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收录高三寒假作业试卷02新题

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wangweiye7840 2024-01-25 15:10:25 +08:00
parent 984ab4a5de
commit c7dc5e19f7
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3
工具v2/文本文件/新题收录列表.txt
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@ -214,3 +214,6 @@
20240125-145904
024158:024160,023657,024161:024170,011324
20240125-150948
024171:024172,000737,024173,013397,024174:024183

2
工具v2/讲义生成.py
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@ -1,4 +1,4 @@
lessonpattern = r"V202405(([01234]\d)|(5[0123]))" # 正则表达式, 数据库中讲义的编号([A-Z][0-9]{4}[(01)|(02)][[0-9]{2}), 字母表示类型, 四位数字表示届别, 2位数字表示学期及其他, 2位数字表示序号
lessonpattern = r"U20240501" # 正则表达式, 数据库中讲义的编号([A-Z][0-9]{4}[(01)|(02)][[0-9]{2}), 字母表示类型, 四位数字表示届别, 2位数字表示学期及其他, 2位数字表示序号
outputdir = "d:/temp/26届材料" # 输出文件夹, 不建议修改
answered = True # 设置是否编译答案

293
题库0.3/Problems.json
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@ -13557,7 +13557,9 @@
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"content": "某市 $A, B, C$ 三个区共有高中学生 $20000$ 人, 其中 $A$ 区高中学生 $7000$ 人, 若采用分层抽样的方法从这三个区所有高中学生中抽取一个容量为 $600$ 人的样本进行学习兴趣调查, 则 $A$ 区应抽取\\blank{50}人.",
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"content": "某班 $48$ 名学生参加建校 $100$ 周年知识竞赛, 若成绩都在区间 $[40,100]$ 上, 其频率分布直方图如图所示, 则成绩不低于 $60$ 分的人数为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.06, yscale = 80]\n\\draw [->] (30,0) -- (32,0) -- (33,-0.002) -- (35,0.002) -- (36,0)-- (115,0) node [below] {成绩/分};\n\\draw [->] (30,0) -- (30,0.04) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (30,0) node [below left] {$O$};\n\\foreach \\i/\\j in {40/0.01,50/0.015,60/0.015,70/0.03,80/0.025,90/0.005}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (10,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {40/0.01,60/0.015,70/0.03,80/0.025,90/0.005}\n{\\draw [dashed] (\\i,\\j) -- (30,\\j) node [left] {$\\k$};};\n\\draw (100,0) node [below] {$100$};\n\\end{tikzpicture}\n\\end{center}",
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"content": "若某班级要从 $4$ 名男生和 $3$ 名女生中选取 $3$ 名同学参加志愿者活动, 则选出的 $3$ 人中既有男生又要有女生的概率为\\blank{50}.",
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"024174": {
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"content": "某副食品店对某月的前 $11$ 天内每天的顾客人数进行统计得到样本数据的茎叶图如图所示, 则样本的中位数和方差 (方差的结果保留一位小数)分别是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{l|llllll}\n3 & 1 & 2 & 4\\\\\n4 & 4 & 5 & 5 & 7 & 7 & 8 \\\\\n5 & 0 & 0 \n\\end{tabular}\n\\end{center}",
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"content": "在二项式 $(1+x)^5$ 的展开式中任取两项, 则所取两项中至少有一项的系数为偶数的概率是\\blank{50}.",
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"024176": {
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"content": "若从一副 $52$ 张的扑克牌中随机抽取 $1$ 张, 放回后再抽取 $1$ 张, 则两张牌都是``K''的概率为\\blank{50}.",
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"024177": {
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"content": "若在含有 $3$ 件次品的 $10$ 件产品中任取 $4$ 件, $X$ 表示取到的次品数, 则 $P(X=2)=$\\blank{50}.",
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"content": "非空集合 $A$ 中所有元素乘积记为 $T(A)$. 已知集合 $M=\\{1,4,5,7,8\\}$, 若从集合 $M$ 的所有非空子集中任选一个子集 $A$, 则 $T(A)$ 为偶数的概率是\\blank{50}.",
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"content": "某校计划在秋季运动会期间开展``运动与健康''知识大赛. 为此某班开展了 $10$ 次模拟测试, 以此选拔选手代表班级参赛. 下表为甲、乙两名学生的历次模拟测试成绩.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n场次 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\n\\hline\n甲 & 98 & 94 & 97 & 97 & 95 & 93 & 93 & 95 & 93 & 95 \\\\\n\\hline\n乙 & 92 & 94 & 93 & 94 & 95 & 94 & 96 & 97 & 97 & 98 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n甲、乙两名学生测试成绩的平均数分别记作 $\\overline{x}, \\overline{y}$, 方差分别记作 $S_1^2, S_2^2$.\\\\\n(1) 求 $\\overline{x}, \\overline{y}, S_1^2, S_2^2$;\\\\\n(2) 以这 $10$ 次模拟测试成绩及(1)中的结果为参考, 请你从甲、乙两名学生中选出一人代表班级参加比赛, 并说明你作出选择的理由.",
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"024180": {
"id": "024180",
"content": "从甲地到乙地要经过 $3$ 个十字路路, 设各路路信号灯工作相互独立, 且在各路路遇到红灯的概率分别为 $\\dfrac{1}{2}, \\dfrac{1}{3}, \\dfrac{1}{4}$.\\\\\n(1) 设 $X$ 表示一辆车从甲地到乙地遇到红灯的个数, 求随机变量 $X$ 的分布;\\\\\n(2) 若有两辆车独立地从甲地到乙地, 求这两辆车共遇到 $1$ 个红灯的概率.",
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"024181": {
"id": "024181",
"content": "已知 $(2 x-1)^n=a_0+a_1(x-1)+a_2(x-1)^2+\\cdots+a_n(x-1)^n$, $n$ 为正整数, $a_2=60$.\\\\\n(1) 求 $a_0+a_1+a_2+\\cdots+a_n$ 的值;\\\\\n(2) 设 $r \\in\\{0,1,2, \\cdots, n\\}$, 求 $a_r$ 的最大值.",
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"024182": {
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"content": "某学校进行体检, 现得到所有男生的身高数据, 从中随机抽取 $50$ 人进行统计 (已知这 $50$ 人身高介于 $155 \\mathrm{cm}$ 到 $195 \\mathrm{cm}$ 之间), 现将抽取结果按如下方式分成八组: 第一组 $[155,160)$ 、第二组 $[160,165)$、$\\cdots$ 、第八组 $[190,195)$, 并按此分组绘制如图所示的频率分布直方图, 其中第六组和第七组还没有绘制完成, 已知第一组与第八组人数相同, 第六组和第七组人数的比为 $5: 2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.15, yscale = 70]\n\\draw [->] (150,0) -- (151,0) -- (151.5,-0.003) -- (152.5,0.003) -- (153,0)-- (205,0) node [below] {身高/cm};\n\\draw [->] (150,0) -- (150,0.07) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (150,0) node [below left] {$O$};\n\\foreach \\i/\\j in {155/0.008,160/0.016,165/0.04,170/0.04,175/0.06,180/0,185/0,190/0.008}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (5,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {160/0.016,165/0.04,175/0.06,190/0.008}\n{\\draw [dashed] (\\i,\\j) -- (150,\\j) node [left] {$\\k$};};\n\\draw (195,0) node [below] {$195$};\n\\end{tikzpicture}\n\\end{center}\n(1) 计算第六组和第七组的频率;\\\\\n(2) 用分层抽样的方法在身高为 $[170,180)$ 内抽取一个容量为 $5$ 的样本, 从样本中任意抽取 $2$ 位男生, 求这两位男生身高都在 $[175,180)$ 内的概率.",
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"024183": {
"id": "024183",
"content": "某部门为了解一企业在生产过程中的用水量情况, 对其每天的用水量做了记录, 得到了大量该企业的日用水量的统计数据, 从这些统计数据中随机抽取 $12$ 天的数据作为样本, 得到如图所示的茎叶图(单位: 吨). 若用水量不低于 $95$ 吨, 则称这一天的用水量超标.\n\\begin{center}\n\\begin{tabular}{c|cccccc}\n7&3&1\\\\\n8&3&5&6&7&8&9\\\\\n9&5&7&8&9\n\\end{tabular}\n\\end{center}\n(1) 从这 $12$ 天的数据中随机抽取 $3$ 个, 求至多有 $1$ 天的用水量超标的概率;\\\\\n(2) 以这 $12$ 天的样本数据中用水量超标的频率作为概率, 估计该企业未来 $3$ 天中用水量超标的天数, 记随机变量 $X$ 为未来这 $3$ 天中用水量超标的天数, 求 $X$ 的分布、数学期望和方差.",
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"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.",
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