From 412074cb34fe2a5ee9dd558153fb3118cdf9ea35 Mon Sep 17 00:00:00 2001 From: Wang Weiye Date: Fri, 2 Dec 2022 13:10:18 +0800 Subject: [PATCH] 20221202 afternoon --- 工具/寻找阶段末尾空闲题号.ipynb | 2 +- 工具/添加题目到数据库.ipynb | 22 +- 工具/识别题库中尚未标注的题目类型.ipynb | 57 ++- 文本处理工具/剪贴板文本整理_word文件.ipynb | 6 +- 文本处理工具/文本整理_图片转文字后.ipynb | 6 +- 题库0.3/Problems.json | 399 +++++++++++++++++++++ 6 files changed, 441 insertions(+), 51 deletions(-) diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index 4c06cce4..70c37b8d 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -11,7 +11,7 @@ "text": [ "首个空闲id: 12096 , 直至 020000\n", "首个空闲id: 20227 , 直至 030000\n", - "首个空闲id: 30483 , 直至 999999\n" + "首个空闲id: 30496 , 直至 999999\n" ] } ], diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 8d4ca732..caf649ca 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -2,20 +2,20 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 30485\n", - "origin = \"空中课堂必修第三册复习课例题\"\n", - "filename = r\"C:\\Users\\Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", - "editor = \"20221127\\t王伟叶\"" + "starting_id = 12096\n", + "origin = \"2023届高三上学期考试院提供适应性测试卷\"\n", + "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目5.tex\"\n", + "editor = \"20221202\\t王伟叶\"" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -70,8 +70,8 @@ " pid = str(id).zfill(6)\n", " if pid in pro_dict:\n", " duplicate_flag = True\n", - " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin , dict = pro_dict,editor = editor)\n", - " # NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n", + " # NewProblem = CreateNewProblem(id = pid, content = p, origin = origin , dict = pro_dict,editor = editor)\n", + " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n", " pro_dict[pid] = NewProblem\n", " id += 1\n", "\n", @@ -101,7 +101,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -115,12 +115,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb index 7d734f2c..ee7256a6 100644 --- a/工具/识别题库中尚未标注的题目类型.ipynb +++ b/工具/识别题库中尚未标注的题目类型.ipynb @@ -9,36 +9,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "012075 填空题\n", - "012076 填空题\n", - "012077 填空题\n", - "012078 填空题\n", - "012079 填空题\n", - "012080 填空题\n", - "012081 填空题\n", - "012082 填空题\n", - "012083 填空题\n", - "012084 填空题\n", - "012085 填空题\n", - "012086 填空题\n", - "012087 选择题\n", - "012088 选择题\n", - "012089 选择题\n", - "012090 选择题\n", - "012091 解答题\n", - "012092 解答题\n", - "012093 解答题\n", - "012094 解答题\n", - "012095 解答题\n", - "030485 解答题\n", - "030486 解答题\n", - "030487 解答题\n", - "030488 解答题\n", - "030489 解答题\n", - "030490 解答题\n", - "030491 解答题\n", - "030492 解答题\n", - "030493 解答题\n" + "012096 填空题\n", + "012097 填空题\n", + "012098 填空题\n", + "012099 填空题\n", + "012100 填空题\n", + "012101 填空题\n", + "012102 填空题\n", + "012103 填空题\n", + "012104 填空题\n", + "012105 填空题\n", + "012106 填空题\n", + "012107 填空题\n", + "012108 选择题\n", + "012109 选择题\n", + "012110 选择题\n", + "012111 选择题\n", + "012112 解答题\n", + "012113 解答题\n", + "012114 解答题\n", + "012115 解答题\n", + "012116 解答题\n" ] } ], @@ -80,7 +71,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -94,12 +85,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/文本处理工具/剪贴板文本整理_word文件.ipynb b/文本处理工具/剪贴板文本整理_word文件.ipynb index 2e059c87..0d137649 100644 --- a/文本处理工具/剪贴板文本整理_word文件.ipynb +++ b/文本处理工具/剪贴板文本整理_word文件.ipynb @@ -480,7 +480,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -494,12 +494,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/文本处理工具/文本整理_图片转文字后.ipynb b/文本处理工具/文本整理_图片转文字后.ipynb index 60189e2d..6a6f54c8 100644 --- a/文本处理工具/文本整理_图片转文字后.ipynb +++ b/文本处理工具/文本整理_图片转文字后.ipynb @@ -456,7 +456,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -470,12 +470,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index f309bc2c..85717089 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -298029,6 +298029,405 @@ "remark": "", "space": "12ex" }, + "012096": { + "id": "012096", + "content": "已知集合$A=\\{x|\\dfrac{2x}{x-1}\\le 1\\}$, $B=\\{-1,0,1,2\\}$, 则$A\\cap B=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题1", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012097": { + "id": "012097", + "content": "设$a\\in \\mathbf{R}$, $\\mathrm{i}$为虚数单位. 若$(a-\\mathrm{i})(1-2\\mathrm{i})$为纯虚数, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题2", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012098": { + "id": "012098", + "content": "在空间直角坐标系中, 点$A(1,2,-3)$关于$xOz$平面对称的点的坐标是$\\blank{50}$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题3", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012099": { + "id": "012099", + "content": "已知$m\\in \\mathbf{R}$, 直线$l_1:\\sqrt{3}x-y+7=0$, $l_2:mx+y-1=0$. 若$l_1\\parallel l_2$, 则$l_1$与$l_2$之间的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题4", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012100": { + "id": "012100", + "content": "为了解某校高三年级男生的体重, 从该校高三年级男生中抽取$17$名, 测得他们的体重数据如下(按从小到大的顺序排列, 单位: kg): $56\\ 56 \\ 57\\ 58\\ 59\\ 59\\ 61\\ 63\\ 64\\ 65\\ 66\\ 68\\ 69\\ 70\\ 73\\ 74\\ 83$\\\\\n据此估计该校高三年级男生体重的第$75$百分位数为\\blank{50}kg.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题5", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012101": { + "id": "012101", + "content": "设$a,b$为实数. 若关于$x$的方程$x^2+abx+b=0$的解集为$\\{1,3\\}$, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题6", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012102": { + "id": "012102", + "content": "已知常数$m>0$. 在$(x+\\dfrac mx)^6$的二项展开式中, $x^2$项的系数是$\\dfrac{1}{x^2}$项的系数的$4$倍, 则$m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题7", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012103": { + "id": "012103", + "content": "在平面上, 已知$\\overrightarrow{a}$, $\\overrightarrow{b}$为两个不平行的单位向量, $O$为定点, 集合$\\Omega = \\{P|\\overrightarrow{OP}=\\lambda \\overrightarrow{a}+\\mu \\overrightarrow{b}, \\ 0\\le \\lambda \\le 1, \\ 0\\le \\mu \\le 2\\}$. 若$\\Omega$中所有点构成图形的面积为$1$, 则$\\overrightarrow{a}$与$\\overrightarrow{b}$夹角的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题8", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012104": { + "id": "012104", + "content": "已知定义在$(-3,3)$上的奇函数$y=f(x)$的导函数是$f'(x)$, 当$x\\ge 0$时, $y=f(x)$的图像如图所示, 则关于$x$的不等式$\\dfrac{f'(x)}{x}>0$的解集为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=stealth, line cap = round, line join = round,scale = 0.6]\n\\draw [->] (-1,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:3] plot (\\x,{1-pow(\\x-1,2)});\n\\draw [dashed] (1,0) node [below] {$1$} -- (1,1) (3,-3) -- (3,0) node [below right] {$3$};\n\\draw (2,0) node [below left] {$2$};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题9", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012105": { + "id": "012105", + "content": "第$14$届国际数学教育大会(ICME-14)于$2021$年$7$月$12$日至$18$日在上海举办, 已知张老师和李老师都在$7$天中随机选择了连续的$3$天参会, 则两位老师所选的日期恰好都不相同的概率为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题10", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012106": { + "id": "012106", + "content": "已知$A$、$B$、$C$是半径为$1$的球面上的三点, 若$AB=AC=1$, 则$BC$的最大值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题11", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012107": { + "id": "012107", + "content": "设$a\\in \\mathbf{R}$, $m\\in \\mathbf{Z}$. 若存在唯一的$m$使得关于$x$的不等式组$\\dfrac 12 x^2-\\dfrac 12=stealth, line cap = round, line join = round]\n\\draw (0,0) node {$1$};\n\\draw (0,-0.5) node {$2$};\n\\draw (0,-1) node {$3$};\n\\draw (0.3,0) node {$6$};\n\\draw (0.6,0) node {$8$};\n\\draw (0.3,-0.5) node {$1$} (0.6,-0.5) node {$2$} (0.9,-0.5) node {$2$};\n\\draw (0.3,-1) node {$1$};\n\\draw (0.15,0.25) -- (0.15,-1.25);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$21$}{$21.5$}{$22$}{$22.5$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题13", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012109": { + "id": "012109", + "content": "已知双曲线$\\Gamma_1:\\dfrac{x^2}{a_1^2}-\\dfrac{y^2}{b_1^2}=1$($a_1>0$, $b_1>0$)与$\\Gamma_2:\\dfrac{x^2}{a_2^2}-\\dfrac{y^2}{b_2^2}=1$($a_2>0$, $b_2>0$)有共同的渐近线, 则它们一定有相等的\\bracket{20}.\n\\fourch{实轴长}{虚轴长}{焦距}{离心率}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题14", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012110": { + "id": "012110", + "content": "已知数列$\\{a_n\\}$的前$n$项和为$S_n$, 若$S_{2023}=a_{2023}$, 则$\\{a_n\\}$不可能是\\bracket{20}. \n\\twoch{公差大于$0$的等差数列}{公差小于$0$的等差数列}{公比大于$0$的等比数列}{公比小于$0$的等比数列}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题15", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012111": { + "id": "012111", + "content": "已知$\\omega \\in \\mathbf{R}$, $\\varphi \\in [0, 2\\pi)$. 若对任意实数$x$均有$\\sin x\\ge \\cos (\\omega x+\\varphi)$, 则满足条件的有序实数对$(\\omega , \\varphi)$的个数为\\bracket{20}. \n\\fourch{$1$个}{$2$个}{$3$个}{无数个}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题16", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012112": { + "id": "012112", + "content": "设等差数列$\\{a_n\\}$的前$n$项和为$S_n$, 且$a_4=10$.\\\\\n(1) 若$S_{20}=590$, 求$\\{a_n\\}$的公差;\\\\\n(2) 若$a_1\\in \\mathbf{Z}$, 且$S_7$是数列$\\{S_n\\}$中最大的项, 求$a_1$所有可能的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题17", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012113": { + "id": "012113", + "content": "如图, 正四棱柱$ABCD-A_1B_1C_1D_1$的底面边长为$1$, 高为$2$, $AC$、$BD$相交于点$O$.\n\\begin{center}\n\\begin{tikzpicture}[>=stealth, line cap = round, line join = round, scale = 1.7]\n\\def\\l{1}\n\\def\\m{1}\n\\def\\n{2}\n\\draw (0,0,0) node [below left] {\\footnotesize $A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {\\footnotesize $B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {\\footnotesize $C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {\\footnotesize $D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {\\footnotesize $A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [above] {\\footnotesize $B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {\\footnotesize $C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {\\footnotesize $D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw (A1)-- (C1);\n\\draw [dashed] (A1) -- (D) (C1) -- (D) (A) -- (C) (B) -- (D);\n\\draw ($(A)!0.5!(C)$) node [below] {\\footnotesize $O$} coordinate (O);\n\\draw [dashed] (O) -- (B1);\n\\end{tikzpicture}\n\\end{center}\n(1)证明: 直线$B_1O$与平面$A_1C_1D$平行;\\\\\n(2)求三棱锥$O-A_1C_1D$的体积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题18", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012114": { + "id": "012114", + "content": "闲置房出租是增加社会住房供给量, 满足人们居住需求的重要途径. 王先生有一套住房以每月$7000$元的价格出租, 但合同租期本月到期. 房客直接向王先生提出希望从下月起续租三年, 并愿意每月支付$8000$元的租金. 王先生通过中介公司了解到: 该房屋所在小区的类似住宅, 目前的租金为每月$8000$-$9000$元, 在委托中介公司后, 一般$2$-$4$周左右可以\n找到承租人, 同时每次租赁交易成功后, 中介公司向出租方和承租方各收取一个月租金的$50\\%$作为中介费. 对于是否同意房客续租, 王先生需要作出决策.\\\\\n(1) 除了上述了解到的情况, 还有哪些因素王先生可能需要考虑? 写出这些因素(不超过$5$个);\\\\ \n(2) 为了简化问题, 请对相关因素作出合情假设, 由此帮助王先生作出决策, 并说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题19", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012115": { + "id": "012115", + "content": "已知椭圆$\\Gamma:\\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的左、右焦点分别为$F_1,F_2$, 直线$l$的斜率为$k$, 在$y$轴上的截距为$m$.\\\\\n(1) 设$k=1$, 若$\\Gamma$的焦距为$2$, $l$过点$F_1$, 求$l$的方程;\\\\\n(2) 设$m=0$. 若$P(\\sqrt{3},\\dfrac 12)$是$\\Gamma$上的一点, 且$|\\overrightarrow{PF_1}|+|\\overrightarrow{PF_2}|=4$, $l$与$\\Gamma$交于不同的两点$A,B$, $Q$为$\\Gamma$的上顶点, 求$\\triangle ABQ$面积的最大值;\\\\\n(3) 设$\\overrightarrow{n}$是$l$的一个法向量, $M$是$l$上一点, 对于坐标平面内的点$N$, 定义$\\delta_N=\\dfrac{\\overrightarrow{n}\\cdot \\overrightarrow{MN}}{|\\overrightarrow{n}|}$. 用$a,b,k,m$表示$\\delta_{F_1}\\cdot \\delta_{F_2}$, 并利用$\\delta_{F_1}\\cdot \\delta_{F_2}$与$b^2$的大小关系, 提出一个关于$l$与$\\Gamma$位置关系的真命题, 给出该命题的证明.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题20", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012116": { + "id": "012116", + "content": "已知$a\\in \\mathbf{R}$, 函数$f(x)=\\sin^2 x-a\\sin x$.\\\\\n(1) 当$a=2$时, 求$f(x)$的值域;\\\\\n(2) 若函数$y=f(x)-f(\\dfrac \\pi 2-x)$在区间$[0,\\dfrac\\pi 2]$上是严格增函数, 求$a$的最大值;\\\\\n(3) 设$a=\\dfrac 12$, $u\\in \\mathbf{R}$. 方程$f(x)=u$的所有正实数解按从小到大的顺序排列后, 是否能构成等差数列? 若能, 求所有满足条件的$u$的值; 若不能, 说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三上学期考试院提供适应性测试卷试题21", + "edit": [ + "20221202\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",