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20230326 evening

This commit is contained in:
weiye.wang 2023-03-26 21:40:42 +08:00
parent acb72d6c01
commit 91a6e9b897
9 changed files with 1148 additions and 153 deletions
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2
工具/修改题目数据库.ipynb
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@ -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",

2
工具/关键字筛选题号.ipynb
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@ -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",

2
工具/寻找阶段末尾空闲题号.ipynb
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@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 1,
"metadata": {},
"outputs": [
{

11
工具/批量题号选题pdf生成.ipynb
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@ -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",

2
工具/文本文件/题号筛选.txt
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@ -1 +1 @@
031332,031333,031334,031335,031336,031337,031338,031339,031340,031341,031342,031343,031344,031345,031346,031347,031348,031349,031350,031351,031352
040283,040284,040285,040286,040287,040288,040289,040290,040291,040292,040293,040294,040295,040296,040297,040298

159
工具/新题比对.ipynb
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@ -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",

82
工具/添加题目到数据库.ipynb
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@ -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"
]
}
],

72
工具/识别题库中尚未标注的题目类型.ipynb
View File

@ -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"
]
}
],

969
题库0.3/Problems.json
View File

@ -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$\\{f(x) | a<x<a+1\\}=\\{f(x) | x \\in \\mathbf{R}\\}$, 则$k$的最小值为\\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": ""
},
"040362": {
"id": "040362",
"content": "下列函数是奇函数的为\\bracket{20}.\n\\fourch{$y=\\sin (x+\\dfrac{\\pi}{2})$}{$y=\\sin x+1$}{$y=\\sin ^2 x$}{$y=\\sin (\\pi+x)$}",
"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": ""
},
"040363": {
"id": "040363",
"content": "给出下列命题: \\textcircled{1} 若$\\alpha \\neq \\beta$, 则$\\sin \\alpha \\neq \\sin \\beta$; \\textcircled{2} 若$\\sin \\alpha>0$, 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)",
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"remark": "",
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},
"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)",
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"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)",
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],
"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": [
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],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
}
}