解题方法
1 . 某港口在一天之内的水深变化曲线近似满足函数
,其中h为水深(单位:米),t为时间(单位:小时),该函数部分图象如图所示.若一艘货船的吃水深度(船底与水面的距离)为4米,安全条例规定至少要有1.5米的安全间隙(船底与水底的距离),则该船一天之内能在该港口停留多久?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b207f342d0153301e859535e698a8f.png)
![](https://img.xkw.com/dksih/QBM/2022/5/13/2978532343529472/2980819154616320/STEM/e57f0f58-1125-4b12-97ec-ec236761a0bc.png?resizew=217)
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名校
解题方法
2 . “南昌之星”摩天轮于2006年竣工,总高度160
,直径153
.匀速旋转一圈需时30
.以摩天轮的中心为原点建立平面直角坐标系,画示意图,如图1.
为起始位置如图2,经过![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
后,
逆时针旋转到
,此时点
距离地面的高度
(
)满足
,其中
,
,
.
(1)根据条件求出
(
)关于
(
)的解析式;
(2)在摩天轮转动的第一圈内,有多长时间P点距离地面不低于45.25
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ce48eafd36547782174eb304d4a003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ce48eafd36547782174eb304d4a003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1dd158811a1ecc73bb3c32fa0fc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad0928c1ec5c77529715aa84085fcee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e945f654178c56202efce1a71f9e27.png)
(1)根据条件求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1dd158811a1ecc73bb3c32fa0fc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ce48eafd36547782174eb304d4a003.png)
(2)在摩天轮转动的第一圈内,有多长时间P点距离地面不低于45.25
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
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2022-05-06更新
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3卷引用:河南省南阳市2021-2022学年高一下学期期中质量评估数学试题
名校
解题方法
3 . 如图所示
的两边
,
,设
是
的重心,
边上的高为
,过
的直线与
,
分别交于
,
,已知
,
;
的值;
(2)若
,
,
,求
的值;
(3)若
的最大值为
,求边
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f322f8f148fbbaa38b6c0218ae68fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e9a5092afe1af9b0a2eb01c5f25a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587b693b82241eb9c32cdbb96c209f33.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45373166e0a004b3b4d910655d409b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c6d5aeee562064b9bb703fa538413d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d2d153c31e0a4a9ca234ba3331590f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8971f209e5596ccf8a5a983e166f5d52.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29a364ce73d0abe8bf37f80450f8ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24473546b4e77ce3091dd840f72ccea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2022-05-02更新
|
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6卷引用:浙江省温州市知临教育集团2021-2022学年高一下学期期中数学试题
浙江省温州市知临教育集团2021-2022学年高一下学期期中数学试题(已下线)期末押题预测卷02安徽省合肥市第八中学2022-2023学年高一下学期期中检测数学试题(已下线)必修二全册综合测试卷(提高篇)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)湖南省长沙市宁乡市2022-2023学年高一下学期期末数学试题(已下线)第一次月考解答题压轴题十六大题型专练(1)-举一反三系列(人教A版2019必修第二册)
4 . 如图,在四边形ABCD中,
,
,E是线段CD上的点,直线BD与直线AE相交于点P,设
,
,
.
,
,
,E是线段CD的中点,求与
同向的单位向量的坐标;
(2)若
,用
,
表示
,并求出实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d730ae4307db56b47849c3a19dedfb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4575a365b8e619654a7327d216f23783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfca12290a98993f84d7ee4b8caaa9d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d587e96eb8c73f677da202d5255b690b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711f1c9e52c41b71e16c8dc85a58eae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e3a62c262064b5ea919da7eab436de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d231ae53e3341fec3e56bc59b3acaed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c04646983028a2088682a2c116672d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6df2d9d2afb376c3c54894b915705f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e7b83a2497d1662d1a95ec4cbb7495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2173a791f504749b01c97b951be4b940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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5卷引用:湖北省六校新高考联盟2021-2022学年高一下学期4月联考数学试题
湖北省六校新高考联盟2021-2022学年高一下学期4月联考数学试题贵州省六盘水市第二中学2021-2022学年高一6月月考数学试题(已下线)第02讲 平面向量基本定理及坐标表示 (精讲)-2023年高考数学一轮复习讲练测(新教材新高考)江西省上饶市横峰中学2022-2023学年高二上学期开学考试数学试题辽宁省大连市滨城高中联盟2022-2023学年高一下学期3月月考数学试题
5 . 在平面直角坐标系中,O为坐标原点,梯形ABCD的四个顶点分别为
,
,
,
,且
.
(1)若
,求点D的坐标;
(2)若
,求点D的坐标;
(3)若点P是平面内任意一点,且
,写出
的最大值.(只需写出结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d31cd03879d5c69ff11d0923f1ee82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c2df1ec4f5d17fa8590e920fac61af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4e5bf2fc46de6d148602f505614c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4575a365b8e619654a7327d216f23783.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
(3)若点P是平面内任意一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b9603b03810c4b388dba92df72cc08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f0e6d3115e900f1a359ec4f894e8896.png)
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6 . 高一某班小赵同学在解答“利用五点法画出函数
在一个周期上的简图,并根据图象讨论它的性质”题目时,有如下解答过程,请补全解答过程.
解:第一步:列表.
第二步:画出
在一个周期上的简图.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/69adf868-b25e-4288-b07d-9e619a02fab4.png?resizew=210)
第三步:讨论
的性质.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83158ac8e214c8763863b22ddc82e03c.png)
解:第一步:列表.
x | 0 | ||||
0 | |||||
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83158ac8e214c8763863b22ddc82e03c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/69adf868-b25e-4288-b07d-9e619a02fab4.png?resizew=210)
第三步:讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83158ac8e214c8763863b22ddc82e03c.png)
函数 | |
定义域 | R |
最小正周期 | ______ |
单调性 | 单调递增区间为______; 单调递减区间为______ |
最大值与最小值 | 当 当 |
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解题方法
7 . 如图,在
中,
,
.点D在边BC上,且
.
,
,求
;
(2)
,AD恰为BC边上的高,求角A;
(3)
,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb89e4f1d401020adebdbfed22a3c855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3129ddd2ea97fd010b9e0b644225da8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d09196d6643e64ab5b9b5df02d98a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045fab982486b0dbb57969a7546759f7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81d46247b6c57774da6fd0a804e679.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
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2022-04-25更新
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7卷引用:上海交通大学附属中学2021-2022学年高一下学期期中数学试题
上海交通大学附属中学2021-2022学年高一下学期期中数学试题安徽省蚌埠市2022-2023学年高一下学期期末学业水平监测数学试题(已下线)重难点01平面向量的实际应用与新定义(1)(已下线)专题6.7 平面向量的综合应用大题专项训练-举一反三系列(已下线)第9章 平面向量 章末检测卷-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)高一下学期期中复习解答题压轴题十八大题型专练(1)-举一反三系列(人教A版2019必修第二册)(已下线)高一下学期期末复习解答题压轴题二十四大题型专练(1)-举一反三系列(人教A版2019必修第二册)
8 . 在
中,向量等式
或
,沟通了几何与代数的联系,利用它并结合向量的运算,可以很好地帮助我们研究问题,体现向量法的特性.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/a2b06e52-e559-4b77-a48b-07d2c630a7fd.png?resizew=210)
(1)如图,
的三个角A,B,C所对的边分别为a,b,c.设向量
为
在平面的一个单位向量,记向量
与
的夹角为
.现构造等式
,据此,请你探究
及
时
的边和角之间的等量关系;
(2)已知AD是
的角平分线,请你用向量法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94327111fa1a63cfac65ebb1dd77d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570ae20fbd0dae546730e306502267b6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/a2b06e52-e559-4b77-a48b-07d2c630a7fd.png?resizew=210)
(1)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd5c976aae6dc8881ddaa045692c246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd5c976aae6dc8881ddaa045692c246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e81ae4b641e593ab21131036df5a66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcca436b9f38396dafd79f5e302a6a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0f96c4dfd44a0412601f183a8c7443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)已知AD是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02bad7fac070822f4c8b4f8b64bda72.png)
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解题方法
9 .
的内角为A,B,C,
边上的高为
.
(1)用
表示
;
(2)若E为
边上一点,且
,试确定E点的位置,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccd5af8518c3021a065c4383783076f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbef69bb5ce04abc8a2daaf8da00d9ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
(2)若E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cc79091dd7796a87ad51e61079fe5d.png)
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2022-03-30更新
|
494次组卷
|
3卷引用:山东省名校2021-2022学年高一下学期大联考考试数学试题
名校
10 . 已知扇形
(如图所示),圆心角
,半径
,在弧
上取一点P,作扇形
的内接矩形
,记
,矩形
的面积为y.
(2)求矩形
面积的最大值,并求此时x的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd33fd61545ef78df7bcde667baba30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adf8bccbc5113a6d8f85285c6dc28cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa340c9d5edd3e26e1fc8969029761c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc4eff53a75a14a675562e8e3bfc13f.png)
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