13-14高三·北京·开学考试
名校
解题方法
1 . 设
,向量
,若
∥
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85527d190d4e1d6bac4145d1c716e65e.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b992104248a854e6e033c26602aff813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de92c53f311fb6f5fd0dd122fd384e91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85527d190d4e1d6bac4145d1c716e65e.png)
您最近一年使用:0次
2024-05-13更新
|
609次组卷
|
25卷引用:2015届北京市重点中学高三8月开学测试数学试卷
(已下线)2015届北京市重点中学高三8月开学测试数学试卷江西省南昌市第二中学2016-2017学年高一下学期第三次月考数学试题(已下线)2019年一轮复习讲练测 5.2 平面向量的基本定理及坐标表示【浙江版】【测】(已下线)2019高考热点题型和提分秘籍 【理数】专题19 平面向量的基本定理及其坐标表示( 教学案)【全国百强校】天津市河西区新华中学2017-2018学年高一上学期期末考试数学试题广东省佛山市禅城区2019-2020学年高三统一调研测试卷(一)数学(理)试题上海市七宝中学2016届高三上学期期中(理科)数学试题上海市实验学校2017届高三上学期第三次月考数学试题(已下线)题型01 特殊向量(单位向量、平行或共线向量)-2020届秒杀高考数学题型之平面向量(已下线)专题15 平面向量的概念、线性运算、平面向量基本定理-十年(2011-2020)高考真题数学分项(已下线)专题13 三角函数的综合应用-十年(2011-2020)高考真题数学分项(二)(已下线)考点17 平面向量的线性运算与基本定理-2021年新高考数学一轮复习考点扫描(二)(已下线)题型01 平面向量性质-2021年高考数学题型秒杀之平面向量福建省龙岩市长汀县三级达标校2020-2021学年高一下学期期中考试数学试题(已下线)考点19 平面向量的基本定理及坐标表示-备战2022年高考数学(理)一轮复习考点帮(已下线)考点20 平面向量的概念及线性运算、平面向量的基本定理-备战2022年高考数学典型试题解读与变式陕西省西安中学2022届高三下学期第一次仿真考试理科数学试题江苏省连云港高级中学2021-2022学年高一下学期期末模拟数学试题江苏省新海高级中学2023-2024学年高一下学期学情检测一数学试题(已下线)数学(全国卷文科03)(已下线)专题09 三角函数填空题(理科)-1陕西省安康市高新中学2024届高三模拟考试最后一卷理科数学试题(已下线)专题02 三角恒等变换题型归纳-《期末真题分类汇编》(江苏专用)(已下线)专题01 平面向量重难题型(1)-期末真题分类汇编(江苏专用)陕西省安康市高新中学2024届高三模拟考试最后一卷文科数学试题
名校
解题方法
2 . 已知
则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de458d9daeae3e48a9916fefb834037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992922f2f0ab9f07b7ccdcb91aa3e691.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-24更新
|
169次组卷
|
3卷引用:第六届高一试题(初赛)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
名校
解题方法
3 . 设集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d077252f46b6b1496cd8ce963e8404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933347fd4d93628c8a9cb6a540560471.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-27更新
|
1359次组卷
|
9卷引用:天津市南开大学附中2020-2021学年高三上学期第二次月考数学试题
4 . 有一电脑程序:每按一次按键,屏幕的
区就会自动加上
,同时
区就会自动减去
,且均显示化简后的结果.已知
两区初始显示的分别是
和
,如图,第一次按键后,
两区分别显示:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/54c243d1-3018-4f7c-8878-46d595048b2b.png?resizew=261)
(1)从初始状态按2次后,分别求
两区显示的结果;
(2)从初始状态按4次后,计算
两区代数式的和,请判断这个和能为负数吗?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cc0b4997cae4d8aec791a1d3923314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06fc7811f9525e8b8c833746d6af5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec54f53122364c46e1e43d1a84f210fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/54c243d1-3018-4f7c-8878-46d595048b2b.png?resizew=261)
(1)从初始状态按2次后,分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(2)从初始状态按4次后,计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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5 . 如图1,在平面直角坐标系中,直线
与直线
相交于点
,点A是直线
上的动点,过点A作
于点
,点
的坐标为
,连接
.设点A的纵坐标为
的面积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://img.xkw.com/dksih/QBM/2023/12/14/3388901252603904/3389081626116096/STEM/db4cbdc765054195a84bec305037bfea.png?resizew=334)
(1)当
时,请直接写出点
的坐标;
(2)
关于
的函数解析式为
,其图象如图2所示,结合图1、2的信息,求出
与
的值;
(3)在
上是否存在点A,使得
是直角三角形?若存在,请求出此时点A的坐标和
的面积;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb51096f4d54ad3cc2aa72a26151904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9f9375b79d1c2591bef9c147a9c441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd2d246f0850db73fe2e6b1e26eb549.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/fb0e705301752424a492f6277ed7774e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3c8c0d7a9eebcf92e49659a58a0a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://img.xkw.com/dksih/QBM/2023/12/14/3388901252603904/3389081626116096/STEM/db4cbdc765054195a84bec305037bfea.png?resizew=334)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486d75d269000f65978a4922abdd53f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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6 . 如图,在Rt
中,
平分
交
于点
为
上一点,经过点
的
分别交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/5f6dc370-6dbc-4580-a2dc-6fbb6c4796ce.png?resizew=153)
(1)求证:
是
的切线;
(2)若
,求
的半径;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbfec790ed848aa4f51dca80b2d4919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed5ea3e7db5a6943f2915d32339709c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ee159aea403220848b14b8e81dc20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adaa82a6500e3a95a24168f7df243790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ae536809b1161fd4e83fdc7f42be96.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/5f6dc370-6dbc-4580-a2dc-6fbb6c4796ce.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881f21399c7da4e1761450e88ccb19c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e6dfdb4e5049440c2ad0ec5eed5f63.png)
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7 . 已知:如图,一次函数的图象与反比例函数的图象交于
两点,与
轴正半轴交于点
,与
轴负半轴交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/69df1a9f-7667-4af0-a9bf-563fe150edb7.png?resizew=176)
(1)求反比例函数的解析式;
(2)当
时,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c25b1fd10831f3aed13a862aa93e24.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/69df1a9f-7667-4af0-a9bf-563fe150edb7.png?resizew=176)
(1)求反比例函数的解析式;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc27da9d3158ea1caeaac45618a09b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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8 . 如图,点
为
中点,分别延长
到点
到点
,使
.以点
为圆心,分别以
为半径在
上方作两个半圆.点
为小半圆上任一点(不与点
重合),连接
并延长交大半圆于点
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/1ddf5ce2-4468-4d8c-b5ec-b71201674b43.png?resizew=390)
(1)①求证:
;
②写出
和
三者间的数量关系,并说明理由.
(2)若
,当
最大时,直接指出
与小半圆的位置关系,并求此时
(答案保留
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa48616f1944739471d03422859b8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cbad6599796efc1c177ae9349feda9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8044faecc4d5a611814a7f1e64dbf8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f0cb663c82fc5de837fa273f983ce8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/1ddf5ce2-4468-4d8c-b5ec-b71201674b43.png?resizew=390)
(1)①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb0368d6e9824a085e5b41c2da993d7.png)
②写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497b955fd8c7d39a388ed329624d9bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b6aed6102edbc4138df13cba9c264b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637f7d8b87adc59c9b06b09803a06553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
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9 . 用承重指数
衡量水平放置的长方体木板的最大承重量.实验室有一些同材质同长同宽而厚度不一的木板,实验发现:木板承重指数
与木板厚度
(厘米)的平方成正比,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/bb308bd5-f038-4a2e-a582-60444187cc90.png?resizew=208)
(1)求
与
的函数关系式.
(2)如图,选一块厚度为6厘米的木板,把它分割成与原来同长同宽但薄厚不同的两块板(不计分割损耗).设薄板的厚度为
(厘米),
.
①求
与
的函数关系式;
②x为何值时,Q是
的3倍?[注:(1)及(2)中的①不必写x的取值范围].
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdde9539c359cd6f4793fd8190cecd44.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/bb308bd5-f038-4a2e-a582-60444187cc90.png?resizew=208)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)如图,选一块厚度为6厘米的木板,把它分割成与原来同长同宽但薄厚不同的两块板(不计分割损耗).设薄板的厚度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d39f07fccf84bab725f45497e29a01.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②x为何值时,Q是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26398218820ab57e8c6b414c6ff1db6.png)
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10 . 如图,甲、乙两人(看成点)分别在数轴
和5的位置上,沿数轴做移动游戏.每次移动游戏规则:
裁判先捂住一枚硬币,再让两人猜向上一面是正是反,而后根据所猜结果进行移动.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a3aa0688-0ca3-4788-bdea-948bf41104cd.png?resizew=233)
①若都对或都错,则甲向东移动1个单位,同时乙向西移动1个单位;
②若甲对乙错,则甲向东移动4个单位,同时乙向东移动2个单位;
③若甲错乙对,则甲向西移动2个单位,同时乙向西移动4个单位.
(1)经过第一次移动游戏,求甲的位置停留在正半轴上的概率
;
(2)从如图的位置开始,若完成了10次移动游戏,发现甲、乙每次所猜结果均为一对一错.设乙猜对
次,且他最终停留的位置对应的数为
,试用含
的代数式表示
,并求该位置距离原点
最近时
的值;
(3)从如图的位置开始,若进行了
次移动游戏后,甲与乙的位置相距2个单位,直接写出
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
裁判先捂住一枚硬币,再让两人猜向上一面是正是反,而后根据所猜结果进行移动.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a3aa0688-0ca3-4788-bdea-948bf41104cd.png?resizew=233)
①若都对或都错,则甲向东移动1个单位,同时乙向西移动1个单位;
②若甲对乙错,则甲向东移动4个单位,同时乙向东移动2个单位;
③若甲错乙对,则甲向西移动2个单位,同时乙向西移动4个单位.
(1)经过第一次移动游戏,求甲的位置停留在正半轴上的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)从如图的位置开始,若完成了10次移动游戏,发现甲、乙每次所猜结果均为一对一错.设乙猜对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)从如图的位置开始,若进行了
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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