1 . 如图,在
中,
为
边上一点,
与
分别为
和
的平分线.
![](https://img.xkw.com/dksih/QBM/2022/8/24/3051581032407040/3054416256311296/STEM/432c6f09ddd742e0800436bc37acdea7.png?resizew=265)
(1)判断
是什么三角形,并证明你的结论;
(2)比较
与
的大小;
(3)以
为直径的
交
于点
,连接
与
交于
,若
,
,求证:
,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c42b59b76eafbbe36f13b2daa60132c.png)
![](https://img.xkw.com/dksih/QBM/2022/8/24/3051581032407040/3054416256311296/STEM/432c6f09ddd742e0800436bc37acdea7.png?resizew=265)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(3)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29224be6a2381b38bc64b144d26dad26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f364bf9d8b0bfc299e51097b3ca512f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b092922acd073edfc3a3887822af40.png)
您最近一年使用:0次
名校
2 . 定理(三角不等式),对于任意的
、
,恒有
.定义:已知
且
,对于有序数组
、
、
、
,称
为有序数组
、
、
、
的波动距离,记作
,即
,请根据上述俼息解决以下几个问题:
(1)求函数
的最小值,并指出函数取到最小值时
的取值范围;
(2)①求有序数组
、
、
、
的波动距离
;
②求证:若
、
、
、
且
,则
;题(注:该命题无需证明,需要时可直接使用).设两两不相等的四个实数
、
、
、
,求有序数组
、
、
、
的波动距离
的最大值.
![](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/49506c61cf5c61605f1cf90a440348cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec475a4298eab592d6589aab8915276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef141315bf951ddcd300f0743a16897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7cfd590897d8d908066c781c63a812d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3b887215cd1514d3e2e79063729a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)①求有序数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330e52932883877de428cfe91962b96.png)
②求证:若
![](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/7a876ecb804eb0553c246e5fcc40b708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effb89a4bffb74028211ecfe671b79d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46944e1594eec140cacd7b454342561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc0ce632fa217dc77f6c92afd311815.png)
您最近一年使用:0次
2022-08-22更新
|
417次组卷
|
7卷引用:上海市控江中学2021-2022学年高一上学期期中数学试题
上海市控江中学2021-2022学年高一上学期期中数学试题上海市高桥中学2022-2023学年高一上学期期中数学试题(已下线)期中模拟预测卷03(测试范围:前三章)-2022-2023学年高一数学上学期期中期末考点大串讲(沪教版2020必修第一册)(已下线)上海高一上学期期中【压轴42题专练】(2)(已下线)第二章 等式与不等式(压轴题专练)-速记·巧练(沪教版2020必修第一册)上海市吴淞中学2023-2024学年高一上学期期中数学试题(已下线)专题02 等式与不等式(练习)-2
名校
解题方法
3 . 如图,已知
为二次函数
的图像上异于顶点的两个点,曲线
在点
处的切线相交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/b1c9ee20-7af4-4018-a49a-6703b2da8013.png?resizew=203)
(1)利用抛物线的定义证明:曲线
上的每一个点都在一条抛物线上,并指出这条抛物线的焦点坐标和准线方程;
(2)求证:
成等差数列,
成等比数列;
(3)设抛物线
焦点为
,过
作
垂直准线
,垂足为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031da5d48fbe63745429b1add253344f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60b6eee6448a408616e1b61bd793f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf210c8c9e83e70f2d3ede1e18a5f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031da5d48fbe63745429b1add253344f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/b1c9ee20-7af4-4018-a49a-6703b2da8013.png?resizew=203)
(1)利用抛物线的定义证明:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf210c8c9e83e70f2d3ede1e18a5f3d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297426b8f7938c8d14f42a481a19c3a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b440f7aac4b432fef8f4c9f8e3f76.png)
(3)设抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf210c8c9e83e70f2d3ede1e18a5f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b7a8d232e9a11f5d471f47a1294cd4.png)
您最近一年使用:0次
4 . 我们学习过利用用尺规作图平分一个任意角,而“利用尺规作图三等分一个任意角”曾是数学史上一大难题,之后被数学家证明是不可能完成的,人们根据实际需要,发明了一种简易操作工具——三分角器.图1是它的示意图,其中
与半圆
的直径
在同一直线上,且
的长度与半圆的半径相等;
与
重直于点
足够长.使用方法如图2所示,若要把
三等分,只需适当放置三分角器,使
经过
的顶点
,点
落在边
上,半圆
与另一边
恰好相切,切点为
,则
就把
三等分了.为了说明这一方法的正确性,需要对其进行证明.如下给出了不完整的“已知”和“求证”,请补充完整,并写出“证明”过程.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/62a403f1-c232-4d37-a853-0c1ecfc8e5d5.png?resizew=355)
已知:如图2,点
在同一直线上,
垂足为点
,
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529c8336c1a523cccbdda7cf183cf219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435f30095577dc714634354f5ad27715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435f30095577dc714634354f5ad27715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04122fc1074cff7e73beea9c2ec76ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435f30095577dc714634354f5ad27715.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/62a403f1-c232-4d37-a853-0c1ecfc8e5d5.png?resizew=355)
已知:如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7d41f6e9ebcd509b0c3446029d9ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833b91a24eb0fe0b2ee960193e83065d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
求证:
您最近一年使用:0次
名校
5 . 如图1,AB为⊙O的直径,点P是直径AB上任意一点,过点P作弦
,垂足为P,过点B的直线与线段AD的延长线交于点F,且∠F=∠ABC.
![](https://img.xkw.com/dksih/QBM/2022/8/3/3036407790297088/3042341699436544/STEM/1f38f551e5a54e12bfa08392d396732b.png?resizew=302)
(1)若CD=
,BP=4,求⊙O的半径;
(2)求证:直线BF是⊙O的切线;
(3)当点P与点O重合时,过点A作⊙O的切线交线段BC的延长线于点E,在其它条件不变的情况下,判断四边形AEBF是什么特殊的四边形?请在图2中补全图象并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://img.xkw.com/dksih/QBM/2022/8/3/3036407790297088/3042341699436544/STEM/1f38f551e5a54e12bfa08392d396732b.png?resizew=302)
(1)若CD=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(2)求证:直线BF是⊙O的切线;
(3)当点P与点O重合时,过点A作⊙O的切线交线段BC的延长线于点E,在其它条件不变的情况下,判断四边形AEBF是什么特殊的四边形?请在图2中补全图象并证明你的结论.
您最近一年使用:0次
解题方法
6 . 用光线照射物体,在某个平面上得到的影子叫做物体的投影,照射光线叫做投影线,投影所在的平面叫做投影面.由平行光线形成的投影叫做平行投影,由点光源发出的光线形成的投影叫做中心投影.投影线垂直于投影面产生的平行投影叫做正投影,投影线不垂直于投影而产生的平行投影叫做斜投影.物体投影的形状、大小与它相对于投影面的位置和角度有关.如图所示,已知平行四边形
在平面
内的平行投影是四边形
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/71cf6fa5-9cb4-4d8d-a907-fa7ccdcd6d3d.png?resizew=314)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9fc4f21f-3f78-4976-887c-0642c3365737.png?resizew=314)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/462c058d-eb41-4d4a-ac0e-89fb806fef7a.png?resizew=314)
(1)若平行四边形
平行于投影面(如图
),求证:四边形
是平行四边形;
(2)在图
中作出平面
与平面
的交线(保留作图痕迹,不需要写出过程);
(3)如图
,已知四边形
和平行四边形
的面积分别为
,平面
与平面
的交线是直线
,且这个平行投影是正投影.设二面角
的平面角为
(
为锐角),猜想并写出角
的余弦值(用
表示),再给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/71cf6fa5-9cb4-4d8d-a907-fa7ccdcd6d3d.png?resizew=314)
图
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9fc4f21f-3f78-4976-887c-0642c3365737.png?resizew=314)
图
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/462c058d-eb41-4d4a-ac0e-89fb806fef7a.png?resizew=314)
图
(1)若平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
(2)在图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7021666155884a8aa345ed8eec3d2a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
您最近一年使用:0次
名校
解题方法
7 . 对于定义域为R的函数
,如果存在常数T,
,使得
是以T为周期的函数,则称函数
为正弦周期函数,且称常数T为
的正弦周期.
已知函数
满足以下四个条件:
①函数
是以T为正弦周期的正弦周期函数;
②函数
的值域为R;
③函数
在区间
上单调递增:
④
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294bab9bbfb414f2d1fb0844aee4fc9e.png)
(1)分别判断函数
、
是否为正弦周期函数.如果是正弦周期函数,写出它的正弦周期,(不需证明).
(2)设
,求证:对任意
,存在唯一的
使得
.
(3)求证:对于任意的
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eecacbdc5c2a7e7ac00daea8c448098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a0ab6eeb2b475795eae6f432789105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaafa094244d569dd54bd8036c7f0b6d.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93941e7f4bea588b5020035760ba0e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294bab9bbfb414f2d1fb0844aee4fc9e.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f19e893159870d911d83af4f4b2b70ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6978ab291c9908f871c1178a2dea35a9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761e8a1b81490a2db7aa84f2104cb3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea34ffa60956e957a07faf386e43a20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b836129720c860faf76f2703b61016.png)
(3)求证:对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7999305fcdf5fd209920cc42cfe6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab11dce5b8ee5cbe5f1439c1b9e4dc3.png)
您最近一年使用:0次
解题方法
8 . 如图,在直角梯形
中,
,
,
,并将直角梯形
绕AB边旋转至ABEF.
平面ADF;
(2)求证:直线
平面ADF;
(3)当平面
平面ABEF时,再从条件①、条件②、条件③这三个条件中选择一个作为已知,使平面ADE与平面BCE垂直.并证明你的结论.
条件①:
;
条件②:
;
条件③:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6045266f6db39e41b7abde762d9e9a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
(3)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6166b9a5437671bcba31e17c375eb39.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c182a9d9fd0a7023b710cd671d9468e7.png)
您最近一年使用:0次
2022-07-08更新
|
1296次组卷
|
11卷引用:北京市丰台区2021-2022学年高一下学期期末练习数学试题
北京市丰台区2021-2022学年高一下学期期末练习数学试题(已下线)8.6.1 空间直线、平面的垂直(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)模块三 专题9(劣构题)拔高能力练(北师大版)(已下线)模块三 专题9(劣构题)基础夯实练(人教B)(已下线)模块三 专题9(劣构题)拔高能力练人教A版)(已下线)模块三 专题10(劣构题)拔高能力练(苏教版)(已下线)专题06 空间中点线面的位置关系6种常考题型归类(1)-期期末真题分类汇编(北京专用)(已下线)7.2 空间几何中的垂直(精练)(已下线)7.1 空间几何中的平行与垂直(精讲)(已下线)高考新题型-立体几何初步(已下线)2023年高考全国乙卷数学(理)真题变式题16-20
名校
9 . 汽车前灯反射镜曲面设计为抛物曲面(即由抛物绕其轴线旋转一周而成的曲面).其设计的光学原理是:由放置在焦点处的点光源发射的光线经抛物镜面反射,光线均沿与轴线平行方向路径反射,而抛物镜曲面的每个反射点的反射镜面就是曲面(线)在该点处的切面(线).定义:经光滑曲线上一点,且与曲线在该点处切线垂直的直线称为曲线在该点处的法线.设计一款汽车前灯,已知灯口直径为20cm,灯深25cm(如图1).设抛物镜面的一个轴截面为抛物线C,以该抛物线顶点为原点,以其对称轴为x轴建立平面直角坐标系(如图2)抛物线上点P到焦点距离为5cm,且在x轴上方.研究以下问题:
(2)求P点坐标.
(3)求抛物线在点P处法线方程.
(4)为证明(检验)车灯的光学原理,求证:由在抛物线焦点F处的点光源发射的光线经点P反射,反射光线所在的直线平行于抛物线对称轴.
(2)求P点坐标.
(3)求抛物线在点P处法线方程.
(4)为证明(检验)车灯的光学原理,求证:由在抛物线焦点F处的点光源发射的光线经点P反射,反射光线所在的直线平行于抛物线对称轴.
您最近一年使用:0次
2022高一·全国·专题练习
解题方法
10 . 证明:平行四边形两条对角线的平方和等于四条边的平方和.已知:平行四边形ABCD.求证:AC2+BD2=AB2+BC2+CD2+DA2.
您最近一年使用:0次
2022-04-14更新
|
262次组卷
|
6卷引用:6.4.1向量在平面几何和物理的应用-【师说智慧课堂】课后作业(人教A版2019)
(已下线)6.4.1向量在平面几何和物理的应用-【师说智慧课堂】课后作业(人教A版2019)(已下线)第05讲 平面向量的应用-《知识解读·题型专练》(人教A版2019必修第二册)(已下线)6.4.1平面几何中的向量方法+6.4.2向量在物理中的应用举例【第一练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)6.4.1 平面几何中的向量方法-高频考点通关与解题策略(人教A版2019必修第二册)(已下线)6.2.2?向量的减法运算——课后作业(巩固版)(已下线)6.4.1 平面几何中的向量方法——课后作业(巩固版)