20230222 noon
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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"0"
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]
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},
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"execution_count": 9,
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"execution_count": 13,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -19,7 +19,7 @@
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"source": [
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"import os,re,json\n",
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"\"\"\"这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块\"\"\"\n",
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"problems = \"21481\"\n",
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"problems = \"11388\"\n",
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"\n",
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"def generate_number_set(string,dict):\n",
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" string = re.sub(r\"[\\n\\s]\",\"\",string)\n",
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@ -51,7 +51,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"execution_count": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"0"
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]
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},
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"execution_count": 2,
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -21,7 +21,7 @@
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"\n",
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"\"\"\"---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",
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"keywords_dict_table = [\n",
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" {\"tags\":[\"第二单元\"],\"genre\":[\"选择题\"]}\n",
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" {\"genre\":[\"解答题\"],\"tags\":[r\"第[二四]单元\"],\"content\":[r\"\\(3\\)\"],\"content_not\":[r\"\\(4\\)\"]}\n",
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"]\n",
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"\"\"\"---关键字设置完毕---\"\"\"\n",
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"# 示例： keywords_dict_table = [\n",
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@ -96,7 +96,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "mathdept",
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"display_name": "pythontest",
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"language": "python",
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"name": "python3"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
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"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
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}
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}
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},
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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@ -11,8 +11,8 @@
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"text": [
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"首个空闲id: 14532 , 直至 020000\n",
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"首个空闲id: 22048 , 直至 030000\n",
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"首个空闲id: 31236 , 直至 040000\n",
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"首个空闲id: 40037 , 直至 999999\n"
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"首个空闲id: 40037 , 直至 999999\n",
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"首个空闲id: 31241 , 直至 040000\n"
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]
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}
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],
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"首行题目数量: 82\n",
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"剩余题目数量: 78\n"
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"首行题目数量: 301\n",
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"剩余题目数量: 259\n"
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]
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}
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],
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@ -1 +1 @@
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000049,000055,000062,000070,001152,001210,001287,002838,002853,002854,002863,002864,002865,002874,002875,002880,002902,002909,002913,002924,002925,002938,002954,002965,002987,003022,003601,003625,003667,003718,003730,003757,003770,003772,003801,003815,003862,003892,003907,003921,003936,003966,003980,003981,004074,004094,004116,004155,004157,004220,004284,004305,004347,004366,004368,004385,004401,004403,004422,004439,004440,004523,004525,004544,004546,004563,004631,004697,004739,004757,004760,004902,004907,005008,005016,005103,005104,005105,005193,005194,005195,005196,005197,005198,005283,005284,005285,005286,005287,005288,005296,005298,005299,005300,005301,005302,005303,005329,005330,005331,005332,005333,005362,005368,005369,005370,005371,005372,005373,005374,005375,005376,005377,005378,005379,005380,005381,005382,005383,005384,005385,005386,005424,005445,005446,005447,005448,005449,005450,005472,005473,005474,005475,005476,005477,005491,005492,005493,005494,005495,005496,005501,005502,005503,005504,005505,005506,005507,005508,005523,005524,005525,005526,005527,005528,005529,005530,005541,005542,005543,005563,005564,005565,005566,005567,005568,005569,005570,005571,005572,005573,005574,005612,005613,005614,005615,005616,005617,005618,005619,005620,005621,005653,005654,005655,005656,005657,005658,005659,005660,005687,005688,005689,005690,005691,005692,005693,005694,005695,005696,005713,005714,005718,005719,005720,005721,005722,005723,005724,005758,005759,005760,005761,005762,005763,005764,005782,005783,005784,005785,005786,007861,007892,007958,007959,007966,007984,008036,008037,008081,008082,008094,008095,008371,008372,008387,008388,008389,009476,009508,009537,010137,010149,010150,010173,010938,010977,010999,011041,011042,011043,011126,011145,011147,011148,011196,011212,011215,011233,011236,011256,011320,011404,011446,011529,011548,011594,011616,011687,011733,011911,011915,011927,011929,011947,011985,012001,012003,012022,012023,012090,012130,012132,012153,012173,012194,012215,012257,012259,012278,012300,012301,012302,012320,012344,012365,012367,012371,012374,012399,012401,012428,012430,012466,012471,012502,012543,012564,012605,012626,012628,012709,012733,012751,012783,012792,012836,012843,012849,012850,012860,012861,012863,012884,012885,012890,012895,012904,012905,012906,012907,012913,013297,013314,013342,013388,013418,013433,013447,013449,013477,013479,013508,013523,013539,013553,013554,013583,013600,013621,013768,013798,013799,013801,013829,013841,020358,020359,020365,020366,020377,020378,020379,020386,020387,020406,020407,020408,020417,020418,020419,020439,020440,020441,020442,020451,020465,020476,020477,020478,020487,020498,020499,020504,020524,020525,020526,020529,020554,020555,020561,020562,020566,020678,020679,020680,020681,021369,021388,030300,030307,030372,030379,030393,030400,030442,030667,030668,030671,030672,030673,030674,030675,030689,030690,030691,030692,030701,030722,030723,030728,030729,030755,030756
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000063,000064,000077,000325,001157,001185,001186,001212,001322,001820,002841,002906,002948,003033,003248,003308,003325,003609,003630,003651,003672,003693,003696,003924,003954,004005,004006,004079,004100,004121,004142,004163,004183,004205,004226,004268,004289,004310,004331,004352,004373,004407,004408,004445,004488,004530,004551,004571,004638,004660,004723,004744,004765,004980,005136,005549,005596,005597,005607,005716,005814,005830,005832,005834,005850,006728,006734,006799,006823,006824,006955,006959,006963,006974,006977,007867,007879,007920,007947,007970,008017,008018,008020,008050,008089,008377,008378,008394,008404,008420,009480,009486,009494,009889,009905,009918,010004,010117,010118,010120,010124,010130,010142,010157,010164,010170,010193,010199,010200,010757,010769,010790,010791,010795,010799,010800,010808,011005,011006,011047,011069,011111,011219,011220,011241,011262,011304,011325,011346,011367,011388,011408,011409,011430,011451,011472,011492,011493,011514,011535,011556,011577,011622,011646,011669,011692,011714,011715,011737,011738,011861,011865,011868,011874,011897,011907,011913,011925,011979,012007,012008,012028,012137,012159,012160,012201,012223,012264,012265,012286,012307,012326,012328,012350,012382,012505,012507,012528,012570,012591,012612,012654,012672,012675,012696,012759,012780,012845,012880,013007,013239,013526,013607,013649,013670,013691,013922,013943,013945,013946,013952,013953,013954,013959,013960,020409,020421,020443,020503,020514,020545,020559,020636,020649,020786,021372,021378,021380,021398,021413,030310,030311,030313,030325,030339,030341,030447,030727,030730,030731,030732,030733,030734,030735,030736,030737,030738,030739,030740,030882,030908,030909,030910,030911,030913,030914,030915,030916,030917,030918,030919,030920,030921,030922,030923,030924,030925,030926,030927
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"import os,re,json,time\n",
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"\n",
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"\"\"\"---设置原题目id与新题目id列表, 新id的数目不能小于旧id的数目---\"\"\"\n",
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"old_ids = \"221,7528,8380,9626\"\n",
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"new_ids = \"31237:31240\"\n",
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"old_ids = \"12847,12851\"\n",
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"new_ids = \"31241:31242\"\n",
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"\"\"\"---设置完毕---\"\"\"\n",
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"\"\"\"---完成编辑后记得运行第二个单元格---\"\"\"\n",
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"\n",
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"题块 2 处理完毕.\n",
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"正在处理题块 3 .\n",
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"题块 3 处理完毕.\n",
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"开始编译教师版本pdf文件: 临时文件/高三下月考01预选_教师_20230220.tex\n",
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"开始编译教师版本pdf文件: 临时文件/高三下学期测验02_教师_20230222.tex\n",
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"0\n",
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"开始编译学生版本pdf文件: 临时文件/高三下月考01预选_学生_20230220.tex\n",
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"开始编译学生版本pdf文件: 临时文件/高三下学期测验02_学生_20230222.tex\n",
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"0\n"
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]
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}
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"\"\"\"---设置题块编号---\"\"\"\n",
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"\n",
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"problems = [\n",
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"\"3675,12165,31237,31238,31239,4252,4256,31240,4499,4132,4217,4235\",\"8972,9082,12445,30691\",\"11301,10000,3691,11450,31236\"\n",
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"\"4292,4143,4190,4169,31241,4128,4189,4129,31242,4130,4233,4174\",\"12021,12437,14087,12346\",\"20958,4657,11218,4508,11388\"\n",
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"]\n",
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"\n",
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"\"\"\"---设置结束---\"\"\"\n",
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"elif paper_type == 2:\n",
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" enumi_mode = 1 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n",
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" template_file = \"模板文件/测验周末卷模板.txt\" #设置模板文件名\n",
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" exec_list = [(\"标题替换\",\"高三下月考01预选\")] #设置讲义标题\n",
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" exec_list = [(\"标题替换\",\"高三下学期测验02\")] #设置讲义标题\n",
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" destination_file = \"临时文件/\"+exec_list[0][1] # 设置输出文件名\n",
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"elif paper_type == 3:\n",
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" enumi_mode = 0 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n",
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 5,
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"开始编译教师版本pdf文件: 临时文件/高一前三次作业_教师用_20230221.tex\n",
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"开始编译教师版本pdf文件: 临时文件/预选_教师用_20230222.tex\n",
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"0\n",
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"开始编译学生版本pdf文件: 临时文件/高一前三次作业_学生用_20230221.tex\n",
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"开始编译学生版本pdf文件: 临时文件/预选_学生用_20230222.tex\n",
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"0\n"
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]
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}
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"\"\"\"---设置题目列表---\"\"\"\n",
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"#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",
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"problems = r\"\"\"\n",
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"021441,021442,021443,021444,021445,021446,021447,021448,021449,021450,021451,021452,021453,021454,021455,021469,021470,021471,021472,021473,021474,021475,021476,021477,021478,021479,021480,021481\n",
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"a\n",
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"\n",
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"\n",
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"\"\"\"\n",
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"\"\"\"---设置题目列表结束---\"\"\"\n",
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"\n",
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"\"\"\"---设置文件名---\"\"\"\n",
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"#目录和文件的分隔务必用/\n",
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"filename = \"临时文件/高一前三次作业\"\n",
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"filename = \"临时文件/预选\"\n",
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"\"\"\"---设置文件名结束---\"\"\"\n",
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"\n",
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"\n",
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},
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"004189": {
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"id": "004189",
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"content": "已知无穷数列$a_n=\\dfrac 2{(-3)^n}$, $n\\in \\mathbf{N}^*$, 则数列$\\{a_n\\}$的各项和为\\blank{50}.",
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"content": "已知无穷数列$a_n=\\dfrac 2{(-3)^n}$, $n\\in \\mathbf{N}$, $n\\ge 1$, 则数列$\\{a_n\\}$的各项和为\\blank{50}.",
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"objs": [
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"K0405003X"
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],
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},
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"004292": {
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"id": "004292",
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"content": "已知集合$P=\\{x|(x+1)(x–3)<0\\}$, $Q=\\{x||x|>2\\}$, 则$P\\cap Q=$\\blank{50}.",
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"content": "已知集合$P=\\{x|(x+1)(x-3)<0\\}$, $Q=\\{x||x|>2\\}$, 则$P\\cap Q=$\\blank{50}.",
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"objs": [
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"K0114001B",
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"K0117001B",
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},
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"011388": {
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"id": "011388",
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"content": "给定数列$\\{a_n\\}$, 若满足$a_1=a$($a>0$且$a\\ne 1$), 对于任意的$n, m\\in \\mathbf{N}^*$, 都有$a_{n+m}=a_n\\cdot a_m$, 则称数列$\\{a_n\\}$为指数数列.\\\\\n(1) 已知数列$\\{a_n\\}$, $\\{b_n\\}$的通项公式分别为$a_n=3\\cdot 2^{n-1}$, $b_n=3^n$, 试判断$\\{a_n\\}$, $\\{b_n\\}$是不是指数数列(需说明理由);\\\\\n(2) 若数列$\\{a_n\\}$满足: $a_1=2$, $a_2=4$, $a_{n+2}=3a_{n+1}-2a_n$, 证明: $\\{a_n\\}$是指数数列;\\\\\n(3) 若数列$\\{a_n\\}$是指数数列, $a_1=\\dfrac{t+3}{t+4}$($t\\in \\mathbf{N}^*$), 证明: 数列$\\{a_n\\}$中任意三项都不能构成等差数列.",
|
||||
"content": "给定数列$\\{a_n\\}$, 若满足$a_1=a$($a>0$且$a\\ne 1$), 对于任意正整数$n, m$, 都有$a_{n+m}=a_n\\cdot a_m$, 则称数列$\\{a_n\\}$为指数数列.\\\\\n(1) 已知数列$\\{a_n\\}$, $\\{b_n\\}$的通项公式分别为$a_n=3\\cdot 2^{n-1}$, $b_n=3^n$, 试判断$\\{a_n\\}$, $\\{b_n\\}$是不是指数数列(需说明理由);\\\\\n(2) 若数列$\\{a_n\\}$满足: $a_1=2$, $a_2=4$, $a_{n+2}=3a_{n+1}-2a_n$, 证明: $\\{a_n\\}$是指数数列;\\\\\n(3) 若数列$\\{a_n\\}$是指数数列, $a_1=\\dfrac{t+3}{t+4}$($t\\in \\mathbf{N}$, $t\\ge 1$), 证明: 数列$\\{a_n\\}$中任意三项都不能构成等差数列.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第四单元"
|
||||
|
|
@ -317337,7 +317337,9 @@
|
|||
"20230118\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"related": [
|
||||
"031241"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
|
|
@ -317473,7 +317475,9 @@
|
|||
"20230118\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"related": [
|
||||
"031242"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
|
|
@ -429276,6 +429280,158 @@
|
|||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031237": {
|
||||
"id": "031237",
|
||||
"content": "从编号分别为$1$、$2$、$3$、$4$、$5$、$6$的$6$个大小与质地相同的小球中随机取出$3$个, 则恰有$2$个小球编号相邻的概率为\\blank{50}.",
|
||||
"objs": [
|
||||
"K0803002B",
|
||||
"K0818001X"
|
||||
],
|
||||
"tags": [
|
||||
"第八单元",
|
||||
"概率"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "教材复习题-20230220修改",
|
||||
"edit": [
|
||||
"20220624\t王伟叶, 余利成",
|
||||
"20230220\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"000221"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031238": {
|
||||
"id": "031238",
|
||||
"content": "在$(\\sqrt x+\\dfrac 1{\\sqrt[3]x})^{100}$的展开式中, 有理项有\\blank{50}项.",
|
||||
"objs": [
|
||||
"K0819002X"
|
||||
],
|
||||
"tags": [
|
||||
"第八单元",
|
||||
"二项式定理"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "有$17$项是有理项",
|
||||
"solution": "考虑$(x^{\\frac 12}+x^{-\\frac 13})^{100}$展开式的通项$T_{r+1}=\\mathrm{C}_{100}^rx^{\\frac{100-r}2}\\cdot (x^{-\\frac 13})^r=\\mathrm{C}_{100}^rx^{50-\\dfrac{3r}6}$.\n令$r=6k$($k\\in \\mathbf{Z}$), 则$0\\le 6k\\le 100$, 即$r=0,6,12,\\cdots ,96$.\n因此共有$17$个有理项.",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "代数精编第九章排列组合-20230220修改",
|
||||
"edit": [
|
||||
"20220720\t王伟叶",
|
||||
"20230220\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"007528"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031239": {
|
||||
"id": "031239",
|
||||
"content": "已知$\\tan \\alpha =3$, 则$\\dfrac 1{\\sin ^2\\alpha +2\\sin \\alpha \\cos \\alpha}$的值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第三单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "二期课改练习册高一第二学期-20230220修改",
|
||||
"edit": [
|
||||
"20220726\t王伟叶",
|
||||
"20230220\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"009553",
|
||||
"008380"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031240": {
|
||||
"id": "031240",
|
||||
"content": "设向量$\\overrightarrow a$、$\\overrightarrow b$满足$|\\overrightarrow a|=5$, $|\\overrightarrow b|=6$, $(\\overrightarrow a+\\overrightarrow b)\\cdot \\overrightarrow b=21$, 则$\\langle \\overrightarrow a, \\overrightarrow b\\rangle =$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第五单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "新教材必修第二册课堂练习-20230220修改",
|
||||
"edit": [
|
||||
"20220730\t王伟叶",
|
||||
"20230220\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"009626"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031241": {
|
||||
"id": "031241",
|
||||
"content": "函数$y=\\dfrac{x^2+7}{\\sqrt{x^2+4}}$的值域是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第二单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2022届高三第二轮复习讲义-20230222修改",
|
||||
"edit": [
|
||||
"20230118\t王伟叶",
|
||||
"20230222\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"012847"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031242": {
|
||||
"id": "031242",
|
||||
"content": "已知$f(x)=\\begin{cases}(2-a) x+1, & x<1, \\\\ 2ax, & x \\geq 1\\end{cases}$满足: 对任意$x_1 \\neq x_2$, 都有$\\dfrac{f(x_1)-f(x_2)}{x_1-x_2}>0$成立, 则实数$a$的取值范围是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第二单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2022届高三第二轮复习讲义-20230222修改",
|
||||
"edit": [
|
||||
"20230118\t王伟叶",
|
||||
"20230222\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"012851"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040001": {
|
||||
"id": "040001",
|
||||
"content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",
|
||||
|
|
@ -429959,109 +430115,5 @@
|
|||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031237": {
|
||||
"id": "031237",
|
||||
"content": "从编号分别为$1$、$2$、$3$、$4$、$5$、$6$的$6$个大小与质地相同的小球中随机取出$3$个, 则恰有$2$个小球编号相邻的概率为\\blank{50}.",
|
||||
"objs": [
|
||||
"K0803002B",
|
||||
"K0818001X"
|
||||
],
|
||||
"tags": [
|
||||
"第八单元",
|
||||
"概率"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "教材复习题-20230220修改",
|
||||
"edit": [
|
||||
"20220624\t王伟叶, 余利成",
|
||||
"20230220\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"000221"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031238": {
|
||||
"id": "031238",
|
||||
"content": "在$(\\sqrt x+\\dfrac 1{\\sqrt[3]x})^{100}$的展开式中, 有理项有\\blank{50}项.",
|
||||
"objs": [
|
||||
"K0819002X"
|
||||
],
|
||||
"tags": [
|
||||
"第八单元",
|
||||
"二项式定理"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "有$17$项是有理项",
|
||||
"solution": "考虑$(x^{\\frac 12}+x^{-\\frac 13})^{100}$展开式的通项$T_{r+1}=\\mathrm{C}_{100}^rx^{\\frac{100-r}2}\\cdot (x^{-\\frac 13})^r=\\mathrm{C}_{100}^rx^{50-\\dfrac{3r}6}$.\n令$r=6k$($k\\in \\mathbf{Z}$), 则$0\\le 6k\\le 100$, 即$r=0,6,12,\\cdots ,96$.\n因此共有$17$个有理项.",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "代数精编第九章排列组合-20230220修改",
|
||||
"edit": [
|
||||
"20220720\t王伟叶",
|
||||
"20230220\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"007528"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031239": {
|
||||
"id": "031239",
|
||||
"content": "已知$\\tan \\alpha =3$, 则$\\dfrac 1{\\sin ^2\\alpha +2\\sin \\alpha \\cos \\alpha}$的值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第三单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "二期课改练习册高一第二学期-20230220修改",
|
||||
"edit": [
|
||||
"20220726\t王伟叶",
|
||||
"20230220\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"009553",
|
||||
"008380"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031240": {
|
||||
"id": "031240",
|
||||
"content": "设向量$\\overrightarrow a$、$\\overrightarrow b$满足$|\\overrightarrow a|=5$, $|\\overrightarrow b|=6$, $(\\overrightarrow a+\\overrightarrow b)\\cdot \\overrightarrow b=21$, 则$\\langle \\overrightarrow a, \\overrightarrow b\\rangle =$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第五单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "新教材必修第二册课堂练习-20230220修改",
|
||||
"edit": [
|
||||
"20220730\t王伟叶",
|
||||
"20230220\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"009626"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
}
|
||||
}
|
||||
Reference in New Issue