From 6baa736c9286d47522d13591958c606dec90938a Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Mon, 12 Dec 2022 23:27:15 +0800 Subject: [PATCH] 20221212 night --- 工具/关键字筛选题号.ipynb | 12 +- 工具/寻找tex文件中未赋答案的题目.ipynb | 8 +- 工具/寻找阶段末尾空闲题号.ipynb | 12 +- 工具/文本文件/题号筛选.txt | 2 +- 工具/添加题目到数据库.ipynb | 16 +- 工具/识别题库中尚未标注的题目类型.ipynb | 206 +- 工具/题号选题pdf生成.ipynb | 10 +- 文本处理工具/剪贴板文本整理_word文件.ipynb | 16 +- 题库0.3/Problems.json | 3302 +++++++++++++++++++- 9 files changed, 3355 insertions(+), 229 deletions(-) diff --git a/工具/关键字筛选题号.ipynb b/工具/关键字筛选题号.ipynb index b30c7901..1d40b272 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 6, + "execution_count": 1, "metadata": {}, "output_type": "execute_result" } @@ -21,7 +21,7 @@ "\n", "\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n", "keywords_dict_table = [\n", - " {\"origin\":[\"2020\"],\"origin1\":[\"春季\"]}\n", + " {\"_nottags\":[\"单元\",\"暂\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", @@ -89,7 +89,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.15 ('mathdept')", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -103,12 +103,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.15" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb index c82d6045..7713dac5 100644 --- a/工具/寻找tex文件中未赋答案的题目.ipynb +++ b/工具/寻找tex文件中未赋答案的题目.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -47,7 +47,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.15 ('mathdept')", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -61,12 +61,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.15" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, 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 277938d9..15dbd9e4 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 @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "首个空闲id: 12329 , 直至 020000\n", + "首个空闲id: 12480 , 直至 020000\n", "首个空闲id: 20227 , 直至 030000\n", - "首个空闲id: 30496 , 直至 999999\n" + "首个空闲id: 30502 , 直至 999999\n" ] } ], @@ -45,7 +45,7 @@ ], "metadata": { "kernelspec": { - "display_name": "base", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -59,12 +59,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.13" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index 43475d13..e63faf23 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1 +1 @@ -012224,012225,012226,012227,012228,012229,012230,012231,012232,012233,012234,012235,012236,012237,012238,012239,012240,012241,012242,012243,012244 \ No newline at end of file +012075,012076,012077,012078,012079,012080,012081,012082,012083,012084,012085,012086,012087,012088,012089,012090,012091,012092,012093,012094,012095,012096,012097,012098,012099,012100,012101,012102,012103,012104,012105,012106,012107,012108,012109,012110,012111,012112,012113,012114,012115,012116,012117,012118,012119,012120,012121,012122,012123,012124,012125,012126,012127,012128,012129,012130,012131,012132,012133,012134,012135,012136,012137,012138,012139,012140,012141,012142,012143,012144,012145,012146,012147,012148,012149,012150,012151,012152,012153,012154,012155,012156,012157,012158,012159,012160,012161,012162,012163,012164,012165,012166,012167,012168,012169,012170,012171,012172,012173,012174,012175,012176,012177,012178,012179,012180,012181,012182,012183,012184,012185,012186,012187,012188,012189,012190,012191,012192,012193,012194,012195,012196,012197,012198,012199,012200,012201,012202,012203,012204,012205,012206,012207,012208,012209,012210,012211,012212,012213,012214,012215,012216,012217,012218,012219,012220,012221,012222,012223,012224,012225,012226,012227,012228,012229,012230,012231,012232,012233,012234,012235,012236,012237,012238,012239,012240,012241,012242,012243,012244,012245,012246,012247,012248,012249,012250,012251,012252,012253,012254,012255,012256,012257,012258,012259,012260,012261,012262,012263,012264,012265,012266,012267,012268,012269,012270,012271,012272,012273,012274,012275,012276,012277,012278,012279,012280,012281,012282,012283,012284,012285,012286,012287,012288,012289,012290,012291,012292,012293,012294,012295,012296,012297,012298,012299,012300,012301,012302,012303,012304,012305,012306,012307,012308,012309,012310,012311,012312,012313,012314,012315,012316,012317,012318,012319,012320,012321,012322,012323,012324,012325,012326,012327,012328,012329,012330,012331,012332,012333,012334,012335,012336,012337,012338,012339,012340,012341,012342,012343,012344,012345,012346,012347,012348,012349,012350,012351,012352,012353,012354,012355,012356,012357,012358,012359,012360,012361,012362,012363,012364,012365,012366,012367,012368,012369,012370,012371,012372,012373,012374,012375,012376,012377,012378,012379,012380,012381,012382,012383,012384,012385,012386,012387,012388,012389,012390,012391,012392,012393,012394,012395,012396,012397,012398,012399,012400,012401,012402,012403,012404,012405,012406,012407,012408,012409,012410,012411,012412,012413,012414,012415,012416,012417,012418,012419,012420,012421,012422,012423,012424,012425,012426,012427,012428,012429,012430,012431,012432,012433,012434,012435,012436,012437,012438,012439,012440,012441,012442,012443,012444,012445,012446,012447,012448,012449,012450,012451,012452,012453,012454,012455,012456,012457,012458,012459,012460,012461,012462,012463,012464,012465,012466,012467,012468,012469,012470,012471,012472,012473,012474,012475,012476,012477,012478,012479,012480,012481,012482,012483,012484,012485,012486,030485,030486,030487,030488,030489,030490,030491,030492,030493,030501 \ No newline at end of file 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 7fccb625..45ab4140 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": 12, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 12308\n", - "origin = \"2023届崇明区一模\"\n", + "starting_id = 12480\n", + "origin = \"2016届春季高考附加卷\"\n", "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", - "editor = \"20221210\\t王伟叶\"" + "editor = \"20221212\\t王伟叶\"" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -101,7 +101,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -115,12 +115,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, 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 6b729683..462551d2 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 @@ -9,48 +9,164 @@ "name": "stdout", "output_type": "stream", "text": [ - "012287 填空题\n", - "012288 填空题\n", - "012289 填空题\n", - "012290 填空题\n", - "012291 填空题\n", - "012292 填空题\n", - "012293 填空题\n", - "012294 填空题\n", - "012295 填空题\n", - "012296 填空题\n", - "012297 填空题\n", - "012298 填空题\n", - "012299 选择题\n", - "012300 选择题\n", - "012301 选择题\n", - "012302 选择题\n", - "012303 解答题\n", - "012304 解答题\n", - "012305 解答题\n", - "012306 解答题\n", - "012307 解答题\n", - "012308 填空题\n", - "012309 填空题\n", - "012310 填空题\n", - "012311 填空题\n", - "012312 填空题\n", - "012313 填空题\n", - "012314 填空题\n", - "012315 填空题\n", - "012316 填空题\n", - "012317 填空题\n", - "012318 填空题\n", - "012319 填空题\n", - "012320 选择题\n", - "012321 选择题\n", - "012322 选择题\n", - "012323 选择题\n", - "012324 解答题\n", - "012325 解答题\n", - "012326 解答题\n", - "012327 解答题\n", - "012328 解答题\n" + "012329 填空题\n", + "012330 填空题\n", + "012331 填空题\n", + "012332 填空题\n", + "012333 填空题\n", + "012334 填空题\n", + "012335 填空题\n", + "012336 填空题\n", + "012337 填空题\n", + "012338 填空题\n", + "012339 填空题\n", + "012340 填空题\n", + "012341 填空题\n", + "012342 填空题\n", + "012343 选择题\n", + "012344 选择题\n", + "012345 选择题\n", + "012346 选择题\n", + "012347 解答题\n", + "012348 解答题\n", + "012349 解答题\n", + "012350 解答题\n", + "012351 解答题\n", + "012352 填空题\n", + "012353 填空题\n", + "012354 填空题\n", + "012355 填空题\n", + "012356 填空题\n", + "012357 填空题\n", + "012358 填空题\n", + "012359 填空题\n", + "012360 填空题\n", + "012361 填空题\n", + "012362 填空题\n", + "012363 填空题\n", + "012364 选择题\n", + "012365 选择题\n", + "012366 选择题\n", + "012367 选择题\n", + "012368 选择题\n", + "012369 选择题\n", + "012370 选择题\n", + "012371 选择题\n", + "012372 选择题\n", + "012373 选择题\n", + "012374 选择题\n", + "012375 选择题\n", + "012376 解答题\n", + "012377 解答题\n", + "012378 解答题\n", + "012379 解答题\n", + "012380 解答题\n", + "012381 解答题\n", + "012382 解答题\n", + "012383 填空题\n", + "012384 填空题\n", + "012385 填空题\n", + "012386 填空题\n", + "012387 填空题\n", + "012388 填空题\n", + "012389 填空题\n", + "012390 填空题\n", + "012391 填空题\n", + "012392 填空题\n", + "012393 填空题\n", + "012394 填空题\n", + "012395 选择题\n", + "012396 选择题\n", + "012397 选择题\n", + "012398 选择题\n", + "012399 选择题\n", + "012400 选择题\n", + "012401 选择题\n", + "012402 选择题\n", + "012403 选择题\n", + "012404 选择题\n", + "012405 选择题\n", + "012406 选择题\n", + "012407 解答题\n", + "012408 解答题\n", + "012409 解答题\n", + "012410 解答题\n", + "012411 解答题\n", + "012412 解答题\n", + "012413 解答题\n", + "012414 解答题\n", + "012415 填空题\n", + "012416 填空题\n", + "012417 填空题\n", + "012418 填空题\n", + "012419 填空题\n", + "012420 填空题\n", + "012421 填空题\n", + "012422 填空题\n", + "012423 填空题\n", + "012424 填空题\n", + "012425 填空题\n", + "012426 填空题\n", + "012427 选择题\n", + "012428 选择题\n", + "012429 选择题\n", + "012430 选择题\n", + "012431 选择题\n", + "012432 选择题\n", + "012433 选择题\n", + "012434 选择题\n", + "012435 选择题\n", + "012436 选择题\n", + "012437 选择题\n", + "012438 选择题\n", + "012439 解答题\n", + "012440 解答题\n", + "012441 解答题\n", + "012442 解答题\n", + "012443 解答题\n", + "012444 选择题\n", + "012445 选择题\n", + "012446 选择题\n", + "012447 填空题\n", + "012448 填空题\n", + "012449 填空题\n", + "012450 解答题\n", + "012451 填空题\n", + "012452 填空题\n", + "012453 填空题\n", + "012454 填空题\n", + "012455 填空题\n", + "012456 填空题\n", + "012457 填空题\n", + "012458 填空题\n", + "012459 填空题\n", + "012460 填空题\n", + "012461 填空题\n", + "012462 填空题\n", + "012463 选择题\n", + "012464 选择题\n", + "012465 选择题\n", + "012466 选择题\n", + "012467 选择题\n", + "012468 选择题\n", + "012469 选择题\n", + "012470 选择题\n", + "012471 选择题\n", + "012472 选择题\n", + "012473 选择题\n", + "012474 选择题\n", + "012475 解答题\n", + "012476 解答题\n", + "012477 解答题\n", + "012478 解答题\n", + "012479 解答题\n", + "012480 选择题\n", + "012481 选择题\n", + "012482 选择题\n", + "012483 填空题\n", + "012484 填空题\n", + "012485 填空题\n", + "012486 解答题\n" ] } ], @@ -92,7 +208,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -106,12 +222,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb index 66d1f2f1..37c4098e 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -9,9 +9,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/题库_教师用_20221210.tex\n", + "开始编译教师版本pdf文件: 临时文件/待标注_教师用_20221212.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/题库_学生用_20221210.tex\n", + "开始编译学生版本pdf文件: 临时文件/待标注_学生用_20221212.tex\n", "0\n" ] } @@ -26,7 +26,7 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n", "problems = r\"\"\"\n", - "\n", + "a\n", "\n", "\n", "\"\"\"\n", @@ -34,7 +34,7 @@ "\n", "\"\"\"---设置文件名---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "filename = \"临时文件/题库\"\n", + "filename = \"临时文件/待标注\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", @@ -189,7 +189,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15 (main, Nov 24 2022, 14:39:17) [MSC v.1916 64 bit (AMD64)]" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { 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 df26bf63..509aba34 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 @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -374,6 +374,8 @@ " equation1 = re.sub(\" *\\)\",\")\",equation1)\n", " equation1 = re.sub(\"\\$ *\",\"$\",equation1)\n", " equation1 = re.sub(\" *\\$\",\"$\",equation1)\n", + " for i in range(2):\n", + " equation1 = re.sub(r\"([A-Z0-9]) ([A-Z0-9])\",lambda matchobj: matchobj.group(1)+matchobj.group(2),equation1)\n", " #改善大括号20220715\n", " layer = 0\n", " equation1 = re.sub(r\"\\\\\\{\",\"leftset\",equation1)\n", @@ -471,6 +473,12 @@ " modified_data = re.sub(r\" \\$\",\"$\",modified_data)\n", "#mathpix的错别字修改\n", "modified_data = modified_data.replace(\"雉\",\"锥\")\n", + "#mathpix的自由向量修改\n", + "modified_data = modified_data.replace(r\"\\vec\",r\"\\overrightarrow \")\n", + "#mathpix的极限修改\n", + "modified_data = modified_data.replace(r\"\\lim _{n \\rightarrow \\infty}\",r\"\\displaystyle\\lim_{n\\to\\infty}\")\n", + "#mathpix的顿号修改\n", + "modified_data = modified_data.replace(r\" 、 \",r\"$、$\")\n", "\n", "\n", "setCopy(modified_data)\n", @@ -489,7 +497,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -503,12 +511,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index f7a3ecb6..ffdcad91 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -300216,7 +300216,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题1", + "origin": "2011届春季高考试题1", "edit": [ "20221208\t王伟叶" ], @@ -300235,7 +300235,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题2", + "origin": "2011届春季高考试题2", "edit": [ "20221208\t王伟叶" ], @@ -300254,7 +300254,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题3", + "origin": "2011届春季高考试题3", "edit": [ "20221208\t王伟叶" ], @@ -300273,7 +300273,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题4", + "origin": "2011届春季高考试题4", "edit": [ "20221208\t王伟叶" ], @@ -300292,7 +300292,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题5", + "origin": "2011届春季高考试题5", "edit": [ "20221208\t王伟叶" ], @@ -300311,7 +300311,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题6", + "origin": "2011届春季高考试题6", "edit": [ "20221208\t王伟叶" ], @@ -300330,7 +300330,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题7", + "origin": "2011届春季高考试题7", "edit": [ "20221208\t王伟叶" ], @@ -300349,7 +300349,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题8", + "origin": "2011届春季高考试题8", "edit": [ "20221208\t王伟叶" ], @@ -300368,7 +300368,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题9", + "origin": "2011届春季高考试题9", "edit": [ "20221208\t王伟叶" ], @@ -300387,7 +300387,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题10", + "origin": "2011届春季高考试题10", "edit": [ "20221208\t王伟叶" ], @@ -300406,7 +300406,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题11", + "origin": "2011届春季高考试题11", "edit": [ "20221208\t王伟叶" ], @@ -300425,7 +300425,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题12", + "origin": "2011届春季高考试题12", "edit": [ "20221208\t王伟叶" ], @@ -300444,7 +300444,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题13", + "origin": "2011届春季高考试题13", "edit": [ "20221208\t王伟叶" ], @@ -300463,7 +300463,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题14", + "origin": "2011届春季高考试题14", "edit": [ "20221208\t王伟叶" ], @@ -300482,7 +300482,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题15", + "origin": "2011届春季高考试题15", "edit": [ "20221208\t王伟叶" ], @@ -300501,7 +300501,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题16", + "origin": "2011届春季高考试题16", "edit": [ "20221208\t王伟叶" ], @@ -300520,7 +300520,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题17", + "origin": "2011届春季高考试题17", "edit": [ "20221208\t王伟叶" ], @@ -300539,7 +300539,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题18", + "origin": "2011届春季高考试题18", "edit": [ "20221208\t王伟叶" ], @@ -300558,7 +300558,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题19", + "origin": "2011届春季高考试题19", "edit": [ "20221208\t王伟叶" ], @@ -300577,7 +300577,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题20", + "origin": "2011届春季高考试题20", "edit": [ "20221208\t王伟叶" ], @@ -300596,7 +300596,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题21", + "origin": "2011届春季高考试题21", "edit": [ "20221208\t王伟叶" ], @@ -300615,7 +300615,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题22", + "origin": "2011届春季高考试题22", "edit": [ "20221208\t王伟叶" ], @@ -300634,7 +300634,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2011年春季高考试题23", + "origin": "2011届春季高考试题23", "edit": [ "20221208\t王伟叶" ], @@ -300653,7 +300653,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题1", + "origin": "2017届春季高考试题1", "edit": [ "20221209\t王伟叶" ], @@ -300672,7 +300672,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题2", + "origin": "2017届春季高考试题2", "edit": [ "20221209\t王伟叶" ], @@ -300691,7 +300691,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题3", + "origin": "2017届春季高考试题3", "edit": [ "20221209\t王伟叶" ], @@ -300710,7 +300710,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题4", + "origin": "2017届春季高考试题4", "edit": [ "20221209\t王伟叶" ], @@ -300729,7 +300729,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题5", + "origin": "2017届春季高考试题5", "edit": [ "20221209\t王伟叶" ], @@ -300748,7 +300748,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题6", + "origin": "2017届春季高考试题6", "edit": [ "20221209\t王伟叶" ], @@ -300767,7 +300767,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题7", + "origin": "2017届春季高考试题7", "edit": [ "20221209\t王伟叶" ], @@ -300786,7 +300786,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题8", + "origin": "2017届春季高考试题8", "edit": [ "20221209\t王伟叶" ], @@ -300805,7 +300805,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题9", + "origin": "2017届春季高考试题9", "edit": [ "20221209\t王伟叶" ], @@ -300824,7 +300824,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题10", + "origin": "2017届春季高考试题10", "edit": [ "20221209\t王伟叶" ], @@ -300843,7 +300843,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题11", + "origin": "2017届春季高考试题11", "edit": [ "20221209\t王伟叶" ], @@ -300862,7 +300862,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题12", + "origin": "2017届春季高考试题12", "edit": [ "20221209\t王伟叶" ], @@ -300881,7 +300881,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题13", + "origin": "2017届春季高考试题13", "edit": [ "20221209\t王伟叶" ], @@ -300900,7 +300900,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题14", + "origin": "2017届春季高考试题14", "edit": [ "20221209\t王伟叶" ], @@ -300919,7 +300919,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2017年春季高考试题15", + "origin": "2017届春季高考试题15", "edit": [ "20221209\t王伟叶" ], @@ -300938,7 +300938,7 @@ "solution": "", "duration": -1, "usages": [], - 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"origin": "2018年春季高考试题16", + "origin": "2018届春季高考试题16", "edit": [ "20221209\t王伟叶" ], @@ -301356,7 +301356,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2018年春季高考试题17", + "origin": "2018届春季高考试题17", "edit": [ "20221209\t王伟叶" ], @@ -301375,7 +301375,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2018年春季高考试题18", + "origin": "2018届春季高考试题18", "edit": [ "20221209\t王伟叶" ], @@ -301394,7 +301394,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2018年春季高考试题19", + "origin": "2018届春季高考试题19", "edit": [ "20221209\t王伟叶" ], @@ -301413,7 +301413,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2018年春季高考试题20", + "origin": "2018届春季高考试题20", "edit": [ "20221209\t王伟叶" ], @@ -301432,7 +301432,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2018年春季高考试题21", + "origin": "2018届春季高考试题21", "edit": [ "20221209\t王伟叶" ], @@ -301451,7 +301451,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题1", + "origin": "2019届春季高考试题1", "edit": [ "20221209\t王伟叶" ], @@ -301470,7 +301470,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题2", + "origin": "2019届春季高考试题2", "edit": [ "20221209\t王伟叶" ], @@ -301489,7 +301489,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题3", + "origin": "2019届春季高考试题3", "edit": [ "20221209\t王伟叶" ], @@ -301508,7 +301508,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题4", + "origin": "2019届春季高考试题4", "edit": [ "20221209\t王伟叶" ], @@ -301527,7 +301527,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题5", + "origin": "2019届春季高考试题5", "edit": [ "20221209\t王伟叶" ], @@ -301546,7 +301546,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题6", + "origin": "2019届春季高考试题6", "edit": [ "20221209\t王伟叶" ], @@ -301565,7 +301565,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题7", + "origin": "2019届春季高考试题7", "edit": [ "20221209\t王伟叶" ], @@ -301584,7 +301584,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题8", + "origin": "2019届春季高考试题8", "edit": [ "20221209\t王伟叶" ], @@ -301603,7 +301603,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题9", + "origin": "2019届春季高考试题9", "edit": [ "20221209\t王伟叶" ], @@ -301622,7 +301622,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题10", + "origin": "2019届春季高考试题10", "edit": [ "20221209\t王伟叶" ], @@ -301641,7 +301641,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题11", + "origin": "2019届春季高考试题11", "edit": [ "20221209\t王伟叶" ], @@ -301660,7 +301660,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题12", + "origin": "2019届春季高考试题12", "edit": [ "20221209\t王伟叶" ], @@ -301679,7 +301679,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题13", + "origin": "2019届春季高考试题13", "edit": [ "20221209\t王伟叶" ], @@ -301698,7 +301698,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题14", + "origin": "2019届春季高考试题14", "edit": [ "20221209\t王伟叶" ], @@ -301717,7 +301717,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题15", + "origin": "2019届春季高考试题15", "edit": [ "20221209\t王伟叶" ], @@ -301736,7 +301736,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题16", + "origin": "2019届春季高考试题16", "edit": [ "20221209\t王伟叶" ], @@ -301755,7 +301755,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题17", + "origin": "2019届春季高考试题17", "edit": [ "20221209\t王伟叶" ], @@ -301774,7 +301774,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题18", + "origin": "2019届春季高考试题18", "edit": [ "20221209\t王伟叶" ], @@ -301793,7 +301793,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题19", + "origin": "2019届春季高考试题19", "edit": [ "20221209\t王伟叶", "20221212\t王慎有" @@ -301813,7 +301813,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题20", + "origin": "2019届春季高考试题20", "edit": [ "20221209\t王伟叶", "20221212\t王慎有" @@ -301835,7 +301835,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题21", + "origin": "2019届春季高考试题21", "edit": [ "20221209\t王伟叶" ], @@ -301854,7 +301854,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题1", + "origin": "2020届春季高考试题1", "edit": [ "20221209\t王伟叶" ], @@ -301873,7 +301873,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题2", + "origin": "2020届春季高考试题2", "edit": [ "20221209\t王伟叶" ], @@ -301892,7 +301892,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题3", + "origin": "2020届春季高考试题3", "edit": [ "20221209\t王伟叶" ], @@ -301911,7 +301911,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题4", + "origin": "2020届春季高考试题4", "edit": [ "20221209\t王伟叶" ], @@ -301930,7 +301930,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题5", + "origin": "2020届春季高考试题5", "edit": [ "20221209\t王伟叶" ], @@ -301949,7 +301949,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题6", + "origin": "2020届春季高考试题6", "edit": [ "20221209\t王伟叶" ], @@ -301968,7 +301968,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题7", + "origin": "2020届春季高考试题7", "edit": [ "20221209\t王伟叶" ], @@ -301987,7 +301987,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题8", + "origin": "2020届春季高考试题8", "edit": [ "20221209\t王伟叶" ], @@ -302006,7 +302006,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题9", + "origin": "2020届春季高考试题9", "edit": [ "20221209\t王伟叶" ], @@ -302025,7 +302025,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题10", + "origin": "2020届春季高考试题10", "edit": [ "20221209\t王伟叶" ], @@ -302044,7 +302044,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题11", + "origin": "2020届春季高考试题11", "edit": [ "20221209\t王伟叶" ], @@ -302063,7 +302063,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题12", + "origin": "2020届春季高考试题12", "edit": [ "20221209\t王伟叶" ], @@ -302082,7 +302082,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题13", + "origin": "2020届春季高考试题13", "edit": [ "20221209\t王伟叶" ], @@ -302101,7 +302101,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题14", + "origin": "2020届春季高考试题14", "edit": [ "20221209\t王伟叶" ], @@ -302120,7 +302120,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题15", + "origin": "2020届春季高考试题15", "edit": [ "20221209\t王伟叶", "20221212\t徐慧" @@ -302140,7 +302140,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题16", + "origin": "2020届春季高考试题16", "edit": [ "20221209\t王伟叶" ], @@ -302159,7 +302159,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题17", + "origin": "2020届春季高考试题17", "edit": [ "20221209\t王伟叶" ], @@ -302178,7 +302178,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题18", + "origin": "2020届春季高考试题18", "edit": [ "20221209\t王伟叶" ], @@ -302197,7 +302197,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题19", + "origin": "2020届春季高考试题19", "edit": [ "20221209\t王伟叶" ], @@ -302216,7 +302216,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题20", + "origin": "2020届春季高考试题20", "edit": [ "20221209\t王伟叶" ], @@ -302235,7 +302235,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2020年春季高考试题21", + "origin": "2020届春季高考试题21", "edit": [ "20221209\t王伟叶", "20221211\t徐慧" @@ -302255,7 +302255,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题1", + "origin": "2021届春季高考试题1", "edit": [ "20221209\t王伟叶" ], @@ -302274,7 +302274,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题2", + "origin": "2021届春季高考试题2", "edit": [ "20221209\t王伟叶" ], @@ -302293,7 +302293,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题3", + "origin": "2021届春季高考试题3", "edit": [ "20221209\t王伟叶" ], @@ -302312,7 +302312,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题4", + "origin": "2021届春季高考试题4", "edit": [ "20221209\t王伟叶" ], @@ -302331,7 +302331,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题5", + "origin": "2021届春季高考试题5", "edit": [ "20221209\t王伟叶" ], @@ -302350,7 +302350,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题6", + "origin": "2021届春季高考试题6", "edit": [ "20221209\t王伟叶" ], @@ -302369,7 +302369,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题7", + "origin": "2021届春季高考试题7", "edit": [ "20221209\t王伟叶" ], @@ -302388,7 +302388,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题8", + "origin": "2021届春季高考试题8", "edit": [ "20221209\t王伟叶" ], @@ -302407,7 +302407,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题9", + "origin": "2021届春季高考试题9", "edit": [ "20221209\t王伟叶" ], @@ -302426,7 +302426,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题10", + "origin": "2021届春季高考试题10", "edit": [ "20221209\t王伟叶" ], @@ -302445,7 +302445,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题11", + "origin": "2021届春季高考试题11", "edit": [ "20221209\t王伟叶" ], @@ -302464,7 +302464,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题12", + "origin": "2021届春季高考试题12", "edit": [ "20221209\t王伟叶" ], @@ -302483,7 +302483,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题13", + "origin": "2021届春季高考试题13", "edit": [ "20221209\t王伟叶" ], @@ -302502,7 +302502,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题14", + "origin": "2021届春季高考试题14", "edit": [ "20221209\t王伟叶" ], @@ -302521,7 +302521,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题15", + "origin": "2021届春季高考试题15", "edit": [ "20221209\t王伟叶" ], @@ -302540,7 +302540,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题16", + "origin": "2021届春季高考试题16", "edit": [ "20221209\t王伟叶" ], @@ -302559,7 +302559,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题17", + "origin": "2021届春季高考试题17", "edit": [ "20221209\t王伟叶" ], @@ -302578,7 +302578,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题18", + "origin": "2021届春季高考试题18", "edit": [ "20221209\t王伟叶" ], @@ -302597,7 +302597,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题19", + "origin": "2021届春季高考试题19", "edit": [ "20221209\t王伟叶" ], @@ -302616,7 +302616,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题20", + "origin": "2021届春季高考试题20", "edit": [ "20221209\t王伟叶" ], @@ -302635,7 +302635,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2021年春季高考试题21", + "origin": "2021届春季高考试题21", "edit": [ "20221209\t王伟叶" ], @@ -302654,7 +302654,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题1", + "origin": "2022届春季高考试题1", "edit": [ "20221209\t王伟叶" ], @@ -302673,7 +302673,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题2", + "origin": "2022届春季高考试题2", "edit": [ "20221209\t王伟叶" ], @@ -302692,7 +302692,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题3", + "origin": "2022届春季高考试题3", "edit": [ "20221209\t王伟叶" ], @@ -302711,7 +302711,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题4", + "origin": "2022届春季高考试题4", "edit": [ "20221209\t王伟叶" ], @@ -302730,7 +302730,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题5", + "origin": "2022届春季高考试题5", "edit": [ "20221209\t王伟叶" ], @@ -302749,7 +302749,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题6", + "origin": "2022届春季高考试题6", "edit": [ "20221209\t王伟叶" ], @@ -302768,7 +302768,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题7", + "origin": "2022届春季高考试题7", "edit": [ "20221209\t王伟叶" ], @@ -302787,7 +302787,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题8", + "origin": "2022届春季高考试题8", "edit": [ "20221209\t王伟叶" ], @@ -302806,7 +302806,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题9", + "origin": "2022届春季高考试题9", "edit": [ "20221209\t王伟叶" ], @@ -302825,7 +302825,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题10", + "origin": "2022届春季高考试题10", "edit": [ "20221209\t王伟叶" ], @@ -302844,7 +302844,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题11", + "origin": "2022届春季高考试题11", "edit": [ "20221209\t王伟叶" ], @@ -302863,7 +302863,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题12", + "origin": "2022届春季高考试题12", "edit": [ "20221209\t王伟叶" ], @@ -302882,7 +302882,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题13", + "origin": "2022届春季高考试题13", "edit": [ "20221209\t王伟叶" ], @@ -302901,7 +302901,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题14", + "origin": "2022届春季高考试题14", "edit": [ "20221209\t王伟叶" ], @@ -302920,7 +302920,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题15", + "origin": "2022届春季高考试题15", "edit": [ "20221209\t王伟叶" ], @@ -302939,7 +302939,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题16", + "origin": "2022届春季高考试题16", "edit": [ "20221209\t王伟叶" ], @@ -302958,7 +302958,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题17", + "origin": "2022届春季高考试题17", "edit": [ "20221209\t王伟叶" ], @@ -302977,7 +302977,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题18", + "origin": "2022届春季高考试题18", "edit": [ "20221209\t王伟叶" ], @@ -302996,7 +302996,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题19", + "origin": "2022届春季高考试题19", "edit": [ "20221209\t王伟叶" ], @@ -303015,7 +303015,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题20", + "origin": "2022届春季高考试题20", "edit": [ "20221209\t王伟叶" ], @@ -303034,7 +303034,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2022年春季高考试题21", + "origin": "2022届春季高考试题21", "edit": [ "20221209\t王伟叶" ], @@ -303844,6 +303844,3008 @@ "remark": "", "space": "12ex" }, + "012329": { + "id": "012329", + "content": "已知集合$A=\\{1,2,k\\}, B=\\{2,5\\}$, 若$A \\cup B=\\{1,2,3,5\\}$, 则$k=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题1", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012330": { + "id": "012330", + "content": "函数$y=\\sqrt {x+1}$的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题2", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012331": { + "id": "012331", + "content": "抛物线$y^2=8 x$的焦点坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题3", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012332": { + "id": "012332", + "content": "若复数$z$满足$\\mathrm{i} z=1+\\mathrm{i}$($\\mathrm{i}$为虚数单位), 则$z=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题4", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012333": { + "id": "012333", + "content": "函数$f(x)=\\sin (2 x+\\dfrac{\\pi}4)$的最小正周期为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题5", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012334": { + "id": "012334", + "content": "方程$4^x-2^{x+1}=0$的解为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题6", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012335": { + "id": "012335", + "content": "若$(2 x-1)^5=a_0+a_1 x+a_2 x^2+a_3 x^3+a_4 x^4+a_5 x^5$, 则$a_0+a_1+a_2+a_3+a_4+a_5=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题7", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012336": { + "id": "012336", + "content": "若$f(x)=\\dfrac{(x+2)(x+m)}x$为奇函数, 则实数$m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题8", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012337": { + "id": "012337", + "content": "函数$y=\\log_2 x+\\dfrac 4{\\log_2 x} (x \\in[2,4])$的最大值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题9", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012338": { + "id": "012338", + "content": "若复数$z$满足$|z-\\mathrm{i}|\\leq \\sqrt 2$($\\mathrm{i}$为虚数单位), 则$z$在复平面内所对应的图形的面积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题10", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012339": { + "id": "012339", + "content": "某校要从$2$名男生和$4$名女生中选出$4$人担任某游泳赛事的志愿者工作, 则在选出的志愿者中, 男、女都有的概率为\\blank{50}. (结果用数值表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题11", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012340": { + "id": "012340", + "content": "若不等式$x^2-k x+k-1>0$对$x \\in(1,2)$恒成立, 则实数$k$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题12", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012341": { + "id": "012341", + "content": "已知等差数列$\\{a_n\\}$的首项及公差均为正数, 令$b_n=\\sqrt {a_n}+\\sqrt {a_{2012-n}}$($n \\in \\mathbf{N}$, $1\\le n<2012$), 当$b_k$是数列$\\{b_n\\}$的最大项时, $k=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题13", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012342": { + "id": "012342", + "content": "若矩阵$\\begin{pmatrix}a_{11} & a_{12} \\\\a_{21} & a_{22}\\end{pmatrix}$满足: $a_{11}$、$a_{12}$、$a_{21}$、$a_{22} \\in\\{-1,1\\}$, 且$\\begin{vmatrix}a_{11} & a_{12} \\\\a_{21} & a_{22}\\end{vmatrix}=0$, 则这样的互不相等的矩阵共有\\blank{50}个.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题14", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012343": { + "id": "012343", + "content": "已知粗圆$C_1: \\dfrac{x^2}{12}+\\dfrac{y^2}4=1$, $C_2: \\dfrac{x^2}{16}+\\dfrac{y^2}8=1$, 则\\bracket{20}.\n\\fourch{$C_1$与$C_2$顶点相同}{$C_1$与$C_2$长轴长相同}{$C_1$与$C_2$短轴长相同}{$C_1$与$C_2$焦距相等}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题15", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012344": { + "id": "012344", + "content": "记函数$y=f(x)$的反函数为$y=f^{-1}(x)$, 如果函数$y=f(x)$的图像过点$(1,0)$, 那么函数$y=f^{-1}(x)+1$的图像过点\\bracket{20}.\n\\fourch{$(0,0)$}{$(0,2)$}{$(1,1)$}{$(2,0)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题16", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012345": { + "id": "012345", + "content": "已知空间三条直线$l$、$m$、$n$, 若$l$与$m$异面, 且$l$与$n$异面, 则\\bracket{20}.\n\\twoch{$m$与$n$异面}{$m$与$n$相交}{$m$与$n$平行}{$m$与$n$异面、相交、平行均有可能}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题17", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012346": { + "id": "012346", + "content": "设$O$为$\\triangle ABC$所在平面上一点, 若实数$x$、$y$、$z$满足$x \\overrightarrow{OA}+y \\overrightarrow{OB}+z \\overrightarrow{OC}=\\overrightarrow 0$($x^2+y^2+z^2 \\neq 0$), 则``$xyz=0$''是``点$O$在$\\triangle ABC$的边所在直线上''的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{既不充分又不必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题18", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012347": { + "id": "012347", + "content": "如图, 正四棱柱$ABCD-A_1B_1C_1D_1$的底面边长为$1$, 高为$2$, $M$为线段$AB$的中点, 求:\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.3]\n\\def\\l{1}\n\\def\\m{1}\n\\def\\n{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,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(A)!0.5!(B)$) node [below] {$M$} coordinate (M);\n\\draw [dashed] (M) -- (C1);\n\\end{tikzpicture}\n\\end{center}\n(1) 三棱锥$C_1-MBC$的体积;\\\\\n(2) 异面直线$CD$与$MC_1$所成角的大小. (结果用反三角函数值表示)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题19", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012348": { + "id": "012348", + "content": "某环线地铁按内、外环线同时运行, 内、外环线的长均为$30$千米. (忽略内、外环线长度差异)\\\\\n(1) 当$9$列列车同时在内环线上运行时, 要使内环线乘客最长候车时间为$10$分钟, 求内环线列车的最小平均速度;\\\\\n(2) 新调整的方案要求内环线列车平均速度为$25$千米/小时, 外环线列车平均速度为$30$千米/小时, 现内、外环线共有$18$列列车全部投入运行, 要使内、外环线乘客的最长候车时间之差不超过$1$分钟, 问: 内、外环线应名投入几列列车运行?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题20", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012349": { + "id": "012349", + "content": "已知双曲线$C_1: x^2-\\dfrac{y^2}4=1$.\\\\\n(1) 求与双曲线$C_1$有相同的焦点, 且过点$P(4, \\sqrt 3)$的双曲线$C_2$的标准方程;\\\\\n(2) 直线$l: y=x+m$分别交双曲线$C_1$的两条渐近线于$A$、$B$两点, 当$\\overrightarrow{OA} \\cdot \\overrightarrow{OB}=3$时, 求实数$m$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题21", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012350": { + "id": "012350", + "content": "已知数列$\\{a_n\\}$、$\\{b_n\\}$、$\\{c_n\\}$满足$(a_{n+1}-a_n)(b_{n+1}-b_n)=c_n$($n \\in \\mathbf{N}$, $n\\ge 1$).\\\\\n(1) 设$c_n=3 n+6$, $\\{a_n\\}$是公差为$3$的等差数列, 当$b_1=1$时, 求$b_2$、$b_3$的值;\\\\\n(2) 设$c_n=n^3$, $a_n=n^2-8 n$, 求正整数$k$, 使得一切$n \\in \\mathbf{N}$, $n\\ge 1$, 均有$b_n \\geq b_k$;\\\\\n(3) 设$c_n=2^n+n$, $a_n=\\dfrac{1+(-1)^n}2$, 当$b_1=1$时, 求数列$\\{b_n\\}$的通项公式.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题22", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012351": { + "id": "012351", + "content": "定义向量$\\overrightarrow{OM}=(a, b)$的``相伴函数''为$f(x)=a \\sin x+b \\cos x$; 函数$f(x)=a \\sin x+b \\cos x$的``相伴向量''为$\\overrightarrow{OM}=(a, b)$(其中$O$为坐标原点), 记平面内所有向量的``相伴函数''构成的集合为$S$.\\\\\n(1) 设$g(x)=3 \\sin (x+\\dfrac{\\pi}2)+4 \\sin x$, 求证: $g(x) \\in S$;\\\\\n(2) 已知$h(x)=\\cos (x+\\alpha)+2 \\cos x$, 且$h(x) \\in S$, 求其``相伴向量''的模;\\\\\n(3) 已知$M(a, b)$($b \\neq 0$)为圆$C:(x-2)^2+y^2=1$上一点, 向量$\\overrightarrow{OM}$的``相伴函数''$f(x)$在$x=x_0$处取得最大值, 当点$M$在圆$C$上运动时, 求$\\tan 2 x_0$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2012届春季高考试题23", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012352": { + "id": "012352", + "content": "函数$y=\\log_2(x+2)$的定义域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题1", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012353": { + "id": "012353", + "content": "方程$2^x=8$的解是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题2", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012354": { + "id": "012354", + "content": "抛物线$y^2=8 x$的准线方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题3", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012355": { + "id": "012355", + "content": "函数$y=2 \\sin x$的最小正周期是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题4", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012356": { + "id": "012356", + "content": "已知向量$\\overrightarrow a=(1, k)$, $\\overrightarrow b=(9, k-6)$, 若$\\overrightarrow a \\parallel \\overrightarrow b$, 则实数$k=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题5", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012357": { + "id": "012357", + "content": "函数$y=4 \\sin x+3 \\cos x$的最大值是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题6", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012358": { + "id": "012358", + "content": "复数$2+3 \\mathrm{i}$($\\mathrm{i}$是虚数单位)的模是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题7", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012359": { + "id": "012359", + "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$所对边长分别为$a$、$b$、$c$, 若$a=5$, $c=8$, $B=60^{\\circ}$, 则$b=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题8", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012360": { + "id": "012360", + "content": "在如图所示的正方体$ABCD-A_1B_1C_1D_1$中, 异面直线$A_1B$与$B_1C$所成角的大小为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{1.5}\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 (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题9", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012361": { + "id": "012361", + "content": "从$4$名男同学和$6$名女同学中随机选取$3$人参加某社团活动, 选出的$3$人中男女同学都有的概率为\\blank{50}.(结果用数值表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题10", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012362": { + "id": "012362", + "content": "若等差数列的前$6$项和为$23$, 前$9$项和为$57$, 则数列的前$n$项和$S_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题11", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012363": { + "id": "012363", + "content": "$36$的所有正约数之和可按如下方法得到: 因为$36=2^2 \\times 3^2$, 所以$36$的所有正约数之和为$(1+3+3^2)+(2+2 \\times 3+2 \\times 3^2)+(2^2+2^2 \\times 3+2^2 \\times 3^2)=(1+2+2^2)(1+3+3^2)=91$, 参照上述方法, 可求得 $2000$的所有正约数之和为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题12", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012364": { + "id": "012364", + "content": "展开式为$a d-b c$的行列式是\\bracket{20}.\n\\fourch{$\\begin{vmatrix}a & b \\\\d & c\\end{vmatrix}$}{$\\begin{vmatrix}a & c \\\\b & d\\end{vmatrix}$}{$\\begin{vmatrix}a & d \\\\b & c\\end{vmatrix}$}{$\\begin{vmatrix}b & a \\\\d & c\\end{vmatrix}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题13", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012365": { + "id": "012365", + "content": "设$f^{-1}(x)$为函数$f(x)=\\sqrt x$的反函数, 下列结论正确的是\\bracket{20}.\n\\fourch{$f^{-1}(2)=2$}{$f^{-1}(2)=4$}{$f^{-1}(4)=2$}{$f^{-1}(4)=4$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题14", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012366": { + "id": "012366", + "content": "直线$2 x-3 y+1=0$的一个方向向量是\\bracket{20}.\n\\fourch{$(2,-3)$}{$(2,3)$}{$(-3,2)$}{$(3,2)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题15", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012367": { + "id": "012367", + "content": "函数$f(x)=x^{-\\frac 12}$的大致图像是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-0.5,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.12:3] plot (\\x,{pow(\\x,-0.5)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-0.5,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:3] plot (\\x,{pow(\\x,0.5)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-1.75,0) -- (1.75,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:1.75] plot (\\x,{pow(\\x,0.5)});\n\\draw [domain = 0:1.75] plot (-\\x,{pow(\\x,0.5)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-1.75,0) -- (1.75,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.12:1.75] plot (\\x,{pow(\\x,-0.5)});\n\\draw [domain = 0.12:1.75] plot (-\\x,{pow(\\x,-0.5)});\n\\end{tikzpicture}}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题16", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012368": { + "id": "012368", + "content": "如果$a=latex,scale = 0.4]\n\\def\\l{2*sqrt(3)}\n\\def\\h{6}\n\\draw ({-\\l/2},0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,{\\l/2*sqrt(3)}) node [below] {$B$} coordinate (B);\n\\draw ({\\l/2},0,0) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,\\h) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\h) node [below right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\h) node [right] {$C_1$} coordinate (C_1);\n\\draw (A) -- (B) -- (C) (A) -- (A_1) (B) -- (B_1) (C) -- (C_1) (A_1) -- (B_1) -- (C_1) (A_1) -- (C_1);\n\\draw (B) -- (C_1);\n\\draw [dashed] (A) -- (C);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题25", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012377": { + "id": "012377", + "content": "如图, 某校有一块形如直角三角形$ABC$的空地, 其中$\\angle B$为直角, $A B$长$40$米, $BC$长$50$米, 现欲在此空地上建造一间健身房, 其占地形状为矩形, 且$B$为矩形的一个顶点, 求该健身房的最大占地面积.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (2.5,0) node [right] {$C$} coordinate (C);\n\\draw (0,2) node [left] {$A$} coordinate (A);\n\\draw (A) -- (B) -- (C) (A) -- (C);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题26", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012378": { + "id": "012378", + "content": "已知数列$\\{a_n\\}$的前$n$项和为$S_n=-n^2+n$, 数列$\\{b_n\\}$满足$b_n=2^{a_n}$, 求$\\displaystyle \\lim_{n \\to \\infty}(b_1+b_2+\\cdots+b_n)$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题27", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012379": { + "id": "012379", + "content": "已知椭圆$C$的两个焦点分别为$F_1(-1,0)$、$F_2(1,0)$, 短轴的两个端点分别为$B_1$、$B_2$.\\\\\n(1) 若$\\triangle F_1B_1B_2$为等边三角形, 求椭圆$C$的方程;\\\\\n(2) 若椭圆$C$的短轴长为$2$, 过点$F_2$的直线$l$与椭圆$C$相交于$P$、$Q$两点, 且$\\overrightarrow{F_1P} \\perp \\overrightarrow{F_1Q}$, 求直线$l$的方程.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题28", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012380": { + "id": "012380", + "content": "已知抛物线$C: y^2=4 x$的焦点为$F$.\\\\\n(1) 点$A$、$P$满足$\\overrightarrow{AP}=-2 \\overrightarrow{FA}$, 当点$A$在抛物线$C$上运动时, 求动点$P$的轨迹方程;\\\\\n(2) 在$x$轴上是否存在点$Q$, 使得点$Q$关于直线$y=2 x$的对称点在抛物线$C$上? 如果存在, 求所有满足条件的点$Q$的坐标; 如果不存在, 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题29", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012381": { + "id": "012381", + "content": "在平面直角坐标系$xOy$中, 点$A$在$y$轴正半轴上, 点$P_n$在$x$轴上, 其横坐标为$x_n$, 且$\\{x_n\\}$是首项为$1$、公比为$2$的等比数列, 记$\\angle P_nAP_{n+1}=\\theta_n$, $n \\in \\mathbf{N}$, $n\\ge 1$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.35]\n\\draw [->] (-1,0) -- (11,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {1,2,3,4} {\\draw ({pow(2,\\i-1)},0) -- (0,4); \\draw ({pow(2,\\i-1)},0) node [below] {$P_\\i$};};\n\\draw (10,0) node [below] {$\\cdots$};\n\\draw (0,4) node [left] {$A$};\n\\end{tikzpicture}\n\\end{center}\n(1) 若$\\theta_3=\\arctan \\dfrac 13$, 求点$A$的坐标;\\\\\n(2) 若点$A$的坐标为$(0,8 \\sqrt 2)$, 求$\\theta_n$的最大值及相应$n$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题30", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012382": { + "id": "012382", + "content": "已知真命题: ``函数$y=f(x)$的图像关于点$P(a, b)$成中心对称图形''的充要条件为``函数$y=f(x+a)-b$是奇函数''.\n(1) 将函数$g(x)=x^3-3 x^2$的图像向左平移$1$个单位, 再向上平移$2$个单位, 求此时图像对应的函数解析式, 并利用题设中的真命题求函数$g(x)$图像对称中心的坐标;\\\\\n(2) 求函数$h(x)=\\log_2 \\dfrac{2 x}{4-x}$图像对称中心的坐标;\\\\\n(3) 已知命题: ``函数$y=f(x)$的图像关于某直线成轴对称图形''的充要条件为``存在实数$a$和$b$, 使得函数$y=f(x+a)-b$是偶函数'' , 判断该命题的真假, 如果是真命题, 请给予证明; 如果是假命题, 请说明理由, 并类比题设的真命题对它进行修改, 使之成为真命题(不必证明).", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2013届春季高考试题31", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012383": { + "id": "012383", + "content": "若$4^x=16$, 则$x=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题1", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012384": { + "id": "012384", + "content": "计算:$\\mathrm{i}(1+\\mathrm{i})=$\\blank{50}.($\\mathrm{i}$为虚数单位)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题2", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012385": { + "id": "012385", + "content": "$1$、$1$、$2$、$2$、$5$这五个数的中位数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题3", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012386": { + "id": "012386", + "content": "若函数$f(x)=x^3+a$为奇函数, 则实数$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题4", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012387": { + "id": "012387", + "content": "点$O(0,0)$到直线$x+y-4=0$的距离是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题5", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012388": { + "id": "012388", + "content": "函数$y=\\dfrac 1{x+1}$的反函数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题6", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012389": { + "id": "012389", + "content": "已知等差数列$\\{a_n\\}$的首项为$1$, 公差为$2$, 则该数列的前$n$项和$S_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题7", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012390": { + "id": "012390", + "content": "已知$\\cos \\alpha=\\dfrac 13$, 则$\\cos 2 \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题8", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012391": { + "id": "012391", + "content": "已知$a$、$b \\in (0,+\\infty)$, 若$a+b=1$, 则$ab$的最大值是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题9", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012392": { + "id": "012392", + "content": "在$10$件产品中, 有$3$件次品, 从中随机取出$5$件, 则恰含$1$件次品的概率是\\blank{50}.(结果用数值表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题10", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012393": { + "id": "012393", + "content": "某货船在$O$处看灯塔$M$在北偏东$30^{\\circ}$方向, 它以每小时$18$海里的速度向正北方向航行, 经过$40$分钟到达$B$处, 看到灯塔$M$在北偏东$75^{\\circ}$方向, 此时货船到灯塔$M$的距离为\\blank{50}海里.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题11", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012394": { + "id": "012394", + "content": "已知函数$f(x)=\\dfrac{x-2}{x-1}$与$g(x)=m x+1-m$的图像相交于$A$、$B$两点, 若动点$P$满足$|\\overrightarrow{PA}+\\overrightarrow{PB}|=2$, 则$P$的轨迹方程为\\blank{50}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题12", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012395": { + "id": "012395", + "content": "两条异面直线所成的角的范围是\\bracket{20}.\n\\fourch{$(0, \\dfrac{\\pi}2)$}{$(0, \\dfrac{\\pi}2]$}{$[0, \\dfrac{\\pi}2)$}{$[0, \\dfrac{\\pi}2]$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题13", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012396": { + "id": "012396", + "content": "复数$2+\\mathrm{i}$($\\mathrm{i}$为虚数单位) 的共轭复数为 \\bracket{20}.\n\\fourch{$2-\\mathrm{i}$}{$-2+i$}{$-2-\\mathrm{i}$}{$1+2 \\mathrm{i}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题14", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012397": { + "id": "012397", + "content": "如图是下列函数中某个函数的部分图像, 则该函数是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -1:4,samples = 100] plot (\\x,{sin(\\x/pi*360)});\n\\draw [dashed] ({pi/4},1) -- (0,1) node [left] {$1$};\n\\draw [dashed] ({3*pi/4},-1) -- (0,-1) node [left] {$-1$};\n\\draw ({pi/2},0) node [below left] {$\\frac\\pi 2$};\n\\draw (pi,0) node [below right] {$\\pi$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$y=\\sin x$}{$y=\\sin 2 x$}{$y=\\cos x$}{$y=\\cos 2 x$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题15", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012398": { + "id": "012398", + "content": "在$(x+1)^4$的二项展开式中,$x^2$项的系数为\\bracket{20}.\n\\fourch{$6$}{$4$}{$2$}{$1$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题16", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012399": { + "id": "012399", + "content": "下列函数中, 在$\\mathbf{R}$上为增函数的是\\bracket{20}.\n\\fourch{$y=x^2$}{$y=|x|$}{$y=\\sin x$}{$y=x^3$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题17", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012400": { + "id": "012400", + "content": "$\\begin{vmatrix}\\cos \\theta & -\\sin \\theta \\\\\\sin \\theta & \\cos \\theta\\end{vmatrix}=$\\bracket{20}.\n\\fourch{$\\cos 2 \\theta$}{$\\sin 2 \\theta$}{$1$}{$-1$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题18", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012401": { + "id": "012401", + "content": "设$x_0$为函数$f(x)=2^x+x-2$的零点, 则$x_0 \\in$\\bracket{20}.\n\\fourch{$(-2,-1)$}{$(-1,0)$}{$(0,1)$}{$(1,2)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题19", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012402": { + "id": "012402", + "content": "若$a>b$, $c \\in \\mathbf{R}$, 则下列不等式中恒成立的是\\bracket{20}.\n\\fourch{$\\dfrac 1a<\\dfrac 1b$}{$a^2>b^2$}{$a|c|>b|c|$}{$\\dfrac a{c^2+1}>\\dfrac b{c^2+1}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题20", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012403": { + "id": "012403", + "content": "若两个球的体积之比为$8: 27$, 则它们的表面积之比为\\bracket{20}.\n\\fourch{$2: 3$}{$4: 9$}{$8: 27$}{$2 \\sqrt 2: 3 \\sqrt 3$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题21", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012404": { + "id": "012404", + "content": "已知数列$\\{a_n\\}$是以$q$为公比的等比数列, 若$b_n=-2 a_n$, 则数列$\\{b_n\\}$是\\bracket{20}.\n\\twoch{以$q$为公比的等比数列}{以$-q$为公比的等比数列}{以$2 q$为公比的等比数列}{以$-2 q$为公比的等比数列}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题22", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012405": { + "id": "012405", + "content": "若点$P$的坐标为$(a, b)$, 曲线$C$的方程为$F(x, y)=0$, 则``$F(a, b)=0$''是``点$P$在曲线$C$上''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充分必要条件}{既非充分又非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题23", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012406": { + "id": "012406", + "content": "如图, 在底面半径和高均为$1$的圆锥中, $AB$、$CD$是底面圆$O$的两条互相垂直的直径, $E$是母线$PB$的中点, 已知过$CD$与$E$的平面与圆锥侧面的交线是以$E$为顶点的抛物线的一部分, 则该抛物线的焦点到圆锥顶点$P$的距离为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 2]\n\\def\\r{1}\n\\def\\h{1}\n\\draw ({-\\r},0,0) node [left] {$A$} coordinate (A) -- (0,\\h,0) node [above] {$P$} coordinate (P) -- (\\r,0,0) node [right] {$B$} coordinate (B);\n\\draw (0,0,0) node [below left] {$O$} coordinate (O);\n\\draw (A) arc (180:360:{\\r} and {\\r/4});\n\\draw [dashed] (A) arc (180:0:{\\r} and {\\r/4});\n\\draw [dashed] (A) -- (B) (O) -- (P);\n\\draw ($(P)!0.5!(B)$) node [above right] {$E$} coordinate (E);\n\\draw [dashed] (O) -- (E);\n\\draw ({\\r*cos(-70)},{\\r/4*sin(-70)}) node [below] {$C$} coordinate (C);\n\\draw ({\\r*cos(110)},{\\r/4*sin(110)}) node [below] {$D$} coordinate (D);\n\\draw (C) .. controls +({\\r/10},{\\r/10}) and +({\\r*cos(-70)/3},{\\r/4*sin(-70)/3}) .. (E);\n\\draw [dashed] (D) .. controls +({\\r/10},{\\r/10}) and +({-\\r*cos(-70)/3},{-\\r/4*sin(-70)/3}) .. (E) (C) -- (D);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$1$}{$\\dfrac{\\sqrt 3}2$}{$\\dfrac{\\sqrt 6}2$}{$\\dfrac{\\sqrt{10}}4$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题24", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012407": { + "id": "012407", + "content": "已知不等式$\\dfrac{x-2}{x+1}<0$的解集为$A$, 函数$y=\\lg (x-1)$的定义域为集合$B$, 求$A \\cap B$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题25", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012408": { + "id": "012408", + "content": "已知函数$f(x)=x^2-4 x+a, x \\in[-3,3]$, 若$f(1)=2$, 求$y=f(x)$的最大值和最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题26", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012409": { + "id": "012409", + "content": "如图, 在体积为$\\dfrac 13$的三棱锥$P-ABC$中, $PA$与平面$ABC$垂直, $AP=AB=1$, $\\angle BAC=\\dfrac{\\pi}2$, $E$、$F$分别是$PB$、$AB$的中点, 求异面直线$EF$与$PC$所成的角的大小. (结果用反三角函数值表示)\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 2]\n\\draw (0,0,0) node [above right] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,0,1) node [left] {$B$} coordinate (B);\n\\draw (0,1,0) node [above] {$P$} coordinate (P);\n\\draw (B) -- (P) -- (C);\n\\draw (B) -- (C);\n\\draw [dashed] (B) -- (A) -- (C) (A) -- (P);\n\\draw ($(A)!0.5!(B)$) node [right] {$F$} coordinate (F);\n\\draw ($(P)!0.5!(B)$) node [above left] {$E$} coordinate (E);\n\\draw [dashed] (E) -- (F);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题27", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012410": { + "id": "012410", + "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+y^2=1(a>1)$的左焦点为$F$, 上顶点为$B$.\\\\\n(1) 若直线$FB$的一个方向向量为$(1, \\dfrac{\\sqrt 3}3)$, 求实数$a$的值;\\\\\n(2) 若$a=\\sqrt 2$, 直线$l: y=k x-2$与椭圆$C$相交于$M$、$N$两点, 且$\\overrightarrow{FM} \\cdot \\overrightarrow{FN}=3$, 求实数$k$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题28", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012411": { + "id": "012411", + "content": "已知数列$\\{a_n\\}$满足$a_n>0$, 双曲线$C_n: \\dfrac{x^2}{a_n}-\\dfrac{y^2}{a_{n+1}}=1$($n \\in \\mathbf{N}$, $n\\ge 1$).\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (\\x,{sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (-\\x,{sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (\\x,{-sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (-\\x,{-sqrt(\\x*\\x-2)});\n\\draw (-4,-4) -- (4,4) (-4,4) -- (4,-4);\n\\draw (2,2) node [left] {$Q_n$} coordinate (Q_n);\n\\draw ({sqrt(6)},2) node [right] {$P_n$} coordinate (P_n);\n\\filldraw [pattern = north west lines] (O) -- (P_n) -- (Q_n);\n\\end{tikzpicture}\n\\end{center}\n(1) 若$a_1=1$, $a_2=2$, 双曲线$C_n$的焦距为$2 c_n$, $c_n=\\sqrt {4 n-1}$, 求$\\{a_n\\}$的通项公式;\\\\\n(2) 如图, 在双曲线$C_n$的右支上取点$P_n(x_{P_n}, n)$, 过$P_n$作$y$轴的垂线, 在第一象限内交$C_n$的渐近线于点$Q_n$, 联结$O P_n$, 记$\\triangle OP_nQ_n$的面积为$S_n$, 若$\\displaystyle\\lim_{n \\to \\infty} a_n=2$, 求$\\displaystyle \\lim_{n \\to \\infty} S_n$.(关于数列极限的运算, 还可参考如下性质: 若$\\displaystyle \\lim_{n \\to \\infty} u_n=A(u_n \\geq 0)$, 则$\\displaystyle \\lim_{n \\to \\infty} \\sqrt {u_n}=\\sqrt A$)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题29", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012412": { + "id": "012412", + "content": "已知直角三角形$A B C$的两直角边$A C$、$B C$的边长分别为$b$、$a$, 如图, 过$A C$边的$n$等分点$A_i$作$A C$边的垂线$d_i$, 过$B C$边的$n$等分点$B_i$和顶点$A$作直线$l_i$, 记$d_i$与$l_i$的交点为$P_i$($i=1,2, \\cdots, n-1$), 是否存在一条圆锥曲线, 对任意的正整数$n \\geq 2$, 点$P_i$($i=1,2, \\cdots, n-1$)都在这条曲线上? 说明理由.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (4,0) node [right] {$C$} coordinate (C);\n\\draw (4,3) node [right] {$B$} coordinate (B);\n\\draw (A) -- (C) -- (B) (A) -- (B);\n\\foreach \\i in {1,2,3,4,5} {\\draw ($(A)!{\\i/6}!(C)$) --++ (0,{0.5*\\i});};\n\\foreach \\i in {1,2,3,4,5} {\\draw ($(B)!{\\i/6}!(C)$) -- (A);};\n\\foreach \\i/\\j in {1/1,2/2,4/i} {\\draw ($(A)!{\\i/6}!(C)$) node [below] {$A_\\j$}; \\draw ($(C)!{\\i/6}!(B)$) node [right] {$B_\\j$};};\n\\foreach \\i/\\j in {3,5} {\\draw ($(A)!{\\i/6}!(C)$) node [below] {$\\cdots$}; \\draw ($(C)!{\\i/6}!(B)$) node [right] {$\\cdots$};};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题30", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012413": { + "id": "012413", + "content": "某人造卫星在地球赤道平面绕地球飞行, 甲、乙两个监测点分别位于赤道上东经$131^{\\circ}$和$147^{\\circ}$, 在某时刻测得甲监测点到卫星的距离为$1537.45$千米, 乙监测点到卫星的距离为$887.64$千米, 假设地球赤道是一个半径为$6378$千米的圆, 求此时卫星所在位置的高度(结果精确到$0.01$千米)和经度(结果精确到$0.01^{\\circ}$).", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题31", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012414": { + "id": "012414", + "content": "如果存在非零常数$c$, 对于函数$y=f(x)$定义域$\\mathbf{R}$上的任意$x$, 都有$f(x+c)>f(x)$成立, 那么称函数为``$Z$函数''.\\\\\n(1) 求证: 若$y=f(x)$($x \\in \\mathbf{R}$)是单调函数, 则它是``$Z$函数'';\\\\\n(2) 若函数$g(x)=a x^3+b x^2$是``$Z$函数'', 求实数$a$、$b$满足的条件.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2014届春季高考试题32", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012415": { + "id": "012415", + "content": "设全集为$U=\\{1,2,3\\}$, 若集合$A=\\{1,2\\}$, 则$\\complement_UA=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题1", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012416": { + "id": "012416", + "content": "计算:$\\dfrac{1+\\mathrm{i}}{\\mathrm{i}}=$\\blank{50}.(其中$\\mathrm{i}$为虚数单位)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题2", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012417": { + "id": "012417", + "content": "函数$y=\\sin (2 x+\\dfrac{\\pi}4)$的最小正周期为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题3", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012418": { + "id": "012418", + "content": "计算:$\\displaystyle\\lim_{n \\to \\infty} \\dfrac{n^2-3}{2 n^2+n}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题4", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012419": { + "id": "012419", + "content": "以$(2,6)$为圆心, $1$为半径的圆的标准方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题5", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012420": { + "id": "012420", + "content": "已知向量$\\overrightarrow a=(1,3)$, $\\overrightarrow b=(m,-1)$, 若$\\overrightarrow a \\perp \\overrightarrow b$, 则$m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题6", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012421": { + "id": "012421", + "content": "函数$y=x^2-2 x+4, x \\in[0,2]$的值域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题7", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012422": { + "id": "012422", + "content": "若线性方程组的增广矩阵为$\\begin{pmatrix}a & 0 & 2 \\\\0 & 1 & b\\end{pmatrix}$, 解为$\\begin{cases}x=2, \\\\y=1,\\end{cases}$ 则$a+b=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题8", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012423": { + "id": "012423", + "content": "方程$\\lg (2 x+1)+\\lg x=1$的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题9", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012424": { + "id": "012424", + "content": "在$(x+\\dfrac 1{x^2})^9$的二项展开式中, 常数项的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题10", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012425": { + "id": "012425", + "content": "用数字组成无重复数字的三位数, 其中奇数的个数为\\blank{50}. (结果用数值表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题11", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012426": { + "id": "012426", + "content": "已知点$A(1,0)$, 直线$l: x=-1$, 两个动圆均过点$A$且与$l$相切, 其圆心分别为$C_1$、$C_2$, 若动点$M$满足$2 \\overrightarrow{C_2M}=\\overrightarrow{C_2C_1}+\\overrightarrow{C_2A}$, 则$M$的轨迹方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题12", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012427": { + "id": "012427", + "content": "若$a<0\\dfrac 1b$}{$-a>b$}{$a^2>b^2$}{$a^30$的解集为\\bracket{20}\n\\fourch{$(-\\infty, \\dfrac 34)$}{$(-\\infty, \\dfrac 23)$}{$(-\\infty, \\dfrac 23) \\cup(1,+\\infty)$}{$(\\dfrac 23, 1)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题15", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012430": { + "id": "012430", + "content": "下列函数中, 是奇函数且在$(0,+\\infty)$上单调递增的为\\bracket{20}.\n\\fourch{$y=x^2$}{$y=x^{\\frac 13}$}{$y=x^{-1}$}{$y=x^{-\\frac 12}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题16", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012431": { + "id": "012431", + "content": "直线$3 x-4 y-5=0$的倾斜角为\\bracket{20}.\n\\fourch{$\\arctan \\dfrac 34$}{$\\pi-\\arctan \\dfrac 34$}{$\\arctan \\dfrac 43$}{$\\pi-\\arctan \\dfrac 43$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题17", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012432": { + "id": "012432", + "content": "底面半径为 1 , 母线长为 2 的圆锥的体积为\\bracket{20}.\n\\fourch{$2 \\pi$}{$\\sqrt 3 \\pi$}{$\\dfrac{2 \\pi}3$}{$\\dfrac{\\sqrt 3 \\pi}3$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题18", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012433": { + "id": "012433", + "content": "以$(-3,0)$和$(3,0)$为焦点, 长轴长为$8$的椭圆方程为\\bracket{20}.\n\\fourch{$\\dfrac{x^2}{16}+\\dfrac{y^2}{25}=1$}{$\\dfrac{x^2}{16}+\\dfrac{y^2}7=1$}{$\\dfrac{x^2}{25}+\\dfrac{y^2}{16}=1$}{$\\dfrac{x^2}7+\\dfrac{y^2}{16}=1$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题19", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012434": { + "id": "012434", + "content": "在复平面上, 满足$|z-1|=|z+\\mathrm{i}|$($\\mathrm{i}$为虚数单位) 的复数$z$对应的点的轨迹为\\bracket{20}.\n\\fourch{椭圆}{圆}{线段}{直线}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题20", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012435": { + "id": "012435", + "content": "若无穷等差数列$\\{a_n\\}$的首项$a_1>0$, 公差$d<0$, $\\{a_n\\}$的前$n$项和为$S_n$, 则\\bracket{20}.\n\\fourch{$S_n$单调递减}{$S_n$单调递增}{$S_n$有最大值}{$S_n$有最小值}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题21", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012436": { + "id": "012436", + "content": "已知$a>0$, $b>0$, 若$a+b=4$, 则\\bracket{20}。\n\\fourch{$a^2+b^2$有最小值}{$\\sqrt {a b}$有最小值}{$\\dfrac 1a+\\dfrac 1b$有最大值}{$\\dfrac 1{\\sqrt a+\\sqrt b}$有最大值}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题22", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012437": { + "id": "012437", + "content": "组合数$\\mathrm{C}_n^m+2\\mathrm{C}_n^{m-1}+\\mathrm{C}_n^{m-2}$($n \\geq m \\geq 2$, $m, n \\in \\mathbf{N}$)恒等于\\bracket{20}.\n\\fourch{$\\mathrm{C}_{n+2}^m$}{$\\mathrm{C}_{n+2}^{m+1}$}{$\\mathrm{C}_{n+1}^m$}{$\\mathrm{C}_{n+1}^{m+1}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题23", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012438": { + "id": "012438", + "content": "设集合$P_1=\\{x | x^2+a x+1>0\\}, P_2=\\{x| x^2+a x+2>0\\}, Q_1=\\{x | x^2+x+b>0\\}$, $Q_2=\\{x | x^2+2 x+b>0\\}$, 其中$a, b \\in \\mathbf{R}$, 下列说法正确的是\\bracket{20}.\n\\onech{对任意$a$, $P_1$是$P_2$的子集; 对任意的$b$, $Q_1$不是$Q_2$的子集}{对任意$a$, $P_1$是$P_2$的子集; 存在$b$, 使得$Q_1$是$Q_2$的子集}{存在$a$, 使得$P_1$不是$P_2$的子集; 对任意的$b$, $Q_1$不是$Q_2$的子集}{存在$a$, 使得$P_1$不是$P_2$的子集; 存在$b$, 使得$Q_1$是$Q_2$的子集}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题24", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012439": { + "id": "012439", + "content": "如图, 在正四棱柱$ABCD-A_1B_1C_1D_1$中, $AB=1$, $D_1B$和平面$ABCD$所成的角的大小为$\\arctan \\dfrac{3 \\sqrt 2}4$, 求该四棱柱的表面积.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\m{2}\n\\def\\n{3}\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,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw [dashed] (B) -- (D1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题25", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012440": { + "id": "012440", + "content": "已知$a$为实数, 函数$f(x)=\\dfrac{x^2+a x+4}x$是奇函数, 求$f(x)$在$(0,+\\infty)$上的最小值及取到最小值时所对应的$x$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题26", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012441": { + "id": "012441", + "content": "某船在海平面$A$处测得灯塔$B$在北偏东$30^{\\circ}$方向, 与$A$相距$6.0$海里, 船由$A$向正北方向航行$8.1$海里到达$C$处, 这时灯塔$B$与船相距多少海里(精确到$0.1$海里)?$B$ 在船的什么方向(精确到$1^\\circ$)?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题27", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012442": { + "id": "012442", + "content": "已知点$F_1$、$F_2$依次为双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a, b>0$)的左右焦点, $|F_1F_2|=6$, $B_1(0,-b)$, $B_2(0, b)$.\\\\\n(1) 若$a=\\sqrt 5$, 以$\\overrightarrow d=(3,-4)$为方向向量的直线$l$经过$B_1$, 求$F_2$到$l$的距离;\\\\\n(2) 若双曲线$C$上存在点$P$, 使得$\\overrightarrow{PB_1} \\cdot \\overrightarrow{PB_2}=-2$, 求实数$b$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题28", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012443": { + "id": "012443", + "content": "已知函数$f(x)=|2^{x-2}-2|$($x \\in \\mathbf{R}$).\n(1) 解不等式$f(x)<2$;\\\\\n(2) 数列$\\{a_n\\}$满足$a_n=f(n)$($n \\in \\mathbf{N}$, $n\\ge 1$), $S_n$为$\\{a_n\\}$的前$n$项和, 若对任意的$n \\geq 4$, 不等式$S_n+\\dfrac 12 \\geq k a_n$恒成立, 求实数$k$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考正卷试题29", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012444": { + "id": "012444", + "content": "对于集合$A$、$B, `` A \\neq B$''是``$A \\cap B \\subset A \\cup B$''的\\bracket{20}.\n\\fourch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考附加卷试题1", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012445": { + "id": "012445", + "content": "对于任意实数$a$、$b$, $(a-b)^2 \\geq k a b$均成立, 则实数$k$的取值范围是\\bracket{20}.\n\\twoch{$\\{-4,0\\}$}{$[-4,0]$}{$(-\\infty, 0]$}{$(-\\infty,-4] \\cup[0,+\\infty)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考附加卷试题2", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012446": { + "id": "012446", + "content": "已知数列$\\{a_n\\}$满足$a_n+a_{n+4}=a_{n+1}+a_{n+3}$($n \\in \\mathbf{N}$, $n\\ge 1$), 那么\\bracket{20}.\n\\fourch{$\\{a_n\\}$是等差数列}{$\\{a_{2 n-1}\\}$是等差数列}{$\\{a_{2 n}\\}$是等差数列}{$\\{a_{3 n}\\}$是等差数列}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考附加卷试题3", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012447": { + "id": "012447", + "content": "关于$x$的实系数一元二次方程$x^2+p x+2=0$的两个虚数根为$z_1$、$z_2$, 若$z_1$、$z_2$在复平面上对应的点是经过原点的椭圆的两个焦点, 则该椭圆的长轴长为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考附加卷试题4", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012448": { + "id": "012448", + "content": "已知圆心为$O$, 半径为$1$的圆上有三点$A$、$B$、$C$, 若$7 \\overrightarrow{OA}+5 \\overrightarrow{OB}+8 \\overrightarrow{OC}=\\overrightarrow 0$, 则$|\\overrightarrow{BC}|=$\\blank{50}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考附加卷试题5", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012449": { + "id": "012449", + "content": "函数$f(x)$与$g(x)$的图像拼成如图所示``$Z$''字形折线段$ABOCD$, 不含$A(0,1)$, $B(1,1)$, $O(0,0)$, $C(-1,-1)$, $D(0,-1)$五个点, 若$f(x)$的图像关于原点对称的图形即为$g(x)$的图像, 则其中一个函数的解析式可以为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$} coordinate (O);\n\\draw (-1,0.1) -- (-1,0) node [below] {$-1$};\n\\draw (1,0.1) -- (1,0) node [below] {$1$};\n\\draw (0,-1) node [below left] {$-1$} (0,1) node [below right] {$1$};\n\\draw (0,1) node [left] {$A$} coordinate (A) -- (1,1) node [right] {$B$} coordinate (B) -- (-1,-1) node [left] {$C$} coordinate (C) -- (0,-1) node [right] {$D$} coordinate (D);\n\\foreach \\i in {A,B,C,D,O} {\\filldraw [white] (\\i) circle (0.03); \\draw (\\i) circle (0.03);};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考附加卷试题6", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012450": { + "id": "012450", + "content": "对于函数$f(x)$、$g(x)$, 若存在函数$h(x)$, 使得$f(x)=g(x) \\cdot h(x)$, 则称$f(x)$是$g(x)$的``$h(x)$关联函数''.\\\\\n(1) 已知$f(x)=\\sin x$, $g(x)=\\cos x$, 是否存在定义域为$\\mathbf{R}$的函数$h(x)$, 使得$f(x)$是$g(x)$的``$h(x)$关联函数''? 若存在, 写出$h(x)$的解析式; 若不存在, 说明理由;\\\\\n(2) 已知函数$f(x)$、$g(x)$的定义域为$[1,+\\infty)$, 当$x \\in[n, n+1)$($n \\in \\mathbf{N}$, $n\\ge 1$)时, $f(x)=2^{n-1} \\sin \\dfrac xn-1$, 若存在函数$h_1(x)$及$h_2(x)$, 使得$f(x)$是$g(x)$的``$h_1(x)$关联函数'', 且$g(x)$是$f(x)$的``$h_2(x)$关联函数'', 求方程$g(x)=0$的解.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2015届春季高考附加卷试题7", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012451": { + "id": "012451", + "content": "复数$3+4 \\mathrm{i}$($\\mathrm{i}$为虚数单位)的实部是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题1", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012452": { + "id": "012452", + "content": "若$\\log_2(x+1)=3$, 则$x=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题2", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012453": { + "id": "012453", + "content": "直线$y=x-1$与直线$y=2$的夹角为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题3", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012454": { + "id": "012454", + "content": "函数$f(x)=\\sqrt {x-2}$的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题4", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012455": { + "id": "012455", + "content": "三阶行列式$\\begin{vmatrix}1 & -3 & 5 \\\\4 & 0 & 0 \\\\-1 & 2 & 1\\end{vmatrix}$中, 元素$5$的代数余子式的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题5", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012456": { + "id": "012456", + "content": "函数$f(x)=\\dfrac 1x+a$的反函数的图像经过点$(2,1)$, 则实数$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题6", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012457": { + "id": "012457", + "content": "在$\\triangle ABC$中, 若$A=30^{\\circ}$, $B=45^{\\circ}$, $BC=\\sqrt 6$, 则$AC=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题7", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012458": { + "id": "012458", + "content": "$4$个人排成一排照相, 不同排列方式的种数为\\blank{50}. (结果用数值表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题8", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012459": { + "id": "012459", + "content": "无穷等比数列$\\{a_n\\}$的首项为$2$, 公比为$\\dfrac 13$, 则$\\{a_n\\}$的各项和为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题9", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012460": { + "id": "012460", + "content": "若$2+\\mathrm{i}$($\\mathrm{i}$为虚数单位)是关于$x$的实系数一元二次方程$x^2+a x+5=0$的一个虚根, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题10", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012461": { + "id": "012461", + "content": "函数$y=x^2-2 x+1$在区间$[0, m]$上的最小值为$0$, 最大值为$1$, 则实数$m$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题11", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012462": { + "id": "012462", + "content": "在平面直角坐标系$xOy$中, 点$A$、$B$是圆$x^2+y^2-6 x+5=0$上的两个动点, 且满足$|AB|=2 \\sqrt 3$, 则$|\\overrightarrow{OA}+\\overrightarrow{OB}|$的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题12", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012463": { + "id": "012463", + "content": "满足$\\sin \\alpha>0$且$\\tan \\alpha<0$的角$\\alpha$属于\\bracket{20}.\n\\fourch{第一象限}{第二象限}{第三象限}{第四象限;}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题13", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012464": { + "id": "012464", + "content": "半径为 1 的球的表面积为\\bracket{20}.\n\\fourch{$\\pi$}{$\\dfrac 43 \\pi$}{$2 \\pi$}{$4 \\pi$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题14", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012465": { + "id": "012465", + "content": "在$(1+x)^6$的二项展开式中,$x^2$项的系数为\\bracket{20}.\n\\fourch{$2$}{$6$}{$15$}{$20$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题15", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012466": { + "id": "012466", + "content": "幂函数$y=x^{-2}$的大致图像是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {sqrt(2)/2}:2] plot (\\x,{pow(\\x,-2)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2] plot (\\x,{pow(\\x,{1/2})});\n\\draw [domain = 0:2] plot (-\\x,{pow(\\x,{1/2})});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {sqrt(2)/2}:2] plot (\\x,{pow(\\x,-2)});\n\\draw [domain = {sqrt(2)/2}:2] plot (-\\x,{pow(\\x,-2)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {sqrt(2)/2}:2] plot (\\x,{pow(\\x,-2)});\n\\draw [domain = {sqrt(2)/2}:2] plot (-\\x,{-pow(\\x,-2)});\n\\end{tikzpicture}}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题16", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012467": { + "id": "012467", + "content": "已知向量$\\overrightarrow a=(1,0), \\overrightarrow b=(1,2)$, 则向量$\\overrightarrow b$在向量$\\overrightarrow a$方向上的数量投影为\\bracket{20}.\n\\fourch{$1$}{$2$}{$(1,0)$}{$(0,2)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题17", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012468": { + "id": "012468", + "content": "设直线$l$与平面$\\alpha$平行, 直线$m$在平面$\\alpha$上, 那么\\bracket{20}.\n\\twoch{直线$l$平行于直线$m$}{直线$l$与直线$m$异面}{直线$l$与直线$m$没有公共点}{直线$l$与直线$m$不垂直}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题18", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012469": { + "id": "012469", + "content": "用数学归纳法证明等式$1+2+3+\\ldots+2 n=2 n^2+n$($n \\in \\mathbf{N}$, $n\\ge 1$)的第(ii)步中, 假设$n=k$时原等式成立, 那么在$n=k+1$时, 需要证明的等式为\\bracket{20}.\n\\onech{$1+2+3+\\ldots+2 k+2(k+1)=2 k^2+k+2(k+1)^2+(k+1)$}{$1+2+3+\\ldots+2 k+2(k+1)=2(k+1)^2+(k+1)$}{$1+2+3+\\ldots+2 k+(2 k+1)+2(k+1)=2 k^2+k+2(k+1)^2+(k+1)$}{$1+2+3+\\ldots+2 k+(2 k+1)+2(k+1)=2(k+1)^2+(k+1)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题19", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012470": { + "id": "012470", + "content": "关于双曲线$\\dfrac{x^2}{16}-\\dfrac{y^2}4=1$与$\\dfrac{y^2}{16}-\\dfrac{x^2}4=1$的焦距和渐近线, 下列说法正确的是\\bracket{20}.\n\\twoch{焦距相等, 渐近线相同}{焦距相等, 渐近线不相同}{焦距不相等, 渐近线相同}{焦距不相等, 渐近线不相同}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题20", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012471": { + "id": "012471", + "content": "设函数$y=f(x)$的定义域为$\\mathbf{R}$, 则``$f(0)=0$''是``$y=f(x)$为奇函数''的\\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": "2016届春季高考正卷试题21", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012472": { + "id": "012472", + "content": "下列关于实数$a$、$b$的不等式中, 不恒成立的是\\bracket{20}.\n\\fourch{$a^2+b^2 \\geq 2 a b$}{$a^2+b^2 \\geq-2 a b$}{$(\\dfrac{a+b}2)^2 \\geq a b$}{$(\\dfrac{a+b}2)^2 \\geq-a b$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题22", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012473": { + "id": "012473", + "content": "设单位向量$\\overrightarrow{e_1}$与$\\overrightarrow{e_2}$既不平行也不垂直, 对非零向量$\\overrightarrow a=x_1 \\overrightarrow{e_1}+y_1 \\overrightarrow{e_2}, \\overrightarrow b=x_2 \\overrightarrow{e_1}+y_2 \\overrightarrow{e_2}$, 有结论: \\textcircled{1} 若$x_1 y_2-x_2 y_1=0$, 则$\\overrightarrow a / / \\overrightarrow b$; \\textcircled{2} 若$x_1 x_2+y_1 y_2=0$, 则$\\overrightarrow a \\perp \\overrightarrow b$; 关于以上两个结论, 正确的判断是\\bracket{20}.\n\\fourch{\\textcircled{1}成立, \\textcircled{2}不成立}{\\textcircled{1}不成立, \\textcircled{2}成立}{\\textcircled{1}成立, \\textcircled{2}成立}{\\textcircled{1}不成立, \\textcircled{2}不成立}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题23", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012474": { + "id": "012474", + "content": "对于椭圆$C_{(a, b)}: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a, b>0$, $a \\neq b$), 若点$(x_0, y_0)$满足$\\dfrac{x_0^2}{a^2}+\\dfrac{y_0^2}{b^2}<1$, 则称该点在椭圆$C_{(a, b)}$内, 在平面直角坐标系中, 若点$A$在过点$(2,1)$的任意椭圆$C_{(a, b)}$内或椭圆$C_{(a, b)}$上, 则满足条件的点$A$构成的图形为\\bracket{20}.\n\\fourch{三角形及其内部}{矩形及其内部}{圆及其内部}{椭圆及其内部}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题24", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012475": { + "id": "012475", + "content": "如图, 已知正三棱柱$ABC-A_1B_1C_1$的体积为$9 \\sqrt 3$, 底面边长为$3$, 求异面直线$BC_1$与$AC$所成的角的大小.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\def\\l{3}\n\\def\\h{4}\n\\draw ({-\\l/2},0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,{\\l/2*sqrt(3)}) node [below] {$B$} coordinate (B);\n\\draw ({\\l/2},0,0) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,\\h) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\h) node [below right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\h) node [right] {$C_1$} coordinate (C_1);\n\\draw (A) -- (B) -- (C) (A) -- (A_1) (B) -- (B_1) (C) -- (C_1) (A_1) -- (B_1) -- (C_1) (A_1) -- (C_1);\n\\draw [dashed] (A) -- (C);\n\\draw (B) -- (C_1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题25", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012476": { + "id": "012476", + "content": "已知函数$f(x)=\\sin x+\\sqrt 3 \\cos x$, 求$f(x)$的最小正周期及最大值, 并指出$f(x)$取得最大值时$x$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题26", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012477": { + "id": "012477", + "content": "如图, 汽车前灯反射镜与轴截面的交线是抛物线的一部分, 灯口所在的圆面与反射镜的轴垂直, 灯泡位于抛物线的焦点$F$处, 已知灯口直径是$24 \\text{cm}$, 灯深$10 \\text{cm}$, 求灯泡与反射镜的顶点$O$的距离.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.15]\n\\filldraw (3.6,0) circle (0.1) node [right] {$F$} coordinate (F);\n\\filldraw (10,0) circle (0.1);\n\\draw [domain = -12:12] plot ({pow(\\x,2)/14.4},\\x);\n\\draw (10,0) ellipse (3 and 12);\n\\draw (0,0) node [left] {$O$} coordinate (O) --++ (0,-14);\n\\draw (10,-12) --++ (0,-2);\n\\draw [<->] (0,-13) -- (10,-13) node [midway, below] {$10\\text{cm}$};\n\\draw (10,-12) --++ (5,0) (10,12) --++ (5,0);\n\\draw [<->] (14,-12) -- (14,12) node [midway, right] {$24\\text{cm}$};\n\\draw [dashed] (10,0) --++ (0,-12);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题27", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012478": { + "id": "012478", + "content": "已知数列$\\{a_n\\}$是公差为$2$的等差数列.\\\\\n(1) 若$a_1$、$a_3$、$a_4$成等比数列, 求$a_1$的值;\\\\\n(2) 设$a_1=-19$, 数列$\\{a_n\\}$的前$n$项和为$S_n$, 数列$\\{b_n\\}$满足$b_1=1$, $b_{n+1}-b_n=(\\dfrac 12)^n$, 记$c_n=S_n+2^{n-1} \\cdot b_n$($n \\in \\mathbf{N}$, $n\\ge 1$), 求数列$\\{c_n\\}$的最小值$c_{n_0}$. (即$c_{n_0} \\leq c_n$对任意$n \\in \\mathbf{N}$, $n\\ge 1$成立)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题28", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012479": { + "id": "012479", + "content": "对于函数$f(x)$与$g(x)$, 记集合$D_{f>g}=\\{x \\mid f(x)>g(x)\\}$.\\\\\n(1) 设$f(x)=2|x|$, $g(x)=x+3$, 求$D_{f>g}$;\\\\\n(2) 设$f_1(x)=x-1$, $f_2(x)=(\\dfrac 13)^x+a \\cdot 3^x+1$, $h(x)=0$, 如果$D_{f_1>h} \\cup D_{f_2>h}=\\mathbf{R}$, 求实数$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考正卷试题29", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012480": { + "id": "012480", + "content": "若函数$f(x)=\\sin (x+\\varphi)$是偶函数, 则$\\varphi$的一个值是\\bracket{20}.\n\\fourch{$0$}{$\\dfrac{\\pi}2$}{$\\pi$}{$2 \\pi$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考附加卷试题1", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012481": { + "id": "012481", + "content": "在复平面上, 满足$|z-1|=4$的复数$z$所对应的点的轨迹是\\bracket{20}.\n\\fourch{两个点}{一条线段}{两条直线}{一个圆}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考附加卷试题2", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012482": { + "id": "012482", + "content": "已知函数$f(x)$的图像是折线段$ABCDE$, 如图, 其中$A(1,2)$、$B(2,1)$、$C(3,2)$、$D(4,1)$、$E(5,2)$, 若直线$y=k x+b$($k, b \\in \\mathbf{R}$)与$f(x)$的图像恰有$4$个不同的公共点, 则$k$的取值范围是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-0.5,0) -- (5.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (1,2) node [above] {$A$} coordinate (A) -- (2,1) node [below] {$B$} coordinate (B) -- (3,2) node [above] {$C$} coordinate (C) -- (4,1) node [below] {$D$} coordinate (D) -- (5,2) node [above] {$E$} coordinate (E);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$(-1,0) \\cup(0,1)$}{$(-\\dfrac 13, \\dfrac 13)$}{$(0,1]$}{$[0, \\dfrac 13]$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考附加卷试题3", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012483": { + "id": "012483", + "content": "椭圆$\\dfrac{x^2}{25}+\\dfrac{y^2}9=1$的长半轴的长为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考附加卷试题4", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012484": { + "id": "012484", + "content": "已知圆锥的母线长为$10$, 母线与轴的夹角为$30^{\\circ}$, 则该圆锥的侧面积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考附加卷试题5", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012485": { + "id": "012485", + "content": "小明用数列$\\{a_n\\}$记录某地区$2015$年$12$月份$31$天中每天是否下过雨, 方法为: 当第$k$天下过雨时, 记$a_k=1$, 当第$k$天没下过雨时, 记$a_k=-1$($1 \\leq k \\leq 31$); 他用数列$\\{b_n\\}$记录该地区该月每天气象台预报是否有雨, 方法为: 当预报第$k$天有雨时, 记$b_k=1$, 当预报第$k$天没有雨时, 记$b_k=-1$($1 \\leq k \\leq 31$); 记录完毕后, 小明计算出$a_1 b_1+a_2 b_2+a_3 b_3+\\ldots+a_{31} b_{31}=25$, 那么该月气象台预报准确的总天数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考附加卷试题6", + "edit": [ + "20221212\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012486": { + "id": "012486", + "content": "对于数列$\\{a_n\\}$与$\\{b_n\\}$, 若对数列$\\{c_n\\}$的每一项$c_k$, 均有$c_k=a_k$或$c_k=b_k$, 则称数列$\\{c_n\\}$是$\\{a_n\\}$与$\\{b_n\\}$的一个``并数列''.\\\\\n(1) 设数列$\\{a_n\\}$与$\\{b_n\\}$的前三项分别为$a_1=1$, $a_2=3$, $a_3=5$, $b_1=1$, $b_2=2$, $b_3=3$, 若数列$\\{c_n\\}$是$\\{a_n\\}$与$\\{b_n\\}$的一个``并数列'', 求所有可能的有序数组$(c_1, c_2, c_3)$;\\\\\n(2) 已知数列$\\{a_n\\}$、$\\{c_n\\}$均为等差数列, $\\{a_n\\}$的公差为$1$, 首项为正整数$t$, $\\{c_n\\}$的前$10$项和为$-30$, 前$20$项和为$-260$, 若存在唯一的数列$\\{b_n\\}$, 使得$\\{c_n\\}$是$\\{a_n\\}$与$\\{b_n\\}$的一个``并数列'', 求$t$的值所构成的集合.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届春季高考附加卷试题7", + "edit": [ + "20221212\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.", @@ -323451,7 +326453,7 @@ "solution": "", "duration": -1, "usages": [], - "origin": "2019年春季高考试题20-20221212修改", + "origin": "2019届春季高考试题20-20221212修改", "edit": [ "20221209\t王伟叶", "20221212\t王慎有",