名校
解题方法
1 . 设
,若
与
的等差中项是2,则
的最小值为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ca13beb13005f586d6503fa2dafc2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270357be57e00dfc1efeb3ce8fdcbd36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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名校
解题方法
2 . 已知
,
,若
,则
的最小值为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254aebe3ef7eabdf41e46c1cd857c705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df852e5c8d439fbf69f83fa9e080a638.png)
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名校
解题方法
3 . 如图,A、C两岛相距
海里,上午9点整有一客轮在位于C岛的北偏西40°且距C岛10海里的D处,沿直线方向匀速开往A岛,在A岛停留10分钟后前往B市,上午9:30测得客轮位于C岛的北偏西70°且距C岛
海里的E处,此时小张从C岛乘坐速度为v海里/小时的小艇沿直线方向前往A岛换乘客轮去B市.
(2)若小张能乘上这班客轮,问小艇的速度至少为多少海里/小时?(由小艇换乘客轮的时间忽略不计)
(3)现测得
,
,已知速度为
海里/时
的小艇每小时的总费用为
元,若小张由岛C直接乘小艇去B市,则至少需要多少费用?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254f942341f65547368c0206d1d748f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e4123975f257306440158659634c4a.png)
(2)若小张能乘上这班客轮,问小艇的速度至少为多少海里/小时?(由小艇换乘客轮的时间忽略不计)
(3)现测得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/601db16fd0de0dc16f99302da464e8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b82ca3f26564d127cfe81a90b1bb4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbac0fb8cc2e5eec37b63c7faddc29b.png)
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4 . 矩形
中,
,
,动点
满足
,
,则下列说法中正确的是______ .
①若
,则
的面积为定值 ②若
,则
的最小值为4
③若
,则满足
的点
不存在 ④若
,
,则
的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9545017eee79a71befee621b52c8cae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535964b59870f898bf1907ee5a3c56f8.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2753dc1c83d54044b89e628a7eb247f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95494fff79fac79913879645730eba57.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76819195cffab10d81638dd673f3af98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66790293bccf6d4410e38dbcfe41f770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa2e529ffee0c5b492279f588cd5576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
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名校
解题方法
5 . 在△ABC中,角A、B、C所对的边分别为a、b、c,
.
(1)求
的值;
(2)若
,求bc的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf623a808eaaef1acef2bd44d92d34a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c54399cfb59213a484664d7fd44018.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
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解题方法
6 . 运货卡车以
千米/时的速度匀速行300千米,按交通法规限制
(单位千米/时),假设汽油价格是每升8元,汽车每小时耗油
升,司机的工资是每小时46元.
(1)求这次行车总费用
(元)关于
(千米/时)的表达式;
(2)当
为何值时,这次行车的总费用
最低?并求出最低总费用(精确到0.01)(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a442028e1158d57eeed2b33e34316efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da630f0af94072a65367932648a40397.png)
(1)求这次行车总费用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](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/a39ca04011ba2f89189b19dd056eee47.png)
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7 . 足球教练带领运动员对“带球射门”进行专项训练.如图,教练员指导运动员沿着与边路
平行的路线带球并起脚射门,教练员强调要在路线上的相应位置
处起脚射门进球的可能性最佳(即点
对球门
所张的角
最大),假如每条虚线都表示在规定的区域
内为运动员预设的带球路线,而每条路线上都有一个最佳起脚射门点
,为了研究方便,如图建立坐标系,设
、
,
在
轴的上方.
,求此时
的外接圆的圆心坐标
(2)过点
作
轴的垂线,垂足为
,若
,求当
最大时,点
的坐标
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb898663f98b8400a897913b4d3102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e7030cc9fb09f86c6cdab7d912ed31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506512c81d3523a4a6c307ccc14f1583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
8 . 在平面直角坐标系
中,任意角
,
的终边交单位圆(圆心在坐标原点
于
,
两点.
(1)若
为锐角,且
,求
的值
(2)若角
为锐角,且终边绕原点逆时针转过
后,终边交单位圆于
,求
的值;
(3)若
两点的纵坐标分别为正数
,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3904463e169fb25dbd36fa257edd2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb7066af4a86840937fa1ae57de7351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8114e78ac5798c981a09a8d282875f99.png)
(2)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5d89e927a5b5c7129511a5f79a38c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f798a9af75a091a8be0b71f2038260.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3a93260a81067443fe512cdd46abbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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2024高三·全国·专题练习
解题方法
9 . 在
中,角
所对的边分别为
,
是
的角平分线,若
,
,则
的最小值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1371fe98a65d8ebd840c8d98346b6d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7efca8735d51460c4de6726291d6817c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2ed49b4be25eac88aa2af01aa84c15.png)
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名校
解题方法
10 . 已知函数
.
(1)当
时,直接写出
的单调区间(不要求证明),并求出
的值域;
(2)设函数
,若对任意
,总有
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b2d3738f56987d159a343dc160f384.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdabdbbbde9b3ee68df66171b0145785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d5a5e70f64f0933ae1e4ddec5fa2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61761abb364ece2281af24d9b1f008de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2024-03-07更新
|
514次组卷
|
11卷引用:大题好拿分期中考前必做30题(压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)
(已下线)大题好拿分期中考前必做30题(压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)安徽省合肥市一中、六中、八中三校2020-2021学年高一上学期期末数学试题安徽省合肥一中、六中、八中2020-2021学年高一上学期期末联考数学试题安徽省淮南市寿县第一中学2020-2021学年高一下学期入学考试数学试题安徽省淮北市树人高级中学2020-2021学年高一下学期开学考试数学试题(已下线)第7章 三角函数 单元测试(单元综合检测)(难点)(单元培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)(已下线)7.3 三角函数的图像和性质(难点)(课堂培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)山东省淄博市美达菲双语高级中学2022-2023学年高一下学期3月月考数学试题四川省德阳市德阳中学校2023-2024学年高一下学期入学考试数学试卷湖南省株洲市第二中学2022届高三下学期期中数学试题(已下线)专题17 三角值域问题