名校
1 . 在初中阶段的函数学习中,我们经历了“确定函数的表达式—利用函数图象研究其性质”函数图象在探索函数的性质中有非常重要的作用,下面我们对已知经过点
的函数
的图象和性质展开研究.探究过程如下,请补全过程:
(1)①请根据解析式列表,则
______________,
______________;
②在给出的平面直角坐标系中描点,并画出函数图象;
(2)并写出这个函数的一条性质:______________________________;
(3)已知函数
,结合两函数图象,请直接写出当
时,自变量
的取值范围_________________________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c63f9522aa44add2a2d3c2acd6a795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dd24e3a83a7663f0c4dd1cb9246170.png)
![]() | ![]() | ![]() | ![]() | ![]() | 0 | 1 | 7 | 9 | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | 0 | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
②在给出的平面直角坐标系中描点,并画出函数图象;
(2)并写出这个函数的一条性质:______________________________;
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56e2ad86ac48fd306494bb31bc34410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df86b0da538701c08fb214608e062372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/ca763303-c888-4fda-bc12-41480bd051e1.png?resizew=419)
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2 . 如图,四边形
是平行四边形,E为
上任意一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/4/304dd5a3-182e-480a-a5e2-7e448d05a2b3.jpg?resizew=323)
(1)如图①,只用无刻度的直尺在
边上作出点F,使
;
(2)如图②,用直尺和圆规作出菱形
,使得点F、G、H分别在边
、
、
上.(不写作法,只保留作图痕迹)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/4/304dd5a3-182e-480a-a5e2-7e448d05a2b3.jpg?resizew=323)
(1)如图①,只用无刻度的直尺在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f40b3bf6b27f936e0747de92151a1f77.png)
(2)如图②,用直尺和圆规作出菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
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3 . 如图,在菱形
中,按以下步骤作图:
①分别以点
和点
为圆心,大于
为半径作弧,两弧交于点
,
;
②作直线
,且
恰好经过点
,与
交于点
,连接
.
则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/8336477d-95ea-42ae-aae2-c11300d92562.png?resizew=179)
①分别以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b840be5852709e18ea985954545e78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
②作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
则下列说法正确的是( )
A.![]() | B.![]() |
C.若![]() ![]() | D.![]() |
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4 . 如图,四边形ABCD为菱形,延长AB至点E,使得BE=AB,过点E作EF∥AD,交DB的延长线于点F,请仅用无刻度直尺 按下列要求作图(保留作图痕迹).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/14/b8790470-7046-45c0-a687-15c24433c674.png?resizew=404)
(1)在图1中,过BD的中点作直线l∥AE.
(2)在图2中,作出一个矩形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/14/b8790470-7046-45c0-a687-15c24433c674.png?resizew=404)
(1)在图1中,过BD的中点作直线l∥AE.
(2)在图2中,作出一个矩形.
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5 . 如图,已知钝角
,依下列步骤尺规作图,并保留作图痕迹.
步骤1:以
为圆心,以
为半径画弧①;
步骤2:以
为圆心,以
为半径画弧②,交弧①于点
;
步骤3:连接
,再连接
,与
的延长线交于点
.
下列叙述正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/e1e792ac-50ed-4f26-8e10-3364c6767ad2.png?resizew=145)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
步骤1:以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
步骤2:以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
步骤3:连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb9b29668bafeccf32ca33022e96d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
下列叙述正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/e1e792ac-50ed-4f26-8e10-3364c6767ad2.png?resizew=145)
A.![]() ![]() | B.![]() ![]() |
C.![]() | D.![]() |
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解题方法
6 . 小说《三体》中的“水滴”是三体文明派往太阳系的探测器,由强相互作用力材料制成,被形容为“像一滴圣母的眼泪”.小刘是《三体》的忠实读者,他利用几何作图软件画出了他心目中的水滴(如图),由线段AB,AC和优弧BC围成,其中BC连线竖直,AB,AC与圆弧相切,已知“水滴”的水平宽度与竖直高度之比为
,则
( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/1/2dc78718-ea0e-4b87-b152-32411da60648.png?resizew=299)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d297eab7380f6a28ec010218d9ab4ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a27dc396251a4453094d19baa79816.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/1/2dc78718-ea0e-4b87-b152-32411da60648.png?resizew=299)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-02-09更新
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16卷引用:辽宁省实验中学2022-2023学年高二实验班上学期期初测试数学试题
辽宁省实验中学2022-2023学年高二实验班上学期期初测试数学试题广东省潮汕地区精英名校2022届高三第一次联考数学试题福建省莆田第二中学2022届高三3月模拟考数学试题(已下线)押新高考第10题 三角函数-备战2022年高考数学临考题号押题(新高考专用)江苏省南通市海安市曲塘中学2021-2022学年高一下学期期中数学试题辽宁省大连育明高级中学2022届高三第一次模拟考试数学试卷广东省广州市铁一中学等三校2022届高三三模联考数学试题山东省济南市第一中学2021-2022学年高一下学期5月月考数学试题湖北省部分重点中学(六校)2021-2022学年高一下学期五月联考数学试题山东省德州市第一中学2021-2022学年高一下学期6月月考数学试题(已下线)5.7三角函数的应用B卷江苏省宿迁市北大附属宿迁实验学校2022-2023学年高三上学期11月期中数学试题湖北省十堰市郧阳中学2021-2022学年高一下学期6月月考数学试题5.7 三角函数的应用练习(已下线)第五章 三角函数单元测试基础卷-人教A版(2019)必修第一册(已下线)第六章 突破立体几何创新问题 专题一 跨学科交汇问题 微点1 跨学科交汇问题(一)【培优版】
名校
解题方法
7 . 如图为一块直四棱柱木料,其底面ABCD满足:
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/5eff88d9-bb16-415a-a4ff-583715036902.png?resizew=161)
(1)要经过平面
内的一点P和棱
将木料锯开,在木料表面应该怎样画线?(借助尺规作图,并写出作图说明,无需证明)
(2)若
,
,当点P在点C处时,求直线AP与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/5eff88d9-bb16-415a-a4ff-583715036902.png?resizew=161)
(1)要经过平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8745717601cd14b46c2298919b41b502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f9660760804ff01bbc9319b7342191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
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|
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3卷引用:福建省安溪一中、养正中学、惠安一中、泉州实验中学四校2023-2024学年高三下学期返校联考数学试题
福建省安溪一中、养正中学、惠安一中、泉州实验中学四校2023-2024学年高三下学期返校联考数学试题吉林省吉林市2021-2022学期高三上学期第二次调研测试数学(理)试题(已下线)模块一 专题2 A 空间向量的应用基础卷 期末终极研习室高二人教A版
8 . 如图,在
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/c26f151d-4ae2-44f3-862b-25026d6c8f61.png?resizew=159)
(1)尺规作图:按要求完成下列作图,不写做法,保留作图痕迹,并标明字母.作
的平分线交
于点F,连接
、
;
(2)在(1)的条件下,若
,
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42218a68301d770accaaefb96b19f8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/c26f151d-4ae2-44f3-862b-25026d6c8f61.png?resizew=159)
(1)尺规作图:按要求完成下列作图,不写做法,保留作图痕迹,并标明字母.作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1164750466d461f0a415d3a6407589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aea80060d179ec1e88b0db7d88c13a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcae9d00980803e5955228d1e217abe.png)
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9 . 如图是
的正方形网格,请仅用无刻度的直尺按要求完成以下作图(保留作图痕迹).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/40e9dd31-8997-4273-885f-5b1f0800ded1.png?resizew=229)
(1)在图1中作
的角平分线;
(2)在图2中过点
作一条直线
,使点
,
到直线
的距离相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb9d60d456560e9bac66c8b20c49bb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/40e9dd31-8997-4273-885f-5b1f0800ded1.png?resizew=229)
(1)在图1中作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
(2)在图2中过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
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10 . 如图,四边形
是平行四边形,
是对角线
(1)基本尺规作图:过点
作
于点
,再在线段
上截取
.(尺规作图,保留作图痕迹,不写作法)
(2)连接
、
、
,猜想四边形
的形状,将下面的推理过程补充完整.
证明:∵四边形
是平行四边形,
∴
,①__________,
∴
.
在
和
中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72179b99f0b14e4e04214adbb0c02bc7.png)
∴
,
∴
,②___________.
∴
.
∴③__________
∴四边形
是④__________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/f66a9bfd-cb31-451c-9aff-c00ef3f283f4.png?resizew=169)
(1)基本尺规作图:过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d320f180419175d75eebc618cc458b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607cfabc1d421835b6b64109ad18f571.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2330c01a4d2b5b20f106e3e48834d5c0.png)
证明:∵四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb27272b4eb9ed057dd3b4d40697e7c.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e1dc3473ec67beb52aaaba5645cacb.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df7626240940eb340420a605e95aeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72179b99f0b14e4e04214adbb0c02bc7.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d99bb3ab66b8884bf23cffe1bddcb33.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc61ded2b8ea5dea2fd9bc17c409a59c.png)
∴③__________
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466a12cf2d11494ec4f7173e904932a9.png)
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