录入25届周末卷14并关联相似
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"20230503\t王伟叶"
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"20231109\t王伟叶"
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@ -623445,6 +623449,450 @@
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"space": "4em",
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"023296": {
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"id": "023296",
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"content": "某课外小组的同学们从社会实践活动中调查了 20 户家庭某月的用电量, 如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\\hline 用电量/度 & 120 & 140 & 160 & 180 & 200 \\\\\n\\hline 户数 & 2 & 3 & 5 & 8 & 2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n则这 20 户家庭该月用电量的众数和中位数分别是\\bracket{20}.\n\\fourch{180,170}{160,180}{160,170}{180,160}",
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"objs": [],
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"genre": "选择题",
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"023297": {
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"id": "023297",
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"content": "在样本频率分布直方图中, 共有 9 个小长方形, 若中间一个小长方形的面积等于其他 8 个长方形的面积和的 $\\dfrac{2}{5}$,且样本容量为 140 . 则中间一组的频数为\\bracket{20}.\n\\fourch{28}{40}{56}{60}",
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"genre": "选择题",
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"023298": {
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"id": "023298",
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"content": "10 名小学生的身高(单位: $\\mathrm{cm}$ )分成了甲、乙两组数据, 甲组: $115,122,105,111,109$; 乙组: $125,132,115,121,119$ . 两组数据中相等的数字特征是\\bracket{20}.\n\\fourch{中位数、极差}{平均数、方差}{方差、极差}{极差、平均数}",
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"023299": {
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"id": "023299",
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"content": "某校随机抽取 100 名同学进行``垃圾分类''的问卷测试, 测试结果显示这 100 名同学的得分都在 $[50,100]$ 内, 按得分分成 5 组: $[50,60),[60,70),[70,80),[80,90),[90,100]$,得到如图所示的频率分布直方图, 则这 100 名同学的得分的中位数不可能为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.06, yscale = 70]\n\\draw [->] (40,0) -- (42,0) -- (43.5,-0.0025) -- (46.5,0.0025) -- (48,0) -- (115,0) node [below] {得分};\n\\draw [->] (40,0) -- (40,0.05) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (40,0) node [below left] {$O$};\n\\foreach \\i/\\j in {50/0.01,60/0.03,70/0.04,80/0.015,90/0.005}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (10,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {50/0.01,60/0.03,70/0.04,80/0.015,90/0.005}\n{\\draw [dashed] (\\i,\\j) -- (40,\\j) node [left] {$\\k$};};\n\\draw (100,0) node [below] {$100$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$72.5$}{$75$}{$77.5$}{$80$}",
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"023300": {
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"id": "023300",
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"content": "某创业公司共有 36 名职工, 为了了解该公司职工的年龄构成情况, 随机采访了 9 位代表, 得到的数据分别为 $36,36,37,37,40,43,43,44,44$, 若用样本估计总体, 则年龄在 $(\\overline{x}-s, \\overline{x}+s)$ 内的人数占公司人数的百分比是(其中 $\\overline{x}$ 是平均数, $s$ 为标准差, 结果精确到 $1 \\%)$\\bracket{20}.\n\\fourch{$14 \\%$}{$25 \\%$}{$56 \\%$}{$67 \\%$}",
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"genre": "选择题",
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"ans": "",
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"023301": {
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"id": "023301",
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"content": "``一带一路''是``丝绸之路经济带''和``21 世纪海上丝绸之路''的简称, 旨在积极发展我国与沿线国家经济合作关系, 共同打造政治互信、经济融合、文化包容的命运共同体. 自 2013 年以来,``一带一路''建设成果显著. 如图是 2013-2017 年, 我国对``一带一路''沿线国家进出口情况统计图, 下列描述错误的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 1.5, yscale = 0.5]\n\\foreach \\i/\\j in {2013/1,2014/2,2015/3,2016/4,2017/5}\n{\\draw (\\j,0) node [below] {$\\i$年};};\n\\foreach \\i/\\j/\\k in {2/2000/0,4/4000/20,6/6000/40,8/8000/60}\n{\\draw [dashed] (0.5,\\i) node [left] {$\\j$}-- (5.5,\\i) node [right] {$\\k\\%$};};\n\\foreach \\i/\\j/\\k in {1/6.6/6.8,2/7.7/7.3,3/7.5/6,4/7.4/5.7,5/7.6/6.4}\n{\\filldraw [fill = white] (\\i,0) --++ (0,\\j) --++ (-0.2,0) --++ (0,{-\\j});\n\\filldraw [pattern = north east lines] (\\i,0) --++ (0,\\k) --++ (0.2,0) --++ (0,{-\\k});}; \n\\draw (0.5,0) node [left] {$0$} -- (5.5,0) node [right] {$-20\\%$};\n\\draw (1,2.7) -- (2,3.67) -- (3,1.74) -- (4,1.87) -- (5,2.27);\n\\draw [ultra thick] (1,2.9) -- (2,2.73) -- (3,0.22) -- (4,1.5) -- (5,3.23);\n\\draw (7,6.5) rectangle (7.3,6.7);\n\\filldraw [pattern = north east lines] (7,4.5) rectangle (7.3,4.7);\n\\draw (7,2.6) -- (7.3,2.6);\n\\draw [ultra thick] (7,0.6) -- (7.3,0.6);\n\\draw (7.3,6.6) node [right] {出口额};\n\\draw (7.3,4.6) node [right] {进口额};\n\\draw (7.3,2.6) node [right] {出口增速};\n\\draw (7.3,0.6) node [right] {进口增速};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{这五年, 2013 年出口额最少}{这五年, 出口总额比进口总额多}{这五年, 出口增速前四年逐年下降}{这五年, 2017 年进口增速最快}",
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"023302": {
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"id": "023302",
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"content": "《中国诗词大会》是央视推出的一档以``赏中华诗词, 寻文化基因,品生活之美''为宗旨的大型文化类竟赛节目. 某班在班级里开展诗词默写比赛, 班里 40 名学生得分诗句的茎叶图如图所示. 若规定得分不小于 90 的学生得到``诗词达人''称号, 小于 90 且不小于 80 的学生获得``诗词能手''的称号, 现随机抽取一名学生, 则这个学生获得``诗词达人''或``诗词能手''称号的概率是\\blank{50}, 这 40 名学生成绩的第 75 百分位数是\\blank{50}.\n\\begin{center}\\begin{tabular}{c|cccccccccccc}\n9 & 1&2&5&6&8 \\\\\n8 & 0&0&1&2&4&5&7&8 \\\\\n7 & 0&2&2&3&3&3&4&5&5&6&9 \\\\\n6 & 0&2&2&3&4&4&4&5&7&7&8&9 \\\\\n5 & 6&6&8&9\n\\end{tabular}\\end{center}",
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"objs": [],
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"genre": "填空题",
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"ans": "",
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"duration": -1,
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"023303": {
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"id": "023303",
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"content": "已知一组数据 $x_1, x_2, \\cdots, x_{10}$ 的平均数是 $2$, 方差是 $\\dfrac{1}{3}$, 那么另一组数据 $3 x_1-2,3 x_2-2, \\cdots, 3 x_{10}-2$ 的平均数为\\blank{50}, 标准差为\\blank{50}.",
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"genre": "填空题",
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"duration": -1,
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"023304": {
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"id": "023304",
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"content": "已知样本 $x_1, x_2, \\cdots, x_{2021}$ 的平均数和方差分别是 1 和 4 , 若 $y_i=a x_i+b$($i=1,2, \\cdots, 2021$) 的平均数和方差也分别是 1 和 4 , 则 $a^b=$\\blank{50}.",
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"023305": {
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"id": "023305",
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"content": "对某市``四城同创''活动中 800 名志愿者的年龄抽样调查统计后得到频率分布直方图(如图), 但是年龄组为 $[25,30)$ 的数据不慎丢失, 则依据此图可得: \n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.2, yscale = 40]\n\\filldraw [pattern = north east lines] (20,0) rectangle (25,0.01);\n\\filldraw [pattern = north east lines] (30,0) rectangle (35,0.07);\n\\filldraw [pattern = north east lines] (35,0) rectangle (40,0.06);\n\\filldraw [pattern = north east lines] (40,0) rectangle (45,0.02);\n\\draw [->] (15,0) --(16.5,0) -- (17,0.005) -- (18,-0.005) -- (18.5,0)-- (50,0) node [below] {年龄};\n\\draw [->] (15,0) -- (15,0.1) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (15,0) node [below left] {$O$};\n\\foreach \\i in {20,25,30,35,40,45}\n{\\draw [dashed] (\\i,0) node [below] {$\\i$} -- (\\i,0.08);};\n\\foreach \\j in {0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08}\n{\\draw [dashed] (15,\\j) node [left] {$\\j$} -- (45,\\j);};\n\\end{tikzpicture}\n\\end{center}\n(1) $[25,30)$ 年龄组对应小矩形的高度为\\blank{50}.\\\\\n(2) 据此估计该市``四城同创''活动中志愿者年龄在 $[25,35)$ 的人数为\\blank{50}.",
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"023306": {
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"id": "023306",
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"content": "下图为某地区 2008-2020 年地方财政预算内收入、城乡居民储蓄年末余额折线图. 根据该折线图可知, 该地区 2008-2020 年\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.8, yscale = 0.01]\n\\draw (1,48) coordinate (S) (1,1) coordinate (T);\n\\filldraw (T) ++ (-0.05,{-0.05*80}) rectangle ++ (0.1,{0.1*80});\n\\filldraw (S) ++ (0,{-0.07*80}) --++ (-0.07,{0.07*80}) --++ (0.07,{0.07*80}) --++ (0.07,{-0.07*80}) --cycle;\n\\foreach \\i/\\j/\\k in {2/54/1,3/66/1,4/84/1,5/96/9,6/117/15,7/130/19,8/147/24,9/185/33,10/231/42,11/262/53,12/291/72,13/336/88}\n{\\draw (S) -- (\\i,\\j) coordinate (S) (T) --(\\i,\\k) coordinate (T);\n\\filldraw (T) ++ (-0.05,{-0.05*80}) rectangle ++ (0.1,{0.1*80});\n\\filldraw (S) ++ (0,{-0.07*80}) --++ (-0.07,{0.07*80}) --++ (0.07,{0.07*80}) --++ (0.07,{-0.07*80}) --cycle;};\n\\foreach \\i/\\j in {1/2008,2/2009,3/2010,4/2011,5/2012,6/2013,7/2014,8/2015,9/2016,10/2017,11/2018,12/2019,13/2020}\n{\\draw (\\i,5) -- (\\i,0) node [below] {\\rotatebox{90}{$\\j$年}};};\n\\draw (1,0) -- (13,0);\n\\foreach \\i in {0,10,...,80}\n{\\draw (1.1,{\\i/10*48}) --++ (-0.1,0) node [left] {$\\i$};};\n\\draw (1,1) -- (1,{8*48});\n\\draw (14,320) coordinate (S);\n\\filldraw (S) ++ (0,{-0.07*80}) --++ (-0.07,{0.07*80}) --++ (0.07,{0.07*80}) --++ (0.07,{-0.07*80}) --cycle;\n\\draw (S) ++ (-0.3,0) --++ (0.6,0) coordinate (S);\n\\draw (14,160) coordinate (T);\n\\filldraw (T) ++ (-0.05,{-0.05*80}) rectangle ++ (0.1,{0.1*80});\n\\draw (T) ++ (-0.3,0) --++ (0.6,0) coordinate (T);\n\\draw (S) node [right] {城乡居民储蓄年末余额/百亿元};\n\\draw (T) node [right] {地方财政预算内收入/百亿元};\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} 地方财政预算内收入、城乡居民储蓄年末余额均呈增长趋势;\\\\\n\\textcircled{2} 地方财政预算内收入、城乡居民储蓄年末余额的逐年增长速度相同;\\\\\n\\textcircled{3} 地方财政预算内收入年平均增长量高于城乡居民储蓄年末余额年平均增长量;\\\\\n\\textcircled{4} 城乡居民储蓄年末余额与地方财政预算内收入的差额逐年增大.",
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"023307": {
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"id": "023307",
|
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"content": "某电视台在每天新闻类节目观众的收看时长的抽样调查中,\n随机抽取了 $100$ 名电视观众, 相关的数据如下: 其中男性人数为 $55$ 名, 女性人数为 $45$ 名, 男性收看时长的样本平均数为 $23$ 分钟, 方差为 $3.5$ ; 女性收看时长的样本平均数为 $16$ 分钟, 方差为 $2.4$ . 请用这些数据求 $100$ 名观众的样本平均数和方差, 并估计所有观众新闻类节目收看时长的总体方差. (结果精确到 $0.1$ 分钟)",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
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||||
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||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"023308": {
|
||||
"id": "023308",
|
||||
"content": "(1) 某机构随机访问 50 名居民, 这 50 名居民对政府的评分(满分 100 分)如下表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\\hline 分数 &{$[70,75)$}&{$[75,80)$}&{$[80,85)$}&{$[85,90)$}&{$[90,95)$}&{$[95,100]$}\\\\\n\\hline 频数 & 2 & 3 & 11 & 14 & 11 & 9 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n请作出居民对政府评分的频率分布直方图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.15, yscale = 80]\n\\draw [->] (65,0) --(66.5,0) -- (67,0.003) -- (68,-0.003) -- (68.5,0)-- (105,0) node [below] {分数};\n\\draw [->] (65,0) -- (65,0.068) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (65,0) node [below left] {$O$};\n\\foreach \\i in {70,75,...,100}\n{\\draw [dashed] (\\i,0) node [below] {$\\i$} -- (\\i,0.06);};\n\\foreach \\j in {0.004,0.008,0.012,0.016,0.020,0.024,0.028,0.032,0.036,0.040,0.044,0.048,0.052,0.056,0.06}\n{\\draw [dashed] (65,\\j) node [left] {$\\j$} -- (100,\\j);};\n\\end{tikzpicture}\n\\end{center}\n(2) 当地环保部门随机抽测了 2019 年 6 月的空气质量指数, 其数据如下表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\\hline 空气质量指数 & $0 \\sim 50$ & $51 \\sim 100$ & $101 \\sim 150$ & $151 \\sim 200$ \\\\\n\\hline 天数 & 2 & 18 & 8 & 2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n用空气质量指数的平均值作为判断该月空气质量指数级别的依据, 求出该月空气质量指数级别为几级? (同一组数据用该组数据的区间中点值作代表, 将频率视为概率)(相关知识参见附表)\\\\\n(3) 空气受到污染, 呼吸系统等疾病患者最易感染. 根据历史经验, 凡遇到空气轻度污染, 小李每天会服用有关药品, 花费 $50$ 元, 遇到中度污染每天服药的费用达到 $100$ 元. 环境整治前的 2015 年 11 月份小李因受到空气污染患呼吸系统等疾病花费了 $5000$ 元, 试估计 2019 年 11 月份(参考(2)中表格数据)小李比 2015 年 11 月份少花了多少钱的医药费?\n附:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline 空气质量指数 & $0 \\sim 50$ & $51 \\sim 100$ & $101 \\sim 150$ & $151 \\sim 200$ & $201 \\sim 300$ & $>300$ \\\\\n\\hline 空气质量指数级别 & 一级 & 二级 & 三级 & 四级 & 五级 & 六级 \\\\\n\\hline 空气质量指数类别 & 优 & 良 & 轻度污染 & 中度污染 & 重度污染 & 严重污染 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
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|
||||
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|
||||
"20240107\t杨懿荔"
|
||||
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|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"023309": {
|
||||
"id": "023309",
|
||||
"content": "已知球的半径为 $3$, 则该球的表面积为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "25届周末卷补充题目",
|
||||
"edit": [
|
||||
"20240107\t杨懿荔"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"022718"
|
||||
],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"023310": {
|
||||
"id": "023310",
|
||||
"content": "直线 $PA$ 与平面 $ABC$ 所成角为 $\\dfrac{\\pi}{3}$, 则直线 $PA$ 与平面 $ABC$ 内的任意一条直线所成角的取值范围是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
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|
||||
"edit": [
|
||||
"20240107\t杨懿荔"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"023311": {
|
||||
"id": "023311",
|
||||
"content": "已知递增的等比数列 $\\{a_n\\}$ 满足: 前 3 项和 $S_3=26$, 且 $a_1=2$, 则公比 $q=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
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|
||||
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|
||||
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|
||||
],
|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"023312": {
|
||||
"id": "023312",
|
||||
"content": "直三棱柱 $ABC-A_1B_1C_1$ 中, $\\angle ACB=90^{\\circ}$, $AC=AA_1=a$, 则点 $A$ 到平面 $A_1BC$ 的距离是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "25届周末卷补充题目",
|
||||
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|
||||
"20240107\t杨懿荔"
|
||||
],
|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"023313": {
|
||||
"id": "023313",
|
||||
"content": "某个命题与自然数 $n$ 有关, 且已证得``假设 $n=k$($k \\in \\mathbf{N}$, $k\\ge 1$) 时该命题成立, 则 $n=k+1$ 时该命题也成立''现已知当 $n=7$ 时, 该命题不成立, 那么\\bracket{20}.\n\\twoch{当 $n=8$ 时, 该命题不成立}{当 $n=8$ 时, 该命题成立}{当 $n=6$ 时, 该命题不成立}{当 $n=6$ 时, 该命题成立}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "25届周末卷补充题目",
|
||||
"edit": [
|
||||
"20240107\t杨懿荔"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"023314": {
|
||||
"id": "023314",
|
||||
"content": "已知三棱柱 $ABC-A_1B_1C_1$ 的侧棱与底面边长都相等, $A_1$ 在底面 $ABC$ 内的射影为 $\\triangle ABC$ 的中心, 则 $AB_1$ 与底面 $ABC$ 所成角的正弦值等于\\bracket{20}.\n\\fourch{$\\dfrac{1}{3}$}{$\\dfrac{\\sqrt{2}}{3}$}{$\\dfrac{\\sqrt{3}}{3}$}{$\\dfrac{2}{3}$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "25届周末卷补充题目",
|
||||
"edit": [
|
||||
"20240107\t杨懿荔"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"016888"
|
||||
],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"023315": {
|
||||
"id": "023315",
|
||||
"content": "如图, 在棱长为 $2$ 的正方体 $ABCD-A_1B_1C_1D_1$ 中, $E$、$F$ 分别是 $A_1D_1$ 和 $CC_1$ 的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw ($(A_1)!0.5!(D_1)$) node [left] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(C_1)$) node [right] {$F$} coordinate (F);\n\\draw [dashed] (E)--(F);\n\\end{tikzpicture}\n\\hspace*{3em}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw ($(C)!0.5!(B)$) node [below right] {$P$} coordinate (P);\n\\draw ($(A)!0.5!(B)$) node [below] {$Q$} coordinate (Q);\n\\draw [dashed] (P)--(Q);\n\\end{tikzpicture}\n\\hspace*{3em}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw ($(B)!{sqrt(2)/sqrt(3)/2}!(B_1)$) node [above right] {$P$} coordinate (P);\n\\draw (A)--(P)--(C);\n\\draw [dashed] (A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求异面直线 $EF$ 与 $AB$ 所成角的余弦值;\\\\\n(2) 若 $P, Q$ 分别是 $CB, BA$ 的中点, 求异面直线 $DD_1$ 与 $PQ$ 的距离.\\\\\n(3) 已知在棱 $BB_1$ 上存在一点 $P$, 使得二面角 $P-AC-B$ 的大小为 $30^{\\circ}$, 求 $BP$ 的长.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "25届周末卷补充题目",
|
||||
"edit": [
|
||||
"20240107\t杨懿荔"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"023316": {
|
||||
"id": "023316",
|
||||
"content": "如图, 用半径为 $10 \\sqrt{2}\\mathrm{cm}$, 面积为 $100 \\sqrt{2}\\pi \\mathrm{cm}^2$ 的扇形铁皮制作一个无盖的圆锥形容器 (衔接部分忽略不计), 该容器最多盛水多少? (结果精确到 $0.1 \\mathrm{cm}^3$)",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "25届周末卷补充题目",
|
||||
"edit": [
|
||||
"20240107\t杨懿荔"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"023317": {
|
||||
"id": "023317",
|
||||
"content": "已知数列 $\\{a_n\\}$ 是等比数列, $T_n=n a_1+(n-1) a_2+(n-2) a_3+\\cdots+2 a_{n-1}+a_n$, 且 $T_1=1$, $T_2=4$.\\\\\n(1) 求 $S_n=a_1+a_2+a_3+\\cdots+a_{n-1}+a_n$;\\\\\n(2) 求 $\\{T_n\\}$ 的通项公式.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "25届周末卷补充题目",
|
||||
"edit": [
|
||||
"20240107\t杨懿荔"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"030001": {
|
||||
"id": "030001",
|
||||
"content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
|
||||
|
|
|
|||
Reference in New Issue