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录入高二周末卷07新题

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wangweiye7840 2024-04-02 15:43:17 +08:00
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3
工具v2/文本文件/新题收录列表.txt
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@ -475,3 +475,6 @@
20240402-131834 高二周末卷06
041097:041099,018928,041100,012745,041101:041104,040148,041105,040146,040011:040012,040015,023553,041106,018949,041107,040017
20240402-154302 高二周末卷07
041108:041113,030201,041114:041121

336
题库0.3/Problems.json
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@ -9549,7 +9549,9 @@
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@ -782672,5 +782692,301 @@
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"space": "4em",
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"id": "041108",
"content": "若对一枚均匀的硬币连续抛掷 3 次, 则出现结果为二次正面, 一枚反面的概率是\\bracket{20}.\n\\fourch{$\\dfrac{1}{4}$}{$\\dfrac{1}{3}$}{$\\dfrac{1}{8}$}{$\\dfrac{3}{8}$}",
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"041109": {
"id": "041109",
"content": "从集合 $\\{0,1,2,3,5,7,11\\}$ 中任取 3 个不同元素分别作直线方程 $a x+b y+c=0$中的 $a, b, c$, 所得直线经过坐标原点的概率为\\bracket{20}.\n\\fourch{$\\dfrac{1}{4}$}{$\\dfrac{1}{5}$}{$\\dfrac{1}{7}$}{$\\dfrac{3}{8}$}",
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"041110": {
"id": "041110",
"content": "把 15 名新生平均分到三个班级, 其中有 3 名是优秀生.每班分到 1 名优秀生的概率为\\bracket{20}.\n\\fourch{$\\dfrac{25}{91}$}{$\\dfrac{60}{91}$}{$\\dfrac{7}{91}$}{$\\dfrac{6}{91}$}",
"objs": [],
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"041111": {
"id": "041111",
"content": "在 $1,2,3, \\cdots, 100$ 这 100 个数中任取一数, 求该数或能被 2 整除或能被 5 整除的概率\\bracket{20}.\n\\fourch{$\\dfrac{1}{4}$}{$\\dfrac{3}{5}$}{$\\dfrac{1}{10}$}{$\\dfrac{2}{5}$}",
"objs": [],
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"041112": {
"id": "041112",
"content": "从某项综合能力测试中抽取 100 人的成绩, 统计如表, 则这 100 人成绩的标准差为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline 分数 & 5 & 4 & 3 & 2 & 1 \\\\\n\\hline 人数 & 20 & 10 & 30 & 30 & 10 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
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"041113": {
"id": "041113",
"content": "在发生某公共卫生事件期间, 某地在某一段时间内连续统计 10 天的每天确诊病例人数, 得到总体均值为 2 , 总体方差为 1 . 设这 10 天中的各天确诊人数的最大值为 $M$, 则在满足条件的所有可能数据中, $M$ 的最大值为\\bracket{20}.\n\\fourch{4}{5}{6}{7}",
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"041114": {
"id": "041114",
"content": "为了了解某地区高三学生的身体发育情况, 抽查了该地区 100 名年龄为 17.5 岁-18 岁的男生体重 $(\\mathrm{kg})$, 得到频率分布直方图如下:\n根据上图可得这 100 名学生中体重在 $[56.5,64.5)$ 的学生人数是\\bracket{20}.\n\\fourch{40}{45}{50}{55}\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.45, yscale = 50]\n\\draw [->] (53.5,0) -- (53.6,0) -- (53.7,0.003) -- (53.9,-0.003) -- (54,0) -- (80.5,0) node [below] {体重(kg)};\n\\draw [->] (53.5,0) -- (53.5,0.09) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\foreach \\i/\\j in {54.5/0.01,56.5/0.03,58.5/0.05,60.5/0.05,62.5/0.07,64.5/0.08,66.5/0.07,68.5/0.06,70.5/0.04,72.5/0.03,74.5/0.01}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (2,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {56.5/0.03,58.5/0.05,62.5/0.07}\n{\\draw [dashed] (\\i,\\j) -- (53.5,\\j) node [left] {$\\k$};};\n\\draw (76.5,0) node [below] {$76.5$};\n\\end{tikzpicture}\n\\end{center}",
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"041115": {
"id": "041115",
"content": "若直线 $x+\\sqrt{3}y-m=0$ 与圆 $x^2+y^2=1$ 在第一象限内有两个不同的交点, 则 $m$ 的取值范围是\\blank{50}.",
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"041116": {
"id": "041116",
"content": "平行六面体的每条棱长均为 1 , 若有一个公共顶点的三条棱两两成 $60^{\\circ}$ 角,则此平行六面体的体积为\\blank{50}.",
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"041117": {
"id": "041117",
"content": "正方体 $ABCD-A_1B_1C_1D_1$ 中,\\\\\n(1) 若 $E$、$F$ 分别为棱 $A_1B_1$、$BB_1$ 的中点, 求异面直线 $AE$ 和 $CF$ 所成角. \\\\\n(2) 若 $G$ 是 $CD$ 的中点, 求异面直线 $B_1C$ 与 $AG$ 所成角的正弦值. \\\\\n(3) 求直线 $BA_1$ 与平面 $ABC_1D_1$ 所成角大小;",
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"genre": "解答题",
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"001603"
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"041118": {
"id": "041118",
"content": "设 $A(3,2)$, 一直线 $l$ 与两直线 $4 x+y+6=0$ 和 $3 x-5 y-6=0$ 分别交于 $B, C$, 若 $\\overrightarrow{AB}=2 \\overrightarrow{BC}$, 求直线 $l$ 的方程.",
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"ans": "",
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"duration": -1,
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"041119": {
"id": "041119",
"content": "已知直线 $x+2 y-3=0$ 和圆 $x^2+y^2+x-2 a y+a=0$ 相交于 $A$、$B$ 两点, 且 $OA \\perp OB$ ($O$ 为原点), 求圆的方程.",
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"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
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"041120": {
"id": "041120",
"content": "已知点 $A(1,0)$ 与直线 $l: x=3$, 动点 $P$ 到点 $A$ 的距离为 $d_1$, 到 $l$ 的距离为 $d_2$, 且满足 $d_1+d_2=4$ 动点 $P$ 的轨迹为曲线 $C$, 求曲线 $C$ 的方程;",
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"041121": {
"id": "041121",
"content": "已知 $A(1,0)$ 为圆 $x^2+y^2=4$ 内的一个定点, 作矩形 $ABCD$, 且 $B$、$D$ 两点在圆上, 求点 $C$ 的轨迹方程.",
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"ans": "",
"solution": "",
"duration": -1,
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