1 .
:若
,则
;
:_____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f735290691112deb4686a0b4e05ae7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d367a8feeea3de8199efbb404be16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc1bb9d53a27d484396ad74d6a26e0.png)
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2023-11-03更新
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182次组卷
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2卷引用:广东省2024年普通高中学业水平合格性考试考前冲刺数学试题三
2 . 幸福指数是衡量人们对自身生存和发展状况的感受和体验,即人们的幸福感的一种指数.某机构从某社区随机调查了10人,得到他们的幸福指数(满分:10分)分别是7.6,8.5,7.8,9.2,8.1,9,7.9,9.5,8.3,8.8,则这组数据的中位数是
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2023-04-30更新
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959次组卷
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6卷引用:2024年广东省普通高中学业水平合格性考试模拟(三)数学试题
2024年广东省普通高中学业水平合格性考试模拟(三)数学试题四川省资阳市2023届高考适应性考试数学(理科)试题四川省资阳市2023届高考适应性考试数学(文科)试题贵州省2023届高三下学期联合考试数学(理)试题辽宁省辽阳市2023届高三二模数学试题(已下线)第九章 统计 单元复习提升-单元速记·巧练(人教A版2019必修第二册)
解题方法
3 . 阅读下面题目及其解答过程.
如图,在直三棱柱
中,
,D,E分别为BC,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/d053b157-0829-465a-b6dc-3ea9c85cb713.png?resizew=138)
(1)求证:
平面
;
(2)求证:
.
解:(1)取
的中点F,连接EF,FC,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/0a94878a-2f4f-4376-980a-eaccd4e4ed9b.png?resizew=139)
在
中,E,F分别为
,
的中点,
所以
,
.
由题意知,四边形
为 ① .
因为D为BC的中点,所以
,
.
所以
,
.
所以四边形DCFE为平行四边形,
所以
.
又 ② ,
平面
,
所以,
平面
.
(2)因为
为直三棱柱,所以
平面ABC.
又
平面ABC,所以 ③ .
因为
,且
,所以 ④ .
又
平面
,所以
.
因为 ⑤ ,所以
.
以上题目的解答过程中,设置了①~⑤五个空格,如下的表格中为每个空格给出了两个选项,其中只有一个符合逻辑推理.请选出符合逻辑推理的选项,并填写在答题卡的指定位置(只需填写“A”或“B”).
如图,在直三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/d053b157-0829-465a-b6dc-3ea9c85cb713.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874eca4abea481fa84eb772a920f9c7.png)
解:(1)取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/0a94878a-2f4f-4376-980a-eaccd4e4ed9b.png?resizew=139)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac03bd962f6fbfecb16b558f3c374784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfbf154e19cbd0580d58ccc9bac077c.png)
由题意知,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
因为D为BC的中点,所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1ab54c55e934d0263f0aa33acb6116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d0463b6e3d27b5cfc1df0e6c14fbef.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70099a8a0e7cff25485a63e8811a6aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeeadcae4a2964c73187962918724ae7.png)
所以四边形DCFE为平行四边形,
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dced11455b3e31a9090915f80a046fa3.png)
又 ② ,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e3ffd599e4fb57893b141bad96c66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
所以,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be509ef5101aae24609ff9941cb246fc.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83499936f532ddce9068dd1ff8eb2b01.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e3ffd599e4fb57893b141bad96c66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f76925ed99b7172956319974258a9b.png)
因为 ⑤ ,所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874eca4abea481fa84eb772a920f9c7.png)
以上题目的解答过程中,设置了①~⑤五个空格,如下的表格中为每个空格给出了两个选项,其中只有一个符合逻辑推理.请选出符合逻辑推理的选项,并填写在答题卡的指定位置(只需填写“A”或“B”).
空格序号 | 选项 |
① | A.矩形 B.梯形 |
② | A.![]() ![]() ![]() ![]() |
③ | A.![]() ![]() |
④ | A.![]() ![]() ![]() ![]() |
⑤ | A.![]() ![]() |
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4 . 某校初一年级共有三个班,为了解课外阅读情况,随机抽取部分学生调查他们一周的课外阅读时长(单位:小时),整理数据得到下表:
①设样本中1班数据的均值为
,2班数据的均值为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b915ea3069054b7389cee9827dd613c.png)
______
(填“>”或“<”);
②设样本中2班数据的方差为
,3班数据的方差为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1295cbd36fdc55a55b549aa2dd5887.png)
______
(填“>”或“<”).
1班 | 8 | 9 | 10 | 11 | 11 | 15 | |
2班 | 7 | 7 | 8 | 9 | 9 | 11 | 12 |
3班 | 5 | 7 | 9 | 9 | 9 | 10 | 14 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b915ea3069054b7389cee9827dd613c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55ec3fc6a2a218803229a6fe3ab2679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b915ea3069054b7389cee9827dd613c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55ec3fc6a2a218803229a6fe3ab2679.png)
②设样本中2班数据的方差为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1295cbd36fdc55a55b549aa2dd5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f314812ee1e19b4e15c505afc40935c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1295cbd36fdc55a55b549aa2dd5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f314812ee1e19b4e15c505afc40935c.png)
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5 . 1796年,年仅19岁的高斯发现了正十七边形的尺规作图法,要用尺规作出正十七边形就要将圆十七等分,高斯墓碑上刻着如图所示的图案.设将圆十七等分后每等份圆弧所对的圆心角为
,则
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8583196f0892a0ac6abad30ff6e514.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/1832986e-a3c0-4159-a0ec-cb7ecbd16851.png?resizew=199)
您最近一年使用:0次
2022-10-11更新
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369次组卷
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2卷引用:广东省2024年普通高中学业水平合格性考试考前冲刺数学试题三
6 . 对于温度的计量,世界上大部分国家使用摄氏温标(
),少数国家使用华氏温标(
),两种温标间有如下对应关系:
根据表格中数值间呈现的规律,给出下列三个推断:
①
对应
;
②
对应
;
③存在某个温度,其摄氏温标的数值等于其华氏温标的数值.
其中所有正确推断的序号是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de96374212b9a5df820d78d10e7d1291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2e6f453529f67d47029e676e101fa1.png)
摄氏温标(![]() | … | 0 | 10 | 20 | 30 | 40 | 50 | … |
华氏温标(![]() | … | 32 | 50 | 68 | 86 | 104 | 122 | … |
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7889f265b1bac6f19624eb93f5dbdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e84f0752917be8193ae8904597eb93.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3ee57b9d71d700e78f43ed84d11e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce05b7fe7399da4f3b66f05f6bdf8b8.png)
③存在某个温度,其摄氏温标的数值等于其华氏温标的数值.
其中所有正确推断的序号是
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7 . 从6种不同的蔬菜种子
,
,
,
,
,
中选出4种,分别种在4块不同的土壤
,
,
,
中进行试验,已有资料表明
土壤不宜种植
,
土壤不宜种植
,但
、
品种产量高.现
、
品种必种的试验方案有________ 种.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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