From 8f7a5e63fbac70ecf01dd64e43d7bd9ef420c1b0 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sat, 27 Jan 2024 16:50:37 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=9524=E5=B1=8A=E9=95=BF=E5=AE=81?= =?UTF-8?q?=E5=8C=BA=E4=B8=80=E6=A8=A1?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 507 ++++++++++++++++++++++++++++++- 2 files changed, 494 insertions(+), 16 deletions(-) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 92df77d4..04e446a1 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -232,3 +232,6 @@ 20240125-153606 024239:024241,020797,024242:024250,004660 +20240127-165000 +024251:024271 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 1e576d77..ab2992b3 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -129694,7 +129694,9 @@ "20220705\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024259" + ], "remark": "", "space": "", "unrelated": [] @@ -139052,7 +139054,9 @@ "20220709\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024254" + ], "remark": "", "space": "", "unrelated": [] @@ -287834,7 +287838,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024265" + ], "remark": "", "space": "4em", "unrelated": [] @@ -303117,7 +303123,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024255" + ], "remark": "", "space": "4em", "unrelated": [] @@ -330593,7 +330601,9 @@ "20220901\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024258" + ], "remark": "", "space": "4em", "unrelated": [] @@ -341186,7 +341196,9 @@ "20221209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024253" + ], "remark": "", "space": "", "unrelated": [] @@ -412452,7 +412464,9 @@ "20230407\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024263" + ], "remark": "", "space": "", "unrelated": [] @@ -459761,7 +459775,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024268" + ], "remark": "", "space": "4em", "unrelated": [] @@ -467331,7 +467347,8 @@ "same": [], "related": [ "023279", - "023320" + "023320", + "024257" ], "remark": "", "space": "", @@ -480264,7 +480281,8 @@ ], "same": [], "related": [ - "023320" + "023320", + "024257" ], "remark": "", "space": "", @@ -574760,7 +574778,8 @@ ], "same": [], "related": [ - "023638" + "023638", + "024256" ], "remark": "", "space": "4em", @@ -624532,7 +624551,9 @@ "20240105\t毛培菁" ], "same": [], - "related": [], + "related": [ + "024254" + ], "remark": "", "space": "", "unrelated": [] @@ -631410,7 +631431,8 @@ "related": [ "017154", "017725", - "019851" + "019851", + "024257" ], "remark": "", "space": "", @@ -639394,7 +639416,8 @@ "same": [], "related": [ "009905", - "021372" + "021372", + "024256" ], "remark": "", "space": "4em", @@ -652080,6 +652103,454 @@ "space": "4em", "unrelated": [] }, + "024251": { + "id": "024251", + "content": "已知集合 $A=(-\\infty, 4]$, $B=\\{1,3,5,7\\}$, 则 $A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题1", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [ + "030605" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024252": { + "id": "024252", + "content": "复数 $z$ 满足 $z=\\dfrac{1}{1-\\mathrm{i}}$ ($\\mathrm{i}$ 为虚数单位), 则 $|\\overline{z}|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题2", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024253": { + "id": "024253", + "content": "不等式 $\\dfrac{1}{x}>1$ 的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题3", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [ + "012225" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024254": { + "id": "024254", + "content": "设向量 $\\overrightarrow{a}=(1,-2)$, $\\overrightarrow{b}=(-1, m)$, 若 $\\overrightarrow{a}\\parallel \\overrightarrow{b}$, 则 $m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题4", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [ + "004490", + "023028" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024255": { + "id": "024255", + "content": "将 $4$ 个人排成一排, 若甲和乙必须排在一起, 则共有\\blank{50}种不同排法.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题5", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [ + "010844" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024256": { + "id": "024256", + "content": "物体位移 $s$ 和时间 $t$ 满足函数关系 $s=100 t-5 t^2$($00$, 使得 $x^2+a x+1<0$''是假命题, 则实数 $a$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题10", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024261": { + "id": "024261", + "content": "若函数 $f(x)=\\sin x+a \\cos x$ 在 $(\\dfrac{2 \\pi}{3}, \\dfrac{7 \\pi}{6})$ 上是严格单调函数, 则实数 $a$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题11", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024262": { + "id": "024262", + "content": "设 $f(x)=|\\log _2 x+a x+b|$($a>0$), 记函数 $y=f(x)$ 在区间 $[t, t+1]$($t>0$) 上的最大值为 $M_t(a, b)$, 若对任意 $b \\in \\mathbf{R}$, 都有 $M_t(a, b) \\geq a+1$, 则实数 $t$ 的最大值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题12", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024263": { + "id": "024263", + "content": "下列函数中既是奇函数又是增函数的是\\bracket{20}.\n\\fourch{$f(x)=2 x$}{$f(x)=x^2$}{$f(x)=\\ln x$}{$f(x)=\\mathrm{e}^x$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题13", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [ + "014817" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024264": { + "id": "024264", + "content": "``$P(A \\cap B)=P(A) P(B)$''是``事件 $A$ 与事件 $\\overline{B}$ 互相独立''\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充要条件}{既不充分也不必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题14", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024265": { + "id": "024265", + "content": "设点 $P$ 是以原点为圆心的单位圆上的动点, 它从初始位置 $P_0(1,0)$ 出发, 沿单位圆按逆时针方向转动角 $\\alpha$($0<\\alpha<\\dfrac{\\pi}{2}$) 后到达点 $P_1$, 然后继续沿单位圆按逆时针方向转动角 $\\dfrac{\\pi}{4}$ 到达 $P_2$. 若点 $P_2$ 的横坐标为 $-\\dfrac{3}{5}$, 则点 $P_1$ 的纵坐标 \\bracket{20}.\n\\fourch{$\\dfrac{\\sqrt{2}}{10}$}{$\\dfrac{\\sqrt{2}}{5}$}{$\\dfrac{3 \\sqrt{2}}{5}$}{$\\dfrac{7 \\sqrt{2}}{10}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题15", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [ + "010252" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024266": { + "id": "024266", + "content": "豆腐发酵后衣面长出一层白线线的长毛就成了毛豆腐. 将三角形豆腐 $ABC$ 悬空挂在发酵空间内, 记发酵后毛豆腐所构成的儿何体为 $T$. 若忽略三角形豆腐 $ABC$ 的原度, 设 $AB=3$, $BC=4$, $AC=5$, 点 $P$ 在 $\\triangle ABC$ 内部. 假设对于任意点 $P$, 满足 $PQ \\leq 1$ 的点 $Q$ 都在 $T$ 内,且对于 $T$ 内任意一点 $Q$, 都存在点 $P$, 满足 $PQ \\leq 1$, 则 $T$ 的体积为\\bracket{20}.\n\\fourch{$12+7 \\pi$}{$12+\\dfrac{22 \\pi}{3}$}{$14+7 \\pi$}{$14+\\dfrac{22 \\pi}{3}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题16", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024267": { + "id": "024267", + "content": "已知等差数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 公差 $d=2$.\\\\\n(1) 若 $S_{10}=100$, 求 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 从集合 $\\{a_1, a_2, a_3, a_4, a_5, a_6\\}$ 中任取 3 个元素, 记这 3 个元索能成等差数列为事件 $A$,求事件 $A$ 发生的概率 $P(A)$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题17", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024268": { + "id": "024268", + "content": "如图, 在三棱锥 $A-BCD$ 中, 平面 $ABD \\perp$ 平面 $BCD$, $AB=AD$, $O$为 $BD$ 的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\draw (-1,0,0) node [left] {$B$} coordinate (B);\n\\draw (1,0,0) node [right] {$D$} coordinate (D);\n\\draw (0,1,0) node [above] {$A$} coordinate (A);\n\\draw (1,0,2) node [below] {$C$} coordinate (C);\n\\draw (B)--(C)--(D)--(A)--cycle(A)--(C);\n\\draw ($(B)!0.5!(D)$) node [above left] {$O$} coordinate (O);\n\\draw [dashed] (B)--(D)(A)--(O);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $AO \\perp CD$;\\\\\n(2) 若 $BD \\perp DC$, $BD=DC$, $AO=BO$, 求异面直线 $BC$ 与 $AD$ 所成的角的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届长宁区一模试题18", + "edit": [ + "20240127\t王伟叶" + ], + "same": [], + "related": [ + "016811" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024269": { + "id": "024269", + "content": "汽车转弯时遵循阿克曼转向几何原理, 即转向时所有车轮中垂线交于一点, 该点称为转向中心: 如图 1, 某汽车四轮中心分别为 $A$、$B$ 、 $C$、$D$, 向左转向, 左前轮转向角为 $\\alpha$, 右前轮转向角为 $\\beta$, 转向中心为 $O$. 设该汽车左右轮距 $AB$ 为 $w$ 米, 前后轴距 $AD$ 为 $l$ 米.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\def\\l{1.57}\n\\def\\w{2.68}\n\\draw (0,0) node [below left] {$D$} coordinate (D);\n\\draw (\\l,0) node [below right] {$C$} coordinate (C);\n\\draw (C)++(0,\\w) node [above right] {$B$} coordinate (B);\n\\draw (D)++(0,\\w) node [above left] {$A$} coordinate (A);\n\\draw (A)--(B)(C)--(D);\n\\draw ($(C)!0.5!(D)$) coordinate (MB) ($(A)!0.5!(B)$) coordinate (MU);\n\\draw (MB)--(MU);\n\\draw (D)++ ({-sqrt(3)*\\w},0) node [below] {$O$} coordinate (O);\n\\draw [dashed] (O)--(D)(O)--(A)(O)--(B)(A)--(D)(B)--(C);\n\\def\\t{atan(\\w/(sqrt(3)*\\w+\\l))}\n\\draw [ultra thick] (D) ++ (0,0.4) --++ (0,-0.8);\n\\draw [ultra thick] (C) ++ (0,0.4) --++ (0,-0.8);\n\\draw [ultra thick] (A) ++ (120:0.4) --++ (-60:0.8);\n\\draw [ultra thick] (B) ++ ({90+\\t}:0.4) --++ ({\\t-90}:0.8);\n\\draw ($(O)!0.5!(C)$) ++ (0,-1) node [below] {图 1};\n\\end{tikzpicture}\n\\hspace*{3em}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\def\\l{1.57}\n\\def\\w{2.68}\n\\draw (0,0) node [below left] {$D$} coordinate (D);\n\\draw (\\l,0) node [below] {$C$} coordinate (C);\n\\draw (C)++(0,\\w) node [above] {$B$} coordinate (B);\n\\draw (D)++(0,\\w) node [above left] {$A$} coordinate (A);\n\\draw (A)--(B)(C)--(D);\n\\draw ($(C)!0.5!(D)$) coordinate (MB) ($(A)!0.5!(B)$) coordinate (MU);\n\\draw (MB)--(MU);\n\\def\\t{atan(\\w/(sqrt(3)*\\w+\\l))}\n\\draw [ultra thick] (D) ++ (0,0.4) --++ (0,-0.8);\n\\draw [ultra thick] (C) ++ (0,0.4) --++ (0,-0.8);\n\\draw [ultra thick] (A) ++ (120:0.4) --++ (-60:0.8);\n\\draw [ultra thick] (B) ++ ({90+\\t}:0.4) --++ ({\\t-90}:0.8);\n\\draw (-1.5,-1) node [left] {$T$} coordinate (T);\n\\draw (-1.5,1.5) node [below left] {$M$} coordinate (M);\n\\draw (-3.5,1.5) node [below] {$N$} coordinate (N);\n\\draw (N) ++ (0,3.5) node [above] {$E$} coordinate (E);\n\\draw (M) ++ (3.5,3.5) node [above right] {$F$} coordinate (F);\n\\draw (T) ++ (3.5,0) node [right] {$S$} coordinate (S);\n\\draw (T)--(M)--(N)(S)--(F)--(E);\n\\draw ($(O)!0.5!(C)$) ++ (1,-1.5) node [below] {图 2};\n\\end{tikzpicture}\n\\end{center}\n(1) 试用 $w$、$l$ 和 $\\alpha$ 表示 $\\tan \\beta$;\\\\\n(2) 如图 2, 有一直角弯道, $M$ 为内直角顶点, $EF$ 为上路边, 路宽均为 $3.5$ 米, 汽车行驶其中, 左轮 $A$、$D$ 与路边 $FS$ 相距 2 米. 试依据如下假设, 对问题*做出判断, 并说明理由.\n假设: \\textcircled{1} 转向过程中, 左前轮转向角 $\\alpha$ 的值始终为 $30^{\\circ}$; \\textcircled{2}设转向中心 $O$ 到路边 $EF$ 的距离为 $d$, 若 $OB0$), $g(x)=\\sin x$, 求实数 $a$ 的取值范围;\\\\\n(3) 若 $y=g(x)$ 为严格减函数, $f(0)| y|$''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