2024高三·全国·专题练习
1 . 魏晋时刘徽撰写的《海岛算经》是关测量的数学著作,其中第一题是测海岛的高.如图,点
,
,
在水平线
上,
和
是两个垂直于水平面且等高的测量标杆的高度,称为“表高”,
称为“表距”,
和
都称为“表目距”,
与
的差称为“表目距的差”,则海岛的高
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e5f736b1195fef1d2d300168a795f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e5f736b1195fef1d2d300168a795f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024高一下·全国·专题练习
2 . 如图,
不共面,且
且相等,
且相等,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0247b63d3f3cc573a24ba0036899c96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e725362f254f8f39245bd3ed311d6d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2bb400160da0da6df6abbaa5fa0f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5c70782c77be805de33099687afc07.png)
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名校
3 . 某学校附近有条长500米,宽6米的道路(如图1所示的矩形ABCD),路的一侧划有100个长5米,宽2.5米的停车位(如矩形AEFG),由于停车位不足,放学时段道路拥堵,学校安保处李老师提出一个改造方案,在不改变停车位形状大小、不改变汽车通道宽度的条件下,可通过压缩道路旁边绿化带及改变停车位方向来增加停车位,记绿化带被压缩的宽度
(米),停车位相对道路倾斜的角度度
,其中
.
,求
和
的长;
(2)求d关于
的函数表达式
;
(3)若
,按照李老师的方案,该路段改造后的停车位比改造前增加多少个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990a3680645f22737907fc1b5b10d99a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb60187001a6a7bbf887d2a233e5e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09463dc187d5b2574170f1566ac4c382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9088e31e00eaa4e95c1e6717b0c82cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827be85b8f921007a5cf9edb64bd3491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c495fd86e62c3090caba0702bbcffd7.png)
(2)求d关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f74946c4e57365e0de85d277ba8d2a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f2572192cc7ca046e9a3155ef3e56a.png)
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4 . 嘌呤是一种杂环有机化合物,它在能量的供应、代谢的调节等方面都有十分重要的作用,它的化学结构式主要由一个正五边形与一个正六边形构成(设它们的边长均为1),其平面图形如图所示,则( )
A.![]() | B.O到AC的距离是![]() |
C.O是![]() | D.![]() |
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2024-03-14更新
|
895次组卷
|
5卷引用:情境4 重视学科交叉
(已下线)情境4 重视学科交叉(已下线)解三角形-综合测试卷B卷广东省燕博园2024届高三下学期3月综合能力测试(CAT联考)数学试题广东省佛山市南海西樵高级中学2024届高三下学期3月综合能力测试数学试题广东省东莞市东莞中学松山湖学校2023-2024学年高一下学期第一次段考数学试题
2024高三·全国·专题练习
5 . 在
中,已知
为
中内一点,满足
,则
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85e50101a5b7eb2e91b1daa2e235fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804cecc86fb704c51897247a7c864db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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6 . 如图是体育公园步道示意图.从A处测得点B在北偏东
,测得点C在北偏东
,在点C处测得点B在北偏西
,
米.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/ba937be0-418e-491a-9371-8d9f206d1e3f.png?resizew=173)
(1)求步道
的长度(结果保留根号);
(2)游客中心Q在点A的正东方向,步道
与步道
交于点P,测得
,小明和爸爸分别从B处和A处同时出发去游客中心,小明跑步的速度是每分钟
米,请计算说明爸爸的速度要达到每分钟多少米,他俩可同时到达游客中心.(结果精确到0.1)(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a4c9b697e3df2b5469b71d3b5e47a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f194bc021c012d8f373535be3c249e23.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/ba937be0-418e-491a-9371-8d9f206d1e3f.png?resizew=173)
(1)求步道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)游客中心Q在点A的正东方向,步道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9caf47639ff9218ef27068ee10c265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda23637a152ef2a22245957e16cc5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52881be613aa404e553da30d8987cfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb3f35e3db7c1f3a3dd3eb20151b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dad09268b7cb8bfcbea010cb6d2a29e.png)
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7 . 阅读理解:高斯上小学时,有一次数学老师让同学们计算“从1到100这100个正整数的和”.许多同学都采用了依次累加的计算方法,计算起来非常烦琐,且易出错.聪明的小高斯经过探索后,给出了下面漂亮的解答过程.
解:设
①,则
②,
①+②,得
.
(两式左右两端分别相加,左端等于2S,右端等于100个101的和)
所以
,
③,所以
.
后来人们将小高斯的这种解答方法概括为“倒序相加法”
计算:
= _____ .
解:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d05f7125540086a961efd2afddb588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4663fd551144091fcd826a6ecd7a9603.png)
①+②,得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6800c25d59d4bf730f469ce16412a7fe.png)
(两式左右两端分别相加,左端等于2S,右端等于100个101的和)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46540f510d1f3537e0453ebb1bd6e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9c674c761493e544d7af9bb5046a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac52232d822e91ac25df49702ba8c71.png)
后来人们将小高斯的这种解答方法概括为“倒序相加法”
计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d7c6e74c5501a04785b710ffe91ec6.png)
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8 . 如图,以
的两边
分别向外作等边
和等边
,
与
交于点P,已知
.
![](https://img.xkw.com/dksih/QBM/2024/1/22/3416677041340416/3419628471492608/STEM/2813bd9be9c047ab9beded363954ed75.png?resizew=156)
(1)求证:
;
(2)求
的度数及
的长;
(3)若点Q、R分别是等边
和等边
的重心(三边中线的交点),连接
,作出图象,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d54431bbb28ebd98db5c1dc6083a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97898c0102c6bc620abb5ab7442550bf.png)
![](https://img.xkw.com/dksih/QBM/2024/1/22/3416677041340416/3419628471492608/STEM/2813bd9be9c047ab9beded363954ed75.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ccd24d1cdb7db9844a4c20c62970a2.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add18fdf2049abff08a687b950f1cc1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(3)若点Q、R分别是等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1168cd6865542e2a2efe6f6f21caa214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
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9 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f328740bf24bfa5307d5ba23cfaac1.png)
(2)已知
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f328740bf24bfa5307d5ba23cfaac1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d227c4e80e72eb343659193a06daff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e28564e8971ee3cd8deb50d1afab24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629abc79d5be8093ee40ef9f6eb19337.png)
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10 . 已知等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8430c0f580ff69646229842c38fab9.png)
(1)若
均为正整数,求
的值;
(2)设
,
分别是分式
中的
取
(
>
>2)时所对应的值,试比较
的大小,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8430c0f580ff69646229842c38fab9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6703fce72e701fd5d9be3e25448d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9724cf149ccc974596673c8aaae9558f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e327c14ae50f0f10478a6c751c26fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a550c916c64f621010e604a30ef67566.png)
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