解题方法
1 . 勒洛三角形是具有类似圆的“定宽性”的曲线,它是由德国机械工程专家、机构运动学家勒洛首先发现,其作法是:以等边三角形每个顶点为圆心,以边长为半径,在另两个顶点间作一段弧,三段弧围成的曲边三角形就是勒洛三角形.如图中的两个勒洛三角形,它们所对应的等边三角形的边长比为1:3,若从大的勒洛三角形中随机取一点,则此点取自小勒洛三角形内的概率是( )
![](https://img.xkw.com/dksih/QBM/2020/8/3/2520096770760704/2520810598187008/STEM/a0a51077f1314456a7a27720e23fe3e8.png?resizew=161)
![](https://img.xkw.com/dksih/QBM/2020/8/3/2520096770760704/2520810598187008/STEM/a0a51077f1314456a7a27720e23fe3e8.png?resizew=161)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
2 . 已知二项式
的展开式中各项系数和为256,则展开式中的常数项为____ . (用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b8fd66aad0af53b6e24dbe06ce42ad.png)
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2020-08-04更新
|
57次组卷
|
7卷引用:山西省阳泉市2020届高三下学期第二次质量调研数学(理)试题
山西省阳泉市2020届高三下学期第二次质量调研数学(理)试题甘肃省兰州第一中学2018届高三上学期第二次月考(9月)数学(理)试题2020届甘肃省天水市第一中学高三上学期第四次段考数学(理)试题四川省棠湖中学2019-2020学年高三下学期第二次月考数学(理)试题(已下线)专题14 计数原理-2020年高考数学(理)母题题源解密(全国Ⅱ专版)(已下线)专题14 二项式定理-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)考点46 利用二项定理求指定项【理】-备战2022年高考数学典型试题解读与变式
3 . 已知对任意平面向量
,把
绕其起点沿逆时针方向旋转
角得到向量
,叫做把点
绕点
逆时针方向旋转
角得到点
.已知平面内点
,点
.把点
绕点
顺时针方向旋转
后得到点
,则点
的坐标是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06704dc348f0a735d68e540f47ca4c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c47514dc018f6ebc777d6fbeaa16ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cf5bee8eda1ab58237f8854bd22c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知数列
中,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63af91fc49514262e581246dfb72d831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5c81c886e0a331a1ad7f390d221e167.png)
A.![]() | B.![]() | C.![]() | D.5051 |
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5 . 已知集合
,
,若
,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e08ce327873f44d538f0dd07b5cdc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd2e1c54c53f7b1a4eff95c396d1bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知函数
.
(Ⅰ)求函数
的最小值
;
(Ⅱ)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b4295218b23077b487fbf0b218c8da.png)
(Ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8839d8bbe4778a5b66ec04f461f4794a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef5ee12526e91cf79494ea3aafcffb1.png)
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解题方法
7 . 已知函数
,
为
的导数.
(1)求
的最值;
(2)若
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d923352b287a54a572aff22639039ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd8b21dd75c69bb9da9a9efe2e64cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc2ccaad45af8bfcfcedfeb7149ed5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 在传染病学中,通常把从致病刺激物侵入机体或者对机体发生作用起,到机体出现反应或开始呈现该疾病对应的相关症状时止的这一阶段称为潜伏期.
(1)一研究团队统计了某地区1000名患者的相关信息,得到如下表格,
该传染病的潜伏期受诸多因素影响,为研究潜伏期与患者年龄的关系,以潜伏期是否超过6天为标准进行分层抽样,从上述1000名患者中抽取200人,得到如下列联表,请将列联表补充完整,并根据列联表判断是否有95%的把握认为潜伏期与患者年龄有关
(2)以这1000名患者的潜伏期超过6天的频率,代替该地区1名患者潜伏期超过6天发生的概率,每名患者的潜伏期是否超过6天相互独立.为了深入研究,该研究团队随机调查了20名患者,其中潜伏期超过6天的人数最有可能(即概率最大)是多少?
附:下面的临界值表仅供参考.
(参考公式:
,其中
.)
(1)一研究团队统计了某地区1000名患者的相关信息,得到如下表格,
潜伏期(单位:天) | [0,2] | (2,4] | (4,6] | (6,8] | (8,10] | (10,12] | (12,14] |
人数 | 85 | 205 | 310 | 250 | 130 | 15 | 5 |
潜伏期≤6天 | 潜伏期>6天 | 总计 | |
50岁以上(含50岁) | 100 | ||
50岁以下 | 55 | ||
总计 | 200 |
附:下面的临界值表仅供参考.
![]() | 0.05 | 0.025 | 0.010 |
![]() | 3.841 | 5.024 | 6.635 |
(参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
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解题方法
9 . 如图,在四棱锥
中,底面
是正方形,
底面
,
,
、
分别是
、
上的点,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/278b5f8e-390e-401c-afc2-f34a097f3b21.png?resizew=175)
(Ⅰ)求证:
为
的中点;
(Ⅱ)当
与平面
所成的角最大时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbdc5a132d35551a980fcef4e7ea5b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36222db36e348661eb5f616820e4e60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/278b5f8e-390e-401c-afc2-f34a097f3b21.png?resizew=175)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57e0d440e8ccf29fe5f9b3605ad27ca.png)
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10 . 如图,在四面体
中,
、
分别是
、
的中点,
、
分别是
和
上的动点,且
与
相交于点
.下列判断中:
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498164163747840/2500042567884800/STEM/e48999ab93354a97a487cabcb5059cfd.png?resizew=328)
①直线
经过点
;
②
;
③
、
、
、
四点共面,且该平面把四面体
的体积分为相等的两部分.
所有正确的序号为
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498164163747840/2500042567884800/STEM/e48999ab93354a97a487cabcb5059cfd.png?resizew=328)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c6af53069897ada75e91c431645860.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
所有正确的序号为
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