From 91a6e9b897d4c5d8201dc07ac372b2f09eb29727 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sun, 26 Mar 2023 21:40:42 +0800 Subject: [PATCH] 20230326 evening --- 工具/修改题目数据库.ipynb | 2 +- 工具/关键字筛选题号.ipynb | 2 +- 工具/寻找阶段末尾空闲题号.ipynb | 2 +- 工具/批量题号选题pdf生成.ipynb | 11 +- 工具/文本文件/题号筛选.txt | 2 +- 工具/新题比对.ipynb | 159 ++-- 工具/添加题目到数据库.ipynb | 82 +- 工具/识别题库中尚未标注的题目类型.ipynb | 72 +- 题库0.3/Problems.json | 969 ++++++++++++++++++++++++ 9 files changed, 1148 insertions(+), 153 deletions(-) diff --git a/工具/修改题目数据库.ipynb b/工具/修改题目数据库.ipynb index efaee5c0..55d6548f 100644 --- a/工具/修改题目数据库.ipynb +++ b/工具/修改题目数据库.ipynb @@ -19,7 +19,7 @@ "source": [ "import os,re,json\n", "\"\"\"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", - "problems = \"031244,031245,031246,031247,031248,031249,031250,031251,031252,031253,031254,031255,031256,031257,031258,031259,031260,031261,031262,031263,031264,031265,031311,031312,031313,031314,031315,031316,031317,031318,031319,031320,031321,031322,031323,031324,031325,031326,031327,031328,031329,031330,031331\"\n", + "problems = \"30808\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", 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 2b305e84..09d01b2f 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -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\":[r\"素养\"]}\n", + " {\"origin\":[r\"复习\"],\"origin2\":[r\"2025\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", 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 4847e930..cf7b2dd4 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 @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [ { diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb index 77dea21c..348d9c40 100644 --- a/工具/批量题号选题pdf生成.ipynb +++ b/工具/批量题号选题pdf生成.ipynb @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/2022学年下学期高一高二材料_教师用_20230324.tex\n", + "开始编译教师版本pdf文件: 临时文件/2022学年下学期高一高二材料_教师用_20230326.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/2022学年下学期高一高二材料_学生用_20230324.tex\n", + "开始编译学生版本pdf文件: 临时文件/2022学年下学期高一高二材料_学生用_20230326.tex\n", "0\n" ] } @@ -51,7 +51,10 @@ "\"2025届高一下学期周末卷06小测\":\"40274:40282\",\n", "\"2025届高一下学期期中复习一(集合逻辑不等式)\":\"40283:40298\",\n", "\"2024届高二下学期周末卷06\":\"40299:40316\",\n", - "\"2024届高二下学期周末卷07\":\"40317:40335\"\n", + "\"2024届高二下学期周末卷07\":\"40317:40335\",\n", + "\"2025届高一下学期测验01\":\"40336:40349\",\n", + "\"2025届高一下学期测验02\":\"40350:40367\",\n", + "\"2025届高一下学期期中复习二(幂指对函数)\":\"40368:40386\"\n", "\n", "}\n", "\n", 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 b2bf58bd..940571a6 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 @@ -031332,031333,031334,031335,031336,031337,031338,031339,031340,031341,031342,031343,031344,031345,031346,031347,031348,031349,031350,031351,031352 \ No newline at end of file +040283,040284,040285,040286,040287,040288,040289,040290,040291,040292,040293,040294,040295,040296,040297,040298 \ No newline at end of file diff --git a/工具/新题比对.ipynb b/工具/新题比对.ipynb index 94b58277..17b87d92 100644 --- a/工具/新题比对.ipynb +++ b/工具/新题比对.ipynb @@ -2,109 +2,72 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1.000\t1\t004884\n", - "1.000\t2\t003673\n", - "0.903\t3\t000506\n", - "0.984\t4\t003665\n", - "0.921\t5\t012805\n", - "0.949\t6\t011578\n", - "0.987\t7\t011716\n", - "0.987\t8\t011674\n", - "0.867\t9\t000041\n", - "0.939\t10\t002911\n", - "0.876\t11\t011630\n", - "0.785\t12\t002858\n", - "0.990\t13\t011636\n", - "0.848\t14\t011186\n", - "0.763\t15\t011186\n", - "0.662\t16\t003625\n", - "0.971\t17\t011687\n", - "0.910\t18\t011712\n", - "0.685\t19\t003857\n", - "0.887\t20\t012107\n", - "1.000\t21\t011594\n", - "0.803\t22\t040098\n", - "1.000\t23\t011708\n", - "1.000\t24\t011724\n", - "1.000\t25\t011639\n", - "0.819\t26\t012756\n", - "1.000\t27\t011670\n", - "1.000\t28\t011608\n", - "0.995\t29\t011728\n", - "0.780\t30\t001553\n", - "0.876\t31\t009993\n", - "0.948\t32\t003638\n", - "0.628\t33\t003607\n", - "0.702\t34\t012316\n", - "0.686\t35\t022043\n", - "0.671\t36\t021435\n", - "0.957\t37\t011611\n", - "0.551\t38\t040015\n", - "0.935\t39\t012448\n", - "1.000\t40\t011648\n", - "1.000\t41\t011671\n", - "0.665\t42\t000387\n", - "0.777\t43\t003624\n", - "0.993\t44\t003666\n", - "1.000\t45\t012195\n", - "0.942\t46\t009988\n", - "1.000\t47\t011696\n", - "1.000\t48\t011631\n", - "0.602\t49\t004391\n", - "0.879\t50\t010710\n", - "1.000\t51\t011721\n", - "0.903\t52\t013057\n", - "0.799\t53\t009074\n", - "0.984\t54\t011686\n", - "0.975\t55\t011718\n", - "0.993\t56\t003733\n", - "1.000\t57\t000629\n", - "1.000\t58\t011697\n", - "0.998\t59\t011736\n", - "0.994\t60\t011700\n", - "1.000\t61\t003674\n", - "0.632\t62\t007439\n", - "0.986\t63\t012746\n", - "0.850\t64\t000512\n", - "0.684\t65\t012743\n", - "0.590\t66\t009751\n", - "0.800\t67\t010005\n", - "0.730\t68\t013272\n", - "0.975\t69\t004037\n", - "0.614\t70\t010551\n", - "0.867\t71\t013396\n", - "0.875\t72\t012745\n", - "0.994\t73\t012100\n", - "0.680\t74\t012289\n", - "1.000\t75\t021151\n", - "0.557\t76\t013684\n", - "0.527\t77\t031184\n", - "0.683\t78\t000659\n", - "0.795\t79\t012359\n", - "0.698\t80\t000283\n", - "0.761\t81\t009445\n", - "0.849\t82\t008965\n", - "0.618\t83\t005293\n", - "0.589\t84\t005293\n", - "0.785\t85\t020601\n", - "0.613\t86\t031069\n", - "0.775\t87\t009921\n", - "0.700\t88\t001769\n", - "0.636\t89\t010481\n", - "0.703\t90\t012295\n", - "0.734\t91\t011946\n", - "0.670\t92\t012825\n", - "0.728\t93\t020841\n", - "0.686\t94\t009040\n", - "0.549\t95\t009718\n", - "0.554\t96\t004998\n" + "0.789\t1\t005886\n", + "0.805\t2\t006207\n", + "0.812\t3\t006137\n", + "0.798\t4\t012269\n", + "0.831\t5\t040063\n", + "0.888\t6\t021503\n", + "0.932\t7\t040057\n", + "0.959\t8\t003206\n", + "0.817\t9\t011090\n", + "0.796\t10\t003058\n", + "0.768\t11\t005984\n", + "0.744\t12\t021463\n", + "0.872\t13\t008169\n", + "0.843\t14\t021559\n", + "0.758\t15\t006230\n", + "0.888\t16\t008317\n", + "0.682\t17\t012005\n", + "0.630\t18\t006107\n", + "0.765\t19\t021581\n", + "0.763\t20\t014242\n", + "0.661\t21\t013849\n", + "0.716\t22\t008191\n", + "0.504\t23\t003537\n", + "0.934\t24\t000818\n", + "0.755\t25\t012596\n", + "0.893\t26\t012355\n", + "0.835\t27\t000479\n", + "0.950\t28\t001529\n", + "0.797\t29\t000577\n", + "0.737\t30\t003191\n", + "1.000\t31\t012594\n", + "0.824\t32\t003150\n", + "1.000\t33\t004066\n", + "0.707\t34\t003140\n", + "0.648\t35\t030294\n", + "0.752\t36\t014186\n", + "0.621\t37\t014223\n", + "0.700\t38\t004442\n", + "0.813\t39\t030808\n", + "0.669\t40\t013843\n", + "0.654\t41\t000738\n", + "0.682\t42\t013354\n", + "0.830\t43\t030042\n", + "0.977\t44\t020411\n", + "0.661\t45\t011133\n", + "0.681\t46\t004118\n", + "0.667\t47\t011943\n", + "0.683\t48\t005600\n", + "0.691\t49\t011386\n", + "0.711\t50\t002922\n", + "1.000\t51\t020452\n", + "0.736\t52\t020356\n", + "0.666\t53\t020430\n", + "0.685\t54\t020357\n", + "0.713\t55\t005540\n", + "0.643\t56\t012868\n", + "0.845\t57\t005598\n", + "0.860\t58\t002958\n", + "0.646\t59\t004184\n" ] } ], @@ -116,7 +79,7 @@ "threshold = 0.85\n", "\n", "# 待比对的文件\n", - "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\空中课堂第六批.tex\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目9.tex\"\n", "\n", "#生成数码列表, 逗号分隔每个区块, 区块内部用:表示整数闭区间\n", "def generate_number_set(string):\n", diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index d7ac84f4..608b3ec1 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 @@ -2,48 +2,78 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 31361\n", - "raworigin = \"2023届四校联考(复兴奉贤松二金山)\"\n", + "starting_id = 40336\n", + "raworigin = \"\"\n", "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目9.tex\"\n", "editor = \"20230326\\t王伟叶\"\n", - "indexed = True\n" + "indexed = False\n" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "添加题号031361, 来源: 2023届四校联考(复兴奉贤松二金山)试题1\n", - "添加题号031362, 来源: 2023届四校联考(复兴奉贤松二金山)试题2\n", - "添加题号031363, 来源: 2023届四校联考(复兴奉贤松二金山)试题3\n", - "添加题号031364, 来源: 2023届四校联考(复兴奉贤松二金山)试题4\n", - "添加题号031365, 来源: 2023届四校联考(复兴奉贤松二金山)试题5\n", - "添加题号031366, 来源: 2023届四校联考(复兴奉贤松二金山)试题6\n", - "添加题号031367, 来源: 2023届四校联考(复兴奉贤松二金山)试题7\n", - "添加题号031368, 来源: 2023届四校联考(复兴奉贤松二金山)试题8\n", - "添加题号031369, 来源: 2023届四校联考(复兴奉贤松二金山)试题9\n", - "添加题号031370, 来源: 2023届四校联考(复兴奉贤松二金山)试题10\n", - "添加题号031371, 来源: 2023届四校联考(复兴奉贤松二金山)试题11\n", - "添加题号031372, 来源: 2023届四校联考(复兴奉贤松二金山)试题12\n", - "添加题号031373, 来源: 2023届四校联考(复兴奉贤松二金山)试题13\n", - "添加题号031374, 来源: 2023届四校联考(复兴奉贤松二金山)试题14\n", - "添加题号031375, 来源: 2023届四校联考(复兴奉贤松二金山)试题15\n", - "添加题号031376, 来源: 2023届四校联考(复兴奉贤松二金山)试题16\n", - "添加题号031377, 来源: 2023届四校联考(复兴奉贤松二金山)试题17\n", - "添加题号031378, 来源: 2023届四校联考(复兴奉贤松二金山)试题18\n", - "添加题号031379, 来源: 2023届四校联考(复兴奉贤松二金山)试题19\n", - "添加题号031380, 来源: 2023届四校联考(复兴奉贤松二金山)试题20\n", - "添加题号031381, 来源: 2023届四校联考(复兴奉贤松二金山)试题21\n" + "添加题号040336, 来源: 2025届高一下学期测验01\n", + "添加题号040337, 来源: 2025届高一下学期测验01\n", + "添加题号040338, 来源: 2025届高一下学期测验01\n", + "添加题号040339, 来源: 2025届高一下学期测验01\n", + "添加题号040340, 来源: 2025届高一下学期测验01\n", + "添加题号040341, 来源: 2025届高一下学期测验01\n", + "添加题号040342, 来源: 2025届高一下学期测验01\n", + "添加题号040343, 来源: 2025届高一下学期测验01\n", + "添加题号040344, 来源: 2025届高一下学期测验01\n", + "添加题号040345, 来源: 2025届高一下学期测验01\n", + "添加题号040346, 来源: 2025届高一下学期测验01\n", + "添加题号040347, 来源: 2025届高一下学期测验01\n", + "添加题号040348, 来源: 2025届高一下学期测验01\n", + "添加题号040349, 来源: 2025届高一下学期测验01\n", + "添加题号040350, 来源: 2025届高一下学期测验02\n", + "添加题号040351, 来源: 2025届高一下学期测验02\n", + "添加题号040352, 来源: 2025届高一下学期测验02\n", + "添加题号040353, 来源: 2025届高一下学期测验02\n", + "添加题号040354, 来源: 2025届高一下学期测验02\n", + "添加题号040355, 来源: 2025届高一下学期测验02\n", + "添加题号040356, 来源: 2025届高一下学期测验02\n", + "添加题号040357, 来源: 2025届高一下学期测验02\n", + "添加题号040358, 来源: 2025届高一下学期测验02\n", + "添加题号040359, 来源: 2025届高一下学期测验02\n", + "添加题号040360, 来源: 2025届高一下学期测验02\n", + "添加题号040361, 来源: 2025届高一下学期测验02\n", + "添加题号040362, 来源: 2025届高一下学期测验02\n", + "添加题号040363, 来源: 2025届高一下学期测验02\n", + "添加题号040364, 来源: 2025届高一下学期测验02\n", + "添加题号040365, 来源: 2025届高一下学期测验02\n", + "添加题号040366, 来源: 2025届高一下学期测验02\n", + "添加题号040367, 来源: 2025届高一下学期测验02\n", + "添加题号040368, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040369, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040370, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040371, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040372, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040373, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040374, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040375, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040376, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040377, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040378, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040379, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040380, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040381, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040382, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040383, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040384, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040385, 来源: 2025届高一下学期期中复习二(幂指对函数)\n", + "添加题号040386, 来源: 2025届高一下学期期中复习二(幂指对函数)\n" ] } ], 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 3750eb69..16159546 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 @@ -9,27 +9,57 @@ "name": "stdout", "output_type": "stream", "text": [ - "031361 填空题\n", - "031362 填空题\n", - "031363 填空题\n", - "031364 填空题\n", - "031365 填空题\n", - "031366 填空题\n", - "031367 填空题\n", - "031368 填空题\n", - "031369 填空题\n", - "031370 填空题\n", - "031371 填空题\n", - "031372 填空题\n", - "031373 选择题\n", - "031374 选择题\n", - "031375 选择题\n", - "031376 选择题\n", - "031377 解答题\n", - "031378 解答题\n", - "031379 解答题\n", - "031380 解答题\n", - "031381 解答题\n" + "040336 填空题\n", + "040337 填空题\n", + "040338 填空题\n", + "040339 填空题\n", + "040340 填空题\n", + "040341 填空题\n", + "040342 填空题\n", + "040343 填空题\n", + "040344 填空题\n", + "040345 解答题\n", + "040346 选择题\n", + "040347 选择题\n", + "040348 解答题\n", + "040349 解答题\n", + "040350 填空题\n", + "040351 填空题\n", + "040352 填空题\n", + "040353 填空题\n", + "040354 填空题\n", + "040355 填空题\n", + "040356 填空题\n", + "040357 填空题\n", + "040358 填空题\n", + "040359 填空题\n", + "040360 填空题\n", + "040361 填空题\n", + "040362 选择题\n", + "040363 选择题\n", + "040364 解答题\n", + "040365 解答题\n", + "040366 解答题\n", + "040367 解答题\n", + "040368 填空题\n", + "040369 填空题\n", + "040370 解答题\n", + "040371 解答题\n", + "040372 解答题\n", + "040373 解答题\n", + "040374 解答题\n", + "040375 解答题\n", + "040376 解答题\n", + "040377 填空题\n", + "040378 填空题\n", + "040379 填空题\n", + "040380 填空题\n", + "040381 选择题\n", + "040382 选择题\n", + "040383 解答题\n", + "040384 解答题\n", + "040385 解答题\n", + "040386 解答题\n" ] } ], diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index f2bd61fa..ad900d0f 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -451658,5 +451658,974 @@ "related": [], "remark": "", "space": "12ex" + }, + "040336": { + "id": "040336", + "content": "角$\\alpha$是第二象限, $\\sin \\alpha=\\dfrac{4}{5}$, 则$\\sin 2 \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040337": { + "id": "040337", + "content": "已知$\\sin (\\dfrac{\\pi}{6}+\\alpha)=\\dfrac{\\sqrt{3}}{2}$, 则$\\sin (\\dfrac{5 \\pi}{6}-\\alpha)$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040338": { + "id": "040338", + "content": "设扇形$AOB$的周长为$8$, 若这个扇形的面积为$4$, 则圆心角的弧度数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040339": { + "id": "040339", + "content": "把$-\\sin \\alpha+\\sqrt{3} \\cos \\alpha$化为$A \\sin (\\alpha+\\varphi)$($A>0$, $\\varphi \\in(0,2 \\pi)$)的形式\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040340": { + "id": "040340", + "content": "已知$\\tan \\alpha, \\tan \\beta$是方程$3 x^2+5 x-7=0$的两根, 则$\\tan (\\alpha+\\beta)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040341": { + "id": "040341", + "content": "已知$\\tan (\\pi+\\alpha)=-2$, 则$\\dfrac{2 \\sin (\\dfrac{3}{2} \\pi-\\alpha)-3 \\sin (\\pi+\\alpha)}{4 \\cos (-\\alpha)+\\cos (\\dfrac{\\pi}{2}-\\alpha)}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040342": { + "id": "040342", + "content": "方程$\\sin (x+\\dfrac{\\pi}{4})=\\dfrac{1}{2}$在$[0,2 \\pi]$内的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040343": { + "id": "040343", + "content": "已知$\\triangle ABC$中的三边分别为$a$、$b$、$c$, 三边所对的角分别为$A$、$B$、$C$, 且满足$\\dfrac{1}{a+b}+\\dfrac{1}{b+c}=\\dfrac{3}{a+b+c}$, $\\triangle ABC$的外接圆的面积为$3 \\pi$, 则$b=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040344": { + "id": "040344", + "content": "在角$\\theta_1, \\theta_2, \\theta_3, \\cdots, \\theta_{60}$的终边上分别有一点$P_1, P_2, P_3, \\cdots, P_{60}$. 如果点$P_k$的坐标为$(\\sin (30^{\\circ}-k^{\\circ})$, $\\sin (60^{\\circ}+k^{\\circ}))$, $1 \\leq k \\leq 60$, $k \\in \\mathbf{N}$, 则$\\cos \\theta_1+\\cos \\theta_2+\\cos \\theta_3+\\cdots+\\cos \\theta_{60}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040345": { + "id": "040345", + "content": "若$\\sin 2 \\alpha=\\dfrac{1}{4}$, 且$\\alpha \\in(\\dfrac{\\pi}{4}, \\dfrac{\\pi}{2})$, 则$\\cos \\alpha-\\sin \\alpha$的值为().\n\\fourch{$\\dfrac{\\sqrt{3}}{2}$}{$-\\dfrac{\\sqrt{3}}{2}$}{$\\pm \\dfrac{\\sqrt{3}}{2}$}{$\\dfrac{3}{4}$}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040346": { + "id": "040346", + "content": "在$\\triangle ABC$中, ``$\\cos A<\\cos B$''是``$\\sin A>\\sin B$''的\\bracket{20} 条件.\n\\fourch{充分非必要}{必要非充分}{充要}{非充分非必要}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040347": { + "id": "040347", + "content": "已知$\\triangle ABC$的三边长分别为$\\sqrt{a}$、$\\sqrt{b}$、$\\sqrt{c}$, 若存在角$\\theta \\in(0, \\pi)$使得$a^2=b^2+c^2-2 b c \\cos \\theta$, 则$\\triangle ABC$的形状为\\bracket{20}.\n\\fourch{锐角三角形}{直角三角形}{钝角三角形}{以上都不对}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040348": { + "id": "040348", + "content": "已知$\\cos (\\alpha+\\beta)=\\dfrac{2 \\sqrt{5}}{5}$, $\\tan \\beta=\\dfrac{1}{7}$, 且$\\alpha$、$\\beta \\in(0, \\dfrac{\\pi}{2})$.\\\\\n(1) 求$\\tan \\alpha$的值;\\\\\n(2) 求$2 \\alpha+\\beta$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040349": { + "id": "040349", + "content": "如图所示, 我国黄海某处的一个圆形海域上有四个小岛, 小岛$B$与小岛$A$、小岛$C$相距都为$5 k$公里, 与小岛$D$相距为$3 \\sqrt{5} k$公里(其中$k$为常数). 已知角$A$为钝角, 且$\\sin A=\\dfrac{3}{5}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.4]\n\\draw (-2.5,0) node [below left] {$A$} coordinate (A);\n\\draw (2.5,0) node [below right] {$B$} coordinate (B);\n\\draw (0,5) coordinate (O);\n\\draw (O) ++ ({-atan(2)-acos(0.28)}:{2.5*sqrt(5)}) node [left] {$D$} coordinate (D);\n\\draw (O) ++ ({-atan(2)+2*atan(1/2)}:{2.5*sqrt(5)}) node [right] {$C$} coordinate (C);\n\\draw [dashed] (O) circle ({2.5*sqrt(5)});\n\\draw (B)--(A)--(D)--(C)--cycle;\n\\draw [dashed] (B)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 求小岛$A$与小岛$D$之间的距离; (用$k$表示)\\\\\n(2) 求四个小岛所形成的四边形$ABCD$的面积;(用$k$表示)(提示: 角$A$与角$C$互补)\\\\\n(3) 记$\\angle CDB$为$\\alpha$, $\\angle CBD$为$\\beta$, 求$\\sin (2 \\alpha+\\beta)$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验01", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040350": { + "id": "040350", + "content": "若$\\sin \\alpha=\\dfrac{1}{3}$, 则$\\cos (\\dfrac{\\pi}{2}+\\alpha)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040351": { + "id": "040351", + "content": "函数$y=1-\\sin x$取得最小值时所有$x$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040352": { + "id": "040352", + "content": "函数$y=\\cos 2 x$的最小正周期是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040353": { + "id": "040353", + "content": "已知$\\tan \\theta=\\dfrac{1}{2}$, 则$\\sin 2 \\theta-2 \\cos ^2 \\theta=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040354": { + "id": "040354", + "content": "函数$y=\\sqrt{\\tan x}$的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040355": { + "id": "040355", + "content": "已知$\\cos \\theta=-\\dfrac{3}{5}$, 并且$180^{\\circ}<\\theta<270^{\\circ}$, 则$\\tan \\dfrac{\\theta}{2}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040356": { + "id": "040356", + "content": "若$x \\in(-\\pi, 2 \\pi)$, 则方程$\\sin 2 x=\\sin x$的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040357": { + "id": "040357", + "content": "设$y=x^{\\frac{1}{2}}-x^3$, 则满足$y<0$的$x$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040358": { + "id": "040358", + "content": "函数$y=2^{\\cos ^2 x-\\cos x}$的值域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040359": { + "id": "040359", + "content": "函数$y=\\sin (\\dfrac{\\pi}{6}-x)$, $x \\in[0, \\dfrac{3 \\pi}{2}]$的单调递减区间是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040360": { + "id": "040360", + "content": "在三角形$ABC$中, $3 \\sin A+4 \\cos B=6$, $4 \\sin B+3 \\cos A=1$, 则$\\angle C=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040361": { + "id": "040361", + "content": "设函数$f(x)=\\sin ^6 \\dfrac{k x}{10}+\\cos ^6 \\dfrac{k x}{10}$, 其中$k$是一个正整数, 若对任意实数$a$, 均有$\\{f(x) | a0$, 则$\\alpha$为第一或第二象限角; \\textcircled{3}$a, b, c>0$, 则$\\sqrt{a^2+b^2}, \\sqrt{b^2+c^2}, \\sqrt{c^2+a^2}$必是某一个锐角三角形的三边长. 上述命题中, 正确的命题有\\bracket{20}个.\n\\fourch{$0$}{$1$}{$2$}{$3$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040364": { + "id": "040364", + "content": "已知函数$f(x)=\\tan (\\omega x+\\dfrac{\\pi}{4})$($\\omega>0$)的最小正周期为$\\dfrac{\\pi}{2}$.\\\\\n(1) 求$\\omega$的值及函数$f(x)$的定义域;\\\\\n(2) 若$f(\\dfrac{\\alpha}{2})=3$, 求$\\tan 2 \\alpha$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040365": { + "id": "040365", + "content": "某水产养殖户承包一片靠岸水域. 如图, $AO$、$OB$为直线岸线, $OA=1000$\n米, $OB=1500$米, $\\angle AOB=\\dfrac{\\pi}{3}$, 该承包水域的水面边界是某\n圆的一段弧$\\overset\\frown{AB}$, 过弧$\\overset\\frown{AB}$上一点$P$按线段$PA$和$PB$修建养殖网箱, 已知$\\angle APB=\\dfrac{2 \\pi}{3}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (1,{sqrt(3)}) node [right] {$A$} coordinate (A);\n\\draw (-1.5,{1.5*sqrt(3)}) node [left] {$B$} coordinate (B);\n\\draw (A) arc ({atan((sqrt(3)-5/sqrt(12))/1.5)}:{180+atan((1.5*sqrt(3)-5/sqrt(12))/(-1))}:{sqrt(7/3)});\n\\draw (-0.5,{5/sqrt(12)}) ++ (85:{sqrt(7/3)}) node [above] {$P$} coordinate (P);\n\\draw (A) -- (P) -- (B) (O) -- (A) (O) -- (B);\n\\draw [dashed] (A) -- (B);\n\\end{tikzpicture}\n\\end{center}\n(1) 求岸线上点$A$与点$B$之间的直线距离;\\\\\n(2) 如果线段$PA$上的网箱每米可获得$40$元的经济收益, 线段$PB$上的网箱每米可获得$30$元的经济收益. 记$\\angle PAB=\\theta$, 则这两段网箱获得的经济总收益最高为多少? (精确到元)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040366": { + "id": "040366", + "content": "已知函数$f(x)=2^x$($x \\in \\mathbf{R}$), 记$g(x)=f(x)-f(-x)$.\\\\\n(1) 解不等式: $f(2 x)-f(x) \\leq 6$;\\\\\n(2) 设$k$为实数, 若存在实数$x_0 \\in(1,2]$, 使得$g(2 x_0)=k \\cdot g^2(x_0)-1$成立, 求$k$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040367": { + "id": "040367", + "content": "已知函数$f(x)=\\log _3 \\dfrac{m-x}{x+2}$为奇函数.\\\\\n(1) 求实数$m$的值;\\\\\n(2) 判定函数$f(x)$在定义域内的单调性, 并证明;\\\\\n(3) 若不等式$f(\\sin ^2 x)+f(t-2 \\cos x-3) \\geq 0$对任意$x \\in[-\\dfrac{\\pi}{3}, \\dfrac{\\pi}{6}]$恒成立, 求实数$t$的最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期测验02", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040368": { + "id": "040368", + "content": "函数$f(x)=(m^2-m-1) x^{m^2+m-3}$是幂函数, 且函数$f(x)$在区间$(0,+\\infty)$上是严格增函数, 则$f(x)$的解析式为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040369": { + "id": "040369", + "content": "函数$y=\\log _2(3-2 x-x^2)$的严格减区间\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040370": { + "id": "040370", + "content": "若函数$y=(m x^2+m x+2)^{-\\frac{3}{4}}$的定义域为$\\mathbf{R}$, 求实数$m$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040371": { + "id": "040371", + "content": "设$f(x)=\\log _a(1+x)+\\log _a(3-x)$($a>0$, 且$a \\neq 1)$且$f(1)=2$.\\\\\n(1) 求实数$a$的值及$f(x)$的定义域;\\\\\n(2) 求$f(x)$在区间$[0, \\dfrac{3}{2}]$上的最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040372": { + "id": "040372", + "content": "已知$f(x)=a x^2+b x+c$($a$、$b$、$c \\in \\mathbf{R}$).\\\\\n(1) 当$f(1)=-1$, 且$f(x)<0$的解集为$(0,2)$, 求函数$f(x)$的解析式;\\\\\n(2) $b=-2 a$, $c=0$, 若关于$x$的不等式$2^{f(x)}-\\dfrac{1}{4}>0$对一切实数$x$恒成立, 求实数$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040373": { + "id": "040373", + "content": "已知$f(x)=x|x-a|+b$, $x \\in \\mathbf{R}$.\\\\\n(1) 当$a=1$, $b=0$时, 判断$f(x)$的奇偶性, 并说明理由;\\\\\n(2) 当$a=1$, $b=1$时, 若$f(\\log _2 x)=3$, 求$x$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040374": { + "id": "040374", + "content": "求证: 函数$f(x)=\\log _{0.5}(\\dfrac{x-1}{x-2})$在区间$(2,+\\infty)$上是严格增函数;", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040375": { + "id": "040375", + "content": "已知$a>0$且$a \\neq 1$, 若$\\log _a(4 x^2-1)<\\log _a(-2 x^2+x+1)$, 求实数$x$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040376": { + "id": "040376", + "content": "某创业投资公司拟投资开发某种新能源产品, 估计能获得$25$万元至$1600$万元的投资收益, 现准备制定一个对科研课题组的奖励方案: 奖金$y$(单位: 万元) 随投资收益$x$(单位: 万元)的增加而增加, 奖金不超过$75$万元, 同时奖金不超过投资收益的$20 \\%$.\\\\\n(1) 请用数学语言列出公司对函数模型的基本要求;\\\\\n(2) 判断函数$f(x)=\\dfrac{x}{40}+10$是否符合公司奖励方案函数模型的要求, 并说明理由;\\\\\n(3) 已知函数$g(x)=a \\sqrt{x}-5$($a \\geq 1$)符合公司奖励方案函数模型要求, 求实数$a$取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040377": { + "id": "040377", + "content": "设$a \\in\\{-2,-\\dfrac{3}{5},-\\dfrac{1}{2},-\\dfrac{1}{3}, \\dfrac{1}{2}, 1,2,3\\}$, 已知幂函数$y=x^a$图像关于原点中心对称, 且在区间$(0,+\\infty)$上是严格减函数, 则满足条件的$a$值是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040378": { + "id": "040378", + "content": "函数$y=\\sqrt{(\\dfrac{1}{16})^x-64}$的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040379": { + "id": "040379", + "content": "若$\\sqrt[4]{a}+(a-2)^0$有意义, 则实数$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040380": { + "id": "040380", + "content": "函数$y=a^{x+2021}+2021$($a>0$, $a \\neq 1$)的图像恒过定点\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040381": { + "id": "040381", + "content": "对任意的实数$a$, 下列各式一定正确的是\\bracket{20}.\n\\fourch{$(a^{\\frac{2}{3}})^{\\frac{1}{2}}=a^{\\frac{1}{3}}$}{$(a^{\\frac{1}{2}})^{\\frac{2}{3}}=a^{\\frac{1}{3}}$}{$(a^{-\\frac{3}{5}})^{-\\frac{1}{3}}=a^{\\frac{1}{5}}$}{$(a^{\\frac{1}{3}})^{\\frac{3}{5}}=a^{\\frac{1}{5}}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040382": { + "id": "040382", + "content": "已知$f(x)=\\begin{cases}x+1,& x \\in[-1,0), \\\\ x^2+1,& x \\in[0,1],\\end{cases}$ 则下列函数的图像错误的是\\bracket{20}的图像.\n\\fourch{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-0.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) -- (1,1);\n\\draw [domain = 1:2] plot (\\x,{(\\x-1)*(\\x-1)+1});\n\\draw [dashed] (1,0) node [below] {$1$} -- (1,1) -- (0,1) node [left] {$1$} (2,0) node [below] {$2$} -- (2,2) -- (0,2) node [left] {$2$};\n\\draw (1,-1) node {$y=f(x-1)$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (1,0) -- (0,1);\n\\draw [domain = -1:0] plot (\\x,{\\x*\\x+1});\n\\draw [dashed] (0,2) node [right] {$2$} coordinate (2) -- (-1,2) -- (-1,0) node [below] {$-1$};\n\\draw (0,1) node [right] {$1$} (1,0) node [below] {$1$};\n\\draw (0,-1) node {$y=f(-x)$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1] plot (\\x,{\\x*\\x+1});\n\\draw (0,2) node [right] {$2$};\n\\draw (-1,0) node [below] {$-1$};\n\\draw (0,1) node [right] {$1$} (1,0) node [below] {$1$};\n\\draw [dashed] (1,0) -- (1,2) -- (-1,2) -- (-1,0);\n\\draw (0,-1) node {$y=f(|x|)$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:1] plot (\\x,{\\x*\\x+1});\n\\draw (-1,2) -- (0,1);\n\\draw (0,2) node [right] {$2$};\n\\draw (-1,0) node [below] {$-1$};\n\\draw (0,1) node [right] {$1$} (1,0) node [below] {$1$};\n\\draw [dashed] (1,0) -- (1,2) -- (-1,2) -- (-1,0);\n\\draw (0,-1) node {$y=f(|x|)$};\n\\end{tikzpicture}}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040383": { + "id": "040383", + "content": "已知幂函数$f(x)=x^{m^2-2 m-3}$($m \\in \\mathbf{Z}$)为偶函数, 且在区间$(0,+\\infty)$上是严格减函数, 求$f(x)$的解析式, 并讨论函数$g(x)=a \\sqrt{f(x)}-\\dfrac{b}{x f(x)}$的奇偶性.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040384": { + "id": "040384", + "content": "设$0 \\leq x \\leq 2$, 求函数$y=4^{x-\\dfrac{1}{2}}-a \\cdot 2^x+\\dfrac{a^2}{2}+1$的最大值和最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040385": { + "id": "040385", + "content": "设函数$f(x)=\\dfrac{10^x-10^{-x}}{10^x+10^{-x}}$.\\\\\n(1) 证明$f(x)$在$(-\\infty,+\\infty)$上是严格增函数;\\\\\n(2) 求函数$f(x)$的值域.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040386": { + "id": "040386", + "content": "定义: 对函数$y=f(x)$, 对给定的正整数$k$, 若在其定义域内存在实数$x_0$, 使得$f(x_0+k)=f(x_0)+f(k)$, 则称函数$f(x)$为``$k$性质函数''.\\\\\n(1) 若函数$f(x)=2^x$为``$1$性质函数'', 求$x_0$;\\\\\n(2) 证明: 函数$f(x)=\\dfrac{1}{x}$不是``$k$性质函数'';\\\\\n(3) 若函数$f(x)=\\lg \\dfrac{a}{x^2+1}$为``$2$性质函数'', 求实数$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期期中复习二(幂指对函数)", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" } } \ No newline at end of file