5279279d58bf14610d6.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.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/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124d17c76931baa8130c9e4a4a8804fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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解题方法
10 . 如图1,圆O的内接四边形
中,
,
,直径
.将圆沿
折起,并连接
、
、
,使得
为正三角形,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/fa1e9412-2c55-4d83-a859-a32d01660735.png?resizew=289)
(1)证明:图2中的
平面
;
(2)在图2中,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ed407cbb778f76bf879bfcae69ebba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c646c683fbe522edb7ea54fd3ad873d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4686f39b38d5b90309ee73ed89a0640.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/fa1e9412-2c55-4d83-a859-a32d01660735.png?resizew=289)
(1)证明:图2中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)在图2中,求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d63a158f3cd698827a5099a09ba6d7e.png)
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