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1 . 古希腊数学家阿波罗尼斯与欧几里得、阿基米德齐名,他发现:“平面内到两个定点A,B的距离之比为定值
的点的轨迹是圆”.人们将这个圆以他的名字命名为阿波罗尼斯圆,简称阿氏圆.在平面直角坐标系
中,
,点P满足
.设点
的轨迹为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6d06ad6919d8cdfba88350d35d2a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589402e5266963ba0ed077618c22212e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df5d30e4268a4b86a4e098e8cb57da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.圆![]() ![]() | B.轨迹圆![]() ![]() |
C.在![]() ![]() ![]() | D.当![]() ![]() ![]() ![]() ![]() |
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5卷引用:四川省雅安市雅安中学2022-2023学年高二上学期期中数学试题
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2 . 如图所示,在某体育场上,写有专用字体“一”、“起”、“向”、“未”、“来”的五块高度均为2米的标语牌正对看台(B点为看台底部)由近及远沿直线依次竖直摆放,分别记五块标语牌为
,
,…,
,且
米.为使距地面6米高的看台第一排A点处恰好能看到后四块标语牌的底部,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/8fda4b0f-a7fc-4f66-a01f-20b39028f372.png?resizew=635)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82482c50f0eb9786dcaf880fbd7c24f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a2ac80f00802614863923e1acf580b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fe0bd76f9698304c0b65da43a68d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81b05392d956dab7f1302f2f5e3d2a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1975e9d976d75976fd74113752b97dc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/8fda4b0f-a7fc-4f66-a01f-20b39028f372.png?resizew=635)
A.40.5米 | B.54米 | C.81米 | D.121.5米 |
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6卷引用:四川省雅安市天立高级中学2023届高三上学期9月月考数学(理)试题
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解题方法
3 . 我国古代数学家秦九韶在《数书九章》中给出了三角形面积的求法:“以小斜幂并大斜幂减中斜幂,余半之,自乘于上.以小斜幂乘大斜幂减上,余四约之,为实.一为从隅.开平方得积.”如果把以上这段文字写成公式,就是
.根据此公式,
中,角A,B,C的对边分别为a,b,c,若
,且
,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bd5fefb9a7c618d1ef8d73b3c43cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48dd098065edd3c3df70bfb7cfcdf8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5223b3e0e9aec0f301237559d3bd1746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.1 | B.![]() | C.![]() | D.2 |
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4卷引用:四川省雅安中学2021-2022学年高一下学期4月月考数学试题
4 . 造纸术是我国古代四大发明之一,现在我国纸张的规格采用国际标准,常用的
复印纸是幅面采用A系列的
,
,
,…,
规格的一种.其中A系列的幅面规格为:①
规格的纸张的幅宽(用
表示)和长度(用
表示)的比例关系是
;②将
纸张沿长度方向对开成两等分,便成为
规格.将
纸张沿长度方向对开成两等分,便成
规格.……,如此继续对开,得到一张
纸的面积为
,则一张
纸的面积为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249b92e30f3808f5287db70a9eec6a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2f35137e52ec64072635be05605325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edc116345359d7f2b9a4519de2534f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
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5卷引用:四川省雅安市2022届高三第二次诊断性考试数学(理工)试题
5 . 中国古代十进制的算筹记数法在世界数学史上是一个伟大的创造.据史料推测,算筹最晚出现在春秋晚期或战国初年.算筹记数的方法是:个位、百位、万位、…上的数按纵式的数码摆出;十位、千位、十万位、…上的数按横式的数码摆出,如
可用算筹表示为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/3d3b4f2f-5bad-495d-8dc7-a8f51473edd0.png?resizew=329)
这
个数字的纵式与横式的表示数码如图所示,则
的运算结果用算筹表示为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c3d58b919ccf9c1c6bd83438147353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/7626f766-64ba-420d-9344-c03301905c82.png?resizew=79)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/3d3b4f2f-5bad-495d-8dc7-a8f51473edd0.png?resizew=329)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab67110bf0d4aac0c1e5c0e0c337de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e275490038d66b2f46d1b9aa596e9be3.png)
A.![]() ![]() ![]() ![]() | B.![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() | D.![]() ![]() ![]() |
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2卷引用:四川省雅安市2021-2022学年高一上学期期末数学试题
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解题方法
6 . 若函数
的定义域为
,集合
,若存在非零实数
使得任意
都有
,且
,则称
为
上的
-增长函数.
(1)已知函数
,函数
,判断
和
是否为区间
上的
增长函数,并说明理由;
(2)已知函数
,且
是区间
上的
-增长函数,求正整数
的最小值;
(3)如果
是定义域为
的奇函数,当
时,
,且
为
上的
增长函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe5fa85f3ebdfca5b2c131582e54bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137e19310362e379bd5943525b715aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa744c6019195b4edcd21bde5784ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253893d2bf2b944a6de271463c3e7929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222db87c8bf85e4548488f09e2d9dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f6a0eff55217e08cd9c7268ef3eecb.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a1551eabdbfb3d6f089b24fa651bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d94112851ce0deb4761bf00fcf275ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33653e42ded81460f3ae0777a786dcfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92b46d50ecc7ea20c610d9b1217582e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4卷引用:四川省雅安市2021-2022学年高一上学期期末数学试题
四川省雅安市2021-2022学年高一上学期期末数学试题福建省厦门双十中学2022-2023常年高一上学期期中考试数学试题(已下线)第3章 函数概念与性质(基础、典型、新文化、易错、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)上海市杨浦区控江中学2020-2021学年高一上学期期末数学试题