名校
解题方法
1 . 已知
的内角
,
,
的对边分别为
,
,
,且
,
.
(1)若
,求
,
的值;
(2)若
的面积为
,求
的大小及
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4f287c96efeeafcbd6eec03d85dfcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f4e19fcf82af19ae7f70cb49685588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e5d4f93699f8dcffb0e7840ca5597e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52bc912794df9a0cf7e4eecbc2e0f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2 . 在
中,
,
,
,
是
的内切圆圆心,内切圆的半径为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e899c486dc49e560fc4aca05e16835b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
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3 .
的内角
,
,
的对边分别为
,
,
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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4 . 已知函数
的图象如图所示.
的解析式;
(2)首先将函数
的图象上每一点的横坐标伸长到原来的2倍,然后将所得函数的图象向右平移
个单位长度,最后再将所得函数的图象向上平移1个单位长度,得到函数
的图象,求函数
在
内的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fcc776400aaae0f6782f73c6c5098e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)首先将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b172723002461ae60798317e2f10f6c2.png)
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5 . 由倍角公式
,可知
可以表示为
的二次多项式.对于
,我们有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2104a78b37da636d13e09e5bdb2be10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b752c5b70e8bef980994bfbb88df7cbc.png)
,可见
也可以表示成
的三次多项式.以上推理过程体现了数学中的逻辑推理和数学运算等核心素养,同时也蕴含了转化和化归思想.
(1)试用以上素养和思想方法将
表示成
的三次多项式;
(2)化简
,并利用此结果求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91d0d02d04a3f1b777b0d86e2372e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5ff5a2e7663e6a21ccea3149a10113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e039219978242ec380e66de6cf9bab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2104a78b37da636d13e09e5bdb2be10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b752c5b70e8bef980994bfbb88df7cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706585b7d68cd2b99f2f671328c318a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e039219978242ec380e66de6cf9bab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(1)试用以上素养和思想方法将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff1dd2db6f898d70a9adef9a0f2ffad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06680427974d0fb0ca07d306f92d505a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1064e3198a310f74672b7211ba74071.png)
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6 . “乡村振兴”是新时代响应习主席社会主义核心价值观的重要举措,秦岭山中镇水县乾祐河畔某乡镇游乐中心欲对游乐设施——摩天轮的运行参数进行核算,以利于该镇游乐设施的进一步发展.如图,该摩天轮的半径为
,其中心
点距离地面的高度为
,摩天轮按逆时针方向匀速转动,且每20分钟转一圈,若摩天轮上点
的起始位置在最高点处,则摩天轮转动过程中( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/22/b0126a92-712c-4670-82db-e09d8959f587.png?resizew=161)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c56c87fd6bf8a44244ba51a9d244e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8badcdb1e5621f0ac4d9272041185a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/22/b0126a92-712c-4670-82db-e09d8959f587.png?resizew=161)
A.转动10分钟后点![]() ![]() |
B.若摩天轮转速减半,则转动一圈所需的时间变为原来的![]() |
C.第17分钟和第43分钟,点![]() |
D.摩天轮转动一圈,点![]() ![]() ![]() |
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7 . 如图所示,是函数
(
,
,
)图象的一部分,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f521f470efae2d0a124df49c0fe7016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060b3885fcc7578d2a99550c351947ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e60c2772ce378786f84f420c6455dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c22d98ce28002ff139743ed4c15074.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 某市政府计划在一处河道湿地修建一个公园.湿地公园呈五边形形状,如图所示,其中
长为600米,在BC上选择一点
作为公园入口,从公园入口出发修建两条绿道
其中绿道终点
两点分别在边界
上,且
.
(2)为了方便游客,打算在湿地公园原有规划基础上增添一条商业步道EF,若建设绿道平均每米需花费200元,建设商业步道平均每米需花费400元,试求建设绿道与商业步道总花费的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01a2627dbc597235c2e6cab7f0cb71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967698dc6a77f482799a4d09c724de29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fa8bd3792adb4f75697357808cd50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c48f3e76e6ce74e963374b55626f534.png)
(2)为了方便游客,打算在湿地公园原有规划基础上增添一条商业步道EF,若建设绿道平均每米需花费200元,建设商业步道平均每米需花费400元,试求建设绿道与商业步道总花费的最小值.
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解题方法
9 . 下列函数中,既是奇函数又在定义域上单调递增的函数是( )
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 记锐角
的内角
的对边分别为
已知
,设甲:
;乙:
的取值范围为
,以下说法正确的是( )
![](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/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5341ff5a6a1c0bdce691957d43a5d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558494a4594f69b0b679d8d588006efa.png)
A.甲为真命题,乙为真命题 | B.甲为真命题,乙为假命题 |
C.甲为假命题,乙为假命题 | D.甲为假命题,乙为真命题 |
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