From 773b7c4163f3b09ea8acce60bba16086ac5a3876 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sun, 18 Sep 2022 19:22:09 +0800 Subject: [PATCH] 20220918 evening --- .gitignore | 3 +- 工具/关键字筛选题号.ipynb | 27 +- .../小闲平台作业测验数据导入.ipynb | 10 +- .../讲义题目分类按顺序梳理_制答题卡用.ipynb | 6 +- 工具/分年级专用工具/赋能卷生成.ipynb | 122 + 工具/寻找tex文件中未赋答案的题目.ipynb | 137 + 工具/批量添加题库字段数据.ipynb | 62 +- 工具/模板文件/题目清单.synctex.gz | Bin 0 -> 2256 bytes 工具/添加关联题目.ipynb | 16 +- 工具/讲义生成.ipynb | 22 +- 工具/课时目标及课时划分信息汇总.ipynb | 10 +- 工具/题号选题pdf生成.ipynb | 19 +- 题库0.3/Problems.json | 7881 ++++++++++------- 13 files changed, 5094 insertions(+), 3221 deletions(-) create mode 100644 工具/分年级专用工具/赋能卷生成.ipynb create mode 100644 工具/寻找tex文件中未赋答案的题目.ipynb create mode 100644 工具/模板文件/题目清单.synctex.gz diff --git a/.gitignore b/.gitignore index 91a99a14..be9cfb8c 100644 --- a/.gitignore +++ b/.gitignore @@ -2,4 +2,5 @@ **/*.pdf **/临时文件/ **/*测试* -**/*数据导入作业文件/ \ No newline at end of file +**/*数据导入作业文件/ +**/*班级报表*/ \ No newline at end of file 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 af4ee9d1..c021123c 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -2,15 +2,26 @@ "cells": [ { "cell_type": "code", - "execution_count": 10, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "import os,re,json\n", "\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", - " {\"tags\":[\"第三单元\"],\"content\":[r\"A[\\s\\S]*B\"],\"content2\":[r\"c\"],}\n", + " {\"tags\":[\"第五单元\"],\"_notcontent\":[\"三角形式\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", @@ -59,7 +70,9 @@ " match_list.append(id)\n", "\n", "with open(filename,\"w\",encoding=\"utf8\") as f:\n", - " f.write(\",\".join(match_list))" + " f.write(\",\".join(match_list))\n", + "\n", + "os.system(\"code \"+filename)" ] }, { @@ -72,7 +85,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -86,12 +99,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/分年级专用工具/小闲平台作业测验数据导入.ipynb b/工具/分年级专用工具/小闲平台作业测验数据导入.ipynb index 962b6291..765b9294 100644 --- a/工具/分年级专用工具/小闲平台作业测验数据导入.ipynb +++ b/工具/分年级专用工具/小闲平台作业测验数据导入.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -44,7 +44,7 @@ "\n", "for sf in statfiles:\n", " #读取文件生成区域列表与难度列表\n", - " classname = \"2023届\"+re.findall(r\"高三[\\d]*?班\",sf)[0]\n", + " classname = \"2023届高三\"+re.findall(r\"高三([\\d])*?班\",sf)[0].zfill(2)+\"班\"\n", " date = str(time.localtime().tm_year)+str(time.localtime().tm_mon).zfill(2)+str(time.localtime().tm_mday).zfill(2)\n", " if \"statsfile.xlsx\" in os.listdir(\"临时文件\"):\n", " os.remove(\"临时文件/statsfile.xlsx\")\n", @@ -81,7 +81,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -95,12 +95,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb b/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb index 95f812df..d272385f 100644 --- a/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb +++ b/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb @@ -84,7 +84,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -98,12 +98,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/分年级专用工具/赋能卷生成.ipynb b/工具/分年级专用工具/赋能卷生成.ipynb new file mode 100644 index 00000000..9c39d8eb --- /dev/null +++ b/工具/分年级专用工具/赋能卷生成.ipynb @@ -0,0 +1,122 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n" + ] + } + ], + "source": [ + "#在 临时文件/赋能答题纸 目录中保留一个pdf(赋能试卷的答题纸), 不留别的pdf文件. \n", + "#在 临时文件/赋能答题纸 目录中保留 赋能template.tex.\n", + "\"\"\"---设置文件名---\"\"\"\n", + "filename = \"赋能02\"\n", + "\n", + "\"\"\"---设置题目列表---\"\"\"\n", + "problems = r\"\"\"\n", + "1750,337,2675,339:345\n", + "\"\"\"\n", + "#完成后将含有 filename 的文件移至其它目录\n", + "\n", + "import os,re,json,shutil\n", + "\n", + "\n", + "def generate_number_set(string,dict):\n", + " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", + " string_list = string.split(\",\")\n", + " numbers_list = []\n", + " for s in string_list:\n", + " if not \":\" in s:\n", + " numbers_list.append(s.zfill(6))\n", + " else:\n", + " start,end = s.split(\":\")\n", + " for ind in range(int(start),int(end)+1):\n", + " numbers_list.append(str(ind).zfill(6))\n", + " return numbers_list\n", + "\n", + "#读取数据库\n", + "with open(\"../../题库0.3/Problems.json\",\"r\",encoding = \"utf8\") as f:\n", + " jsondata = f.read()\n", + "pro_dict = json.loads(jsondata)\n", + "\n", + "#读取pdf文件并转化为png\n", + "pdffile = \"临时文件/赋能答题纸/\"+[f for f in os.listdir(\"临时文件/赋能答题纸\") if \".pdf\" in f][0]\n", + "try:\n", + " shutil.copy(pdffile,\"tempanswersheet.pdf\")\n", + "except:\n", + " os.remove(\"tempanswersheet.pdf\")\n", + " shutil.copy(pdffile,\"tempanswersheet.pdf\")\n", + "os.system(\"pdftocairo -png tempanswersheet.pdf\")\n", + "try:\n", + " os.rename(\"tempanswersheet-1.png\",\"临时文件/赋能答题纸/output/\"+filename+\"答题纸.png\")\n", + "except:\n", + " os.remove(\"tempanswersheet-1.png\")\n", + "os.rename(pdffile,\"临时文件/赋能答题纸/\"+filename+\"答题纸_raw.pdf\")\n", + "os.remove(\"tempanswersheet.pdf\")\n", + "\n", + "#替换tex模板中的内容\n", + "problem_list = [id for id in generate_number_set(problems.strip(),pro_dict) if id in pro_dict]\n", + "\n", + "with open(\"临时文件/赋能答题纸/赋能template.tex\",\"r\",encoding=\"utf8\") as f:\n", + " texdata = f.read()\n", + "texdata = texdata.replace(\"背景待替换\",filename+\"答题纸.png\")\n", + "data_problems = \"\\n\\n\"\n", + "for id in problem_list:\n", + " problemset = pro_dict[id]\n", + " problem = problemset[\"content\"]\n", + " data_problems += \"\\\\item \" + \"{\\\\tiny (\"+id+\")}\"+problem + \"\\n\\n\"\n", + "texdata = texdata.replace(\"题目待替换\",data_problems)\n", + "\n", + "with open(\"临时文件/赋能答题纸/output/\"+filename+\".tex\",\"w\",encoding=\"utf8\") as f:\n", + " f.write(texdata)\n", + "\n", + "#编译文件\n", + "os.chdir(\"临时文件/赋能答题纸/output\")\n", + "os.system(\"xelatex -interaction=batchmode \" + filename +\".tex\")\n", + "print(os.system(\"xelatex -interaction=batchmode \" + filename +\".tex\"))\n", + "os.chdir(\"../../..\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.8 ('base')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.8" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb new file mode 100644 index 00000000..2aa2e7b1 --- /dev/null +++ b/工具/寻找tex文件中未赋答案的题目.ipynb @@ -0,0 +1,137 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "周末卷01.tex\n", + "010923\n", + "\n", + "\n", + "010924\n", + "\n", + "\n", + "010925\n", + "\n", + "\n", + "010926\n", + "\n", + "\n", + "030013\n", + "\n", + "\n", + "010928\n", + "\n", + "\n", + "010929\n", + "\n", + "\n", + "010930\n", + "\n", + "\n", + "030014\n", + "\n", + "\n", + "010932\n", + "\n", + "\n", + "010933\n", + "\n", + "\n", + "010934\n", + "\n", + "\n", + "010935\n", + "\n", + "\n", + "010936\n", + "\n", + "\n", + "010937\n", + "\n", + "\n", + "010938\n", + "\n", + "\n", + "010939\n", + "\n", + "\n", + "010940\n", + "\n", + "\n", + "010941\n", + "\n", + "\n", + "010942\n", + "\n", + "\n", + "010943\n", + "\n", + "\n" + ] + } + ], + "source": [ + "import os,json,re\n", + "\n", + "#这里需要修改, 设定路径与选择文件\n", + "fileind = 0\n", + "# path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n", + "path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\上学期周末卷\"\n", + "\n", + "with open(\"../题库0.3/Problems.json\",\"r\",encoding = \"utf8\") as f:\n", + " jsondata = f.read()\n", + "pro_dict = json.loads(jsondata)\n", + "\n", + "filelist = [f for f in os.listdir(path) if \".tex\" in f]\n", + "file = filelist[fileind]\n", + "print(file)\n", + "with open(os.path.join(path,file),\"r\",encoding = \"utf8\") as f:\n", + " data = f.read()\n", + " idlist = re.findall(r\"\\(([\\d]{6})\\)\",data)\n", + " for id in idlist:\n", + " if pro_dict[id][\"ans\"].strip() == \"\":\n", + " print(id+\"\\n\\n\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.8 ('base')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.8" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb index d4fbdbf4..b0a74aeb 100644 --- a/工具/批量添加题库字段数据.ipynb +++ b/工具/批量添加题库字段数据.ipynb @@ -2,44 +2,34 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 000136 , 字段: objs 中已有该数据: K0319002B\n", - "题号: 001492 , 字段: objs 中已添加数据: K0319002B\n", - "题号: 009597 , 字段: objs 中已添加数据: K0319002B\n", - "题号: 000136 , 字段: objs 中已有该数据: K0319003B\n", - "题号: 001492 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 001493 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 001495 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 001496 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 001497 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 001498 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 001513 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 003154 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 006096 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 006097 , 字段: objs 中已添加数据: K0319003B\n", - "题号: 003179 , 字段: objs 中已添加数据: K0324003B\n", - "题号: 001534 , 字段: objs 中已添加数据: K0324004B\n", - "题号: 001535 , 字段: objs 中已添加数据: K0324004B\n", - "题号: 001538 , 字段: objs 中已添加数据: K0324004B\n", - "题号: 006058 , 字段: objs 中已添加数据: K0324004B\n", - "题号: 010305 , 字段: objs 中已添加数据: K0324004B\n", - "题号: 003152 , 字段: objs 中已添加数据: K0324005B\n", - "题号: 003172 , 字段: objs 中已添加数据: K0324005B\n", - "题号: 003177 , 字段: objs 中已添加数据: K0324005B\n", - "题号: 001538 , 字段: objs 中已添加数据: K0324006B\n", - "题号: 001537 , 字段: objs 中已添加数据: K0324006B\n", - "题号: 001536 , 字段: objs 中已添加数据: K0324006B\n", - "题号: 003172 , 字段: objs 中已添加数据: K0324006B\n", - "题号: 006062 , 字段: objs 中已添加数据: K0324006B\n", - "题号: 006225 , 字段: objs 中已添加数据: K0324006B\n", - "题号: 009612 , 字段: objs 中已添加数据: K0324006B\n", - "题号: 010109 , 字段: objs 中已添加数据: K0324006B\n" + "题号: 010923 , 字段: ans 中已修改数据: $\\{1,2,3,4,6\\}$\n", + "题号: 010924 , 字段: ans 中已修改数据: $(-1,2)$\n", + "题号: 010925 , 字段: ans 中已修改数据: $(1,2)$\n", + "题号: 010926 , 字段: ans 中已修改数据: $2$\n", + "题号: 030013 , 字段: ans 中已修改数据: $3$\n", + "题号: 010928 , 字段: ans 中已修改数据: $(0,+\\infty)$\n", + "题号: 010929 , 字段: ans 中已修改数据: $60$\n", + "题号: 010930 , 字段: ans 中已修改数据: $[-1,1]$\n", + "题号: 030014 , 字段: ans 中已修改数据: $\\dfrac{\\pi}3$\n", + "题号: 010932 , 字段: ans 中已修改数据: $\\dfrac{5\\sqrt{6}}2$\n", + "题号: 010933 , 字段: ans 中已修改数据: $[1,\\dfrac 54)$\n", + "题号: 010934 , 字段: ans 中已修改数据: $13$\n", + "题号: 010935 , 字段: ans 中已修改数据: B\n", + "题号: 010936 , 字段: ans 中已修改数据: D\n", + "题号: 010937 , 字段: ans 中已修改数据: C\n", + "题号: 010938 , 字段: ans 中已修改数据: C\n", + "题号: 010939 , 字段: ans 中已修改数据: (1) $\\dfrac{4\\sqrt{2}}3$; (2) $\\arccos\\dfrac{\\sqrt{3}}6$.\n", + "题号: 010940 , 字段: ans 中已修改数据: (1) $\\{x|x=k\\pi-\\dfrac\\pi 6, \\ k\\in \\mathbf{Z}\\}$; (2) $\\dfrac{3\\sqrt{3}}4$.\n", + "题号: 010941 , 字段: ans 中已修改数据: (1) 不符合要求, 证明略; (2) $S=\\dfrac{12}{1+\\sin(2\\theta+\\dfrac \\pi 4)}, \\ \\theta\\in [0,\\arctan\\dfrac 34]$, $S$的最小值为$12\\sqrt{2}-12$.\n", + "题号: 010942 , 字段: ans 中已修改数据: (1) $3$; (2) 证明略.\n", + "题号: 010943 , 字段: ans 中已修改数据: (1) 当$k=1$时, $y=f(x)$是偶函数; 当$k=-1$时, $y=f(x)$是奇函数; 当$k\\ne 1$且$k \\ne -1$时, $y=f(x)$既不是奇函数, 又不是偶函数; (2) $m=\\log_4 k$; (3) $\\{-3\\}\\cup (1,+\\infty)$.\n" ] } ], @@ -47,7 +37,7 @@ "import os,re,json\n", "\n", "\"\"\"---明确数据文件位置---\"\"\"\n", - "datafile = \"临时文件/l15objs.txt\"\n", + "datafile = \"临时文件/answers.txt\"\n", "# 双回车分隔，记录内单回车分隔列表，首行为字段名\n", "\"\"\"---文件位置结束---\"\"\"\n", "\n", @@ -137,7 +127,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -151,12 +141,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/模板文件/题目清单.synctex.gz b/工具/模板文件/题目清单.synctex.gz new file mode 100644 index 0000000000000000000000000000000000000000..a7bb1e5d47bf4360d0f66d61ae4382cc8a74371e GIT binary patch literal 2256 zcmV;>2ru^^iwFP!000003bmWfuH&{9$M=4UncW1qx)$|md7D*R6e-XTBq*|wB}(R4 z5*3lUv8T<`wApvlMS-H-4A4!{R|pUwuTk_+l5I+quSmOt!Pt~6{zxAF4|z!H{`yoU 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\"\\n\\n标签: \" + tags + \"\\n\\n答案: \"+answer + \"\\n\\n\" + \"解答或提示: \" + solution + \"\\n\\n使用记录:\\n\\n\"+ usage + \"\\n\" + \"\\n\\n备注: \" + remarks + \"\\n\\n出处: \"+origin + \"\\n\"\n", " students_string = raw_string + space + \"\\n\\n\"\n", " data_teachers += teachers_string\n", " data_students += students_string\n", @@ -163,7 +164,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -177,12 +178,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index e07ab677..de69538f 100644 --- a/题库0.3/Problems.json +++ 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"origin": "教材复习题", "edit": [ @@ -532,11 +532,11 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ - "20220901\t2023届高三2班\t0.364", + "20220901\t2023届高三02班\t0.364", "20220902\t2023届高三10班\t0.970" ], "origin": "教材复习题", @@ -564,7 +564,7 @@ "solution": "", "duration": -1, "usages": [ - "20220906\t2023届高三2班\t0.774" + "20220906\t2023届高三02班\t0.774" ], "origin": "教材复习题", "edit": [ @@ -802,7 +802,7 @@ "solution": "", "duration": -1, "usages": [ - "20220906\t2023届高三2班\t0.903" + "20220906\t2023届高三02班\t0.903" ], "origin": "教材复习题", "edit": [ @@ -850,7 +850,7 @@ "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.688" + "20220904\t2023届高三02班\t0.688" ], "origin": "教材复习题", "edit": [ @@ -1112,12 +1112,12 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ - "20220831\t2023届高三10班\t0.663", - "20220831\t2023届高三2班\t0.656" + "20220831\t2023届高三02班\t0.656", + "20220831\t2023届高三10班\t0.663" ], "origin": "教材复习题", "edit": [ @@ -1166,11 +1166,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\sqrt[3]{5}$, $\\log_3 5$; (2) $a^{\\frac 13}$; (3) $\\dfrac 14$; (4) $125$", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t1.000\t1.000\t1.000\t0.906" + "20220904\t2023届高三02班\t1.000\t1.000\t1.000\t0.906" ], "origin": "教材复习题", "edit": [ @@ -1192,11 +1192,11 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "(1) B (2) D", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.969\t1.000" + "20220904\t2023届高三02班\t0.969\t1.000" ], "origin": "教材复习题", "edit": [ @@ -1289,11 +1289,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t1.000" + "20220904\t2023届高三02班\t1.000" ], "origin": "教材复习题", "edit": [ @@ -1315,11 +1315,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $-3$; (2) $64$; (3) $1$", "solution": "", "duration": -1, "usages": [ - 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"20220824\t2023届高三8班\t0.879\t0.970\t0.970\t0.939\t0.970\t1.000\t0.818\t0.909\t1.000\t0.970\t1.000\t1.000\t0.455" + "20220824\t2023届高三02班\t0.848\t1.000\t0.970\t1.000\t0.970\t0.939\t0.970\t0.909\t1.000\t0.970\t0.909\t0.970\t0.424", + "20220824\t2023届高三08班\t0.879\t0.970\t0.970\t0.939\t0.970\t1.000\t0.818\t0.909\t1.000\t0.970\t1.000\t1.000\t0.455", + "20220824\t2023届高三10班\t0.849" ], "origin": "2016届创新班作业\t1103-假言命题的四种形式及充分必要条件", "edit": [ @@ -24966,13 +24970,13 @@ "usages": [ "2016届11班\t0.513", "2016届12班\t0.553", + "20220821\t2023届高三02班\t0.364", + "20220821\t2023届高三03班\t0.583", + "20220821\t2023届高三09班\t0.355", "20220821\t2023届高三10班\t0.438", "20220821\t2023届高三12班\t0.250", - "20220821\t2023届高三2班\t0.364", - "20220821\t2023届高三3班\t0.583", - "20220821\t2023届高三9班\t0.355", - "20220822\t2023届高三10班\t0.250", - "20220822\t2023届高三8班\t0.290" + "20220822\t2023届高三08班\t0.290", + "20220822\t2023届高三10班\t0.250" ], "origin": "2016届创新班作业\t1105-集合的关系", "edit": [ @@ -25267,10 +25271,10 @@ "usages": [ "2016届11班\t0.410", "2016届12班\t0.308", + "20220822\t2023届高三02班\t0.909", "20220822\t2023届高三10班\t0.567", - "20220822\t2023届高三2班\t0.909", - "20220823\t2023届高三11班\t0.480", - "20220823\t2023届高三8班\t0.688" + "20220823\t2023届高三08班\t0.688", + "20220823\t2023届高三11班\t0.480" ], "origin": "2016届创新班作业\t1106-集合的运算", "edit": [ @@ -25300,13 +25304,13 @@ "usages": [ "2016届11班\t0.667", "2016届12班\t0.590", + "20220821\t2023届高三02班\t0.758", + "20220821\t2023届高三03班\t0.875", + "20220821\t2023届高三09班\t0.806", "20220821\t2023届高三10班\t0.854", "20220821\t2023届高三12班\t0.750", - "20220821\t2023届高三2班\t0.758", - "20220821\t2023届高三3班\t0.875", - "20220821\t2023届高三9班\t0.806", - "20220822\t2023届高三10班\t0.583", - "20220822\t2023届高三8班\t0.774" + "20220822\t2023届高三08班\t0.774", + "20220822\t2023届高三10班\t0.583" ], "origin": "2016届创新班作业\t1106-集合的运算", "edit": [ @@ -25336,10 +25340,10 @@ "usages": [ "2016届11班\t0.795", "2016届12班\t0.692", + "20220822\t2023届高三02班\t0.636", "20220822\t2023届高三10班\t0.700", - "20220822\t2023届高三2班\t0.636", - "20220823\t2023届高三11班\t0.640", - "20220823\t2023届高三8班\t0.531" + "20220823\t2023届高三08班\t0.531", + "20220823\t2023届高三11班\t0.640" ], "origin": "2016届创新班作业\t1106-集合的运算", "edit": [ @@ -26163,7 +26167,7 @@ "usages": [ "2016届11班\t0.923", "2016届12班\t0.949", - "20220904\t2023届高三2班\t0.688" + "20220904\t2023届高三02班\t0.688" ], "origin": "2016届创新班作业\t1113-一次方程与二次方程", "edit": [ @@ -26191,7 +26195,7 @@ "usages": [ "2016届11班\t0.872", "2016届12班\t0.897", - "20220906\t2023届高三2班\t0.871" + "20220906\t2023届高三02班\t0.871" ], "origin": "2016届创新班作业\t1113-一次方程与二次方程", "edit": [ @@ -26696,7 +26700,7 @@ "usages": [ "2016届11班\t0.949", "2016届12班\t0.795", - "20220904\t2023届高三2班\t0.750" + "20220904\t2023届高三02班\t0.750" ], "origin": "2016届创新班作业\t1115-Viete定理", "edit": [ @@ -26779,7 +26783,7 @@ "usages": [ "2016届11班\t0.949", "2016届12班\t0.821", - "20220906\t2023届高三2班\t0.774" + "20220906\t2023届高三02班\t0.774" ], "origin": "2016届创新班作业\t1115-Viete定理", "edit": [ @@ -26806,7 +26810,7 @@ "usages": [ "2016届11班\t0.872", "2016届12班\t0.897", - "20220906\t2023届高三2班\t0.935" + "20220906\t2023届高三02班\t0.935" ], "origin": "2016届创新班作业\t1115-Viete定理", "edit": [ @@ -26833,7 +26837,7 @@ "usages": [ "2016届11班\t0.769", "2016届12班\t0.744", - "20220904\t2023届高三2班\t0.875" + "20220904\t2023届高三02班\t0.875" ], "origin": "2016届创新班作业\t1115-Viete定理", "edit": [ @@ -27116,14 +27120,14 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\times$ (2) $\\checkmark$ (3) $\\times$ (4) $\\times$ (5) $\\times$ (6) $\\times$ (7) $\\checkmark$ (8) $\\checkmark$ (9) $\\checkmark$ (10) $\\times$", "solution": "", "duration": -1, "usages": [ "2016届11班\t1.000\t0.974\t0.974\t0.923\t1.000\t0.974\t1.000\t0.692\t1.000\t0.462", "2016届12班\t0.974\t0.923\t0.974\t0.846\t1.000\t1.000\t1.000\t0.564\t1.000\t0.590", - "20220831\t2023届高三10班\t0.863", - "20220831\t2023届高三2班\t1.000\t1.000\t1.000\t0.906\t1.000\t1.000\t0.969\t0.688\t0.969\t0.594" + "20220831\t2023届高三02班\t1.000\t1.000\t1.000\t0.906\t1.000\t1.000\t0.969\t0.688\t0.969\t0.594", + "20220831\t2023届高三10班\t0.863" ], "origin": "2016届创新班作业\t1117-不等式的性质", "edit": [ @@ -27144,14 +27148,14 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac ab$, $\\dfrac{a+m}{b+m}$, $\\dfrac{b+n}{a+n}$, $\\dfrac ba$", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.821", "2016届12班\t0.846", - "20220831\t2023届高三10班\t0.926", - "20220831\t2023届高三2班\t0.844" + "20220831\t2023届高三02班\t0.844", + "20220831\t2023届高三10班\t0.926" ], "origin": "2016届创新班作业\t1117-不等式的性质", "edit": [ @@ -27408,14 +27412,14 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.718\t0.385", "2016届12班\t0.641\t0.436", - "20220831\t2023届高三10班\t0.704\t0.630", - "20220831\t2023届高三2班\t0.531\t0.688" + "20220831\t2023届高三02班\t0.531\t0.688", + "20220831\t2023届高三10班\t0.704\t0.630" ], "origin": "2016届创新班作业\t1119-含有绝对值的不等式基本性质", "edit": [ @@ -27970,7 +27974,7 @@ "usages": [ "2016届11班\t0.487", "2016届12班\t0.541", - "20220904\t2023届高三2班\t0.594" + "20220904\t2023届高三02班\t0.594" ], "origin": "2016届创新班作业\t1124-带绝对值的不等式", "edit": [ @@ -28045,13 +28049,13 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\checkmark$ (2) $\\checkmark$ (3) $\\checkmark$ (4) $\\times$ (5) $\\times$ (6) $\\times$ (7) $\\checkmark$ (8) $\\times$ (9) $\\times$ (10) $\\checkmark$ (11) $\\times$", "solution": "", "duration": -1, "usages": [ "2016届11班\t1.000\t1.000\t1.000\t1.000\t1.000\t1.000\t0.947\t0.974\t1.000\t1.000\t1.000", "2016届12班\t1.000\t1.000\t0.944\t0.972\t1.000\t0.889\t0.944\t1.000\t0.972\t1.000\t1.000", - "20220901\t2023届高三2班\t0.970\t1.000\t0.970\t0.939\t0.909\t1.000\t0.848\t0.939\t0.909\t0.970\t0.970", + "20220901\t2023届高三02班\t0.970\t1.000\t0.970\t0.939\t0.909\t1.000\t0.848\t0.939\t0.909\t0.970\t0.970", "20220902\t2023届高三10班\t0.871" ], "origin": "2016届创新班作业\t1125-基本不等式及其推广", @@ -28127,13 +28131,13 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$k=\\dfrac 13$", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.895", "2016届12班\t0.889", - "20220901\t2023届高三2班\t0.091", + "20220901\t2023届高三02班\t0.091", "20220902\t2023届高三10班\t0.385" ], "origin": "2016届创新班作业\t1125-基本不等式及其推广", @@ -28233,14 +28237,14 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.923", "2016届12班\t0.892", - "20220831\t2023届高三10班\t0.778", - "20220831\t2023届高三2班\t0.406" + "20220831\t2023届高三02班\t0.406", + "20220831\t2023届高三10班\t0.778" ], "origin": "2016届创新班作业\t1126-基本不等式在最值问题中的应用", "edit": [ @@ -28261,14 +28265,14 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.949", "2016届12班\t0.973", - "20220831\t2023届高三10班\t0.926", - "20220831\t2023届高三2班\t0.500" + "20220831\t2023届高三02班\t0.500", + "20220831\t2023届高三10班\t0.926" ], "origin": "2016届创新班作业\t1126-基本不等式在最值问题中的应用", "edit": [ @@ -28316,14 +28320,14 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$4\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.897", "2016届12班\t0.919", - "20220831\t2023届高三10班\t0.826", - "20220831\t2023届高三2班\t0.344" + "20220831\t2023届高三02班\t0.344", + "20220831\t2023届高三10班\t0.826" ], "origin": "2016届创新班作业\t1126-基本不等式在最值问题中的应用", "edit": [ @@ -28372,13 +28376,13 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "最大面积为$2L^2$, 长与宽分别为$2L$与$L$时面积最大.", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.846", "2016届12班\t0.919", - "20220901\t2023届高三2班\t0.364", + "20220901\t2023届高三02班\t0.364", "20220902\t2023届高三10班\t0.697" ], "origin": "2016届创新班作业\t1126-基本不等式在最值问题中的应用", @@ -28426,14 +28430,14 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.974", "2016届12班\t1.000", - "20220831\t2023届高三10班\t0.852", - "20220831\t2023届高三2班\t0.875" + "20220831\t2023届高三02班\t0.875", + "20220831\t2023届高三10班\t0.852" ], "origin": "2016届创新班作业\t1127-不等式的证明[1]", "edit": [ @@ -28535,14 +28539,14 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.897", "2016届12班\t0.658", - "20220831\t2023届高三10班\t0.911", - "20220831\t2023届高三2班\t0.500" + "20220831\t2023届高三02班\t0.500", + "20220831\t2023届高三10班\t0.911" ], "origin": "2016届创新班作业\t1127-不等式的证明[1]", "edit": [ @@ -28565,14 +28569,14 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.846", "2016届12班\t0.868", - "20220831\t2023届高三10班\t0.685", - "20220831\t2023届高三2班\t0.844" + "20220831\t2023届高三02班\t0.844", + "20220831\t2023届高三10班\t0.685" ], "origin": "2016届创新班作业\t1127-不等式的证明[1]", "edit": [ @@ -28928,7 +28932,9 @@ "001153": { "id": "001153", "content": "集合$A=\\{1,2,3\\}$, 集合$B=\\{1,4\\}$, 则可建立从$A$到$B$的不同映射共\\blank{30}种, 从$B$到$A$的不同映射共\\blank{30}种.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -28952,7 +28958,9 @@ "001154": { "id": "001154", "content": "设映射$f:\\ \\mathbf{N}\\rightarrow \\mathbf{N}; \\ n\\mapsto 2n^2+1$, 则在该映射下, $3$的原像为\\blank{30}, $3$的像为\\blank{30}.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -28976,7 +28984,9 @@ "001155": { "id": "001155", "content": "已知$a,b$是实数, 映射$f:\\ \\mathbf{R}\\rightarrow \\mathbf{R};\\ x\\mapsto ax+b$满足$f(1)=3$, $f(3)=10$, 那么在该映射下, $10$的像为\\blank{30}, $10$ 的原像为\\blank{30}.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -29000,7 +29010,9 @@ "001156": { "id": "001156", "content": "判断下列各映射是否单射, 是否满射(``A''表示单且满, ``B''表示单但不满, ``C''表示满但不单, ``D''表示既不单又不满).\n\\begin{center}\n\\begin{tabular}{|l|c|}\n\\hline\n映射 & 类型\\\\\\hline\n$(1) \\ f: \\{1,2\\}\\rightarrow \\{1,2\\};\\ x\\mapsto 3-x$&\\\\\\hline\n$(2) \\ f: \\{1,3,5,\\cdots,99\\}\\rightarrow \\{2,4,6,\\cdots,100\\};\\ x\\mapsto \\sqrt{(x+1)^2}$&\\\\\\hline\n$(3) \\ f: [1,2]\\rightarrow [1,4];\\ x\\mapsto 2x$&\\\\\\hline\n$(4) \\ f: [-1,1]\\rightarrow [0,1];\\ x\\mapsto x^{2010}$&\\\\\\hline\n$(5) \\ f: [-2,1]\\rightarrow [-8,1];\\ x\\mapsto x^3$&\\\\\\hline\n$(6) \\ f: (0,+\\infty)\\rightarrow (0,+\\infty);\\ x\\mapsto (x+1)^2$&\\\\\\hline\n$(7) \\ f: \\{(x,y)|x,y\\in \\mathbf{R}\\}\\rightarrow \\mathbf{R};\\ (x,y)\\mapsto x$&\\\\\\hline\n$(8) \\ f: \\mathbf{R}\\rightarrow \\{(x,y)|x,y\\in \\mathbf{R}\\};\\ x\\mapsto (x,x)$&\\\\\\hline\n$(9) \\ f: \\{(x,y)|x,y\\in \\mathbf{R}\\}\\rightarrow \\{(x,y)|x,y\\in \\mathbf{R}\\};\\ (x,y)\\mapsto (x+y,x-y)$&\\\\\\hline\n\\end{tabular}\n\\end{center}", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -29024,7 +29036,9 @@ "001157": { "id": "001157", "content": "设$A=\\mathbf{Z}$, $B=\\{n|n=2k+1,\\ k\\in \\mathbf{Z}\\}$, $C=\\mathbf{R}$. $f:\\ A\\rightarrow B;\\ x\\mapsto 2x-1$, $g:\\ B\\rightarrow C;\\ x\\mapsto \\dfrac{1}{2x+1}$. 经过两次映射,\\\\ \n(1) 求$A$中元素$1$在$C$中的对应元素;\\\\ \n(2) $C$中元素$1$在$A$中有没有对应元素?\\\\ \n(3) 如果把这两次映射``合成''成为一个$A$到$C$的映射$h$, 试写出$h$的对应法则.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -29048,7 +29062,9 @@ "001158": { "id": "001158", "content": "(1) 试证明: 映射\n\\begin{align*}\nf:\\ [0,2]&\\rightarrow \\mathbf{R}\\\\\nx&\\mapsto x^2\n\\end{align*}\n的像集为$[0,4]$;\\\\ \n(2) 试证明: 映射\n\\begin{align*}\nf:\\ [-1,2]&\\rightarrow \\mathbf{R}\\\\\nx& \\mapsto x^2\n\\end{align*}\n的像集为$[0,4]$.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -29072,7 +29088,9 @@ "001159": { "id": "001159", "content": "设集合$A=\\{-1, 0, 1\\}$, $B=\\{2,3,4,5,6\\}$, 映射$f:\\ A\\rightarrow B$, 对任意$x\\in A$, 都有$x+f(x)+xf(x)$是奇数. 求满足条件的映射个数.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -29207,13 +29225,13 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,1)\\cup (1,2)\\cup (2,+\\infty)$; (2) $(-\\infty,1)\\cup (1,+\\infty)$; (3) $(\\dfrac 23,+\\infty)$; (4) $\\{\\dfrac 12\\}$; (5) $(-\\infty,-2]\\cup [2,+\\infty)$; (6) $[-\\dfrac 12,3)\\cup (3,+\\infty)$", "solution": "", "duration": -1, "usages": [ "2016届11班\t0.921\t0.895\t0.974\t0.868\t0.921\t1.000", "2016届12班\t0.868\t0.816\t0.895\t0.737\t0.842\t0.895", - "20220913\t2023届高三2班\t0.929\t0.893\t0.964\t0.857\t0.893\t0.929" + "20220913\t2023届高三02班\t0.929\t0.893\t0.964\t0.857\t0.893\t0.929" ], "origin": "2016届创新班作业\t1131-函数与函数的三要素", "edit": [ @@ -29313,7 +29331,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=12ax+\\dfrac{16000a}x+\\dfrac{8000a}3, \\ x\\in (0,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -29394,7 +29412,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\begin{cases} \\dfrac{24}5 x, & 0=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2,samples = 50] plot (\\x,{pow(\\x,2/3)});\n\\draw [domain = 0:2,samples = 50] plot (-\\x,{pow(\\x,2/3)});\n\\end{tikzpicture}\n\\end{center}", "solution": "", "duration": -1, "usages": [ - "20220908\t2023届高三2班\t0.727" + "20220908\t2023届高三02班\t0.727" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -72368,7 +72386,10 @@ "002921": { "id": "002921", "content": "函数$y=-(x+1)^{-3}$的图像可以先将幂函数$y=x^{-3}$的图像向\\blank{50}平移1个单位, 再以\\blank{50}轴为对称轴作对称变换.", - "objs": [], + "objs": [ + "K0208005B", + "K0213001B" + ], "tags": [ "第二单元" ], @@ -72389,7 +72410,10 @@ "002922": { "id": "002922", "content": "设$\\alpha \\in \\{-3,-\\dfrac 23,-\\dfrac 12,-\\dfrac 13,\\dfrac 13,1,\\dfrac 32,2\\}$. 已知幂函数$y=x^{\\alpha}$是奇函数, 且在区间$(0,+\\infty)$上是减函数, 则满足条件的$\\alpha$的值是\\blank{50}.", - "objs": [], + "objs": [ + "K0208002B", + "K0207004B" + ], "tags": [ "第二单元" ], @@ -72410,7 +72434,10 @@ "002923": { "id": "002923", "content": "下列关于幂函数图像及性质的叙述中, 正确的叙述的序号是\\blank{50}.\\\\\n\\textcircled{1} 对于一个确定的幂函数, 第二、三象限不可能同时有该幂函数的图像上的点;\\\\\n\\textcircled{2} 若某个幂函数图像过$(-1,-1)$, 则该幂函数是奇函数;\\\\\n\\textcircled{3} 若某个幂函数在定义域上递增, 则该幂函数图像必经过原点;\\\\\n\\textcircled{4} 幂函数图像不会经过点$(-\\dfrac 12,8)$以及$(-8,-4)$.", - "objs": [], + "objs": [ + "K0207003B", + "K0207004B" + ], "tags": [ "第二单元" ], @@ -72431,7 +72458,11 @@ "002924": { "id": "002924", "content": "设$y=f(x)$与$y=g(x)$是两个不同的幂函数, 集合$M=\\{x|f(x)=g(x) \\}$, 则集合$M$中的元素是\\bracket{20}.\n\\fourch{$1$或$2$}{$1$或$3$}{$1$或$2$或$3$}{$1$或$2$或$3$或$4$}", - "objs": [], + "objs": [ + "K0207001B", + "K0208003B", + "K0207004B" + ], "tags": [ "第二单元" ], @@ -72460,11 +72491,11 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ - "20220908\t2023届高三2班\t0.939" + "20220908\t2023届高三02班\t0.939" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -72478,7 +72509,9 @@ "002926": { "id": "002926", "content": "若$(x+1)^{-\\frac 13}<(3-2x)^{-\\frac 13}$, 求实数$x$的取值范围.", - "objs": [], + "objs": [ + "K0208004B" + ], "tags": [ "第二单元" ], @@ -72499,7 +72532,9 @@ "002927": { "id": "002927", "content": "设常数$a,b$满足$a>b>0$. 已知函数$f(x)=\\dfrac{x+a}{x+b}$.\n(1) 写出函数$y=f(x)$的单调性;\\\\\n(2) 写出函数$y=f(x)$图像的一个对称中心的坐标.", - "objs": [], + "objs": [ + "K0208005B" + ], "tags": [ "第二单元" ], @@ -72520,7 +72555,10 @@ "002928": { "id": "002928", "content": "已知函数$f(x)=\\dfrac{x^{\\frac 13}-x^{-\\frac 13}}5$, $g(x)=\\dfrac{x^{\\frac 13}+x^{-\\frac 13}}5$.\\\\\n(1) 分别计算$f(4)-5f(2)g(2)$和$f(9)-5f(3)g(3)$的值;\\\\\n(2) 由(1)概括出涉及函数$y=f(x)$和$y=g(x)$的, 对所有不等于零的实数$x$都成立的一个等式, 并加以证明.", - "objs": [], + "objs": [ + "K0203002B", + "K0202003B" + ], "tags": [ "第二单元" ], @@ -72541,7 +72579,9 @@ "002929": { "id": "002929", "content": "*设常数$a,b$满足$a>b>0$. 已知函数$f(x)=\\dfrac{x+a}{x+b}$. 证明: 该函数图像的对称中心是唯一的.", - "objs": [], + "objs": [ + "K0207004B" + ], "tags": [ "第二单元" ], @@ -72800,7 +72840,12 @@ "002940": { "id": "002940", "content": "记$y=f^{-1}(x)$是$y=f(x)$的反函数.\\\\\n(1) 若函数$f(x+1)=\\dfrac x{x+1}$, 求函数$y=f^{-1}(x+1)$的解析式;\\\\\n(2) 设函数$f(x)=\\dfrac{1-2x}{1+x}$. 若$y=g(x)$的图像与$y=f^{-1}(x+1)$的图像关于直线$y=x$对称, 求$y=g(x)$的解析式.", - "objs": [], + "objs": [ + "K0215001B", + "K0225005B", + "K0226006B", + "K0226004B" + ], "tags": [ "第二单元" ], @@ -72821,7 +72866,9 @@ "002941": { "id": "002941", "content": "(1) 函数$y=x^2+2x-3\\ (x\\ge 0)$的反函数为\\blank{50};\\\\\n(2) 函数$y=\\dfrac{\\mathrm{e}^x-1}{{\\mathrm{e}}^x+1}$的反函数为\\blank{50};\\\\\n(3) 函数$y=x|x|$的反函数为\\blank{50}.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -72842,7 +72889,10 @@ "002942": { "id": "002942", "content": "已知函数$y=f(x)$是奇函数, 且$y=g(x)$是$y=f(x)$的反函数. 若$x\\ge 0$时, $f(x)=3^x-1$, 则$g(-8)$=\\blank{50}.", - "objs": [], + "objs": [ + "K0225004B", + "K0218001B" + ], "tags": [ "第二单元" ], @@ -72863,7 +72913,9 @@ "002943": { "id": "002943", "content": "设常数$a\\in \\mathbf{R}$. 若函数$y=x+\\dfrac ax$在区间$[1,2]$上存在反函数, 求$a$的取值范围.", - "objs": [], + "objs": [ + "K0225002B" + ], "tags": [ "第二单元" ], @@ -72884,7 +72936,9 @@ "002944": { "id": "002944", "content": "求函数$y=\\begin{cases}x^2-2x+2, & x\\le 1,\\\\(\\dfrac 12)^x, & x>1 \\end{cases}$的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -72905,7 +72959,9 @@ "002945": { "id": "002945", "content": "设常数$a>0$且$a\\ne 1$. 求函数$f(x)=\\log_a(x+\\sqrt{x^2-1})$的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -72926,7 +72982,9 @@ "002946": { "id": "002946", "content": "已知函数$y=f(x)$的图像经过点$(0,-1)$. 若函数$y=f(x+4)$存在反函数$y=g(x)$, 则$y=g(x)$的图像总经过的定点的坐标为\\blank{50}.", - "objs": [], + "objs": [ + "K0225004B" + ], "tags": [ "第二单元" ], @@ -72947,7 +73005,10 @@ "002947": { "id": "002947", "content": "设$y=f^{-1}(x)$, $y=g^{-1}(x)$分别是定义在$\\mathbf{R}$上的函数$y=f(x)$, $y=g(x)$的反函数. 若函数$y=f(x-1)$和$y=g^{-1}(x-3)$的图像关于直线$y=x$对称, 且$g(5)=2018$, 则 $f(4)$的值为\\blank{50}.", - "objs": [], + "objs": [ + "K0226004B", + "K0226006B" + ], "tags": [ "第二单元" ], @@ -72968,7 +73029,10 @@ "002948": { "id": "002948", "content": "设$a>0$, 函数$f(x)=\\dfrac 1{1+a\\cdot 2^x}$.\\\\\n(1) 若$a=1$, 求$f(x)$的反函数$f^{-1}(x)$;\\\\\n(2) 求函数$y=f(x)\\cdot f(-x)$的最大值(用$a$表示);\\\\\n(3) *设$g(x)=f(x)-f(x-1)$. 若对任意$x\\in (-\\infty ,0]$, $g(x)\\ge g(0)$恒成立, 求$a$的取值范围.", - "objs": [], + "objs": [ + "K0225005B", + "K0221002B" + ], "tags": [ "第二单元" ], @@ -72989,7 +73053,10 @@ "002949": { "id": "002949", "content": "已知函数$y=f^{-1}(x)$是$y=f(x)$的反函数. 定义: 若对给定的实数$a(a\\ne 0)$, 函数$y=f(x+a)$与$y=f^{-1}(x+a)$互为反函数, 则称$y=f(x)$满足``$a$和性质''.\\\\\n(1) 判断函数$g(x)=x^2+1(x>0)$是否满足``$1$和性质'', 并说明理由;\\\\\n(2) *求所有满足``$2$和性质''的一次函数.", - "objs": [], + "objs": [ + "K0225005B", + "K0226006B" + ], "tags": [ "第二单元" ], @@ -73136,11 +73203,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1+\\sqrt{5}}2$", "solution": "", "duration": -1, "usages": [ - "20220915\t2023届高三2班\t0.906" + "20220915\t2023届高三02班\t0.906" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -73235,11 +73302,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$g(a)=\\begin{cases} \\dfrac 32a-\\dfrac 34, & a\\ge \\dfrac 12,\\\\ 0, & a\\le \\dfrac 12. \\end{cases}$", "solution": "", "duration": -1, "usages": [ - "20220915\t2023届高三2班\t0.469" + "20220915\t2023届高三02班\t0.469" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -73253,7 +73320,10 @@ "002960": { "id": "002960", "content": "已知函数$f(x)=a\\cdot 2^x+b\\cdot 3^x$, 其中常数$a,b$满足$ab\\ne 0$.\\\\\n(1) 若$ab>0$, 判断函数$y=f(x)$的单调性;\\\\\n(2) 若$ab<0$, 求$f(x+1)>f(x)$时$x$的取值范围.", - "objs": [], + "objs": [ + "K0211001B", + "K0219001B" + ], "tags": [ "第二单元" ], @@ -73276,7 +73346,9 @@ "002961": { "id": "002961", "content": "不等式$\\log_{\\frac 12}(x-1)\\ge 1$的解集为\\blank{50}.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -73301,7 +73373,9 @@ "002962": { "id": "002962", "content": "设常数$a\\in \\mathbf{R}$. 若函数$f(x)=\\dfrac 1{2^x-1}+a$为奇函数, 则$a$=\\blank{50}.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -73348,7 +73422,10 @@ "002964": { "id": "002964", "content": "对于函数$y=f(x)$的定义域中的任意的$x_1,x_2$($x_1\\ne x_2$), 有如下结论:\\\\\n\\textcircled{1} $f(x_1+x_2)=f(x_1)\\cdot f(x_2)$; \\textcircled{2} $f(x_1\\cdot x_2)=f(x_1)+f(x_2)$;\\\\ \\textcircled{3} $\\dfrac{f(x_1)-f(x_2)}{x_1-x_2}>0$; \\textcircled{4} $f(\\dfrac{x_1+x_2}2)<\\dfrac{f(x_1)+f(x_2)}2$. \n\\\\当$y=\\ln x$时, 上述结论中, 正确结论的序号是\\blank{50}.", - "objs": [], + "objs": [ + "K0205001B", + "K0215001B" + ], "tags": [ "第二单元" ], @@ -73369,7 +73446,9 @@ "002965": { "id": "002965", "content": "(1) *函数$y=\\log_a|x-b|$在$(0,+\\infty)$上递增, 则$a$、$b$满足\\bracket{20}.\n\\fourch{$a>1$且$b\\ge 0$}{$a>1$且$b\\le 0$}{$00,\\ a\\ne 1)$在区间$[3,4]$上是增函数, 则实数$a$的范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -73398,11 +73477,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [ - "20220915\t2023届高三2班\t0.781" + "20220915\t2023届高三02班\t0.781" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -73448,11 +73527,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[-3\\sqrt{3},-\\sqrt{3}]\\cup [\\sqrt{3},3\\sqrt{3}]$; (2) $[13,\\dfrac {69}4]$", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t0.531\t0.063" + "20220907\t2023届高三02班\t0.531\t0.063" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -73615,11 +73694,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\begin{cases} 0, & a\\ge \\dfrac 12, \\\\ 2a-1, & a\\le \\dfrac 12. \\end{cases}$", "solution": "", "duration": -1, "usages": [ - "20220913\t2023届高三2班\t0.484" + "20220913\t2023届高三02班\t0.484" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -74079,11 +74158,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-2,+\\infty)$", "solution": "", "duration": -1, "usages": [ - "20220913\t2023届高三2班\t0.893" + "20220913\t2023届高三02班\t0.893" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -74175,7 +74254,9 @@ "002998": { "id": "002998", "content": "函数$y=\\dfrac{2x-3}{x^2-2x+3}$的值域是\\blank{50}.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -74200,7 +74281,9 @@ "002999": { "id": "002999", "content": "设$x,y\\in \\mathbf{R}$. 若$x^2+y^2=1$, 则$3x^2-4y^2$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -74221,7 +74304,13 @@ "003000": { "id": "003000", "content": "已知函数$f(x)=\\log_a(x+\\sqrt{x^2+1}), \\ a>1$.\\\\\n(1) 求$f(x)$的定义域和值域;\\\\\n(2) 求$f^{-1}(x)$;\\\\\n(3) 判断$f^{-1}(x)$的奇偶性、单调性;\\\\\n(4) 若实数$m$满足$f^{-1}(1-m)+f^{-1}(1-m^2)<0$, 求$m$的范围.", - "objs": [], + "objs": [ + "K0215003B", + "K0215005B", + "K0225005B", + "K0217004B", + "K0219003B" + ], "tags": [ "第二单元" ], @@ -74242,7 +74331,9 @@ "003001": { "id": "003001", "content": "*设常数$m,n\\in \\mathbf{R}$. 若函数$y=\\dfrac{mx^2+4x+n}{x^2+1}$的值域为$[1,6]$, 求$m,n$的值.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -74263,7 +74354,10 @@ "003002": { "id": "003002", "content": "设常数$a\\in \\mathbf{R}$, 区间$E\\subseteq (0,+\\infty)$. 已知函数$f(x)=\\dfrac 1a-\\dfrac 1x$, $x\\in E$.\\\\\n(1) 求证: $y=f(x)$在区间$E$上递增;\\\\\n(2) 是否存在$a$, 使得对于这样的$a$, 总是存在 $E=[m,n]$($m0$恒成立, 求$a$的取值范围.", - "objs": [], + "objs": [ + "K0223005B" + ], "tags": [ "第二单元" ], @@ -75488,7 +75591,9 @@ "003053": { "id": "003053", "content": "已知常数$m, n\\in \\mathbf{R}$, $m<-2$, 函数$f(x)=x^2+mx+n$. 问: 是否存在$x_0\\in [-1,1]$, 使得$|f(x_0)|\\ge |m|$成立?", - "objs": [], + "objs": [ + "K0223005B" + ], "tags": [ "第二单元" ], @@ -85209,10 +85314,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t0.818", "20220822\t2023届高三10班\t0.800", - "20220822\t2023届高三2班\t0.818", - "20220823\t2023届高三11班\t0.920", - "20220823\t2023届高三8班\t1.000" + "20220823\t2023届高三08班\t1.000", + "20220823\t2023届高三11班\t0.920" ], "origin": "2022届高三第一轮复习讲义", "edit": [ @@ -87190,7 +87295,9 @@ "003593": { "id": "003593", "content": "已知$f(x)=\\dfrac3x+2$, 则$f^{-1}(1)=$\\blank{50}.", - "objs": [], + "objs": [ + "K0225004B" + ], "tags": [ "第二单元" ], @@ -87312,7 +87419,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.907" + "20220630\t2022届高三01班\t0.907" ], "origin": "上海2021年秋季高考试题10", "edit": [ @@ -87335,7 +87442,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.860" + "20220630\t2022届高三01班\t0.860" ], "origin": "上海2021年秋季高考试题11", "edit": [ @@ -87358,7 +87465,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.721" + "20220630\t2022届高三01班\t0.721" ], "origin": "上海2021年秋季高考试题12", "edit": [ @@ -87428,7 +87535,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.767" + "20220630\t2022届高三01班\t0.767" ], "origin": "上海2021年秋季高考试题15", "edit": [ @@ -87453,7 +87560,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.791" + "20220630\t2022届高三01班\t0.791" ], "origin": "上海2021年秋季高考试题16", "edit": [ @@ -87558,7 +87665,9 @@ "003609": { "id": "003609", "content": "已知$f(x)$是定义在$\\mathbf{R}$上的函数, 若对任意的$x_1,x_2\\in \\mathbf{R}$, $x_1-x_2\\in S$, 均有$f(x_1)-f(x_2)\\in S$, 则称$f(x)$是``$S-$关联''的.\\\\\n(1) 判断和证明$f(x)=2x+1$是否是``$[0,+\\infty)-$关联''的? 是否是``$[0,1]-$关联''的?\\\\\n(2) 若$f(x)$是``$\\{3\\}-$关联''的, 且当$x\\in [0,3)$时, $f(x)=x^2-2x$, 解不等式$2 \\le f(x)\\le 3$;\\\\\n(3) 证明: ``$f(x)$是`$\\{1\\}-$关联'的, 且是`$[0,+\\infty)-$关联'的''当且仅当``$f(x)$是`$[1,2]-$关联'的''.", - "objs": [], + "objs": [ + "K0223004B" + ], "tags": [ "第二单元" ], @@ -87814,7 +87923,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.907" + "20220630\t2022届高三01班\t0.907" ], "origin": "上海2020年秋季高考试题10", "edit": [ @@ -87828,7 +87937,9 @@ "003620": { "id": "003620", "content": "已知$a\\in \\mathbf{R}$, 若存在定义域为$\\mathbf{R}$的函数$f(x)$同时满足下列两个条件, \\textcircled{1} 对任意$x_0\\in \\mathbf{R}$, $f(x_0)$的值为$x_0$或$x_0^2$; \\textcircled{2} 关于$x$的方程$f(x)=a$无实数解; 则$a$的取值范围为\\blank{50}.", - "objs": [], + "objs": [ + "K0223004B" + ], "tags": [ "第二单元" ], @@ -87837,7 +87948,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.837" + "20220630\t2022届高三01班\t0.837" ], "origin": "上海2020年秋季高考试题11", "edit": [ @@ -87860,7 +87971,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.767" + "20220630\t2022届高三01班\t0.767" ], "origin": "上海2020年秋季高考试题12", "edit": [ @@ -87927,7 +88038,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.837" + "20220630\t2022届高三01班\t0.837" ], "origin": "上海2020年秋季高考试题15", "edit": [ @@ -87941,7 +88052,9 @@ "003625": { "id": "003625", "content": "命题$p$: 存在$a\\in \\mathbf{R}$且$a\\ne 0$, 对任意的$x\\in \\mathbf{R}$, 均有$f(x+a)0$恒成立; 命题$q_2$: $f(x)$单调递增, 且存在${x_0}<0$使得$f({x_0})=0$. 则下列说法正确的是\\bracket{20}.\n\\twoch{$q_1$、$q_2$都是$p$的充分条件}{只有$q_1$是$p$的充分条件}{只有$q_2$是$p$的充分条件}{$q_1$、$q_2$都不是$p$的充分条件}", - "objs": [], + "objs": [ + "K0219001B" + ], "tags": [ "第二单元" ], @@ -87950,7 +88063,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.767" + "20220630\t2022届高三01班\t0.767" ], "origin": "上海2020年秋季高考试题16", "edit": [ @@ -88191,7 +88304,9 @@ "003636": { "id": "003636", "content": "已知函数$f(x)$的周期为$1$, 当$01, \\ a>0)$, $f(x)$的图像与$x$轴的交点为$A$, 若对于$f(x)$的图像上任意一点$P$, 在其图像上总存在另一点$Q$($P$、$Q$异于$A$), 满足$AP\\perp AQ$, 且$|AP|=|AQ|$, 则$a=$\\blank{50}.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -88334,7 +88451,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.767" + "20220630\t2022届高三01班\t0.767" ], "origin": "上海2019年秋季高考试题12", "edit": [ @@ -88399,7 +88516,7 @@ "solution": "", "duration": -1, "usages": [ - "20220630\t2022届高三1班\t0.884" + "20220630\t2022届高三01班\t0.884" ], "origin": 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"20220517\t2022届高三01班\t0.977" ], "origin": "2022届高三下学期测验卷10第5题", "edit": [ @@ -102425,7 +102584,7 @@ "solution": "", "duration": -1, "usages": [ - "20220517\t2022届高三1班\t0.977" + "20220517\t2022届高三01班\t0.977" ], "origin": "2022届高三下学期测验卷10第6题", "edit": [ @@ -102448,7 +102607,7 @@ "solution": "", "duration": -1, "usages": [ - "20220517\t2022届高三1班\t0.977" + "20220517\t2022届高三01班\t0.977" ], "origin": "2022届高三下学期测验卷10第7题", "edit": [ @@ -102471,7 +102630,7 @@ "solution": "", "duration": -1, "usages": [ - "20220517\t2022届高三1班\t0.930" + "20220517\t2022届高三01班\t0.930" ], "origin": "2022届高三下学期测验卷10第8题", "edit": [ @@ -102485,7 +102644,10 @@ "004256": { "id": "004256", "content": "设$f(x)$是定义在$\\mathbf{R}$上的奇函数, 当$x>0$时, $f(x)=a^x+b$($0b,\\end{cases}$, 已知函数$f(x)$、$g(x)$定义域都是$\\mathbf{R}$, 给出下列命题:\\\\\n(1) 若$f(x)$、$g(x)$都是奇函数, 则函数$F(f(x),g(x))$为奇函数;\\\\\n(2) 若$f(x)$、$g(x)$都是减函数, 则函数$F(f(x),g(x))$为减函数;\\\\\n(3) 若$f_{\\min}(x)=m$, $g_{\\min}(x)=n$, 则$F_{\\min}(f(x),g(x))=F(m,n)$;\\\\\n(4) 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"20220711\t2023届高三2班\t1.000", - "20220711\t2023届高三4班\t0.969", - "20220711\t2023届高三7班\t1.000", - "20220711\t2023届高三8班\t0.939" + "20220711\t2023届高三02班\t1.000", + "20220711\t2023届高三04班\t0.969", + "20220711\t2023届高三07班\t1.000", + "20220711\t2023届高三08班\t0.939" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110383,10 +110573,10 @@ "solution": "", "duration": -1, "usages": [ - "20220711\t2023届高三2班\t0.879", - "20220711\t2023届高三4班\t0.938", - "20220711\t2023届高三7班\t1.000", - "20220711\t2023届高三8班\t1.000" + "20220711\t2023届高三02班\t0.879", + "20220711\t2023届高三04班\t0.938", + "20220711\t2023届高三07班\t1.000", + "20220711\t2023届高三08班\t1.000" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110409,10 +110599,10 @@ "solution": "", "duration": -1, "usages": [ - "20220711\t2023届高三2班\t0.939", - "20220711\t2023届高三4班\t0.875", - "20220711\t2023届高三7班\t0.917", - "20220711\t2023届高三8班\t0.939" + "20220711\t2023届高三02班\t0.939", + "20220711\t2023届高三04班\t0.875", + "20220711\t2023届高三07班\t0.917", + "20220711\t2023届高三08班\t0.939" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110435,10 +110625,10 @@ "solution": "", "duration": -1, "usages": [ - "20220711\t2023届高三2班\t0.667\t0.758", - "20220711\t2023届高三4班\t0.594\t0.719", - "20220711\t2023届高三7班\t0.639\t0.778", - "20220711\t2023届高三8班\t0.667\t0.788" + "20220711\t2023届高三02班\t0.667\t0.758", + "20220711\t2023届高三04班\t0.594\t0.719", + "20220711\t2023届高三07班\t0.639\t0.778", + "20220711\t2023届高三08班\t0.667\t0.788" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110461,10 +110651,10 @@ "solution": "", "duration": -1, "usages": [ - "20220711\t2023届高三2班\t0.909", - "20220711\t2023届高三4班\t0.969", - "20220711\t2023届高三7班\t0.944", - "20220711\t2023届高三8班\t0.970" + "20220711\t2023届高三02班\t0.909", + "20220711\t2023届高三04班\t0.969", + "20220711\t2023届高三07班\t0.944", + "20220711\t2023届高三08班\t0.970" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110487,10 +110677,10 @@ "solution": "利用条件概率公式计算$P(A\\cap B)$.", "duration": -1, "usages": [ - "20220711\t2023届高三2班\t0.970", - "20220711\t2023届高三4班\t0.969", - "20220711\t2023届高三7班\t0.972", - "20220711\t2023届高三8班\t1.000" + "20220711\t2023届高三02班\t0.970", + "20220711\t2023届高三04班\t0.969", + "20220711\t2023届高三07班\t0.972", + "20220711\t2023届高三08班\t1.000" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110513,10 +110703,10 @@ "solution": "", "duration": -1, "usages": [ - "20220711\t2023届高三2班\t0.727", - "20220711\t2023届高三4班\t0.625", - "20220711\t2023届高三7班\t0.556", - "20220711\t2023届高三8班\t0.667" + "20220711\t2023届高三02班\t0.727", + "20220711\t2023届高三04班\t0.625", + "20220711\t2023届高三07班\t0.556", + "20220711\t2023届高三08班\t0.667" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110539,11 +110729,11 @@ "solution": "", "duration": -1, "usages": [ - "20220712\t2023届高三2班\t1.000", - "20220712\t2023届高三3班\t0.939", - "20220712\t2023届高三4班\t0.963", - "20220712\t2023届高三7班\t0.971", - "20220712\t2023届高三8班\t0.970" + "20220712\t2023届高三02班\t1.000", + "20220712\t2023届高三03班\t0.939", + "20220712\t2023届高三04班\t0.963", + "20220712\t2023届高三07班\t0.971", + "20220712\t2023届高三08班\t0.970" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110566,11 +110756,11 @@ "solution": "", "duration": -1, "usages": [ - "20220712\t2023届高三2班\t0.909", - "20220712\t2023届高三3班\t0.970", - "20220712\t2023届高三4班\t0.926", - "20220712\t2023届高三7班\t0.971", - "20220712\t2023届高三8班\t0.879" + "20220712\t2023届高三02班\t0.909", + "20220712\t2023届高三03班\t0.970", + "20220712\t2023届高三04班\t0.926", + "20220712\t2023届高三07班\t0.971", + "20220712\t2023届高三08班\t0.879" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110593,11 +110783,11 @@ "solution": "", "duration": -1, "usages": [ - "20220712\t2023届高三2班\t0.970", - "20220712\t2023届高三3班\t1.000", - "20220712\t2023届高三4班\t1.000", - "20220712\t2023届高三7班\t0.943", - "20220712\t2023届高三8班\t0.970" + "20220712\t2023届高三02班\t0.970", + "20220712\t2023届高三03班\t1.000", + "20220712\t2023届高三04班\t1.000", + "20220712\t2023届高三07班\t0.943", + "20220712\t2023届高三08班\t0.970" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110620,11 +110810,11 @@ "solution": "", "duration": -1, "usages": [ - "20220712\t2023届高三2班\t1.000", - "20220712\t2023届高三3班\t1.000", - "20220712\t2023届高三4班\t0.926", - "20220712\t2023届高三7班\t0.971", - "20220712\t2023届高三8班\t0.939" + "20220712\t2023届高三02班\t1.000", + "20220712\t2023届高三03班\t1.000", + "20220712\t2023届高三04班\t0.926", + "20220712\t2023届高三07班\t0.971", + "20220712\t2023届高三08班\t0.939" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110647,11 +110837,11 @@ "solution": "", "duration": -1, "usages": [ - "20220712\t2023届高三2班\t0.818", - "20220712\t2023届高三3班\t0.879", - "20220712\t2023届高三4班\t0.889", - "20220712\t2023届高三7班\t0.943", - "20220712\t2023届高三8班\t0.758" + "20220712\t2023届高三02班\t0.818", + "20220712\t2023届高三03班\t0.879", + "20220712\t2023届高三04班\t0.889", + "20220712\t2023届高三07班\t0.943", + "20220712\t2023届高三08班\t0.758" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110674,11 +110864,11 @@ "solution": "$P(\\overline{B}|A)=\\dfrac{P(A\\cap 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"20220713\t2023届高三03班\t0.880", + "20220713\t2023届高三04班\t0.852", + "20220713\t2023届高三07班\t0.889", + "20220713\t2023届高三08班\t0.788" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110863,11 +111053,11 @@ "solution": "", "duration": -1, "usages": [ - "20220713\t2023届高三2班\t0.909", - "20220713\t2023届高三3班\t0.800", - "20220713\t2023届高三4班\t0.778", - "20220713\t2023届高三7班\t0.889", - "20220713\t2023届高三8班\t0.758" + "20220713\t2023届高三02班\t0.909", + "20220713\t2023届高三03班\t0.800", + "20220713\t2023届高三04班\t0.778", + "20220713\t2023届高三07班\t0.889", + "20220713\t2023届高三08班\t0.758" ], "origin": "2023届高三暑假作业概率初步续", "edit": [ @@ -110890,11 +111080,11 @@ "solution": "", "duration": -1, "usages": [ - "20220713\t2023届高三2班\t0.909", - "20220713\t2023届高三3班\t0.960", - "20220713\t2023届高三4班\t0.926", - "20220713\t2023届高三7班\t1.000", - "20220713\t2023届高三8班\t0.848" + "20220713\t2023届高三02班\t0.909", + "20220713\t2023届高三03班\t0.960", + "20220713\t2023届高三04班\t0.926", + "20220713\t2023届高三07班\t1.000", + 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"20211209\t2022届高三1班\t0.750" + "20211209\t2022届高三01班\t0.750" ], "origin": "2022届高三上月考卷02第16题", "edit": [ @@ -112462,7 +112652,7 @@ "duration": -1, "usages": [ "20211209\t2022届高三\t0.849\t0.692", - "20211209\t2022届高三1班\t0.939\t0.764" + "20211209\t2022届高三01班\t0.939\t0.764" ], "origin": "2022届高三上月考卷02第17题", "edit": [ @@ -112486,7 +112676,7 @@ "duration": -1, "usages": [ "20211209\t2022届高三\t0.893\t0.867", - "20211209\t2022届高三1班\t0.977\t0.977" + "20211209\t2022届高三01班\t0.977\t0.977" ], "origin": "2022届高三上月考卷02第18题", "edit": [ @@ -112500,7 +112690,11 @@ "004658": { "id": "004658", "content": "如图, $A$、$B$、$C$三地有直道相通, $AB=5$千米, $AC=3$千米, $BC=4$千米, 现甲、乙两警员同时从$A$地出发匀速前往$B$地, 经过$t$小时, 他们之间的距离为$f(t)$(单位: 千米), 甲的路线是$AB$, 速度为$5$千米/小时, 乙的路线是$ACB$, 速度为$8$千米/小时, 乙到$B$地后在原地等待, 设$t=t_1$时乙到达$C$地.\n\\begin{center}\n \\begin{tikzpicture}[scale = 0.6]\n \\draw (0,0) node [left] {$C$} -- (4,0) node [right] {$B$} -- (0,3) node [above] {$A$} -- cycle;\n \\end{tikzpicture}\n\\end{center}\n(1) 求$t_1$及$f(t_1)$的值;\\\\\n(2) 已知警员的对讲机的有效通话距离是$3$千米, 当$t_1\\le t\\le 1$时, 求$f(t)$的表达式, 并判断$f(t)$在$[t_1,1]$上的最大值是否超过$3$? 说明理由.", - "objs": [], + "objs": [ + "K0222001B", + "K0222002B", + "K0221002B" + ], "tags": [ "第二单元" ], @@ -112510,7 +112704,7 @@ "duration": -1, "usages": [ "20211209\t2022届高三\t0.850\t0.584", - "20211209\t2022届高三1班\t0.947\t0.773" + "20211209\t2022届高三01班\t0.947\t0.773" ], "origin": "2022届高三上月考卷02第19题", "edit": [ @@ -112534,7 +112728,7 @@ "duration": -1, "usages": [ "20211209\t2022届高三\t0.853\t0.447\t0.480", - "20211209\t2022届高三1班\t0.949\t0.523\t0.678" + "20211209\t2022届高三01班\t0.949\t0.523\t0.678" ], "origin": "2022届高三上月考卷02第20题", "edit": [ @@ -112558,7 +112752,7 @@ "duration": -1, "usages": [ "20211209\t2022届高三\t0.947\t0.430\t0.120", - "20211209\t2022届高三1班\t0.960\t0.720\t0.301" + "20211209\t2022届高三01班\t0.960\t0.720\t0.301" ], "origin": "2022届高三上月考卷02第21题", "edit": [ @@ -112572,7 +112766,9 @@ "004661": { "id": "004661", "content": "函数$f(x)={x^{-\\frac 12}}$的定义域是\\blank{50}.", - "objs": [], + "objs": [ + "K0215003B" + ], "tags": [ "第二单元" ], @@ -112675,7 +112871,9 @@ "004665": { "id": "004665", "content": "方程$\\lg (x+2)=2\\lg x$的解为\\blank{50}.", - "objs": [], + "objs": [ + "K0205001B" + ], "tags": [ "第二单元" ], @@ -112725,7 +112923,10 @@ "004667": { "id": "004667", "content": "若函数$f(x)=\\sqrt{2x+1}$的反函数为$g(x)$, 则函数$g(x)$的零点为\\blank{50}.", - "objs": [], + "objs": [ + "K0223001B", + "K0225004B" + ], "tags": [ "第二单元" ], @@ -112819,7 +113020,9 @@ "004671": { "id": "004671", "content": "设$f(x)$是定义在$\\mathbf{R}$上的函数, 且满足$f(1)=0$.若$y=f(x)+a\\cdot 2^x$是奇函数, $y=f(x)+3^x$是偶函数, 则$a$的值为\\blank{50}.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -113012,7 +113215,11 @@ "004679": { "id": "004679", "content": "为实现``碳达峰'', 减少污染, 某化工企业开发了一个废料回收项目. 经测算, 该项目日回收成本$p$(元)与日回收量$x$(吨)($x\\in [0,50]$)的函数关系可表示为$p=\\begin{cases}20x, & 0\\le x\\le 30, \\\\ x^2+16x-780, & 300$, 均存在区间$I=(M,+\\infty)$, 使得函数$y=f(x)$与$y=g(x)$具有性质$P(I,a)$, 求证: $g(x)=0$;\\\\\n(3)\t已知$I=[1,m]$, $f(x)=x^2$, 若存在一次函数$y=g(x)$与$y=f(x)$具有性质$P(I,1)$, 求实数$m$的最大值.", - "objs": [], + "objs": [ + "K0215001B", + "K0221002B", + "K0319003B" + ], "tags": [ "第二单元" ], @@ -113615,7 +113834,9 @@ "004704": { "id": "004704", "content": "函数$y=\\log_2(x+1)$的反函数为\\blank{50}.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -114003,18 +114224,19 @@ "content": "已知函数$f(x)=x^2+mx+3$, 其中$m\\in \\mathbf{R}$.\\\\\n(1) 若不等式$f(x)<5$的解集是$(-1,2)$, 求$m$的值;\\\\\n(2) 若函数$y=f(x)$在区间$[0,3]$上有且仅有一个零点, 求$m$的取值范围.", "objs": [ "K0223001B", - "K0223004B" + "K0223004B", + "K0221002B" ], "tags": [ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-1$; (2) $(-\\infty,-4)\\cup \\{-2\\sqrt{3}\\}$", "solution": "", "duration": -1, "usages": [ "20220414\t2022届高三\t0.979\t0.665", - "20220915\t2023届高三2班\t0.969\t0.125" + "20220915\t2023届高三02班\t0.969\t0.125" ], "origin": "2022届高三下期中区统考第18题", "edit": [ @@ -114028,7 +114250,11 @@ "004721": { "id": "004721", "content": "如图, 有一块扇形草地$OMN$, 已知半径为$4$, $\\angle MON=\\dfrac\\pi 2$, 现要在其中圈出一块举行场地$ABCD$作为儿童乐园使用, 其中点$A$、$B$在弧$\\overset\\frown{MN}$上, 且线段$AB$平行于线段$MN$.\n\\begin{center}\n \\begin{tikzpicture}[scale = 1.5]\n \\draw (0,0) node [above] {$O$} coordinate (O);\n \\draw (-45:2) node [right] {$N$} coordinate (N);\n \\draw (-135:2) node [left] {$M$} coordinate (M);\n \\draw (-75:2) node [below] {$B$} coordinate (B);\n \\draw (-105:2) node [below] {$A$} coordinate (A);\n \\draw (-45:{2/sin(45)*sin(15)}) node [above right] {$C$} coordinate (C);\n \\draw (-135:{2/sin(45)*sin(15)}) node [above left] {$D$} coordinate (D);\n \\draw (M) -- (O) -- (N) (A) rectangle (C) (O) -- (A);\n \\draw (M) arc (-135:-45:2);\n \\end{tikzpicture}\n\\end{center}\n(1) 若点$A$为弧$\\overset\\frown{MN}$的一个三等分点, 求矩形$ABCD$的面积$S$;\\\\\n(2) 当$A$在何处时, 矩形$ABCD$的面积$S$最大? 最大值为多少?", - "objs": [], + "objs": [ + "K0222001B", + "K0222002B", + "K0221002B" + ], "tags": [ "第二单元" ], @@ -114228,7 +114454,9 @@ "004729": { "id": "004729", "content": "函数$f(x)=1+\\lg x$的反函数是$f^{-1}(x)$=\\blank{50}.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -114277,7 +114505,9 @@ "004731": { "id": "004731", "content": "已知集合$A=\\{-2,-1,-\\dfrac 12,\\dfrac 13,\\dfrac 12,1,2,3\\}$, 从集合$A$中任取一个元素$a$, 使函数$y=x^a$是奇函数且在$(0,+\\infty)$上递增的概率为\\blank{50}.", - "objs": [], + "objs": [ + "K0207001B" + ], "tags": [ "第二单元", "第八单元" @@ -114467,7 +114697,9 @@ "004739": { "id": "004739", "content": "对于定义在集合$D$上的两个函数$y_1=f_1(x)$与$y_2=f_2(x)$, 若对任意的$x\\in D$, 总有$|f_2(x)|\\le |f_1(x)|$成立, 则称函数$f_1(x)$包裹函数$f_2(x)$. 判断如下两个命题真假:\\\\\n\\textcircled{1} 函数$f_1(x)=kx$包裹函数$f_2(x)=x\\cos x$的充要条件是$|k|\\ge 1$;\n\\textcircled{2} 若对于任意$p>0$, $|f_1(x)-f_2(x)|0$;\\\\\n$q_2$: 函数$y=f(x)$是定义域为$\\mathbf{R}$的增函数, 存在$x_0<0$, 使得$f(x_0)=0$;\\\\\n用这三个陈述句组成两个命题, 命题$S$: ``若$q_1$, 则$p$''; 命题$T$: ``若$q_2$, 则$p$''. 关于$S,T$以下说法正确的是\\bracket{20}.\n\\twoch{只有命题$S$是真命题}{只有命题$T$是真命题}{两个命题$S,T$都是真命题}{两个命题$S,T$都不是真命题}", - "objs": [], + "objs": [ + "K0215001B", + "K0219001B", + "K0223001B" + ], "tags": [ "第二单元" ], @@ -114985,7 +115229,7 @@ "solution": "", "duration": -1, "usages": [ - "20220317\t2022届高三1班\t0.767" + "20220317\t2022届高三01班\t0.767" ], "origin": "2022届高三下月考卷01第16题", "edit": [ @@ -115008,7 +115252,7 @@ "solution": "", "duration": -1, "usages": [ - "20220317\t2022届高三1班\t0.992\t0.983" + "20220317\t2022届高三01班\t0.992\t0.983" ], "origin": "2022届高三下月考卷01第17题", "edit": [ @@ -115031,7 +115275,7 @@ "solution": "", "duration": -1, "usages": [ - "20220317\t2022届高三1班\t0.977\t0.968" + "20220317\t2022届高三01班\t0.977\t0.968" ], "origin": "2022届高三下月考卷01第18题", "edit": [ @@ -115045,7 +115289,11 @@ "004763": { "id": "004763", "content": "新冠肺炎疫情造成医用防护服紧缺, 某地政府决定为防护服生产企业A公司扩大生产提供$x$($x\\in [0,10]$)(万元)的专项补贴, 并以每套$80$元的价格收购其生产的全部防护服. $A$公司在收到政府$x$(万元)补贴后, 防护服产量将增加到$t=k\\cdot (6-\\dfrac{12}{x+4})$(万套), 其中$k$为工厂工人的复工率($k\\in [0.5,1]$). $A$公司生产$t$万件防护服还需投入成本$20+8x+50t$(万元).\\\\\n(1) 将$A$公司生产防护服的利润$y$(万元)表示为补贴$x$(万元)的函数(利润不包含政府补贴);\\\\\n(2) 若对任意的$x\\in [0,10]$(万元), $A$公司都不会产生亏损, 求复工率$k$的取值范围.", - "objs": [], + "objs": [ + "K0221002B", + "K0222001B", + "K0222002B" + ], "tags": [ "第二单元" ], @@ -115054,7 +115302,7 @@ "solution": "", "duration": -1, "usages": [ - "20220317\t2022届高三1班\t0.907\t0.890" + "20220317\t2022届高三01班\t0.907\t0.890" ], "origin": "2022届高三下月考卷01第19题", "edit": [ @@ -115077,7 +115325,7 @@ "solution": "", "duration": -1, "usages": [ - "20220317\t2022届高三1班\t1.000\t0.903\t0.442" + "20220317\t2022届高三01班\t1.000\t0.903\t0.442" ], "origin": "2022届高三下月考卷01第20题", "edit": [ @@ -115100,7 +115348,7 @@ "solution": "", "duration": -1, "usages": [ - "20220317\t2022届高三1班\t0.994\t0.535\t0.090" + "20220317\t2022届高三01班\t0.994\t0.535\t0.090" ], "origin": "2022届高三下月考卷01第21题", "edit": [ @@ -115176,13 +115424,13 @@ "solution": "", "duration": -1, "usages": [ + "20220821\t2023届高三02班\t0.939", + "20220821\t2023届高三03班\t0.917", + "20220821\t2023届高三09班\t0.903", "20220821\t2023届高三10班\t1.000", "20220821\t2023届高三12班\t0.875", - "20220821\t2023届高三2班\t0.939", - 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"20220822\t2023届高三08班\t0.774", + "20220822\t2023届高三10班\t0.917" ], "origin": "代数精编第一章集合与命题", "edit": [ @@ -115809,10 +116057,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t0.909", "20220822\t2023届高三10班\t0.933", - "20220822\t2023届高三2班\t0.909", - "20220823\t2023届高三11班\t0.880", - "20220823\t2023届高三8班\t1.000" + "20220823\t2023届高三08班\t1.000", + "20220823\t2023届高三11班\t0.880" ], "origin": "代数精编第一章集合与命题", "edit": [ @@ -116181,22 +116429,22 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$[0,1]$", "solution": "", "duration": -1, "usages": [ + "20220914\t2023届高三01班\t0.970", + "20220914\t2023届高三02班\t0.839", + "20220914\t2023届高三03班\t0.935", + "20220914\t2023届高三04班\t0.906", + "20220914\t2023届高三05班\t0.846", + "20220914\t2023届高三06班\t0.829", + "20220914\t2023届高三07班\t0.879", + "20220914\t2023届高三08班\t0.875", + "20220914\t2023届高三09班\t0.706", "20220914\t2023届高三10班\t0.811", "20220914\t2023届高三11班\t0.652", - "20220914\t2023届高三12班\t0.692", - "20220914\t2023届高三1班\t0.970", - 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-125508,11 +125756,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(\\dfrac 23,\\dfrac 32)$", "solution": "", "duration": -1, "usages": [ - "20220908\t2023届高三2班\t0.970" + "20220908\t2023届高三02班\t0.970" ], "origin": "代数精编第二章不等式", "edit": [ @@ -125574,7 +125822,9 @@ "005202": { "id": "005202", "content": "解关于$x$的不等式: $\\lg (x-\\dfrac 1x)<0$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125597,7 +125847,9 @@ "005203": { "id": "005203", "content": "解关于$x$的不等式: $\\log_2|x-\\dfrac 12|<-1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125623,7 +125875,9 @@ "005204": { "id": "005204", "content": "已知集合$M=\\{x|\\log_3(x-m)>1\\}$与$P=\\{x|3^{5-3x} \\ge \\dfrac 13\\}$满足$M\\cap P\\ne \\varnothing$, 求实数$m$的取值范围.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125644,7 +125898,9 @@ "005205": { "id": "005205", "content": "解不等式: $\\log_8(2-x)+\\log_{64}(x+1)\\ge \\log_4x$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125665,7 +125921,9 @@ "005206": { "id": "005206", "content": "解不等式: $\\log_{0.5}(x+13)<\\log_{0.5}(x^2-2x-15)$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125686,7 +125944,9 @@ "005207": { "id": "005207", "content": "解不等式: $\\log_x(3\\sqrt{x-1}-1)>1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125707,7 +125967,9 @@ "005208": { "id": "005208", "content": "解不等式: $\\log_{x-1}(6-x-x^2)>2$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125728,7 +125990,9 @@ "005209": { "id": "005209", "content": "解不等式: $\\dfrac 1{\\log_2(x-1)}<\\dfrac 1{\\log_2\\sqrt{x+1}}$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125749,7 +126013,9 @@ "005210": { "id": "005210", "content": "解不等式: $\\dfrac{\\log_3(1-\\dfrac{3x}2)}{\\log_9(2x)}\\ge 1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125770,7 +126036,9 @@ "005211": { "id": "005211", "content": "解不等式: $\\log_{0.5}({2^x}-1)\\cdot \\log_{0.5}({2^{x-1}}-\\dfrac 12)\\le 2$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125791,7 +126059,9 @@ "005212": { "id": "005212", "content": "解关于$x$的不等式, 其中$a>0$, $a\\ne 1$: $\\log_a(x+1-a)>1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125817,7 +126087,9 @@ "005213": { "id": "005213", "content": "解关于$x$的不等式, 其中$a>0$, $a\\ne 1$: $\\log_a(1-\\dfrac 1x)>1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125841,7 +126113,9 @@ "005214": { "id": "005214", "content": "解关于$x$的不等式, 其中$a>0$, $a\\ne 1$: $\\log_a(2x-1)>\\log_a(x-1)$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125867,7 +126141,9 @@ "005215": { "id": "005215", "content": "解关于$x$的不等式, 其中$a>0$, $a\\ne 1$: $\\log_a^2x<\\log_x^2a$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125892,7 +126168,9 @@ "005216": { "id": "005216", "content": "解关于$x$的不等式, 其中$a>0$, $a\\ne 1$: ${x^{\\log_ax}}>\\dfrac{x^4\\cdot \\sqrt x}{a^2}$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125913,7 +126191,9 @@ "005217": { "id": "005217", "content": "解关于$x$的不等式, 其中$a>0$, $a\\ne 1$: $\\sqrt{\\log_ax-1}>3-\\log_ax$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125938,7 +126218,9 @@ "005218": { "id": "005218", "content": "已知$x$满足不等式$(\\dfrac 12)^{2x-4}-(\\dfrac 12)^x-(\\dfrac 12)^{x-2}+\\dfrac 14\\le 0$, 且$y=\\log_{\\frac 1a}(a^2x)\\cdot \\log_{\\frac 1{a^2}}(ax)$的最大值是$0$, 最小值是$-\\dfrac 18$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -125959,7 +126241,9 @@ "005219": { "id": "005219", "content": "已知关于$x$的方程$x^2-5x\\log_ak+6\\log _a^2k=0$的两根中$(k>1)$, 仅较小的根在区间$(1,2)$内, 试用$a$表示$k$的取值范围($a>0$且$a\\ne 1$).", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -126111,11 +126395,11 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ - "20220901\t2023届高三2班\t0.970", + "20220901\t2023届高三02班\t0.970", "20220902\t2023届高三10班\t1.000" ], "origin": "代数精编第二章不等式", @@ -126232,22 +126516,22 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(2,+\\infty)$", "solution": "", "duration": -1, "usages": [ + "20220914\t2023届高三01班\t0.939", + "20220914\t2023届高三02班\t0.903", + "20220914\t2023届高三03班\t0.935", + "20220914\t2023届高三04班\t0.969", + "20220914\t2023届高三05班\t0.949", + "20220914\t2023届高三06班\t0.951", + "20220914\t2023届高三07班\t0.939", + "20220914\t2023届高三08班\t0.938", + "20220914\t2023届高三09班\t0.882", "20220914\t2023届高三10班\t0.946", "20220914\t2023届高三11班\t0.913", - "20220914\t2023届高三12班\t0.962", - "20220914\t2023届高三1班\t0.939", - "20220914\t2023届高三2班\t0.903", - "20220914\t2023届高三3班\t0.935", - "20220914\t2023届高三4班\t0.969", - "20220914\t2023届高三5班\t0.949", - "20220914\t2023届高三6班\t0.951", - "20220914\t2023届高三7班\t0.939", - "20220914\t2023届高三8班\t0.938", - "20220914\t2023届高三9班\t0.882" + "20220914\t2023届高三12班\t0.962" ], "origin": "代数精编第二章不等式", "edit": [ @@ -126288,7 +126572,9 @@ "005232": { "id": "005232", "content": "若函数$y=\\log_ax$在$x\\in [2,+\\infty)$上恒有$|y|>1$, 则实数$a$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -126391,11 +126677,11 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,\\dfrac 52)$", "solution": "", "duration": -1, "usages": [ - "20220915\t2023届高三2班\t0.781" + "20220915\t2023届高三02班\t0.781" ], "origin": "代数精编第二章不等式", "edit": [ @@ -126465,11 +126751,11 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(1,+\\infty)$", "solution": "", "duration": -1, "usages": [ - "20220901\t2023届高三2班\t0.606", + "20220901\t2023届高三02班\t0.606", "20220902\t2023届高三10班\t0.688" ], "origin": "代数精编第二章不等式", @@ -126484,7 +126770,9 @@ "005240": { "id": "005240", "content": "解不等式: $\\log_{\\frac 14}|x|<\\log_{\\frac 12}|x+1|$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -126505,7 +126793,9 @@ "005241": { "id": "005241", "content": "解不等式: $|\\lg (1-x)|>|\\lg (1+x)|$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -126526,7 +126816,9 @@ "005242": { "id": "005242", "content": "解不等式: $|\\log_{\\frac 13}x|+|\\log_{\\frac 13}\\dfrac 1{3-x}|\\ge 1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -126547,7 +126839,9 @@ "005243": { "id": "005243", "content": "求函数$f(x)=|x-\\dfrac 12|-|x+\\dfrac 12|$的最大值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -126568,7 +126862,10 @@ "005244": { "id": "005244", "content": "已知$|\\lg x-\\lg y|\\le 1$, 则$\\dfrac xy+\\dfrac yx$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0221002B", + "K0214002B" + ], "tags": [ "第二单元" ], @@ -126589,7 +126886,9 @@ "005245": { "id": "005245", "content": "解关于$x$的不等式: $|\\log_{\\sqrt a}x-2|-|\\log_ax-2|<2$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -126610,7 +126909,9 @@ "005246": { "id": "005246", "content": "解关于$x$的不等式: $|\\log_ax|<|\\log_a(ax^2)|-2$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -126633,7 +126934,9 @@ "005247": { "id": "005247", "content": "解关于$x$的不等式: $|3^x-3|+9^x-3>0$.", - "objs": [], + "objs": [ + "K0211001B" + ], "tags": [ "第二单元" ], @@ -126654,7 +126957,9 @@ "005248": { "id": "005248", "content": "解关于$x$的不等式: $|a^x-1|+|a^{2x}-3|>2(a>0)$.", - "objs": [], + "objs": [ + "K0211001B" + ], "tags": [ "第二单元" ], @@ -126774,7 +127079,10 @@ "005253": { "id": "005253", "content": "已知常数$a\\in (0,1)$, 对任意$x>0$, $f(\\log_ax)=\\dfrac{a(x^2-1)}{x(a^2-1)}$.\\\\\n(l) 求$f(x)$($x\\in \\mathbf{R}$)的表达式, 并判断它的单调性;\\\\\n(2) 若$n\\ge 2$, $n\\in \\mathbf{N}$, 求证: $f(n)>n$.", - "objs": [], + "objs": [ + "K0219003B", + "K0223005B" + ], "tags": [ "第二单元" ], @@ -127003,7 +127311,9 @@ "005263": { "id": "005263", "content": "解不等式: $2^{x+1}+x>0$.", - "objs": [], + "objs": [ + "K0211001B" + ], "tags": [ "第二单元" ], @@ -127212,7 +127522,9 @@ "005272": { "id": "005272", "content": "求函数$y=\\dfrac{3x-1}{x+1}$的值域.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127241,7 +127553,9 @@ "005273": { "id": "005273", "content": "求函数$y=\\dfrac{4x+3}{2x-1}$的值域.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127269,7 +127583,9 @@ "005274": { "id": "005274", "content": "求函数$y=\\dfrac{x^2-1}{x^2+2}$的值域.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127297,7 +127613,9 @@ "005275": { "id": "005275", "content": "求函数$y=\\dfrac{x^2-x+1}{2x^2-2x+3}$的值域.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127325,7 +127643,9 @@ "005276": { "id": "005276", "content": "求函数$y=\\dfrac{x^2+4x+3}{x^2+x-6}$的值域.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127351,7 +127671,9 @@ "005277": { "id": "005277", "content": "若实数$x,y$满足$x^2+4y^2=4x$, 求$S=x^2+y^2$的值域.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127372,7 +127694,9 @@ "005278": { "id": "005278", "content": "已知函数$y=f(x)=x^2+ax+3$在区间$x\\in [-1,1]$上的最小值为$-3$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127393,7 +127717,9 @@ "005279": { "id": "005279", "content": "求函数$y=3x^2-12x+18\\sqrt {4x-x^2}-23$的值域.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127414,7 +127740,9 @@ "005280": { "id": "005280", "content": "求函数$y=|x-2|-|x+1|$的值域.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -127435,7 +127763,9 @@ "005281": { "id": "005281", "content": "若$f(x-1)=2x^2+1$, 求$f(x)$.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -127456,7 +127786,9 @@ "005282": { "id": "005282", "content": "已知定义域为$\\mathbf{R}$的函数$f(x)$满足:\n\\textcircled{1} $f(x+y)=f(x)\\cdot f(y)$对任何实数$x,y$都成立;\n\\textcircled{2} 存在实数$x_1,x_2$, 使$f(x_1)\\ne f(x_2)$.\n求证:\\\\\n(1) $f(0)=1$;\\\\\n(2) $f(x)>0$.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -127875,11 +128207,11 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ - "20220913\t2023届高三2班\t0.964" + "20220913\t2023届高三02班\t0.964" ], "origin": "代数精编第三章函数", "edit": [ @@ -128707,7 +129039,9 @@ "005333": { "id": "005333", "content": "函数$f(x)=|1-x|-|x-3|(x\\in \\mathbf{R})$的值域是\\bracket{20}.\n\\fourch{$[-2,2]$}{$[-1,3]$}{$[-3,1]$}{$[0,4]$}", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -128728,7 +129062,9 @@ "005334": { "id": "005334", "content": "若函数$f(x)$的定义域是$[0,1]$, 分别求函数$f(1-2x)$和$f(x+a)$($a>0$)的定义域.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -128749,7 +129085,9 @@ "005335": { "id": "005335", "content": "若函数$f(x+1)$的定义域是$[-2,3)$, 求函数$f(\\dfrac 1x+2)$的定义域.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -128770,7 +129108,9 @@ "005336": { "id": "005336", "content": "求函数$y=\\dfrac{2x}{x^2+x+1}$的值域.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -128797,7 +129137,9 @@ "005337": { "id": "005337", "content": "求函数$y=\\dfrac{x^2+x-1}{x^2+x+1}$的值域.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -128826,7 +129168,9 @@ "005338": { "id": "005338", "content": "求函数$y=\\dfrac{x^2-1}{x^2-5x+4}$的值域.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -128851,7 +129195,9 @@ "005339": { "id": "005339", "content": "若实数$x,y$满足$3x^2+2y^2=6x$, 分别求$x$与$x^2+y^2$的取值范围.", - "objs": [], + "objs": [ + "K0709001X" + ], "tags": [ "第二单元" ], @@ -128874,7 +129220,9 @@ "005340": { "id": "005340", "content": "若实数$x,y$满足$x^2+y^2=2x$, 求$x^2-y^2$的取值范围.", - "objs": [], + "objs": [ + "K0709001X" + ], "tags": [ "第二单元" ], @@ -128897,7 +129245,9 @@ "005341": { "id": "005341", "content": "求函数$y=3x-2+\\sqrt {3-2x}$的值域.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -128920,7 +129270,9 @@ "005342": { "id": "005342", "content": "求函数$y=2x+\\sqrt {2x-1}$的值域.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -128945,7 +129297,9 @@ "005343": { "id": "005343", "content": "求函数$y=(x-1)(x-2)(x-3)(x-4)+15$的值域.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -128989,7 +129343,9 @@ "005345": { "id": "005345", "content": "已知函数$y=x^2+mx-1$在区间$[0,3]$上有最小值$-2$, 求实数$m$的值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -129010,7 +129366,9 @@ "005346": { "id": "005346", "content": "当$x\\ge 0$时, 求函数$f(x)=x^2+2ax$的最小值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -129031,7 +129389,10 @@ "005347": { "id": "005347", "content": "已知函数$f(x)=\\dfrac{ax}{2x+3}$($x\\ne -\\dfrac 32$)满足$f(f(x))=x$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0215001B", + "K0225005B" + ], "tags": [ "第二单元" ], @@ -129052,7 +129413,9 @@ "005348": { "id": "005348", "content": "已知$f(x)$是二次函数, 且满足$f(2x)+f(3x+1)=13x^2+6x-1$, 求$f(x)$的表达式.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -129073,7 +129436,9 @@ "005349": { "id": "005349", "content": "已知函数$f(x)$的定义域是一切非零实数, 且满足$3f(x)+2f(\\dfrac 1x)=4x$, 求, $f(x)$的表达式.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -129094,7 +129459,9 @@ "005350": { "id": "005350", "content": "作出函数$y=1+\\dfrac{|x|}x$的图像.", - "objs": [], + "objs": [ + "K0216002B" + ], "tags": [ "第二单元" ], @@ -129118,7 +129485,9 @@ "005351": { "id": "005351", "content": "作出函数$y=x-|1-x|$的图像.", - "objs": [], + "objs": [ + "K0216002B" + ], "tags": [ "第二单元" ], @@ -129142,7 +129511,9 @@ "005352": { "id": "005352", "content": "作出函数$y=|x^2-4x+3|$的图像.", - "objs": [], + "objs": [ + "K0216002B" + ], "tags": [ "第二单元" ], @@ -129165,7 +129536,9 @@ "005353": { "id": "005353", "content": "作出函数$y=\\dfrac{x^3+x}{|x|}$的图像.", - "objs": [], + "objs": [ + "K0216002B" + ], "tags": [ "第二单元" ], @@ -129188,7 +129561,9 @@ "005354": { "id": "005354", "content": "作出函数$y=\\dfrac{(x+\\dfrac 12)}{|x|-x}^0$的图像.", - "objs": [], + "objs": [ + "K0216002B" + ], "tags": [ "第二单元" ], @@ -129209,7 +129584,9 @@ "005355": { "id": "005355", "content": "已知$f(x)=-x^2+2x+3$, 画出函数$y=\\dfrac 12[f(x)+|f(x)|]$的图像.", - "objs": [], + "objs": [ + "K0216002B" + ], "tags": [ "第二单元" ], @@ -129230,7 +129607,9 @@ "005356": { "id": "005356", "content": "已知$f(x)=|x|$, $x\\in [-1,1]$, 作出函数$y=f(x+1)+1$的图像.", - "objs": [], + "objs": [ + "K0216002B" + ], "tags": [ "第二单元" ], @@ -129251,7 +129630,10 @@ "005357": { "id": "005357", "content": "将进货单价为$40$元的商品按每件$50$元出售时, 每月能卖出$500$个, 已知这批商品在销售单价的基础上每涨价$1$元, 其月销售数就减少$10$个, 为了每月赚取最大利润, 销售单价应定为多少?", - "objs": [], + "objs": [ + "K0222002B", + "K0221002B" + ], "tags": [ "第二单元" ], @@ -129273,7 +129655,8 @@ "id": "005358", "content": "飞机飞行$1$小时的耗费由两部分组成: 固定部分$4900$元, 变动部分$P$与飞机飞行速度$v$(千米/时)的函数关系是$P=0.01v^2$. 已知甲、乙两地相距为一常数$a$(千米), 试写出飞机从甲地飞到乙地的总耗费$y$与飞机速度$v$的函数关系式, 并写出耗费最小时飞机的飞行速度.", "objs": [ - "K0222002B" + "K0222002B", + "K0221002B" ], "tags": [ "第二单元" @@ -129295,7 +129678,9 @@ "005359": { "id": "005359", "content": "求证: 函数$f(x)=x^3$在$x\\in \\mathbf{R}$上是增函数.", - "objs": [], + "objs": [ + "K0219003B" + ], "tags": [ "第二单元" ], @@ -129316,7 +129701,9 @@ "005360": { "id": "005360", "content": "已知奇函数$y=f(x)$在$x<0$时是减函数, 求证: $y=f(x)$在$x>0$时也是减函数.", - "objs": [], + "objs": [ + "K0220003B" + ], "tags": [ "第二单元" ], @@ -129337,7 +129724,9 @@ "005361": { "id": "005361", "content": "已知$f(x)$是奇函数, 且当$x>0$时$f(x)=x(1-x)$, 求$f(x)$在$x<0$时的表达式.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -129358,7 +129747,10 @@ "005362": { "id": "005362", "content": "已知函数$y=f(x)$满足$f(x)=f(4-x)$($x\\in \\mathbf{R}$), 且$f(x)$在$x>2$时为增函数, 记$a=f(\\dfrac 35)$, $b=f(\\dfrac 65)$, $c=f(4)$, 则$a,b,c$之间的大小关系是\\bracket{20}.\n\\fourch{$c>a>b$}{$c>b>a$}{$b>a>c$}{$a>c>d$}", - "objs": [], + "objs": [ + "K0219001B", + "K0218001B" + ], "tags": [ "第二单元" ], @@ -129379,7 +129771,9 @@ "005363": { "id": "005363", "content": "画出函数$y=x^2-2|x|-1$的图像.", - "objs": [], + "objs": [ + "K0216002B" + ], "tags": [ "第二单元" ], @@ -129402,7 +129796,9 @@ "005364": { "id": "005364", "content": "求函数$y=\\dfrac{x-2}{2x+1}$的值域.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -129430,7 +129826,10 @@ "005365": { "id": "005365", "content": "已知函数$f(x)=(x-1)^2$($x\\le 1$), 又$f(x)$和$\\varphi (x)$的图像关于直线$y=x$对称, 求$\\varphi (x)$的表达式.", - "objs": [], + "objs": [ + "K0225005B", + "K0226002B" + ], "tags": [ "第二单元" ], @@ -129451,7 +129850,9 @@ "005366": { "id": "005366", "content": "求实数$m$的范围, 使关于$x$的方程$x^2+2(m-1)x+2m+6=0$:\\\\\n(1) 有两个实数根, 且一个比$2$大, 另一个比$2$小;\\\\\n(2) 有两个实数根, 且都比$1$大;\\\\\n(3) 有两个实数根$\\alpha ,\\beta$, 且满足$0<\\alpha <1<\\beta <4$;\\\\\n(4) 至少有一个正根.", - "objs": [], + "objs": [ + "K0223004B" + ], "tags": [ "第二单元" ], @@ -129472,7 +129873,9 @@ "005367": { "id": "005367", "content": "就参数$m$讨论方程$x^2-2|x|-m=0$的解的情况.", - "objs": [], + "objs": [ + "K0223004B" + ], "tags": [ "第二单元" ], @@ -129493,7 +129896,9 @@ "005368": { "id": "005368", "content": "下列记数中, 符合科学记数法的是\\bracket{20}.\n\\fourch{$35.6\\times 10^{-25}$}{$0.356\\times 10^{-23}$}{$3.56\\times 10^{-24}$}{$356\\times 10^{-26}$}", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -129514,7 +129919,9 @@ "005369": { "id": "005369", "content": "计算$3^{-1}\\times 2^{-2}\\div 4^{-2}$的结果是\\bracket{20}.\n\\fourch{$\\dfrac 1{192}$}{$\\dfrac 43$}{$\\dfrac 1{12}$}{$-\\dfrac 43$}", - "objs": [], + "objs": [ + "K0201001B" + ], "tags": [ "第二单元" ], @@ -129535,7 +129942,9 @@ "005370": { "id": "005370", "content": "下列各式中, 正确的是\\bracket{20}.\n\\fourch{$(-1)^0=-1$}{$(-1)^{-1}=1$}{$3a^{-2}=\\dfrac 1{3a^2}$}{$(-x)^5\\div (-x)^3=x^2$}", - "objs": [], + "objs": [ + "K0201001B" + ], "tags": [ "第二单元" ], @@ -129556,7 +129965,9 @@ "005371": { "id": "005371", "content": "下列各式中, 计算正确的是\\bracket{20}.\n\\twoch{$(-0.125)\\div (-0.5)^{-3}=1$}{$10^{-4}(\\sqrt 5)^0=-10000$}{$(\\dfrac 13)^0\\div 3^{-1}=3$}{$(\\sqrt 3-\\sqrt 2)^0-(\\sqrt 3)^2-(-\\sqrt 2)^2=1-3+2=0$}", - "objs": [], + "objs": [ + "K0201001B" + ], "tags": [ "第二单元" ], @@ -129577,7 +129988,9 @@ "005372": { "id": "005372", "content": "化简$\\dfrac 13x\\sqrt {9x}-x^2\\sqrt {\\dfrac 1x}$的结果是\\bracket{20}.\n\\fourch{$\\sqrt x$}{$x(1-x^2)\\sqrt x$}{$x^2(1-x\\sqrt x)$}{0}", - "objs": [], + "objs": [ + "K0201002B" + ], "tags": [ "第二单元" ], @@ -129598,7 +130011,9 @@ "005373": { "id": "005373", "content": "化简$\\dfrac{a^{-2}-b^{-2}}{a^2-b^2}$的结果是\\bracket{20}.\n\\fourch{-1}{$-\\dfrac 1{a^2b^2}$}{$a^{-1}+b^{-1}$}{$\\dfrac 1{a^2b^2}$}", - "objs": [], + "objs": [ + "K0201001B" + ], "tags": [ "第二单元" ], @@ -129619,7 +130034,9 @@ "005374": { "id": "005374", "content": "已知$x=1-2^s$, $y=1-2^{-s}$, 则$y$等于\\bracket{20}.\n\\fourch{$\\dfrac{x-1}x$}{$\\dfrac{2-x}{1-x}$}{$\\dfrac x{x-1}$}{$\\dfrac{x-2}{x-1}$}", - "objs": [], + "objs": [ + "K0203002B" + ], "tags": [ "第二单元" ], @@ -129640,7 +130057,9 @@ "005375": { "id": "005375", "content": "计算$\\sqrt {(3-\\pi)^2}$的结果是\\bracket{20}.\n\\fourch{$3-\\pi$}{$\\pi -3$}{$\\pi +3$}{$-\\pi -3$}", - "objs": [], + "objs": [ + "K0201002B" + ], "tags": [ "第二单元" ], @@ -129661,7 +130080,9 @@ "005376": { "id": "005376", "content": "若$(\\sqrt [n]{-3})^n$有意义, 则$n$一定是\\bracket{20}.\n\\fourch{正偶数}{自然数}{正奇数}{整数}", - "objs": [], + "objs": [ + "K0201002B" + ], "tags": [ "第二单元" ], @@ -129682,7 +130103,9 @@ "005377": { "id": "005377", "content": "已知$n\\in \\mathbf{N}$, 在\\textcircled{1} $\\sqrt [4]{(-4)^{2n}}$; \\textcircled{2} $\\sqrt [4]{(-4)^{2n+1}}$; \\textcircled{3} $\\sqrt [5]{-x^2}$; \\textcircled{4} $\\sqrt [5]{-x^2}$这四个式子中, 有意义的\\bracket{20}.\n\\fourch{是\\textcircled{1}\\textcircled{2}\\textcircled{3}\\textcircled{4} }{只有\\textcircled{3}\\textcircled{4}}{只有\\textcircled{1}\\textcircled{3}\\textcircled{4}}{只有\\textcircled{4}}", - "objs": [], + "objs": [ + "K0201002B" + ], "tags": [ "第二单元" ], @@ -129703,7 +130126,9 @@ "005378": { "id": "005378", "content": "若$\\sqrt [4]{4a^2-4a+1}=\\sqrt [3]{1-2a}$, 则实数$a$的取值范围是\\bracket{20}.\n\\fourch{$a<2$}{$a=\\dfrac 12$或0}{$a>\\dfrac 12$}{$R$}", - "objs": [], + "objs": [ + "K0201002B" + ], "tags": [ "第二单元" ], @@ -129724,7 +130149,9 @@ "005379": { "id": "005379", "content": "在\\textcircled{1} $0^{-1}$; \\textcircled{2} $0^{-\\frac 12}$; \\textcircled{3} $0^0$; \\textcircled{4} $0^{0.2}$这四个式子中, 有意义的个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{$3$}", - "objs": [], + "objs": [ + "K0201001B" + ], "tags": [ "第二单元" ], @@ -129745,7 +130172,11 @@ "005380": { "id": "005380", "content": "下列各式中正确的是\\bracket{20}.\n\\fourch{$-4^0=1$}{$(5^{-\\frac 12})^2=5$}{$(-3^{m-n})^2=9^{m-n}$}{$(-2)^{-1}=\\dfrac 12$}", - "objs": [], + "objs": [ + "K0201001B", + "K0202003B", + "K0203002B" + ], "tags": [ "第二单元" ], @@ -129766,7 +130197,9 @@ "005381": { "id": "005381", "content": "计算$[ (-3)^2 ]^{\\frac 12}-(-10)^0$的值等于\\bracket{20}.\n\\fourch{$-2$}{$2$}{$-4$}{$4$}", - "objs": [], + "objs": [ + "K0201001B" + ], "tags": [ "第二单元" ], @@ -129787,7 +130220,9 @@ "005382": { "id": "005382", "content": "下列计算中正确的是\\bracket{20}.\n\\fourch{$a^{\\frac 83}\\cdot a^{\\frac 38}=a$}{$a^{\\frac 83}\\cdot a^{-\\frac 83}=0$}{$a^{\\frac 83}\\div a^{\\frac 13}=a^8$}{$a^{\\frac 12}\\div a^{\\frac 13}=a^{\\frac 16}$}", - "objs": [], + "objs": [ + "K0203002B" + ], "tags": [ "第二单元" ], @@ -129808,7 +130243,9 @@ "005383": { "id": "005383", "content": "下列计算中正确的是\\bracket{20}.\n\\fourch{$a^{\\frac 34}\\cdot a^{\\frac 43}=a$}{$a^{\\frac 34}\\div a^{\\frac 34}=a$}{$a^{-4}\\div a^4=0$}{$(a^{\\frac 34})^{\\frac 43}=a$}", - "objs": [], + "objs": [ + "K0203002B" + ], "tags": [ "第二单元" ], @@ -129829,7 +130266,9 @@ "005384": { "id": "005384", "content": "化简$(a^{\\frac 23}b^{\\frac 12})(-3a^{\\frac 12}b^{\\frac 13})\\div (\\frac 13a^{\\frac 16}b^{\\frac 56})$的结果是\\bracket{20}.\n\\fourch{$6a$}{$-a$}{$-9a$}{$9a$}", - "objs": [], + "objs": [ + "K0203002B" + ], "tags": [ "第二单元" ], @@ -131807,11 +132246,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,1)$, $pq=1$", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.839" + "20220904\t2023届高三02班\t0.839" ], "origin": "代数精编第三章函数", "edit": [ @@ -131832,11 +132271,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,0)$", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.903" + "20220904\t2023届高三02班\t0.903" ], "origin": "代数精编第三章函数", "edit": [ @@ -132875,11 +133314,11 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t0.844" + "20220907\t2023届高三02班\t0.844" ], "origin": "代数精编第三章函数", "edit": [ @@ -134155,7 +134594,9 @@ "005563": { "id": "005563", "content": "已知函数$f(x)=4+a^{x-1}$的图像恒过记点$P$, 则点$P$的坐标是\\bracket{20}.\n\\fourch{$(1, 5)$}{$(1, 4)$}{$(0, 4)$}{$(4, 0)$}", - "objs": [], + "objs": [ + "K0210002B" + ], "tags": [ "第二单元" ], @@ -134176,7 +134617,9 @@ "005564": { "id": "005564", "content": "下列函数中, 值域为$(0,+\\infty)$的函数是\\bracket{20}.\n\\fourch{$y=(\\dfrac 18)^{2-x}$}{$y=\\sqrt {1-3^x}$}{$y=\\sqrt {(\\dfrac 13)^x-1}$}{$y=2^{\\frac 1{3-x}}$}", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -134197,7 +134640,9 @@ "005565": { "id": "005565", "content": "若$01$}{$|a|<\\sqrt 2$}{$a>\\sqrt 2$}{$1<|a|<\\sqrt 2$}", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -134396,7 +134854,9 @@ "005574": { "id": "005574", "content": "若函数$f(x)=a^x-(b+1)$($a>0$且$a\\ne 1$)的图像经过第一、三、四象限, 则必有\\bracket{20}.\n\\fourch{$00$}{$01$且$b<1$}{$a>1$且$b>0$}", - "objs": [], + "objs": [ + "K0210005B" + ], "tags": [ "第二单元" ], @@ -134417,7 +134877,10 @@ "005575": { "id": "005575", "content": "用不等号``$>$''或``$<$''填空:\n(1) $1.2^{0.3}$\\blank{50}$1$;\\\\\n(2) $0.3^{5.1}$\\blank{50}$1$;\\\\\n(3) $(\\dfrac 23)^{-\\frac 13}$\\blank{50}$(\\dfrac 32)^{-\\frac 13}$;\\\\\n(4) $9^{\\frac 13}$\\blank{50}$3^{\\frac 43}$;\\\\\n(5) $2^{\\frac 23}$\\blank{50}$3.6^{-\\frac 34}$;\\\\\n(6) $0.8^{-2}$\\blank{50}$(\\dfrac 53)^{-\\frac 12}$.", - "objs": [], + "objs": [ + "K0210006B", + "K0208004B" + ], "tags": [ "第二单元" ], @@ -134438,7 +134901,10 @@ "005576": { "id": "005576", "content": "将下列各数从小到大排列:\n(1) $0.9^{\\frac 34}$, $1.2^{\\frac 34}$, 1:\\blank{50};\\\\\n(2) $2.5^{\\frac 23}$, $(-1.4)^{\\frac 23}$, $(-3)^{\\frac 13}$:\\blank{50};\\\\\n(3) $4.1^{\\frac 23}$, $3.8^{-\\frac 23}$, $(-1.9)^{\\frac 35}$:\\blank{50}.", - "objs": [], + "objs": [ + "K0210006B", + "K0208004B" + ], "tags": [ "第二单元" ], @@ -134459,7 +134925,9 @@ "005577": { "id": "005577", "content": "根据条件确定实数$x$的取值范围:\\\\\n(1) $2^x>0.5$:\\blank{50};\\\\\n(2) $2^x<1$:\\blank{50};\\\\\n(3) $0.2^{2x-1}>\\dfrac 1{25}$:\\blank{50};\\\\\n(4) $8<(\\dfrac 12)^{2x+1}$:\\blank{50};\\\\\n(5) $(a^2+a+2)^x>(a^2+a+2)^{1-x}$:\\blank{50};\\\\\n(6) $(\\dfrac 12)^{x^2+x-2}<1$:\\blank{50}.", - "objs": [], + "objs": [ + "K0223005B" + ], "tags": [ "第二单元" ], @@ -134480,7 +134948,9 @@ "005578": { "id": "005578", "content": "函数$f(x)=\\sqrt {1-6^{x^2+x-2}}$的定义域是\\blank{50}.", - "objs": [], + "objs": [ + "K0215003B" + ], "tags": [ "第二单元" ], @@ -134503,7 +134973,9 @@ "005579": { "id": "005579", "content": "若函数$f(x)$的定义域是$(0, 1)$, 则函数$f(2^{-x})$的定义域是\\blank{50}, $f(3\\times 9^x+2\\times 3^x)$的定义域是\\blank{50}.", - "objs": [], + "objs": [ + "K0215003B" + ], "tags": [ "第二单元" ], @@ -134524,7 +134996,9 @@ "005580": { "id": "005580", "content": "函数$y=3^{x^2-3x-2}$为增函数的区间是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -134548,7 +135022,9 @@ "005581": { "id": "005581", "content": "函数$y=(0.2)^{x^2-6x+9}$为增函数的区间是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -134571,7 +135047,9 @@ "005582": { "id": "005582", "content": "函数$y=2^{-|x|}$为增函数的区间是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -134594,7 +135072,9 @@ "005583": { "id": "005583", "content": "函数$y=(\\dfrac 12)^{|1+2x|}$为增函数的区间是\\blank{50}, 为减函数的区间是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -134615,7 +135095,9 @@ "005584": { "id": "005584", "content": "若函数$y=(\\dfrac 12)^{(m^2-1)x}$在$x\\in \\mathbf{R}$为严格减函数, 则实数$m$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -134636,7 +135118,9 @@ "005585": { "id": "005585", "content": "若$1\\le x\\le 2$, 则函数$y=(\\dfrac 12)^{x^2-6x+10}$的最大值为\\blank{50}.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -134657,7 +135141,9 @@ "005586": { "id": "005586", "content": "函数$f(x)=a^{2x}-3a^x+2$($a>0$且$a\\ne 1$)的最小值为\\blank{50}.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -134678,7 +135164,9 @@ "005587": { "id": "005587", "content": "对于函数$y=a^{x^2-4}$($a>0$且$a\\ne 1$):\\\\\n(1) 若$01$, 则$y$有最小值\\blank{50}.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -134699,7 +135187,9 @@ "005588": { "id": "005588", "content": "函数$f(x)=\\dfrac 1{3^x-1}$的值域是\\blank{50}.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -134722,7 +135212,9 @@ "005589": { "id": "005589", "content": "函数$f(x)=\\dfrac{3^x}{3^x+1}$的值域是\\blank{50}.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -134746,7 +135238,9 @@ "005590": { "id": "005590", "content": "若关于$x$的方程$5^x=\\dfrac{a+3}{5-a}$有负根, 则实数$a$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0223004B" + ], "tags": [ "第二单元" ], @@ -134769,7 +135263,10 @@ "005591": { "id": "005591", "content": "若$0y>1$, 则$a^x$, $x^a$, $a^y$, $y^a$从小到大的排列顺序是\\blank{50}.", - "objs": [], + "objs": [ + "K0210006B", + "K0208004B" + ], "tags": [ "第二单元" ], @@ -134797,11 +135294,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$a0$且$a\\ne 1$), 确定$x$的取值范围, 使得$f(x)>g(x)$.", - "objs": [], + "objs": [ + "K0210006B" + ], "tags": [ "第二单元" ], @@ -134836,7 +135335,9 @@ "005594": { "id": "005594", "content": "若$f(x)=a+\\dfrac 1{4^x+1}$是奇函数, 求常数$a$的值.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -134857,7 +135358,9 @@ "005595": { "id": "005595", "content": "若$f(x)=x^2(\\dfrac 1{a^x-1}+m)$($a>0$且$a\\ne 1$)为奇函数, 求常数$m$的值.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -134878,7 +135381,10 @@ "005596": { "id": "005596", "content": "已知函数$f(x)=(\\dfrac 1{2^x-1}+\\dfrac 12)x^3$.\\\\\n(1) 求函数的定义域;\\\\\n(2) 讨论$f(x)$的奇偶性;\\\\\n(3) 求证: $f(x)>0$.", - "objs": [], + "objs": [ + "K0215003B", + "K0218001B" + ], "tags": [ "第二单元" ], @@ -134899,7 +135405,11 @@ "005597": { "id": "005597", "content": "已知$f(x)=\\dfrac{a^x-1}{a^x+1}$($a>1$).\\\\\n(1) 判断函数$f(x)$的奇偶性;\\\\\n(2) 求函数$f(x)$的值域;\\\\\n(3) 求证: $f(x)$在区间$(-\\infty ,+\\infty)$上是增函数.", - "objs": [], + "objs": [ + "K0215005B", + "K0215003B", + "K0219003B" + ], "tags": [ "第二单元" ], @@ -134920,7 +135430,9 @@ "005598": { "id": "005598", "content": "若$0\\le x\\le 2$, 求函数$y=4^{x-\\frac 12}-3\\cdot 2^x+5$的最大值和最小值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -134941,7 +135453,9 @@ "005599": { "id": "005599", "content": "若函数$f(x)=a^{2x}+2a^x-1$($a>0$且$a\\ne 1$)在$[-1, 1]$上的最大值为$14$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -134962,7 +135476,9 @@ "005600": { "id": "005600", "content": "已知函数$f(x)=\\dfrac a{a^2-2}(a^x-a^{-x})$($a>0$且$a\\ne 1$)在$(-\\infty ,+\\infty)$上是增函数, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0219003B" + ], "tags": [ "第二单元" ], @@ -134983,7 +135499,9 @@ "005601": { "id": "005601", "content": "已知$(a+1)^{-\\frac 13}<(3-2a)^{-\\frac 13}$, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0208004B" + ], "tags": [ "第二单元" ], @@ -135004,7 +135522,9 @@ "005602": { "id": "005602", "content": "已知集合$M=\\{x|(x+1)^2\\le 1\\}$, $P=\\{y|y=4^x-a\\cdot 2^{x+1}+1,\\ x\\in M,\\ \\dfrac 340$, $b\\ne 1$), 则有\\bracket{20}.\n\\fourch{$\\log_2a=b$}{$\\log_2b=a$}{$\\log_ab=2$}{$\\log_ba=2$}", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -135239,7 +135769,9 @@ "005613": { "id": "005613", "content": "若$\\log_x\\sqrt[7]y=z$, 则$x,y,z$之间满足\\bracket{20}.\n\\fourch{$y^7=x^z$}{$y=x^{7z}$}{$y=7x^z$}{$y=z^{7x}$}", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -135260,7 +135792,9 @@ "005614": { "id": "005614", "content": "$2^{\\log_43}$的值等于\\bracket{20}.\n\\fourch{3}{$\\sqrt 3$}{$\\dfrac{\\sqrt 3}3$}{$\\dfrac 13$}", - "objs": [], + "objs": [ + "K0206003B" + ], "tags": [ "第二单元" ], @@ -135426,11 +135960,11 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.875" + "20220904\t2023届高三02班\t0.875" ], "origin": "代数精编第三章函数", "edit": [ @@ -136123,11 +136657,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.625" + "20220904\t2023届高三02班\t0.625" ], "origin": "代数精编第三章函数", "edit": [ @@ -136632,7 +137166,9 @@ "005672": { "id": "005672", "content": "记$\\log_827=m$, 用$m$表示$\\log_616$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -136653,7 +137189,9 @@ "005673": { "id": "005673", "content": "已知$\\log_37=a$, $\\log_34=b$, 求$\\log_{12}21$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -136676,7 +137214,9 @@ "005674": { "id": "005674", "content": "已知$\\log_23=a$, $\\log_35=b$, 求$\\log_{15}20$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -136699,7 +137239,9 @@ "005675": { "id": "005675", "content": "已知$a>b>1$, $\\log_ab+\\log_ba=\\dfrac{10}3$, 求$\\log_ab-\\log_ba$的值.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -136720,7 +137262,10 @@ "005676": { "id": "005676", "content": "已知$\\log_{2a}a=m$, $\\log_{3a}2a=n$, 求证: $2^{1-mn}=3^{n-mn}$.", - "objs": [], + "objs": [ + "K0204004B", + "K0205002B" + ], "tags": [ "第二单元" ], @@ -136741,7 +137286,9 @@ "005677": { "id": "005677", "content": "已知关于$x$的方程$x^2-(\\log_2b+\\log_a2)x+\\log_ab=0$的两根为$-1$和$2$, 求实数$a,b$的值.", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -136771,11 +137318,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t0.469" + "20220907\t2023届高三02班\t0.469" ], "origin": "代数精编第三章函数", "edit": [ @@ -136789,7 +137336,10 @@ "005679": { "id": "005679", "content": "已知正实数$x,y,z$满足$3^x=4^y=6^z$.\\\\\n(1) 求证$\\dfrac 1z-\\dfrac 1x=\\dfrac 1{2y}$;\\\\\n(2) 比较$3x,4y,6z$的大小.", - "objs": [], + "objs": [ + "K0206002B", + "K0204004B" + ], "tags": [ "第二单元" ], @@ -136810,7 +137360,9 @@ "005680": { "id": "005680", "content": "求函数$y=\\dfrac{\\sqrt {\\log_{0.8}x-1}}{2x-1}$的定义域.", - "objs": [], + "objs": [ + "K0215003B" + ], "tags": [ "第二单元" ], @@ -136833,7 +137385,9 @@ "005681": { "id": "005681", "content": "解不等式$\\log_{0.2}(x^2+2x-3)>\\log_{0.2}(3x+1)$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -136854,7 +137408,10 @@ "005682": { "id": "005682", "content": "将$\\log_{0.7}0.8$, $\\log_{1.1}0.9$, $1.1^{0.9}$由小到大排列.", - "objs": [], + "objs": [ + "K0213008B", + "K0210006B" + ], "tags": [ "第二单元" ], @@ -136896,7 +137453,9 @@ "005684": { "id": "005684", "content": "求函数$f(x)=\\log_{0.2}(x-1)(x+2)$为增函数的区间.", - "objs": [], + "objs": [ + "K0220001B" + ], "tags": [ "第二单元" ], @@ -136917,7 +137476,9 @@ "005685": { "id": "005685", "content": "求函数$f(x)=\\log_{\\frac 12}(x^2-6x+17)$的值域.", - "objs": [], + "objs": [ + "K0212002B" + ], "tags": [ "第二单元" ], @@ -136959,7 +137520,9 @@ "005687": { "id": "005687", "content": "与函数$y=x$为同一个函数的是\\bracket{20}.\n\\twoch{$y=\\sqrt {x^2}$}{$y=\\dfrac{x^2}x$}{$y=a^{\\log_ax}$($a>0$且$a\\ne 1$)}{$y=\\log_aa^x$($a>0$且$a\\ne 1$)}", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -136980,7 +137543,9 @@ "005688": { "id": "005688", "content": "若函数$y=f(x)$的反函数是$y=\\lg (x-1)+3$($x>1$), 则$f(x)$等于\\bracket{20}.\n\\fourch{$10^{x+3}+1$}{$10^{x-3}-1$}{$10^{x+3}-1$}{$10^{x-3}+1$}", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -137001,7 +137566,9 @@ "005689": { "id": "005689", "content": "若函数$f(x)=\\log_2x+3$($x\\ge 1$), 则其反函数$f^{-1}(x)$的定义域是\\bracket{20}.\n\\fourch{$\\mathbf{R}$}{$\\{x|x\\ge 1\\}$}{$\\{x|0=latex]\n \\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n \\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw [domain = -1.4:1.8] plot ({0.5^\\x},\\x);\n \\draw (1,0) node [below] {$1$}; \n \\end{tikzpicture}\n\\end{center}\n\\fourch{$y=2^x$}{$y=2^x$的反函数}{$y=2^{-x}$}{$y=2^{-x}$的反函数}", - "objs": [], + "objs": [ + "K0226003B" + ], "tags": [ "第二单元" ], @@ -137127,7 +137696,10 @@ "005695": { "id": "005695", "content": "由关系式$\\log_xy=3$所确定的函数$y=f(x)$的图像是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex,scale = 0.7]\n \\draw [->] (-2.3,0) -- (2.3,0) node [below] {$x$};\n \\draw [->] (0,-2.3) -- (0,2.3) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (1,0.1) -- (1,0) node [below] {$1$} (-1,0.1) -- (-1,0) node [below] {$-1$} (0.1,1) -- (0,1) node [left] {$1$} (0.1,-1) -- (0,-1) node [left] {$-1$};\n \\draw [domain = 0:2] plot ({\\x^(1/3)},\\x);\n \\draw [domain = 0:2] plot ({-\\x^(1/3)},{-\\x});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.7]\n \\draw [->] (-2.3,0) -- (2.3,0) node [below] {$x$};\n \\draw [->] (0,-2.3) -- (0,2.3) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (1,0.1) -- (1,0) node [below] {$1$} (-1,0.1) -- (-1,0) node [below] {$-1$} (0.1,1) -- (0,1) node [left] {$1$} (0.1,-1) -- (0,-1) node [left] {$-1$};\n \\draw [domain = 0:2] plot ({\\x^(1/3)},\\x);\n \\filldraw [white] (0,0) circle (0.05) (1,1) circle (0.05);\n \\draw (0,0) circle (0.05) (1,1) circle (0.05);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.7]\n \\draw [->] (-2.3,0) -- (2.3,0) node [below] {$x$};\n \\draw [->] (0,-2.3) -- (0,2.3) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (1,0.1) -- (1,0) node [below] {$1$} (-1,0.1) -- (-1,0) node [below] {$-1$} (0.1,1) -- (0,1) node [left] {$1$} (0.1,-1) -- (0,-1) node [left] {$-1$};\n \\draw [domain = 0:2] plot ({\\x^(1/3)},\\x);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.7]\n \\draw [->] (-2.3,0) -- (2.3,0) node [below] {$x$};\n \\draw [->] (0,-2.3) -- (0,2.3) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (1,0.1) -- (1,0) node [below] {$1$} (-1,0.1) -- (-1,0) node [below] {$-1$} (0.1,1) -- (0,1) node [left] {$1$} (0.1,-1) -- (0,-1) node [left] {$-1$};\n \\draw [domain = 0:2] plot ({\\x^(1/3)},\\x);\n \\draw [domain = 0:2] plot ({-\\x^(1/3)},\\x);\n\\end{tikzpicture}}", - "objs": [], + "objs": [ + "K0204004B", + "K0216002B" + ], "tags": [ "第二单元" ], @@ -137148,7 +137720,9 @@ "005696": { "id": "005696", "content": "若函数$f(x)=\\dfrac{1-2^x}{1+2^x}$, 则$f^{-1}(\\dfrac 35)$等于\\bracket{20}.\n\\fourch{$3$}{$2$}{$1$}{$-2$}", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -137169,7 +137743,9 @@ "005697": { "id": "005697", "content": "函数$y=\\log_{\\frac 13}(x^2-3x+4)$的定义域为\\blank{50}.", - "objs": [], + "objs": [ + "K0212002B" + ], "tags": [ "第二单元" ], @@ -137193,7 +137769,9 @@ "005698": { "id": "005698", "content": "函数$y=\\dfrac{\\sqrt {x^2-4}}{\\lg (x^2+2x-3)}$的定义域为\\blank{50}.", - "objs": [], + "objs": [ + "K0212002B" + ], "tags": [ "第二单元" ], @@ -137214,7 +137792,9 @@ "005699": { "id": "005699", "content": "函数$y=\\log_{(2x-1)}(32-4^x)$的定义域为\\blank{50}.", - "objs": [], + "objs": [ + "K0212002B" + ], "tags": [ "第二单元" ], @@ -137237,7 +137817,9 @@ "005700": { "id": "005700", "content": "函数$y=\\log_{\\frac 13}(x^2-4x+7)$的值域为\\blank{50}.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -137262,7 +137844,9 @@ "005701": { "id": "005701", "content": "函数$y=\\log_{\\frac 12}\\dfrac 1{x^2-2x+5}$的值域为\\blank{50}.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -137283,7 +137867,9 @@ "005702": { "id": "005702", "content": "函数$y=\\log_{\\frac 12}\\sqrt {3-2x-x^2}$的值域为\\blank{50}.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -137307,7 +137893,9 @@ "005703": { "id": "005703", "content": "函数$y=\\log_{\\frac 13}(x^2-5x+6)$为减函数的区间是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -137328,7 +137916,9 @@ "005704": { "id": "005704", "content": "函数$y=\\lg (12-4x-x^2)$为增函数的区间是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -137349,7 +137939,9 @@ "005705": { "id": "005705", "content": "函数$y=-\\log_{\\frac 12}(-x)$为减函数的区间是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -137370,7 +137962,9 @@ "005706": { "id": "005706", "content": "若函数$y=\\log_a(1-x)$在$[0,1)$上是增函数, 则$a$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -137391,7 +137985,9 @@ "005707": { "id": "005707", "content": "函数$y=\\log_{\\frac 12}^2x-\\log_{\\frac 12}x+1$为增函数的区间是\\blank{50}.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -137412,7 +138008,9 @@ "005708": { "id": "005708", "content": "函数$y=(0.2)^{-x}+1$的反函数是\\blank{50}.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -137438,7 +138036,9 @@ "005709": { "id": "005709", "content": "函数$y=1+\\lg (x+2)$($x\\ge 8$)的反函数是\\blank{50}.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -137464,7 +138064,9 @@ "005710": { "id": "005710", "content": "若$f(x)=\\dfrac{10^x+1}{10^x-1}$($x>1$), 则$f^{-1}(\\dfrac{101}{99})=$\\blank{50}.", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -137485,7 +138087,9 @@ "005711": { "id": "005711", "content": "若$f(x)=\\dfrac{\\lg x-1}{\\lg x+1}$($x>1$且$x\\ne \\dfrac 1{10}$), 则$f^{-1}(\\dfrac 1{10})=$\\blank{50}.", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -137506,7 +138110,9 @@ "005712": { "id": "005712", "content": "若函数$f(x)=a^x-k$的图像过点$(1, 3)$, 其反函数$f^{-1}(x)$的图像过点$(2, 0)$, 则$f(x)$的表达式是\\blank{50}.", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -137548,7 +138154,9 @@ "005714": { "id": "005714", "content": "函数$f(x)=\\ln (\\mathrm{e}^x+1)-\\dfrac x2$\\bracket{20}.\n\\twoch{是奇函数, 但不是偶函数}{是偶函数, 但不是奇函数}{既是奇函数, 又是偶函数}{没有奇偶性}", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -137569,7 +138177,9 @@ "005715": { "id": "005715", "content": "求函数$f(x)=\\lg (1+x)+\\lg (1-x)$ $(-\\dfrac 121$).\\\\\n(1) 求$f(x)$的值域;\\\\\n(2) 求证: $f(x)$在$R$上是增函数;\\\\\n(3) 求$f(x)$的反函数.", - "objs": [], + "objs": [ + "K0215005B", + "K0219003B", + "K0225005B" + ], "tags": [ "第二单元" ], @@ -137611,7 +138225,9 @@ "005717": { "id": "005717", "content": "已知$f(\\log_ax)=\\dfrac{a(x^2-1)}{x(a^2-1)}$($x>0$, $00$, 则$f(x)$\\bracket{20}.\n\\twoch{在$(-\\infty ,0)$上是增函数}{在$(-\\infty ,0)$是减函数}{在$(-\\infty ,-1)$上是增函数}{在$(-\\infty ,-1)$是减函数}", - "objs": [], + "objs": [ + "K0219003B" + ], "tags": [ "第二单元" ], @@ -137653,7 +138271,9 @@ "005719": { "id": "005719", "content": "若$01$}", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -137682,11 +138302,11 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.871" + "20220904\t2023届高三02班\t0.871" ], "origin": "代数精编第三章函数", "edit": [ @@ -137700,7 +138320,10 @@ "005721": { "id": "005721", "content": "若$1\\log_{\\frac 12}x>\\sqrt[3]x$}{$2^x>\\sqrt[3]x>\\log_{\\frac 12}x$}{$\\sqrt[3]x>2^x>\\log_{\\frac 12}x$}{$\\log_{\\frac 12}>x\\sqrt[3]x>2^x$}", - "objs": [], + "objs": [ + "K0213004B", + "K0208004B" + ], "tags": [ "第二单元" ], @@ -137721,7 +138344,9 @@ "005722": { "id": "005722", "content": "若函数$f(x)=\\log_ax$在$x\\in [3,+\\infty)$上恒有$|f(x)|>1$, 则实数$a$的取值范围是\\bracket{20}.\n\\twoch{$03$}{$\\dfrac 133$}", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -137749,11 +138374,11 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.903" + "20220904\t2023届高三02班\t0.903" ], "origin": "代数精编第三章函数", "edit": [ @@ -137790,7 +138415,9 @@ "005725": { "id": "005725", "content": "将下列各数按从小到大排列: $a=|\\log_{\\frac 13}\\dfrac 14|$, $b=|\\log_{\\frac 12}\\dfrac 32|$, $c=|\\log_25|$:\\blank{50}.", - "objs": [], + "objs": [ + "K0213008B" + ], "tags": [ "第二单元" ], @@ -137811,7 +138438,9 @@ "005726": { "id": "005726", "content": "将下列各数按从小到大排列: $\\log_{0.1}0.4$, $\\log_{\\frac 12}0.4$, $\\log_30.4$, $\\lg 0.4$:\\blank{50}.", - "objs": [], + "objs": [ + "K0213008B" + ], "tags": [ "第二单元" ], @@ -137832,7 +138461,9 @@ "005727": { "id": "005727", "content": "将下列各数按从小到大排列: $\\dfrac 32$, $\\log_23$:\\blank{50}.", - "objs": [], + "objs": [ + "K0213008B" + ], "tags": [ "第二单元" ], @@ -137853,7 +138484,9 @@ "005728": { "id": "005728", "content": "将下列各数按从小到大排列: $\\dfrac 2{\\lg 2}$, $\\dfrac 3{\\lg 3}$, $\\dfrac 5{\\lg 5}$:\\blank{50}.", - "objs": [], + "objs": [ + "K0213008B" + ], "tags": [ "第二单元" ], @@ -137874,7 +138507,9 @@ "005729": { "id": "005729", "content": "将下列各数按从小到大排列: $\\lg ^2x$, $\\lg x^2$, $\\lg (\\lg x)$, 其中$10$, $a\\ne 1$), 则$a$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -137918,7 +138555,10 @@ "005731": { "id": "005731", "content": "若$00$且$m\\ne 1$), 求$m$的值.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138002,7 +138648,9 @@ "005735": { "id": "005735", "content": "已知实数$x,y$满足$(\\log_4y)^2=\\log_{\\frac 12}x$, 求$u=\\dfrac xy$的最大值及其相应的$x,y$的值.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138023,7 +138671,10 @@ "005736": { "id": "005736", "content": "已知抛物线$y=x^2\\log_2a+2x\\log_a2+8$位于$x$轴的上方, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0214002B", + "K0219002B" + ], "tags": [ "第二单元" ], @@ -138044,7 +138695,10 @@ "005737": { "id": "005737", "content": "已知函数$f(x)=(\\log_ab)x^2+2(\\log_ba)x+8$的图像在$x$轴的上方, 求$a,b$的取值范围.", - "objs": [], + "objs": [ + "K0214002B", + "K0219002B" + ], "tags": [ "第二单元" ], @@ -138065,7 +138719,10 @@ "005738": { "id": "005738", "content": "若只有一个$x$的值满足方程$(1-\\lg ^2a)x^2+(1-\\lg a)x+2=0$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0204004B", + "K0223002B" + ], "tags": [ "第二单元" ], @@ -138088,7 +138745,10 @@ "005739": { "id": "005739", "content": "若关于$x$的方程$x^2+2(\\log_3a+1)x-\\log_9a=0$有两个相等实根, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0204004B", + "K0223002B" + ], "tags": [ "第二单元" ], @@ -138109,7 +138769,9 @@ "005740": { "id": "005740", "content": "若二次函数$f(x)=(\\lg a)x^2+2x+4\\lg a$有最小值$-3$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138130,7 +138792,9 @@ "005741": { "id": "005741", "content": "已知$f(x)=\\log_a|\\log_ax|$($00$;\\\\\n(2) 判断$f(x)$在$(1,+\\infty)$上的单调性, 并证明之.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138151,7 +138815,9 @@ "005742": { "id": "005742", "content": "实数$a$为何值时, 函数$f(x)=2^x-2^{-x}\\lg a$为奇函数?", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -138172,7 +138838,9 @@ "005743": { "id": "005743", "content": "已知函数$f(x)=\\sqrt {\\log_ax-1}$($a>0$且$a\\ne 1$).\\\\\n(1) 求$f(x)$的定义域;\\\\\n(2) 当$a>1$时, 求证: $f(x)$在$[a,+\\infty)$上是增函数.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138193,7 +138861,9 @@ "005744": { "id": "005744", "content": "已知函数$f(x)=1+\\log_x3$, $g(x)=2\\log_x2$($x>0$, 且$x\\ne 1$), 比较$f(x)$与$g(x)$的大小.", - "objs": [], + "objs": [ + "K0213008B" + ], "tags": [ "第二单元" ], @@ -138214,7 +138884,9 @@ "005745": { "id": "005745", "content": "当$a>1$时, 比较$\\log_ba$与$\\log_{2b}a$的大小.", - "objs": [], + "objs": [ + "K0213008B" + ], "tags": [ "第二单元" ], @@ -138235,7 +138907,9 @@ "005746": { "id": "005746", "content": "已知$\\log_ma>\\log_na$($a>1$), 讨论$m$与$n$的大小关系.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138256,7 +138930,9 @@ "005747": { "id": "005747", "content": "已知$\\log_{1+a}(1-a)<1$, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138277,7 +138953,9 @@ "005748": { "id": "005748", "content": "已知$|\\lg (1-a)|>|\\lg (1+a)|$, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138363,7 +139041,9 @@ "005752": { "id": "005752", "content": "解方程$9^{2x-1}=4^x$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -138384,7 +139064,9 @@ "005753": { "id": "005753", "content": "解方程$(\\dfrac 1{27})^x=9^{1-x}$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -138405,7 +139087,9 @@ "005754": { "id": "005754", "content": "解方程$9^x-2\\cdot 3^{x+1}-27=0$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -138428,7 +139112,9 @@ "005755": { "id": "005755", "content": "解方程$9^x+4^x=\\dfrac 52\\times 6^x$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -138451,7 +139137,10 @@ "005756": { "id": "005756", "content": "解方程$\\log_3(3^x-1)\\cdot \\log_3(3^{x-1}-\\dfrac 13)=2$.", - "objs": [], + "objs": [ + "K0211002B", + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138472,7 +139161,9 @@ "005757": { "id": "005757", "content": "已知关于$x$的方程$\\lg (kx)=2\\lg (x+1)$有且只有一个实数解, 求实数$k$的取值范围.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -138493,7 +139184,9 @@ "005758": { "id": "005758", "content": "若$2^{2x}+4=5\\times 2^x$, 则$x^2+1$等于\\bracket{20}.\n\\fourch{$1$}{$5$}{$5$或$1$}{$3$或$2$}", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -179950,13 +180643,13 @@ "solution": "", "duration": -1, "usages": [ + "20220821\t2023届高三02班\t1.000\t1.000", + "20220821\t2023届高三03班\t0.833\t0.917", + "20220821\t2023届高三09班\t0.839", "20220821\t2023届高三10班\t0.917\t0.875", "20220821\t2023届高三12班\t0.917", - "20220821\t2023届高三2班\t1.000\t1.000", - "20220821\t2023届高三3班\t0.833\t0.917", - "20220821\t2023届高三9班\t0.839", - "20220822\t2023届高三10班\t0.958\t0.917", - "20220822\t2023届高三8班\t0.839\t0.903" + "20220822\t2023届高三08班\t0.839\t0.903", + "20220822\t2023届高三10班\t0.958\t0.917" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -180154,13 +180847,13 @@ "solution": "", "duration": -1, "usages": [ + "20220821\t2023届高三02班\t0.879", + "20220821\t2023届高三03班\t0.792", + "20220821\t2023届高三09班\t0.677", "20220821\t2023届高三10班\t0.792", "20220821\t2023届高三12班\t0.542", - "20220821\t2023届高三2班\t0.879", - "20220821\t2023届高三3班\t0.792", - "20220821\t2023届高三9班\t0.677", - "20220822\t2023届高三10班\t0.667", - "20220822\t2023届高三8班\t0.613" + "20220822\t2023届高三08班\t0.613", + "20220822\t2023届高三10班\t0.667" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -180575,9 +181268,9 @@ "solution": "", "duration": -1, "usages": [ - "20220824\t2023届高三10班\t0.988", - "20220824\t2023届高三2班\t0.909", - "20220824\t2023届高三8班\t0.970" + "20220824\t2023届高三02班\t0.909", + "20220824\t2023届高三08班\t0.970", + "20220824\t2023届高三10班\t0.988" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -180814,8 +181507,8 @@ "duration": -1, "usages": [ "20220824\t2023届高三10班\t0.929", - "20220825\t2023届高三2班\t0.909\t1.000\t1.000", - "20220825\t2023届高三8班\t0.742\t0.935\t0.935" + "20220825\t2023届高三02班\t0.909\t1.000\t1.000", + "20220825\t2023届高三08班\t0.742\t0.935\t0.935" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -181223,8 +181916,8 @@ "duration": -1, "usages": [ "20220824\t2023届高三10班\t0.821", - "20220825\t2023届高三2班\t0.788", - "20220825\t2023届高三8班\t0.710" + "20220825\t2023届高三02班\t0.788", + "20220825\t2023届高三08班\t0.710" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -183019,22 +183712,22 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[\\dfrac 32,2)\\cup (2,\\dfrac 52]$", "solution": "", "duration": -1, "usages": [ + "20220914\t2023届高三01班\t0.909", + "20220914\t2023届高三02班\t0.774", + "20220914\t2023届高三03班\t0.839", + "20220914\t2023届高三04班\t0.875", + "20220914\t2023届高三05班\t0.795", + "20220914\t2023届高三06班\t0.780", + "20220914\t2023届高三07班\t0.909", + "20220914\t2023届高三08班\t0.781", + "20220914\t2023届高三09班\t0.765", "20220914\t2023届高三10班\t0.757", "20220914\t2023届高三11班\t0.913", - "20220914\t2023届高三12班\t0.885", - "20220914\t2023届高三1班\t0.909", - "20220914\t2023届高三2班\t0.774", - "20220914\t2023届高三3班\t0.839", - "20220914\t2023届高三4班\t0.875", - "20220914\t2023届高三5班\t0.795", - "20220914\t2023届高三6班\t0.780", - "20220914\t2023届高三7班\t0.909", - "20220914\t2023届高三8班\t0.781", - "20220914\t2023届高三9班\t0.765" + "20220914\t2023届高三12班\t0.885" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -183450,12 +184143,12 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$1760$元", "solution": "", "duration": -1, "usages": [ - "20220831\t2023届高三10班\t0.807", - "20220831\t2023届高三2班\t0.312" + "20220831\t2023届高三02班\t0.312", + "20220831\t2023届高三10班\t0.807" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -184676,7 +185369,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$S=\\begin{cases} 4t, & 0=latex]\n \\draw [->] (-0.2,0) -- (2.5,0) node [below] {$x$};\n \\draw [->] (0,-0.2) -- (0,2.5) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) -- (2,2);\n \\draw [dashed] (2,0) node [below] {$2$} -- (2,2) -- (0,2) node [left] {$2$};\n \\filldraw [fill = white, draw = black] (0,0) circle (0.05) (2,2) circle (0.05);\n \\end{tikzpicture}\n\\end{center}", - "objs": [], + "objs": [ + "K0216001B" + ], "tags": [ "第二单元" ], @@ -185012,7 +185707,9 @@ "007892": { "id": "007892", "content": "若函数$y=f(x)$的定义域为$\\mathbf{R}$, 则$y=f(x)$为奇函数的充要条件为\\bracket{20}.\n\\twoch{$f(0)=0$}{对任意$x\\in \\mathbf{R},f(x)=0$}{存在某个$x_0\\in \\mathbf{R}$, 使得$f(x_0)+f(-x_0)=0$}{对任意的$x\\in \\mathbf{R}$, $f(x)+f(-x)=0$都成立}", - "objs": [], + "objs": [ + "K0217004B" + ], "tags": [ "第二单元" ], @@ -185035,7 +185732,9 @@ "007893": { "id": "007893", "content": "求证函数$f(x)=x^{-3}$是奇函数.", - "objs": [], + "objs": [ + "K0217004B" + ], "tags": [ "第二单元" ], @@ -185056,7 +185755,9 @@ "007894": { "id": "007894", "content": "求证函数$f(x)=\\dfrac x{1-x^2}$是奇函数.", - "objs": [], + "objs": [ + "K0217004B" + ], "tags": [ "第二单元" ], @@ -185077,7 +185778,9 @@ "007895": { "id": "007895", "content": "判断函数$f(x)=2x+\\sqrt[3]x$的奇偶性.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -185100,7 +185803,9 @@ "007896": { "id": "007896", "content": "判断函数$f(x)=2x^4-x^2$的奇偶性.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -185123,7 +185828,9 @@ "007897": { "id": "007897", "content": "判断函数$f(x)=x^2-x$的奇偶性.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -185148,7 +185855,9 @@ "007898": { "id": "007898", "content": "判断函数$f(x)=\\dfrac{1-x}{1+x}$的奇偶性.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -185171,7 +185880,9 @@ "007899": { "id": "007899", "content": "已知函数$y=f(x)$的定义域为$[0,+\\infty)$.如果对任意的$x>0$, 都有$f(x)=latex]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2.7:2.7] plot (\\x,{pow(\\x,2)-2*abs(\\x)});\n\\end{tikzpicture}\n\\end{center}", "solution": "", "duration": -1, "usages": [ - "20220914\t2023届高三2班\t0.875" + "20220914\t2023届高三02班\t0.875" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -185462,7 +186200,11 @@ "007912": { "id": "007912", "content": "研究函数$f(x)=\\dfrac 1{1+x^2}$的定义域、奇偶性、单调性、最大值.", - "objs": [], + "objs": [ + "K0215003B", + "K0219003B", + "K0221001B" + ], "tags": [ "第二单元" ], @@ -185485,7 +186227,9 @@ "007913": { "id": "007913", "content": "已知函数$f(x)=|x-a|$, 且$f(1)=0$.\\\\\n(1) 求函数$y=f(x)$的解析式;\\\\\n(2) 比较$f(2)$与$f(-3)$的大小.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -185506,7 +186250,9 @@ "007914": { "id": "007914", "content": "已知函数$f(x)=x^2+ax+1,x\\in [b,2]$是偶函数, 求$a$、$b$的值.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -185527,7 +186273,9 @@ "007915": { "id": "007915", "content": "已知函数$f(x)$为偶函数, $g(x)$为奇函数, 且$f(x)+g(x)=x^2+2x+3$, 求$y=f(x)$、$y=g(x)$的解析式.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -185548,7 +186296,9 @@ "007916": { "id": "007916", "content": "已知$a\\ne 0$, 试讨论函数$f(x)=\\dfrac a{1-x^2}$在区间$(0,1)$上的单调性.", - "objs": [], + "objs": [ + "K0219003B" + ], "tags": [ "第二单元" ], @@ -185569,7 +186319,9 @@ "007917": { "id": "007917", "content": "已知$\\alpha,\\beta$是方程$4x^2-4mx+m+2=0$的两个实数根, 当$m$为何值时, $\\alpha ^2+\\beta ^2$有最小值? 并求出这个最小值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -185590,7 +186342,9 @@ "007918": { "id": "007918", "content": "求函数$y=x^2-4x+1$在$x\\in [t,4]$上的最小值和最大值, 其中$t<4$.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -185611,7 +186365,9 @@ "007919": { "id": "007919", "content": "已知集合$A=\\{x|1\\le x\\le 4\\}$, $f(x)=x^2+px+q$和$g(x)=x+\\dfrac 4x$是定义在$A$上的函数, 且在$x_0$处同时取到最小值, 并满足$f(x_0)=g(x_0)$, 求$f(x)$在$A$上的最大值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -185633,7 +186389,8 @@ "id": "007920", "content": "已知某气垫船的最大船速是$48$海里/时, 船每小时使用的燃料费用和船速的平方成正比, 若船速为$30$海里/时, 则船每小时的燃料费用为$600$元.其余费用(不论船速为多少)都是每小时$864$元.甲乙两地相距$100$海里, 船从甲地行驶到乙地.\\\\\n(1) 试把船每小时使用的燃料费用$P$(元)表示成船速$v$(海里/时)的函数;\\\\\n(2) 试把船从甲地到乙地所需的总费用$y$表示成船速$v$(海里/时)的函数;\\\\\n(3) 当船速为每小时多少海里时, 船从甲地到乙地所需的总费用最少?", "objs": [ - "K0222002B" + "K0222002B", + "K0222001B" ], "tags": [ "第二单元" @@ -185657,7 +186414,10 @@ "007921": { "id": "007921", "content": "已知函数$y=f(x)$, 定义$F(x)=f(x+1)-f(x)$.某公司每月最多生产$100$台报警系统装置, 生产$x$台$(x>0)$的收入函数为$R(x)=3000x-20x^2$(单位: 元), 其成本函数为$G(x)=5000x+4000$(单位: 元), 利润是收入与成本之差.\\\\\n(1) 求利润函数$y=f(x)$及相应的$y=F(x)$;\\\\\n(2) 利润函数$y=f(x)$与$y=F(x)$是否具有相等的最大值?", - "objs": [], + "objs": [ + "K0222001B", + "K0222002B" + ], "tags": [ "第二单元" ], @@ -185678,7 +186438,9 @@ "007922": { "id": "007922", "content": "求方程的近似解$x^2+2+\\dfrac 1x=0$(精确到$0.1$).", - "objs": [], + "objs": [ + "K0224002B" + ], "tags": [ "第二单元" ], @@ -185699,7 +186461,10 @@ "007923": { "id": "007923", "content": "研究函数$f(x)=x+\\dfrac ax(a>0)$的定义域、奇偶性、单调性.", - "objs": [], + "objs": [ + "K0215003B", + "K0219003B" + ], "tags": [ "第二单元" ], @@ -185720,7 +186485,9 @@ "007924": { "id": "007924", "content": "求函数$y=\\dfrac 1{2-x}+\\sqrt {x^2-1}$的定义域.", - "objs": [], + "objs": [ + "K0215003B" + ], "tags": [ "第二单元" ], @@ -185743,7 +186510,9 @@ "007925": { "id": "007925", "content": "判断函数$f(x)=|\\dfrac 12x-3|+|\\dfrac 12x+3|$的奇偶性.", - "objs": [], + "objs": [ + "K0217004B" + ], "tags": [ "第二单元" ], @@ -185764,7 +186533,9 @@ "007926": { "id": "007926", "content": "判断函数$f(x)=x^3+\\dfrac 2x$的奇偶性.", - "objs": [], + "objs": [ + "K0217004B" + ], "tags": [ "第二单元" ], @@ -185789,7 +186560,9 @@ "007927": { "id": "007927", "content": "判断函数$f(x)=x^2$, $x\\in (k,2)$的奇偶性.", - "objs": [], + "objs": [ + "K0217004B" + ], "tags": [ "第二单元" ], @@ -185812,7 +186585,9 @@ "007928": { "id": "007928", "content": "已知$y=f(x)$是奇函数, 定义域为$\\mathbf{R}$, $y=g(x)$是偶函数, 定义域为$D$. 设$F(x)=f(x)\\cdot g(x)$, 判断$y=F(x)$奇偶性.", - "objs": [], + "objs": [ + "K0217004B" + ], "tags": [ "第二单元" ], @@ -185833,7 +186608,9 @@ "007929": { "id": "007929", "content": "已知函数$f(x)=(m-1)x^2+3x+(2-n)$, 且此函数为奇函数, 求$m$、$n$的值.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -185854,7 +186631,9 @@ "007930": { "id": "007930", "content": "已知函数$f(x)=x$, $g(x)=-\\dfrac 4x$, $p(x)=f(x)-g(x)$, 求$y=p(x)$的函数表达式, 并写出$y=p(x)$的单调递减区间.", - "objs": [], + "objs": [ + "K0220002B" + ], "tags": [ "第二单元" ], @@ -185876,7 +186655,8 @@ "id": "007931", "content": "作出函数$y=|x^2-4x|$的图像, 并指出其单调区间.", "objs": [ - "K0220001B" + "K0220001B", + "K0220002B" ], "tags": [ "第二单元" @@ -185902,7 +186682,8 @@ "id": "007932", "content": "作出函数$y=2|x|-3$的图像, 并指出其单调区间.", "objs": [ - "K0220001B" + "K0220001B", + "K0220002B" ], "tags": [ "第二单元" @@ -185926,7 +186707,9 @@ "007933": { "id": "007933", "content": "设函数$f(x)=(a^2+4a-5)x^2-4(a-1)x+3$的图像都在$x$轴的上方, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -185947,7 +186730,9 @@ "007934": { "id": "007934", "content": "已知函数$f(x)=x^2+10x-a+3$, 当$x\\in [-2,+\\infty)$时, $f(x)\\ge 0$恒成立, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -185968,7 +186753,10 @@ "007935": { "id": "007935", "content": "设$\\alpha,\\beta$是二次方程$x^2-2kx+k+20=0$的两个实数根, 当$k$为何值时, $(\\alpha +1)^2+(\\beta +1)^2$有最小值?", - "objs": [], + "objs": [ + "K0109004B", + "K0221002B" + ], "tags": [ "第二单元" ], @@ -185989,7 +186777,9 @@ "007936": { "id": "007936", "content": "已知$f(x)=x^2+ax+1$, 若对任意的实数$x$, 均有$f(2+x)=f(2-x)$恒成立, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0109002B" + ], "tags": [ "第二单元" ], @@ -186010,7 +186800,10 @@ "007937": { "id": "007937", "content": "已知二次函数$f(x)=ax^2-2ax+3-a$($a>0$), 比较$f(-1)$和$f(2)$的大小.", - "objs": [], + "objs": [ + "K0111003B", + "K0220001B" + ], "tags": [ "第二单元" ], @@ -186031,7 +186824,10 @@ "007938": { "id": "007938", "content": "已知函数$f(x)=-x^2+2ax+1-a$在$[0,1]$上有最大值$2$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0221001B", + "K0221002B" + ], "tags": [ "第二单元" ], @@ -186053,17 +186849,19 @@ "id": "007939", "content": "已知$y=f(x)$是定义在$(-1,1)$上的奇函数, 在区间$[0,1)$上是严格减函数, 且$f(1-a)+f(1-a^2)<0$, 求实数$a$的取值范围.", "objs": [ - "K0220003B" + "K0220003B", + "K0217003B", + "K0219001B" ], "tags": [ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(0,1)$", "solution": "", "duration": -1, "usages": [ - "20220914\t2023届高三2班\t0.656" + "20220914\t2023届高三02班\t0.656" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -186079,7 +186877,10 @@ "007940": { "id": "007940", "content": "已知函数$f(x)=2-x^2$, 函数$g(x)=x$, 定义函数$F(x)$如下: 当$f(x)\\ge g(x)$时, $F(x)=g(x)$; 当$f(x)=latex]\n \\draw [->] (-0.5,0) -- (2.5,0) node [below] {$t$};\n \\draw [->] (0,-0.5) -- (0,2.5) node [left] {$h$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) -- (2,2);\n \\draw (1,-0.5) node [below] {(a)};\n \\end{tikzpicture}\n \\begin{tikzpicture}[>=latex]\n \\draw [->] (-0.5,0) -- (2.5,0) node [below] {$t$};\n \\draw [->] (0,-0.5) -- (0,2.5) node [left] {$h$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) -- (1.5,1.5) -- (2,1.5);\n \\draw (1,-0.5) node [below] {(b)};\n \\end{tikzpicture}\n \\begin{tikzpicture}[>=latex]\n \\draw [->] (-0.5,0) -- (2.5,0) node [below] {$t$};\n \\draw [->] (0,-0.5) -- (0,2.5) node [left] {$h$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) arc (180:90:0.5 and 1.5) -- (2,1.5);\n \\draw (1,-0.5) node [below] {(c)};\n \\end{tikzpicture}\n \\begin{tikzpicture}[>=latex]\n \\draw [->] (-0.5,0) -- (2.5,0) node [below] {$t$};\n \\draw [->] (0,-0.5) -- (0,2.5) node [left] {$h$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) arc (270:360:0.5 and 1.5) -- (2,1.5);\n \\draw (1,-0.5) node [below] {(d)};\n \\end{tikzpicture}\n\\end{center}\n(2) 下列是两个杯子相应函数$h=f(t)$的图像, 试说明这两个杯子形状有何差别.\n\\begin{center}\n \\begin{tikzpicture}[>=latex]\n \\draw [->] (-0.5,0) -- (2.5,0) node [below] {$t$};\n \\draw [->] (0,-0.5) -- (0,2.5) node [left] {$h$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) -- (0.5,1.5) -- (2,1.5);\n \\draw (1,-0.5) node [below] {(e)};\n \\end{tikzpicture}\n \\begin{tikzpicture}[>=latex]\n \\draw [->] (-0.5,0) -- (2.5,0) node [below] {$t$};\n \\draw [->] (0,-0.5) -- (0,2.5) node [left] {$h$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) -- (1.5,1.5) -- (2,1.5);\n \\draw (1,-0.5) node [below] {(f)};\n \\end{tikzpicture}\n\\end{center}", "objs": [ "K0216002B", - "K0216003B" + "K0216003B", + "K0215001B" ], "tags": [ "第二单元" @@ -186149,7 +186951,9 @@ "007943": { "id": "007943", "content": "已知幂函数$f(x)$的图像经过$(2,\\dfrac{\\sqrt 2}2)$, 试求出这个函数的解析式.", - "objs": [], + "objs": [ + "K0207001B" + ], "tags": [ "第二单元" ], @@ -186170,7 +186974,10 @@ "007944": { "id": "007944", "content": "幂函数$y=x^s$与$y=x^t$的图像在第一象限都通过定点\\blank{50}, 若它们在第一象限的部分关于直线$y=x$对称, 则$s$、$t$应满足的条件是\\blank{50}.", - "objs": [], + "objs": [ + "K0208003B", + "K0226004B" + ], "tags": [ "第二单元" ], @@ -186191,7 +186998,10 @@ "007945": { "id": "007945", "content": "研究幂函数$f(x)=x^{\\frac 25}$的定义域、奇偶性、单调性、值域.", - "objs": [], + "objs": [ + "K0207002B", + "K0215001B" + ], "tags": [ "第二单元" ], @@ -186212,7 +187022,9 @@ "007946": { "id": "007946", "content": "作函数$y=\\dfrac{|x|+1}{|x+1|}$的大致图像.", - "objs": [], + "objs": [ + "K0208005B" + ], "tags": [ "第二单元" ], @@ -186235,7 +187047,10 @@ "007947": { "id": "007947", "content": "已知函数$f(x)=x^3-3x$.\\\\\n(1) 试求函数$y=f(x)$的零点;\\\\\n(2) 求证: 函数$f(x)=x^3-3x$在$[1,+\\infty)$上是增函数;\\\\\n(3) 是否存在自然数$n$, 使$f(n)=1000$? 若存在, 求出一个满足条件的$n$; 若不存在, 请问明理由.", - "objs": [], + "objs": [ + "K0219003B", + "K0223004B" + ], "tags": [ "第二单元" ], @@ -186256,7 +187071,9 @@ "007948": { "id": "007948", "content": "在下列函数中, 哪一个既是奇函数, 又在区间$(+\\infty ,0)$内是减函数?\\\\ \n\\textcircled{1} $y=x^{\\frac 12}$; \\textcircled{2} $y=x^{\\frac 13}$; \\textcircled{3} $y=x^{\\frac 23}$; \\textcircled{4} $y=x^{-\\frac 13}$.", - "objs": [], + "objs": [ + "K0207001B" + ], "tags": [ "第二单元" ], @@ -186278,7 +187095,9 @@ "id": "007949", "content": "已知幂函数$f(x)$的定义域是$(+\\infty ,0)\\cup (0,+\\infty)$, 且它的图像关于$y$轴对称, 写出一个满足要求的幂函数$f(x)$.", "objs": [ - "K0217001B" + "K0217001B", + "K0207001B", + "K0207004B" ], "tags": [ "第二单元" @@ -186307,11 +187126,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "存在, 如$a=0$(小于$\\dfrac 12$的整数都可以)", "solution": "", "duration": -1, "usages": [ - "20220914\t2023届高三2班\t0.750" + "20220914\t2023届高三02班\t0.750" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -186325,7 +187144,9 @@ "007951": { "id": "007951", "content": "比较$3^{0.8},3^{0.7}$两个值的大小.", - "objs": [], + "objs": [ + "K0210006B" + ], "tags": [ "第二单元" ], @@ -186346,7 +187167,9 @@ "007952": { "id": "007952", "content": "比较$0.75^{0.1},0.75^{-0.1}$两个值的大小.", - "objs": [], + "objs": [ + "K0210006B" + ], "tags": [ "第二单元" ], @@ -186367,7 +187190,9 @@ "007953": { "id": "007953", "content": "设$a^{2x}=2$, 且$a>0$, $a\\ne 1$, 求$\\dfrac{a^{3x}+a^{-3x}}{a^x+a^{-x}}$的值.", - "objs": [], + "objs": [ + "K0203005B" + ], "tags": [ "第二单元" ], @@ -186391,7 +187216,9 @@ "007954": { "id": "007954", "content": "已知$f(x)=a\\cdot b^x$, $f(4)=648$, $f(5)=1944$.\\\\\n(1) 估算$f(4.5)$;\\\\\n(2) 计算$f(4.5)$, 利用计算的结果评判你的估算.", - "objs": [], + "objs": [ + "K0203005B" + ], "tags": [ "第二单元" ], @@ -186412,7 +187239,9 @@ "007955": { "id": "007955", "content": "已知$f(x)=3^x$, $u,v\\in \\mathbf{R}$.\\\\\n(1) 求证: 对任意的$u$、$v$, 都有$f(u)\\cdot f(v)=f(u+v)$成立.\\\\\n(2) 写出一个关于$f(u)\\div f(v)$类似上式的等式, 并证明你的结论.", - "objs": [], + "objs": [ + "K0203005B" + ], "tags": [ "第二单元" ], @@ -186433,7 +187262,9 @@ "007956": { "id": "007956", "content": "求证: $f(x)=\\dfrac{a^x-a^{-x}}2$($a>0$, $a\\ne 1$)是奇函数.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -186454,7 +187285,9 @@ "007957": { "id": "007957", "content": "求证: $f(x)=\\dfrac{(a^x-1)\\cdot x}{a^x+1}$($a>0$, $a\\ne 1$)是偶函数.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -186475,7 +187308,9 @@ "007958": { "id": "007958", "content": "若指数函数$y=a^x$是减函数, 则下列不等式中, 能够成立的是\\bracket{20}.\n\\fourch{$a>1$}{$a<1$}{$a(a-1)<0$}{$a(a-1)>0$}", - "objs": [], + "objs": [ + "K0211001B" + ], "tags": [ "第二单元" ], @@ -186496,27 +187331,29 @@ "007959": { "id": "007959", "content": "若函数$y=2^x-m$的图像不经过第二象限, 则$m$的取值范围是\\bracket{20}.\n\\fourch{$m\\ge 1$}{$m<1$}{$m>-1$}{$m\\le -1$}", - "objs": [], + "objs": [ + "K0211001B" + ], "tags": [ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ + "20220914\t2023届高三01班\t0.970", + "20220914\t2023届高三02班\t0.903", + "20220914\t2023届高三03班\t0.968", + "20220914\t2023届高三04班\t0.969", + "20220914\t2023届高三05班\t0.974", + "20220914\t2023届高三06班\t1.000", + "20220914\t2023届高三07班\t0.939", + "20220914\t2023届高三08班\t1.000", + "20220914\t2023届高三09班\t0.971", "20220914\t2023届高三10班\t0.973", "20220914\t2023届高三11班\t0.957", - "20220914\t2023届高三12班\t0.962", - "20220914\t2023届高三1班\t0.970", - "20220914\t2023届高三2班\t0.903", - "20220914\t2023届高三3班\t0.968", - "20220914\t2023届高三4班\t0.969", - "20220914\t2023届高三5班\t0.974", - "20220914\t2023届高三6班\t1.000", - "20220914\t2023届高三7班\t0.939", - "20220914\t2023届高三8班\t1.000", - "20220914\t2023届高三9班\t0.971" + "20220914\t2023届高三12班\t0.962" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -186530,7 +187367,9 @@ "007960": { "id": "007960", "content": "某地区的中小学$2003$年、$2004$年共购置电脑$100$台, 为了加快中小学的电脑普及程度, 准备新购置的电脑数按每两年递增$10\\%$的比例增长, 从$2005$年至$2010$年, 该地区中小学新购置的电脑总数是多少?", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -186551,7 +187390,9 @@ "007961": { "id": "007961", "content": "已知集合$M=\\{y|y=2^x,\\ x\\in \\mathbf{R}\\}$, 集合$N=\\{y|y=x^2,\\ x\\in \\mathbf{R}\\}$, 求$M\\cap N$.", - "objs": [], + "objs": [ + "K0210005B" + ], "tags": [ "第二单元" ], @@ -186572,7 +187413,9 @@ "007962": { "id": "007962", "content": "作函数$y=2^{|x|}$的大致图像.", - "objs": [], + "objs": [ + "K0210005B" + ], "tags": [ "第二单元" ], @@ -186596,7 +187439,9 @@ "007963": { "id": "007963", "content": "作函数$y=2^{-|x|}$的大致图像.", - "objs": [], + "objs": [ + "K0210005B" + ], "tags": [ "第二单元" ], @@ -186620,7 +187465,9 @@ "007964": { "id": "007964", "content": "判断并证明函数$y=\\dfrac{10^x-10^{-x}}{10^x+10^{-x}}$的奇偶性.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -186641,7 +187488,9 @@ "007965": { "id": "007965", "content": "判断并证明函数$y=x(\\dfrac 1{2^x-1}+\\dfrac 12)$的奇偶性.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -186662,7 +187511,9 @@ "007966": { "id": "007966", "content": "函数$y=4^x-2^{x+1}+1(x<0)$的值域是\\bracket{20}.\n\\fourch{$[0,+\\infty)$}{$(1,+\\infty)$}{$(0,1)$}{$(0,1]$}", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -186683,7 +187534,9 @@ "007967": { "id": "007967", "content": "填写下表, 比较$f(x)=3x$和$g(x)=x^3$函数值递增的快慢.\n\\begin{center}\n \\begin{tabular}{|p{.1\\textwidth}<{\\centering}|p{.2\\textwidth}<{\\centering}|p{.2\\textwidth}<{\\centering}|p{.2\\textwidth}<{\\centering}|p{.2\\textwidth}<{\\centering}|}\n \\hline\n $x$ & $f(x)=3x$ & 增加量$f(x)-f(x-1)$ & $g(x)=x^3$ & 增加量$g(x)-g(x-1)$ \\\\ \\hline\n $0$ & & $\\slash$ & & $\\slash$ \\\\ \\hline\n $1$ & & & & \\\\ \\hline\n $2$ & & & & \\\\ \\hline\n $3$ & & & & \\\\ \\hline\n $4$ & & & & \\\\ \\hline\n $5$ & & & & \\\\ \\hline\n \\end{tabular}\n\\end{center}", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -186704,7 +187557,9 @@ "007968": { "id": "007968", "content": "试比较$f(x)=x^2$和$g(x)=x^3$在$x\\in (0,1)$时, 函数值递增的快慢程度.", - "objs": [], + "objs": [ + "K0207003B" + ], "tags": [ "第二单元" ], @@ -186727,7 +187582,9 @@ "007969": { "id": "007969", "content": "试比较$f(x)=x^2$和$g(x)=2x$在$x\\in [0, +\\infty)$时, 函数值递增的快慢程度.", - "objs": [], + "objs": [ + "K0207003B" + ], "tags": [ "第二单元" ], @@ -186750,7 +187607,10 @@ "007970": { "id": "007970", "content": "$A$国现有人口$3500$万, 年粮食产量$800$万吨. 根据历年的资料统计, $A$国人口的平均年增长率为$2\\%$, 每人平均每年消耗粮食$200$千克. 假定他们国家既不出口粮食, 也不进口粮食.\\\\\n(1) 预测多少年后, $A$国会出现粮食短缺的情况;\\\\\n(2) 如果$A$国的粮食每年增产$10$万吨, 还会出现粮食短缺的情况吗? 如果会, 约在多少年以后?\\\\\n(3)如果从现在开始, $A$国的粮食每年增产$10$万吨, 同时将人口的年增长率控制在$1\\%$, 还会出现粮食短缺的情况吗? 如果会, 约在多少年以后?", - "objs": [], + "objs": [ + "K0222001B", + "K0222002B" + ], "tags": [ "第二单元" ], @@ -186771,7 +187631,10 @@ "007971": { "id": "007971", "content": "幂函数$y=f(x)$, 当$x=2$时, $y=16$.\\\\\n(1)求函数$f(x)$的解析式;\\\\\n(2)比较$f(2)$和$f(-3)$的大小.", - "objs": [], + "objs": [ + "K0215001B", + "K0207001B" + ], "tags": [ "第二单元" ], @@ -186792,7 +187655,9 @@ "007972": { "id": "007972", "content": "若关于$x$的方程$5^x=\\dfrac{a+3}{5-a}$有负数根, 则$a$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0210005B" + ], "tags": [ "第二单元" ], @@ -186815,7 +187680,10 @@ "007973": { "id": "007973", "content": "方程$(\\dfrac 12)^x=x^{\\frac 12}$的实数根个数为\\blank{50}.", - "objs": [], + "objs": [ + "K0210005B", + "K0208002B" + ], "tags": [ "第二单元" ], @@ -186836,7 +187704,10 @@ "007974": { "id": "007974", "content": "设在海拔$x$米处的大气压强是$y$帕, $y$与$x$之间的函数关系式是$y=c\\cdot \\mathrm{e}^{k\\tau}$, 其中$c$、$k$是常量.已知某地某天在海平面的大气压强为$1.01\\times 10^5$帕, $1000$米高空的大气压强为$0.90\\times 10^5$帕, 求$600$米高空的大气压强.(结果保留$3$位有效数字)", - "objs": [], + "objs": [ + "K0222001B", + "K0222002B" + ], "tags": [ "第二单元" ], @@ -186859,7 +187730,10 @@ "007975": { "id": "007975", "content": "$2005$年$1$月$6$日, 我国人口总数为$13$亿, 称该天为``中国人口$13$亿日'', 如果$2005$年$1$月$6$日后我国人口的年自然增长率保持在$0.6\\%$, 问到哪一年我国人口总数将超过$14$亿?", - "objs": [], + "objs": [ + "K0222001B", + "K0222002B" + ], "tags": [ "第二单元" ], @@ -186880,7 +187754,10 @@ "007976": { "id": "007976", "content": "当$x$充分大时, 试比较下列各函数: $y_1=10x,y_2=8x^2,y_3=4x^4,y_4=2\\times 3^x,y_5=5^x$值的大小.你能从中归纳出一些规律性的结论吗?", - "objs": [], + "objs": [ + "K0208004B", + "K0210006B" + ], "tags": [ "第二单元" ], @@ -186901,7 +187778,9 @@ "007977": { "id": "007977", "content": "比较$a^2$和$a^a$两个值的大小(其中$a>0$, 且$a\\ne 1$).", - "objs": [], + "objs": [ + "K0210006B" + ], "tags": [ "第二单元" ], @@ -186924,7 +187803,9 @@ "007978": { "id": "007978", "content": "比较$2^a$和$a^a$两个值的大小(其中$a>0$, 且$a\\ne 1$).", - "objs": [], + "objs": [ + "K0208004B" + ], "tags": [ "第二单元" ], @@ -186947,7 +187828,10 @@ "007979": { "id": "007979", "content": "把物体放在温度为$\\theta_0^\\circ\\text{C}$的空气中冷却, 若物体原来的温度是$\\theta _0^\\circ\\text{C}$($\\theta _1>\\theta _0$), $t$分钟后物体温度$\\theta _0^\\circ\\text{C}$可由公式$\\theta =\\theta _0+(\\theta _1-\\theta _0)\\mathrm{e}^{-kt}$求得, 其中$k$是一个随着物体与空气的接触状况而定的常量, 现有$62^\\circ\\text{C}$的物体, 放在$15^\\circ\\text{C}$的空气中冷却$1$分钟以后物体的温度是$52^\\circ\\text{C}$, 求上式中$k$的值(精确到$0.01$). 开始冷却$2$分钟后物体的温度是多少? 开始冷却$10$分钟后, 物体的温度是多少? (精确到$1^\\circ\\text{C}$).", - "objs": [], + "objs": [ + "K0222001B", + "K0222002B" + ], "tags": [ "第二单元" ], @@ -186968,7 +187852,9 @@ "007980": { "id": "007980", "content": "若集合$A=\\{y|y=x^2+2c+3\\}$, 集合$B=\\{y|y=x+\\dfrac 4x\\}$, 则$A\\cup B=$\\blank{50}.", - "objs": [], + "objs": [ + "K0215005B" + ], "tags": [ "第二单元" ], @@ -186989,7 +187875,9 @@ "007981": { "id": "007981", "content": "已知$x,y\\in \\mathbf{R}$, 集合$\\alpha =\\{(x,y)|xy\\ge 0\\}$, 集合$\\beta =\\{(x,y)||x+y|=|x|+|y|\\}$, 用推出关系表示$\\alpha$与$\\beta$的关系\\blank{50}.", - "objs": [], + "objs": [ + "K0105002B" + ], "tags": [ "第二单元" ], @@ -187010,7 +187898,9 @@ "007982": { "id": "007982", "content": "若函数$f(x)=3x+1$的定义域为$\\{1,3,k\\}$.值域为$\\{4,a^4,a^2+3a\\}$, 且$a$、$k$为自然数, 则$a+k=$\\blank{50}.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -187031,7 +187921,9 @@ "007983": { "id": "007983", "content": "已知函数$f(x)=\\begin{cases} -2^x-1, & x\\le 0, \\\\x^{\\frac 12}, & x>0. \\end{cases}$若$f(x_0)=1$, 则$x_0$的值为\\blank{50}.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -187056,17 +187948,18 @@ "id": "007984", "content": "下列图形中, 能作为某个函数的图像的只能是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex]\n \\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n \\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (1,0) node [below right] {$1$} (-1,0) node [below left] {$-1$} (0,1) node [above left] {$1$} (0,-1) node [below left] {$-1$};\n \\draw (0,0) circle (1);\n\\end{tikzpicture}\n}{\\begin{tikzpicture}[>=latex]\n \\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n \\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (1,0) node [below right] {$1$} (0,1) node [above left] {$1$} (0,-1) node [below left] {$-1$};\n \\draw (0,1) arc (90:-90:1);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n \\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n \\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (1,0) node [below right] {$1$} (0,1) node [above left] {$1$} (0,-1) node [below left] {$-1$} (-1,0) node [below left] {$-1$};\n \\draw (0,1) arc (90:0:1) (0,-1) arc (270:180:1);\n \\filldraw [fill = white, draw = black] (0,1) circle (0.05) (0,-1) circle (0.05);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n \\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n \\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (1,0) node [below right] {$1$} (0,1) node [above left] {$1$} (0,-1) node [below left] {$-1$} (-1,0) node [below left] {$-1$};\n \\draw (0,1) arc (90:180:1) (0,-1) arc (270:360:1);\n \\filldraw (0,1) circle (0.05) (0,-1) circle (0.05) (1,0) circle (0.05) (-1,0) circle (0.05);\n\\end{tikzpicture}}", "objs": [ - "K0216004B" + "K0216004B", + "K0215001B" ], "tags": [ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t1.000" + "20220907\t2023届高三02班\t1.000" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -187134,7 +188027,9 @@ "007987": { "id": "007987", "content": "点$(\\sqrt 2,2)$在幂函数$y=f(x)$的图像上, 点$(-2,\\dfrac 14)$在幂函数$y=g(x)$的图像上.当$x$为何值时, $f(x)=g(x)$?", - "objs": [], + "objs": [ + "K0207001B" + ], "tags": [ "第二单元" ], @@ -187180,7 +188075,9 @@ "007989": { "id": "007989", "content": "已知函数$f(x)=a^x(a>0,a\\ne 1)$在区间$[1,2]$上的最大值比最小值大$\\dfrac 14$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -187237,7 +188134,7 @@ "solution": "", "duration": -1, "usages": [ - "20220906\t2023届高三2班\t0.581" + "20220906\t2023届高三02班\t0.581" ], "origin": "二期课改练习册高一第一学期", "edit": [ @@ -187253,7 +188150,9 @@ "007992": { "id": "007992", "content": "某地区某日海拔高度与气温的对照表为:\n\\begin{center}\n \\begin{tabular}{|c|c|c|c|c|}\n \\hline\n 高度$h$(米)\t& $0$ & $500$ & $1000$ & $2000$\\\\ \\hline\n 气温$t$($^\\circ\\text{C}$) &\t$15.00$ & $11.75$ & $8.50$ & $2.00$ \\\\ \\hline\n \\end{tabular}\n\\end{center}\n(1) 根据表中$t$与$h$的对应关系, 写出$t$关于$h$的函数解析式;\\\\\n(2) 根据(1)的结论, 求海拔高度$1500$米处的气温.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -187274,7 +188173,11 @@ "007993": { "id": "007993", "content": "已知函数$f(x)=ax^2+\\dfrac b{x^2}$($a$、$b$是正常数).\n(1) 列出所具有的基本性质, 并加以说明;\\\\\n(2) 当$a=\\dfrac 14,b=4$时, 画出函数$y=f(x)$的简图.", - "objs": [], + "objs": [ + "K0215001B", + "K0216002B", + "K0218001B" + ], "tags": [ "第二单元" ], @@ -187295,7 +188198,9 @@ "007994": { "id": "007994", "content": "若$2x+y=1$, 求$4^x+2^y$的最小值.", - "objs": [], + "objs": [ + "K0119001B" + ], "tags": [ "第二单元" ], @@ -187367,7 +188272,10 @@ "007997": { "id": "007997", "content": "试讨论函数$f(x)=\\dfrac x{1-x^2}$在区间$(-1,1)$上的单调性.", - "objs": [], + "objs": [ + "K0219003B", + "K0220001B" + ], "tags": [ "第二单元" ], @@ -187388,7 +188296,10 @@ "007998": { "id": "007998", "content": "甲乙两地的高速公路全长$166$千米, 在高速公路上最高行驶时速不得高于$120$千米/时, 假设汽车从甲地进入该高速公路以不低于$70$千米/时的速度匀速行驶到乙地, 已知汽车每小时的运输成本(以元为单位)由可变部分和固定部分组成: 可变部分与速度$v$(千米/时)的平方成正比, 比例系数为$0.02$; 固定部分为$220$元.\\\\\n(1) 把全程运输成本$y$(元)表示为速度$v$(千米/时)的函数, 并指出这个函数的定义域;\\\\\n(2) 汽车应以多大速度行驶才能使全程运输成本最小? 最小运输成本约为多少元?", - "objs": [], + "objs": [ + "K0215001B", + "K0221002B" + ], "tags": [ "第二单元" ], @@ -187410,7 +188321,8 @@ "id": "007999", "content": "某居民小区供水站的蓄水池现有水$40$吨, 自来水厂每小时可向蓄水池中注水$8$吨, 同时蓄水池又向居民小区供水, $t$小时内供水总量为$32\\sqrt t$吨.现在开始向池中注水并同时向居民小区供水, 若蓄水池中存水量少于$10$吨, 就会出现供水紧张现象.\\\\\n(1) 试建立蓄水池中存水量$S$与供水时间$t$之间的函数关系;\\\\\n(2) 供水多少时间开始出现供水紧张? 这一天内供水紧张的有几小时?", "objs": [ - "K0222002B" + "K0222002B", + "K0215001B" ], "tags": [ "第二单元" @@ -187432,7 +188344,9 @@ "008000": { "id": "008000", "content": "把下列指数式写成对数式:\\\\\n(1) $10^{-2}=0.01$:\\blank{50};\\\\\n(2) $(\\dfrac 12)^0=1$:\\blank{50};\\\\\n(3) $5^x=6$:\\blank{50}.", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -187453,7 +188367,9 @@ "008001": { "id": "008001", "content": "把下列对数式写成指数式:\\\\\n(1) $x=\\log _{16}32$:\\blank{50};\\\\\n(2) $\\log _{\\pi }x=4$:\\blank{50};\\\\\n(3) $\\log _x9=2$:\\blank{50}.", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -187474,7 +188390,9 @@ "008002": { "id": "008002", "content": "求下列各式中的$x$:\\\\\n(1) $\\log _{\\frac 12}x=3$, $x=$\\blank{50};\\\\\n(2) $\\log _3\\dfrac 1{27}=x$, $x=$\\blank{50};\\\\\n(3) $\\log _{100}1000=x$, $x=$\\blank{50};\\\\\n(4) $\\log _x16=4$, $x=$\\blank{50}.", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -187537,7 +188455,9 @@ "008005": { "id": "008005", "content": "计算: $\\log _{12}6+\\log _{12}2$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187560,7 +188480,9 @@ "008006": { "id": "008006", "content": "计算: $\\log _348-4\\log _32$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187581,7 +188503,9 @@ "008007": { "id": "008007", "content": "用$\\log _aM$、$\\log _aN$表示$\\log _aMN^2$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187604,7 +188528,9 @@ "008008": { "id": "008008", "content": "用$\\log _aM$、$\\log _aN$表示$\\log _a\\dfrac{\\sqrt M}N$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187627,7 +188553,9 @@ "008009": { "id": "008009", "content": "计算: $3^{\\log _31}+\\log _248-\\log _23$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187648,7 +188576,9 @@ "008010": { "id": "008010", "content": "计算: $2\\log _7\\dfrac{35}9+4\\log _73+2\\log _7\\dfrac 1{10}+\\log _74$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187669,7 +188599,9 @@ "008011": { "id": "008011", "content": "计算: $\\log _32\\times \\log _53\\times \\log _85$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -187690,7 +188622,9 @@ "008012": { "id": "008012", "content": "计算: $(\\log _43+\\log _83)\\times \\log _32$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -187713,7 +188647,9 @@ "008013": { "id": "008013", "content": "计算: $\\log _2\\dfrac 1{49}\\times \\log _3\\dfrac 1{16}\\times \\log _7\\dfrac 1{27}$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -187734,7 +188670,9 @@ "008014": { "id": "008014", "content": "计算: $\\log _ab\\cdot \\log _bc\\cdot \\log _ca$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -187755,7 +188693,9 @@ "008015": { "id": "008015", "content": "计算: $(\\log _43+\\log _83)(\\log _32+\\log _94)$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -187778,7 +188718,10 @@ "008016": { "id": "008016", "content": "已知$\\log _32=m$, 试用$m$表示$\\log _{32}18$.", - "objs": [], + "objs": [ + "K0206002B", + "K0206003B" + ], "tags": [ "第二单元" ], @@ -187801,7 +188744,10 @@ "008017": { "id": "008017", "content": "已知$\\lg 2=a$, $\\lg 3=b$.\\\\\n(1) 求$\\lg 5$;\\\\\n(2) 求$\\log _23$;\\\\\n(3) 求$\\log _{12}25$.", - "objs": [], + "objs": [ + "K0206002B", + "K0206003B" + ], "tags": [ "第二单元" ], @@ -187822,7 +188768,9 @@ "008018": { "id": "008018", "content": "求出下列各式中$x$的取值范围: ($a>0$且$a\\ne 1$)\\\\\n(1) $\\log _a(x^2+1)$;\\\\\n(2) $\\log _a(x-2)$;\\\\\n(3) $\\log _a\\dfrac 1{x+2}$.", - "objs": [], + "objs": [ + "K0212001B" + ], "tags": [ "第二单元" ], @@ -187843,7 +188791,10 @@ "008019": { "id": "008019", "content": "在下列各式中的横线上填入适当的值, 使等式成立:\\\\\n(1) $\\log _5$\\blank{20}$=1$;\\\\\n(2) $2^{\\log _31}=$\\blank{20};\\\\\n(3) $(\\dfrac 15)^{\\log _{0.2}3}=$\\blank{20};\\\\\n(4) $\\sqrt 3^{\\log _{\\sqrt 3}}$\\blank{20}$=7$.", - "objs": [], + "objs": [ + "K0204001B", + "K0204002B" + ], "tags": [ "第二单元" ], @@ -187864,7 +188815,11 @@ "008020": { "id": "008020", "content": "用$\\log _ax$、$\\log _ay$、$\\log _a(x+y)$、$\\log _a(x-y)$表示下列各式:\\\\\n(1) $\\log _a(x^2-y^2)$;\\\\\n(2) $\\log _4\\dfrac{x^3y}{(x+y)^4}$;\\\\\n(3) $\\log _a(\\dfrac{\\sqrt x}{\\sqrt y}-\\dfrac{\\sqrt y}{\\sqrt x})$.", - "objs": [], + "objs": [ + "K0204001B", + "K0204002B", + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187885,7 +188840,10 @@ "008021": { "id": "008021", "content": "计算: $\\log _2(\\log _216)$.", - "objs": [], + "objs": [ + "K0204001B", + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187908,7 +188866,9 @@ "008022": { "id": "008022", "content": "计算: $2^{\\log _65}\\times 3^{\\log _65}$.", - "objs": [], + "objs": [ + "K0204002B" + ], "tags": [ "第二单元" ], @@ -187929,7 +188889,9 @@ "008023": { "id": "008023", "content": "计算: $\\sqrt {\\lg^25-2\\lg 5+1}$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187950,7 +188912,9 @@ "008024": { "id": "008024", "content": "计算: $\\lg ^25+\\lg ^2\\times \\lg 50$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -187971,7 +188935,10 @@ "008025": { "id": "008025", "content": "设$56^a=14$, 试用$a$表示$\\log _756$.", - "objs": [], + "objs": [ + "K0205002B", + "K0206002B" + ], "tags": [ "第二单元" ], @@ -187992,7 +188959,10 @@ "008026": { "id": "008026", "content": "已知$5.4^x=3$, $0.6^y=3$, 求$\\dfrac 1x-\\dfrac 1y$的值.", - "objs": [], + "objs": [ + "K0204001B", + "K0205002B" + ], "tags": [ "第二单元" ], @@ -188015,7 +188985,10 @@ "008027": { "id": "008027", "content": "已知函数$f(x)=x^2-4x-5$, $x\\in [1,3]$, 判断其是否存在反函数. 若存在, 求出反函数; 若不存在, 说明理由.", - "objs": [], + "objs": [ + "K0225001B", + "K0225002B" + ], "tags": [ "第二单元" ], @@ -188038,7 +189011,9 @@ "008028": { "id": "008028", "content": "求函数$y=-x^3$的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -188059,7 +189034,9 @@ "008029": { "id": "008029", "content": "求函数$y-\\dfrac x{x+2}$的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -188080,7 +189057,9 @@ "008030": { "id": "008030", "content": "求函数$y=x^2+1$($x<0$)的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -188103,7 +189082,9 @@ "008031": { "id": "008031", "content": "已知$f(x)=1-x^2$($x<-1$), 求$f^{-1}(-3)$的值.", - "objs": [], + "objs": [ + "K0225004B" + ], "tags": [ "第二单元" ], @@ -188126,7 +189107,9 @@ "008032": { "id": "008032", "content": "已知函数$y=\\dfrac a{x+1}$的反函数的图像经过点$(\\dfrac 12,1)$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -188149,7 +189132,9 @@ "008033": { "id": "008033", "content": "已知函数$y=f(x)$的图像与函数$y=\\dfrac{x-1}{x+1}$的图像关于直线$y=x$对称, 求函数$y=f(x)$的解析式.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -188170,7 +189155,10 @@ "008034": { "id": "008034", "content": "判断题: (正确的在括号内用``$\\checkmark$''表示, 错误的用``$\\times$''表示)\\\\\n(1) 存在反函数的函数一定是单调函数.\\blank{20};\\\\\n(2) 偶函数存在反函数.\\blank{20};\\\\\n(3) 奇函数必存在反函数.\\blank{20}.", - "objs": [], + "objs": [ + "K0225001B", + "K0225002B" + ], "tags": [ "第二单元" ], @@ -188191,7 +189179,10 @@ "008035": { "id": "008035", "content": "一次函数$y=-x$的图像与它的反函数的图像重合. 试写出一个非一次函数的函数, 使它的图像与其反函数的图像重合.", - "objs": [], + "objs": [ + "K0225001B", + "K0226005B" + ], "tags": [ "第二单元" ], @@ -188212,7 +189203,9 @@ "008036": { "id": "008036", "content": "如果函数$y=f(x)$的图像过点$(0, 1)$, 那么函数$y=f^{-1}(x)+2$的反函数的图像过点\\bracket{20}.\n\\fourch{$(3, 0)$}{$(0, 3)$}{$(1, 2)$}{$(2, 1)$}", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -188233,7 +189226,9 @@ "008037": { "id": "008037", "content": "如果$y=-\\sqrt {1-x^2}$的反函数是$y=-\\sqrt {1-x^2}$, 那么原来的函数的定义域可以是\\bracket{20}.\n\\fourch{$(0,+\\infty)$}{$[-1,1]$}{$[-1,0]$}{$[0,1]$}", - "objs": [], + "objs": [ + "K0225003B" + ], "tags": [ "第二单元" ], @@ -188254,7 +189249,9 @@ "008038": { "id": "008038", "content": "求函数$y=\\begin{cases} -\\sqrt x, & 0\\le x\\le 1, \\\\ x^2, & -1\\le x<0 \\end{cases}$的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -188275,7 +189272,9 @@ "008039": { "id": "008039", "content": "求函数$y=\\lg (x^2-3x+2)$的定义域.", - "objs": [], + "objs": [ + "K0212001B" + ], "tags": [ "第二单元" ], @@ -188296,7 +189295,9 @@ "008040": { "id": "008040", "content": "求函数$y=\\dfrac{\\sqrt {2x-1}}{\\lg x}$的定义域.", - "objs": [], + "objs": [ + "K0215003B" + ], "tags": [ "第二单元" ], @@ -188320,7 +189321,9 @@ "008041": { "id": "008041", "content": "求函数$y=\\sqrt {\\lg x}+\\lg (5-2x)$的定义域.", - "objs": [], + "objs": [ + "K0215003B" + ], "tags": [ "第二单元" ], @@ -188341,7 +189344,9 @@ "008042": { "id": "008042", "content": "求函数$y=10^x+1$的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -188364,7 +189369,9 @@ "008043": { "id": "008043", "content": "求函数$y=\\log _2(x+1)$的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -188388,7 +189395,9 @@ "008044": { "id": "008044", "content": "求函数$y=\\log _22x$的反函数.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -188411,7 +189420,9 @@ "008045": { "id": "008045", "content": "已知函数$f(x)=a^x+b$的图像经过点$(1, 7)$, 反函数$f^{-1}(x)$的图像经过点$(4, 0)$, 求函数$f(x)$的表达式.", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -188432,7 +189443,9 @@ "008046": { "id": "008046", "content": "若$\\log _a0.2<\\log _a0.1$成立, 求$a$的取值范围.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188453,7 +189466,9 @@ "008047": { "id": "008047", "content": "若$\\log _a\\pi >\\log _a\\mathrm{e}$成立, 求$a$的取值范围.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188474,7 +189489,9 @@ "008048": { "id": "008048", "content": "若$\\log _a3<0$成立, 求$a$的取值范围.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188537,7 +189554,9 @@ "008051": { "id": "008051", "content": "判断函数$y=\\lg\\dfrac{x+1}{x-1}$的奇偶性.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -188558,7 +189577,9 @@ "008052": { "id": "008052", "content": "设$a>0$且$a\\ne 1$, 比较$\\log _a2a$与$\\log _a3a$的大小.", - "objs": [], + "objs": [ + "K0213008B" + ], "tags": [ "第二单元" ], @@ -188579,7 +189600,9 @@ "008053": { "id": "008053", "content": "求证: $y=\\lg(1-x)$在定义域上单调递减.", - "objs": [], + "objs": [ + "K0219003B" + ], "tags": [ "第二单元" ], @@ -188600,7 +189623,9 @@ "008054": { "id": "008054", "content": "求函数$y=\\log _{\\frac 15}(x^2-6x+10)$在区间$[1,2]$上的最大值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -188621,7 +189646,9 @@ "008055": { "id": "008055", "content": "解方程$2^{1-x}=\\dfrac 1{32}$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188642,7 +189669,9 @@ "008056": { "id": "008056", "content": "解方程$3^{-x+2}=9^x$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188663,7 +189692,9 @@ "008057": { "id": "008057", "content": "解方程$4^{2x-1}=1$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188684,7 +189715,9 @@ "008058": { "id": "008058", "content": "解方程$0.38\\cdot 10^{x-3}=0.5$(精确到$0.01$).", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188705,7 +189738,9 @@ "008059": { "id": "008059", "content": "解指数方程$2^{x^2+3}=(\\dfrac 14)^{\\frac 72}$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188726,7 +189761,9 @@ "008060": { "id": "008060", "content": "解指数方程$9^x-8\\cdot 3^x-9=0$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188749,7 +189786,9 @@ "008061": { "id": "008061", "content": "已知关于$x$的方程$2a^{2x-2}-7a^{x-1}+3=0$有一个根是$x=2$, 求$a$的值并求方程的其余的根.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188772,7 +189811,9 @@ "008062": { "id": "008062", "content": "某种放射性物质不断衰减, 若每经过一年剩留的物质是原来的$\\dfrac 45$, 经过多少年, 剩余物质是原来的$\\dfrac{64}{125}$?", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188793,7 +189834,9 @@ "008063": { "id": "008063", "content": "解方程: $9^x+4^x=\\dfrac 52\\cdot 6^x$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188817,7 +189860,9 @@ "008064": { "id": "008064", "content": "解方程: $4^x+4^{-x}-6(2^x+2^{-x})+10=0$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188840,7 +189885,9 @@ "008065": { "id": "008065", "content": "动物尸体内$^{14}C$的含量每年衰减$0.012\\%$, 设动物死亡的时刻$t=0$时, $^{14}C$含量为$100\\%$.\\\\\n(1) 写出$^{14}C$含量$y$关于时间$t$的函数解析式;\\\\\n(2) $^{14}C$含量减少到$50\\%$需多少时间? (精确到$1$年)", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -188861,7 +189908,9 @@ "008066": { "id": "008066", "content": "解方程$\\log _3(x-2)=1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188884,7 +189933,9 @@ "008067": { "id": "008067", "content": "解方程$\\log _2(x^2-3x)=2$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188907,7 +189958,9 @@ "008068": { "id": "008068", "content": "解方程$\\log _2(\\log _5x)=1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188928,7 +189981,9 @@ "008069": { "id": "008069", "content": "解方程$\\log _5(x+1)-\\log _{\\frac 15}(x-3)=1$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188951,7 +190006,9 @@ "008070": { "id": "008070", "content": "解方程$\\log _2^2x+3\\log _2x+2=0$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188972,7 +190029,9 @@ "008071": { "id": "008071", "content": "解方程$\\log _x(x^2-x)=\\log _x2$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -188996,7 +190055,9 @@ "008072": { "id": "008072", "content": "解方程$\\log _{\\frac 12}(9^{x-1}-5)=\\log _{\\frac 12}(3^{x-1}-2)-2$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -189019,7 +190080,9 @@ "008073": { "id": "008073", "content": "解方程$(\\lg x)^2-\\lg x^2=3$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -189040,7 +190103,9 @@ "008074": { "id": "008074", "content": "解方程: $x^{\\log _2x}=32x^4$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -189063,7 +190128,9 @@ "008075": { "id": "008075", "content": "求方程$\\log _2(x+4)=(\\dfrac 13)^x$根的个数, 并说明理由.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -189084,7 +190151,9 @@ "008076": { "id": "008076", "content": "若$x^5=3$, 则$x=$\\blank{50}; 若$5^x=3$, 则$x=$\\blank{50}.", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -189105,7 +190174,9 @@ "008077": { "id": "008077", "content": "计算: $\\log _236-2\\log _23=$\\blank{50}.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -189126,7 +190197,9 @@ "008078": { "id": "008078", "content": "若$\\log _ab\\cdot \\log _5a=3$, 则$b=$\\blank{50}.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -189147,7 +190220,9 @@ "008079": { "id": "008079", "content": "函数$y=\\log _2x(x\\ge 1)$的反函数是\\blank{50}.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -189176,7 +190251,9 @@ "008080": { "id": "008080", "content": "若点$(1, 7)$既在函数$y=\\sqrt {ax+b}$的图像上, 又在其反函数的图像上, 则数对$(a,b)$为\\blank{50}.", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -189197,7 +190274,9 @@ "008081": { "id": "008081", "content": "若$f(x)=3^x+5$, 则$f^{-1}(x)$的定义域是\\bracket{20}.\n\\fourch{$(0,+\\infty)$}{$(5,+\\infty)$}{$(8,+\\infty)$}{$(-\\infty ,+\\infty)$}", - "objs": [], + "objs": [ + "K0225003B" + ], "tags": [ "第二单元" ], @@ -189218,7 +190297,9 @@ "008082": { "id": "008082", "content": "若$\\log _{18}9=a$, $18^b=5$, 则$\\log _{36}45$等于\\bracket{20}.\n\\fourch{$\\dfrac{a+b}{2+a}$}{$\\dfrac{a+b}{2-a}$}{$\\dfrac{a+b}{2a}$}{$\\dfrac{a+b}{a^2}$}", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -189241,7 +190322,9 @@ "008083": { "id": "008083", "content": "已知函数$f(x)=\\dfrac{ax+1}{x-3}$的反函数是$f(x)$本身, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0226005B" + ], "tags": [ "第二单元" ], @@ -189262,7 +190345,9 @@ "008084": { "id": "008084", "content": "作出函数$y=\\log _2(x-1)$的图像.", - "objs": [], + "objs": [ + "K0216003B" + ], "tags": [ "第二单元" ], @@ -189285,7 +190370,9 @@ "008085": { "id": "008085", "content": "作出函数$y=|\\log _2(x-1)|$的图像.", - "objs": [], + "objs": [ + "K0216003B" + ], "tags": [ "第二单元" ], @@ -189308,7 +190395,10 @@ "008086": { "id": "008086", "content": "已知$\\lg x+\\lg y=2$, 求$\\dfrac 1x+\\dfrac 1y$的最小值.", - "objs": [], + "objs": [ + "K0205002B", + "K0119001B" + ], "tags": [ "第二单元" ], @@ -189329,7 +190419,9 @@ "008087": { "id": "008087", "content": "解方程: $4^x+2^{x+1}=80$.", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -189350,7 +190442,9 @@ "008088": { "id": "008088", "content": "解方程: $\\lg (2x+2)+\\lg (15-x)=1+\\lg 3$.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -189371,7 +190465,11 @@ "008089": { "id": "008089", "content": "已知函数$f(x)=\\log _a\\dfrac{1+x}{1-x}$($a>0$, $a\\ne 1$).\n(1) 求$f(x)$的定义域;\\\\\n(2) 判断$f(x)$的奇偶性, 并加以证明;\\\\\n(3) 当$a>1$时, 求使$f(x)>0$的$x$的取值范围.", - "objs": [], + "objs": [ + "K0215003B", + "K0218001B", + "K0214002B" + ], "tags": [ "第二单元" ], @@ -189392,7 +190490,9 @@ "008090": { "id": "008090", "content": "如果光线每通过一块玻璃其强度要减少$10\\%$, 求至少需要多少块这样的玻璃重叠起来, 才能使通过它们的光线强度为原来的强度的$\\dfrac 13$以下?", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -189415,7 +190515,9 @@ "008091": { "id": "008091", "content": "如果函数$f(x)=\\log _a(-x^2+ax)$的定义域为$(0,\\dfrac 12)$, 那么实数$a=$\\blank{50}.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -189436,7 +190538,9 @@ "008092": { "id": "008092", "content": "如果$45^x=3$, $45^y=5$, 那么$2x+y=$\\blank{50}.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -189457,7 +190561,10 @@ "008093": { "id": "008093", "content": "若函数$y=f(x)$的图像与函数$y=2^x-1$的图像关于直线$y=x$成轴对称图形, 则函数$y=f(x)$的解析式为\\blank{50}.", - "objs": [], + "objs": [ + "K0225005B", + "K0226001B" + ], "tags": [ "第二单元" ], @@ -189480,7 +190587,10 @@ "008094": { "id": "008094", "content": "当$a>1$时, 在同一坐标系中, 函数$y=a^{-x}$与$y=\\log _ax$的图像是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[scale = 0.7, >=latex]\n \\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n \\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw [domain = -1:2] plot (\\x, {pow(0.5,\\x)});\n \\draw [domain = -1:2] plot ({pow(0.5,\\x)},-\\x);\n\\end{tikzpicture}}\n{\\begin{tikzpicture}[scale = 0.7, >=latex]\n \\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n \\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw [domain = -1:2] plot (-\\x, {pow(0.5,\\x)});\n \\draw [domain = -1:2] plot ({pow(0.5,\\x)},-\\x);\n\\end{tikzpicture}}{\\begin{tikzpicture}[scale = 0.7, >=latex]\n \\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n \\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw [domain = -1:2] plot (-\\x, {pow(0.5,\\x)});\n \\draw [domain = -1:2] plot ({pow(0.5,\\x)},\\x);\n\\end{tikzpicture}}{\\begin{tikzpicture}[scale = 0.7, >=latex]\n \\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n \\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw [domain = -1:2] plot (\\x, {pow(0.5,\\x)});\n \\draw [domain = -1:2] plot ({pow(0.5,\\x)},\\x);\n\\end{tikzpicture}}", - "objs": [], + "objs": [ + "K0210005B", + "K0213007B" + ], "tags": [ "第二单元" ], @@ -189501,7 +190611,9 @@ "008095": { "id": "008095", "content": "函数$f(x)=4+\\log _a(x-1)(a>0a\\ne 1)$的图像恒经过定点$P$, 则点$P$的坐标是\\bracket{20}.\n\\fourch{$(1, 4)$}{($4, 1)$}{$(2, 4)$}{$(4, 2)$}", - "objs": [], + "objs": [ + "K0213002B" + ], "tags": [ "第二单元" ], @@ -189522,7 +190634,9 @@ "008096": { "id": "008096", "content": "已知$0=latex]\n \\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n \\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw [domain = -1:2] plot (\\x,{pow(2,-\\x)});\n \\draw [domain = -1:2] plot ({-pow(2,-\\x)},-\\x);\n \\draw (0,1) node [above right] {$1$};\n \\draw (-1,0) node [below left] {$-1$};\n \\end{tikzpicture}\n\\end{center}\n\\twoch{$y=a^x$和$y=\\log _a(-x)$}{$y=a^x$和$y=\\log _ax^{-1}$}{$y=a^{-x}$和$y=\\log _ax^{-1}$}{$y=a^{-x}$和$y=\\log _a(-x)$}", - "objs": [], + "objs": [ + "K0213007B", + "K0213006B", + "K0210005B" + ], "tags": [ "第二单元" ], @@ -195662,7 +196798,11 @@ "008372": { "id": "008372", "content": "若$0n>1$}{$n>m>1$}{$00$的$x$的值范围是\\blank{50}.", "objs": [ - "K0220003B" + "K0220003B", + "K0220001B", + "K0213008B" ], "tags": [ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(0,\\dfrac 12)\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [ - "20220914\t2023届高三2班\t0.844" + "20220914\t2023届高三02班\t0.844" ], "origin": "二期课改练习册高一第二学期", "edit": [ @@ -196142,7 +197304,11 @@ "008394": { "id": "008394", "content": "已知函数$f(x)=\\log _a\\dfrac{x+b}{x-b}(a>0,b>0, a\\ne 1)$.\\\\\n(1) 求$f(x)$的定义域;\\\\\n(2) 判断$f(x)$的奇偶性;\\\\\n(3) 求函数$y=f^{-1}(x)$的解析式.", - "objs": [], + "objs": [ + "K0212002B", + "K0218001B", + "K0225005B" + ], "tags": [ "第二单元" ], @@ -196253,7 +197419,10 @@ "008399": { "id": "008399", "content": "设在海拔$x$米处的大气压强是$y$帕, $y$与$x$之间的函数关系式是$y=ce^{kx}$, 其中$c,k$为常量.已知某地某天在海平面的大气压强为$1.01\\times 10^5$帕, $1000$米高空的大气压强为$0.90\\times 10^5$帕, 求$600$米高空的大气压强(结果保留$3$个有效数字)。", - "objs": [], + "objs": [ + "K0204004B", + "K0215001B" + ], "tags": [ "第二单元" ], @@ -218758,7 +219927,7 @@ "solution": "", "duration": -1, "usages": [ - "20220906\t2023届高三2班\t0.355" + "20220906\t2023届高三02班\t0.355" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -219276,11 +220445,11 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ - "20220901\t2023届高三2班\t0.939\t0.939", + "20220901\t2023届高三02班\t0.939\t0.939", "20220902\t2023届高三10班\t1.000\t0.909" ], "origin": "新教材必修第一册课堂练习", @@ -219295,7 +220464,9 @@ "009469": { "id": "009469", "content": "求$-\\dfrac{32}{243}$的$5$次方根.", - "objs": [], + "objs": [ + "K0201003B" + ], "tags": [ "第二单元" ], @@ -219316,7 +220487,9 @@ "009470": { "id": "009470", "content": "求$9$的$4$次方根.", - "objs": [], + "objs": [ + "K0201003B" + ], "tags": [ "第二单元" ], @@ -219337,7 +220510,9 @@ "009471": { "id": "009471", "content": "求下列各根式的值:\\\\\n(1) $\\sqrt[5]{(-4)^5}$;\\\\\n(2) $\\sqrt[6]{(a-b)^6}$(其中$a0$):\\\\\n(1) $a^{\\frac{10}3}\\cdot \\sqrt[5]{a^3}$;\\\\\n(2) $\\sqrt[3]{a\\sqrt[3]{a}}$.", - "objs": [], + "objs": [ + "K0202002B" + ], "tags": [ "第二单元" ], @@ -219402,7 +220581,9 @@ "009474": { "id": "009474", "content": "化简下列各式:\\\\\n(1) $(a^{3+\\sqrt 3})^{3-\\sqrt 3}$(其中$a>0$);\\\\\n(2) $\\dfrac{4a^{\\frac 23}b^2}{(a^{\\frac 16}b^{\\frac 56})(-\\dfrac 23 a^{\\frac 12}b)}$(其中$a>0$, $b>0$).", - "objs": [], + "objs": [ + "K0202002B" + ], "tags": [ "第二单元" ], @@ -219423,7 +220604,9 @@ "009475": { "id": "009475", "content": "已知$00$. 求证: $00$且$a\\ne 1$). 用$A$及$B$表示下列各式:\\\\\n(1) $\\log_axy$;\\\\\n(2) $\\log_ax^2\\sqrt y$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -219528,7 +220719,9 @@ "009480": { "id": "009480", "content": "求下列各式的值:\\\\\n(1) $\\log_{15}3+\\log_{15}5$;\\\\\n(2) $\\log_2\\sqrt[3]{4}$;\\\\\n(3) $\\log_5\\sqrt{10}-\\dfrac 12\\log_5250$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -219549,7 +220742,10 @@ "009481": { "id": "009481", "content": "已知$\\log_73=a$, $7^b=2$. 用$a$及$b$表示$\\log_772$.", - "objs": [], + "objs": [ + "K0204004B", + "K0205002B" + ], "tags": [ "第二单元" ], @@ -219593,7 +220789,10 @@ "009483": { "id": "009483", "content": "已知$\\log_32=a$, 用$a$表示$\\log_296$.", - "objs": [], + "objs": [ + "K0205002B", + "K0206002B" + ], "tags": [ "第二单元" ], @@ -219616,7 +220815,9 @@ "009484": { "id": "009484", "content": "设$a$、$b$是两个不等于$1$的正数, 求证: $\\log_ba=\\dfrac1{\\log_ab}$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -219637,7 +220838,9 @@ "009485": { "id": "009485", "content": "若幂函数$y=x^a$的图像经过点$(3, \\sqrt 3)$, 求此幂函数的表达式.", - "objs": [], + "objs": [ + "K0207001B" + ], "tags": [ "第二单元" ], @@ -219660,7 +220863,10 @@ "009486": { "id": "009486", "content": "求下列函数的定义域, 并作出它们的大致图像:\\\\\n(1) $y=x^{\\frac 13}$;\\\\\n(2) $y=x^{-\\frac 12}$;\\\\\n(3) $y=x^{\\frac 43}$.", - "objs": [], + "objs": [ + "K0207002B", + "K0207003B" + ], "tags": [ "第二单元" ], @@ -219683,7 +220889,9 @@ "009487": { "id": "009487", "content": "若幂函数$y=x^{-m^2+2m+3}$($m$为整数)的定义域为$\\mathbf{R}$, 求$m$的值.", - "objs": [], + "objs": [ + "K0207001B" + ], "tags": [ "第二单元" ], @@ -219711,11 +220919,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=(x-1)^{\\frac 23}$的图像由$y=x^{\\frac 23}$的图像向右平移一个单位长度而得到.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2,samples = 50] plot (\\x,{pow(\\x,2/3)}) node [above right] {$y=x^{\\frac 23}$};\n\\draw [domain = 0:2,samples = 50] plot (-\\x,{pow(\\x,2/3)});\n\\draw [domain = 0:2,samples = 50] plot ({\\x+1},{pow((\\x,2/3)}) node [right] {$y=(x-1)^{\\frac 23}$};\n\\draw [domain = 0:2,samples = 50] plot ({-\\x+1},{pow(\\x,2/3)});\n\\end{tikzpicture}\n\\end{center}\n(2) $y=x^{\\frac 23}+1$的图像由$y=x^{\\frac 23}$的图像向上平移一个单位长度而得到.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2,samples = 50] plot (\\x,{pow(\\x,2/3)}) node [above right] {$y=x^{\\frac 23}$};\n\\draw [domain = 0:2,samples = 50] plot (-\\x,{pow(\\x,2/3)});\n\\draw [domain = 0:2,samples = 50] plot (\\x,{pow(\\x,2/3)+1}) node [right] {$y=x^{\\frac 23}+1$};\n\\draw [domain = 0:2,samples = 50] plot (-\\x,{pow(\\x,2/3)+1});\n\\end{tikzpicture}\n\\end{center}", "solution": "", "duration": -1, "usages": [ - "20220904\t2023届高三2班\t0.742\t0.710" + "20220904\t2023届高三02班\t0.742\t0.710" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -219729,7 +220937,9 @@ "009489": { "id": "009489", "content": "比较下列各题中两个数的大小:\\\\\n(1) $2.5^{-3}$与$3.1^{-3}$;\\\\\n(2) $1.7^{\\frac 32}$与$1.6^{\\frac 32}$.", - "objs": [], + "objs": [ + "K0208004B" + ], "tags": [ "第二单元" ], @@ -219757,11 +220967,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "图像如下:\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [above right] {$O$};\n\\draw [domain = -4:{-7/3}] plot (\\x,{(-\\x-1)/(\\x+2)});\n\\draw [domain = {-9/5}:4] plot (\\x,{(-\\x-1)/(\\x+2)});\n\\draw [dashed] (-4,-1) -- (4,-1) (-2,-4) -- (-2,4);\n\\end{tikzpicture}\n\\end{center}", "solution": "", "duration": -1, "usages": [ - "20220908\t2023届高三2班\t0.879" + "20220908\t2023届高三02班\t0.879" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -219777,7 +220987,10 @@ "009491": { "id": "009491", "content": "判断下列函数哪些是指数函数, 哪些是幂函数:\\\\\n(1) $y=x$;\\\\\n(2) $y=x^3$;\\\\\n(3) $y=\\mathrm{e}^x$;\\\\\n(4) $y=\\sqrt[3]{x}$;\\\\\n(5) $y=2^{-x}$;\\\\\n(6) $y=2^x$.", - "objs": [], + "objs": [ + "K0207001B", + "K0209001B" + ], "tags": [ "第二单元" ], @@ -220184,11 +221397,11 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t1.000" + "20220907\t2023届高三02班\t1.000" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -220255,11 +221468,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\begin{cases} 3x+10, & x\\in [-3,-2],\\\\ 4, & x\\in [-2,2],\\\\ 10-3x, & x\\in [2,3]. \\end{cases}$", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t0.844" + "20220907\t2023届高三02班\t0.844" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -220395,11 +221608,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "不正确, 如$y=\\begin{cases} 0, & x=0, \\\\ \\dfrac 1x, & x>0.\\end{cases}$", "solution": "", "duration": -1, "usages": [ - "20220909\t2023届高三2班\t0.656" + "20220909\t2023届高三02班\t0.656" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -220421,11 +221634,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ - "20220914\t2023届高三2班\t0.969" + "20220914\t2023届高三02班\t0.969" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -220516,11 +221729,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 是的, 证明略", "solution": "", "duration": -1, "usages": [ - "20220909\t2023届高三2班\t0.563\t0.250" + "20220909\t2023届高三02班\t0.563\t0.250" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -220613,7 +221826,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=6-\\dfrac x2, \\ x\\in (0,6)$", "solution": "", "duration": -1, "usages": [], @@ -220705,11 +221918,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(1,+\\infty)$", "solution": "", "duration": -1, "usages": [ - "20220915\t2023届高三2班\t0.906" + "20220915\t2023届高三02班\t0.906" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -220730,11 +221943,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "不是, 例如$f(x)=x^2-1$, $a=-10$, $b=10$等", "solution": "", "duration": -1, "usages": [ - "20220913\t2023届高三2班\t0.903" + "20220913\t2023届高三02班\t0.903" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -220755,11 +221968,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$1.6$", "solution": "", "duration": -1, "usages": [ - "20220915\t2023届高三2班\t0.969" + "20220915\t2023届高三02班\t0.969" ], "origin": "新教材必修第一册课堂练习", "edit": [ @@ -228714,7 +229927,9 @@ "009906": { "id": "009906", "content": "将石子投入水中, 水面产生的圆形波纹不断扩散.\\\\\n(1) 当半径$r$从$a$增加到$a+h$($h>0$)时, 求圆周长相对于半径的平均变化率;\\\\\n(2) 当半径$r=a$时, 求圆周长相对于半径的瞬时变化率.", - "objs": [], + "objs": [ + "K0227004X" + ], "tags": [ "第二单元" ], @@ -228737,7 +229952,9 @@ "009907": { "id": "009907", "content": "已知$f(x)=3x^2$, 分别求曲线$y=f(x)$在点$P(-1,3)$和点$Q(1,3)$处的切线方程.", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元" ], @@ -228758,7 +229975,9 @@ "009908": { "id": "009908", "content": "借助函数图像, 判断下列导数的正负(可利用信息技术工具):\\\\\n(1) $f'(\\dfrac\\pi 4)$, 其中$f(x)=\\sin x$;\\\\\n(2) $f'(0)$, 其中$f(x)=(\\dfrac 12)^x$.", - "objs": [], + "objs": [ + "K0228003X" + ], "tags": [ "第二单元" ], @@ -228781,7 +230000,10 @@ "009909": { "id": "009909", "content": "用导数的定义求函数 $y=x^2+3x-5$的导数.", - "objs": [], + "objs": [ + "K0227005X", + "K0229001X" + ], "tags": [ "第二单元" ], @@ -228802,7 +230024,9 @@ "009910": { "id": "009910", "content": "用公式求下列函数$y=f(x)$的导数, 其中:\\\\\n(1) $f(x)=\\sqrt[3]{x^2}$;\\\\\n(2) $f(x)=x^\\pi$.", - "objs": [], + "objs": [ + "K0229004X" + ], "tags": [ "第二单元" ], @@ -228823,7 +230047,9 @@ "009911": { "id": "009911", "content": "求余弦函数$y=\\cos x$在$x=\\dfrac \\pi2$处的导数.", - "objs": [], + "objs": [ + "K0229004X" + ], "tags": [ "第二单元" ], @@ -228844,7 +230070,10 @@ "009912": { "id": "009912", "content": "证明函数$y=\\ln x$与$y=\\mathrm{e}^x$没有驻点.", - "objs": [], + "objs": [ + "K0229004X", + "K0228005X" + ], "tags": [ "第二单元" ], @@ -228865,7 +230094,10 @@ "009913": { "id": "009913", "content": "求下列函数$y=f(x)$的导数, 其中:\\\\\n(1) $f(x)=3\\mathrm{e}^x-x^{\\mathrm{e}}+\\mathrm{e}$;\\\\\n(2) $f(x)=\\cos x-\\dfrac 2x$;\\\\\n(3) $f(x)=(2x+1)^3$;\\\\\n(4) $f(x)=\\sqrt x\\sin x$;\\\\\n(5) $f(x)=x\\ln x-\\dfrac1{x^2}$;\\\\\n(6) $f(x)=\\dfrac{x^2-1}x$;\\\\\n(7) $f(x)=\\dfrac{x^2-1}{x^2+1}$;\\\\\n(8) $f(x)=\\tan x$.", - "objs": [], + "objs": [ + "K0230004X", + "K0229004X" + ], "tags": [ "第二单元" ], @@ -228886,7 +230118,10 @@ "009914": { "id": "009914", "content": "利用$f(ax+b)$型复合函数的求导法则求下列函数的导数:\\\\\n(1) $y=(3-2x)^2$;\\\\\n(2) $y=\\sin 2x$.", - "objs": [], + "objs": [ + "K0231003X", + "K0229004X" + ], "tags": [ "第二单元" ], @@ -228907,7 +230142,10 @@ "009915": { "id": "009915", "content": "尝试用两种不同的方法求$f(x)=\\dfrac1{2x-1}$的导数.", - "objs": [], + "objs": [ + "K0230004X", + "K0231003X" + ], "tags": [ "第二单元" ], @@ -228928,7 +230166,10 @@ "009916": { "id": "009916", "content": "求曲线$y=2^{1-3x}$在点$(0,2)$处的切线方程.", - "objs": [], + "objs": [ + "K0228003X", + "K0231003X" + ], "tags": [ "第二单元" ], @@ -228949,7 +230190,10 @@ "009917": { "id": "009917", "content": "求下列函数的导数:\\\\\n(1) $y=3x \\sqrt{2-x}$;\\\\\n(2) $y=\\dfrac{\\ln(2x+1)}x$.", - "objs": [], + "objs": [ + "K0230004X", + "K0231003X" + ], "tags": [ "第二单元" ], @@ -228970,7 +230214,11 @@ "009918": { "id": "009918", "content": "利用导数研究下列函数的单调性, 并说明所得结果与你之前的认识是否一致:\\\\\n(1) $y=\\mathrm{e}^x$;\\\\\n(2) $y=\\ln x$;\\\\\n(3) $y=ax^2+bx+c$, 其中$a\\ne 0$.", - "objs": [], + "objs": [ + "K0232002X", + "K0229004X", + "K0230004X" + ], "tags": [ "第二单元" ], @@ -228991,7 +230239,11 @@ "009919": { "id": "009919", "content": "确定下列函数的单调区间:\\\\\n(1) $y=x\\mathrm{e}^x$;\\\\\n(2) $y=4x^3-9x^2+6x+7$.", - "objs": [], + "objs": [ + "K0232002X", + "K0229004X", + "K0230004X" + ], "tags": [ "第二单元" ], @@ -229012,7 +230264,11 @@ "009920": { "id": "009920", "content": "求余弦函数$y=\\cos x$的单调区间和极值.", - "objs": [], + "objs": [ + "K0229004X", + "K0232002X", + "K0233003X" + ], "tags": [ "第二单元" ], @@ -229033,7 +230289,11 @@ "009921": { "id": "009921", "content": "求函数$y=x^3-3x$的单调区间和极值.", - "objs": [], + "objs": [ + "K0229004X", + "K0232002X", + "K0233003X" + ], "tags": [ "第二单元" ], @@ -229054,7 +230314,10 @@ "009922": { "id": "009922", "content": "判断下列说法是否正确, 并说明理由:\\\\\n(1) 函数在某区间上的极大值不会小于它的极小值;\\\\\n(2) 函数在某区间上的最大值不会小于它的最小值;\\\\\n(3) 函数在某区间上的极大值就是它在该区间上的最大值;\\\\\n(4) 函数在某区间上的最大值就是它在该区间上的极大值.", - "objs": [], + "objs": [ + "K0233001X", + "K0234001X" + ], "tags": [ "第二单元" ], @@ -229075,7 +230338,11 @@ "009923": { "id": "009923", "content": "求函数$y=x^2-6x+5$, $x\\in [1, 4]$的值域.", - "objs": [], + "objs": [ + "K0229004X", + "K0230004X", + "K0234003X" + ], "tags": [ "第二单元" ], @@ -229096,7 +230363,11 @@ "009924": { "id": "009924", "content": "求函数$y=x^3-3x$在区间$[-\\dfrac 32,0]$上的最大值与最小值.", - "objs": [], + "objs": [ + "K0229004X", + "K0230004X", + "K0234003X" + ], "tags": [ "第二单元" ], @@ -229117,7 +230388,11 @@ "009925": { "id": "009925", "content": "商品的成本$C$和产量$q$满足函数关系$C=50000+200q$, 该商品的销售单价$p$和产量$q$满足函数关系$p=24200-\\dfrac 15q^2$. 问: 要使利润最大, 应如何确定产量?", - "objs": [], + "objs": [ + "K0229004X", + "K0230004X", + "K0235001X" + ], "tags": [ "第二单元" ], @@ -229138,7 +230413,11 @@ "009926": { "id": "009926", "content": "采矿、采石或取土时, 常用炸药包进行爆破, 部分爆破呈圆锥漏斗形状(如图), 已知圆锥的母线长是炸药包的爆破半径$R$, 它的值是固定的. 问: 炸药包埋多深可使爆破体积最大? \n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.6]\n\\draw (-1,0) -- (1,0) (0.5,0) node [above] {$r$};\n\\draw (-1,0) -- (0,-2) -- (1,0);\n\\draw (0,0) ellipse (1 and 0.25);\n\\draw [dashed] (0,0) -- (0,-2) (0,-1) node [left] {$h$};\n\\draw (0.5,-1) node [below right] {$R$};\n\\filldraw (0,-2) circle (0.08) (0,-2.3) node {炸药包};\n\\end{tikzpicture}\n\\end{center}", - "objs": [], + "objs": [ + "K0229004X", + "K0230004X", + "K0235001X" + ], "tags": [ "第二单元" ], @@ -230513,7 +231792,9 @@ "009991": { "id": "009991", "content": "设$a$是常数, 若函数$f(x)=\\begin{cases} a^2x-1, & x<0, \\\\ x+a, & x>0, \\\\ 0, & x=0 \\end{cases}$为奇函数, 则$a$的值为\\blank{50}.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -230597,7 +231878,9 @@ "009995": { "id": "009995", "content": "设定义在$[0,+\\infty)$上的函数$f(x)$的值域为$A_f$. 若对任意满足$f(x)=f(\\dfrac 1{x+1})$的函数$f(x)$, 集合$\\{y|y=f(x), \\ x\\in [0,a]\\}$总可以取得$A_f$中的所有值, 则实数$a$的取值范围为\\blank{50}.", - "objs": [], + "objs": [ + "K0215001B" + ], "tags": [ "第二单元" ], @@ -230728,7 +232011,10 @@ "010001": { "id": "010001", "content": "已知$f(x)=\\log_3(x+a)+\\log_3(6-x)$.\\\\\n(1) 若将函数$y=f(x)$的图像向下平移$m$($m>0$)个单位后, 所得的图像经过点$(3,0)$与点$(5,0)$, 求$a$与$m$的值;\\\\\n(2) 若$a>-3$且$a\\ne 0$, 解关于$x$的不等式$f(x)\\le f(6-x)$.", - "objs": [], + "objs": [ + "K0216002B", + "K0206002B" + ], "tags": [ "第二单元" ], @@ -230821,18 +232107,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.910", + "20220802\t2023届高三02班\t0.844", + "20220802\t2023届高三03班\t0.806", + "20220802\t2023届高三04班\t0.875", + "20220802\t2023届高三05班\t0.600", + "20220802\t2023届高三06班\t0.600", + "20220802\t2023届高三07班\t0.824", + "20220802\t2023届高三08班\t0.545", + "20220802\t2023届高三09班\t0.812", "20220802\t2023届高三10班\t0.579", "20220802\t2023届高三11班\t0.708", - "20220802\t2023届高三12班\t0.577", - "20220802\t2023届高三1班\t0.910", - "20220802\t2023届高三2班\t0.844", - "20220802\t2023届高三3班\t0.806", - "20220802\t2023届高三4班\t0.875", - "20220802\t2023届高三5班\t0.600", - "20220802\t2023届高三6班\t0.600", - "20220802\t2023届高三7班\t0.824", - "20220802\t2023届高三8班\t0.545", - "20220802\t2023届高三9班\t0.812" + "20220802\t2023届高三12班\t0.577" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -230855,18 +232141,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.970", + "20220802\t2023届高三02班\t0.969", + "20220802\t2023届高三03班\t0.968", + "20220802\t2023届高三04班\t0.969", + "20220802\t2023届高三05班\t0.925", + "20220802\t2023届高三06班\t0.950", + "20220802\t2023届高三07班\t1.000", + "20220802\t2023届高三08班\t0.939", + "20220802\t2023届高三09班\t0.906", "20220802\t2023届高三10班\t0.947", "20220802\t2023届高三11班\t1.000", - "20220802\t2023届高三12班\t0.962", - "20220802\t2023届高三1班\t0.970", - "20220802\t2023届高三2班\t0.969", - "20220802\t2023届高三3班\t0.968", - "20220802\t2023届高三4班\t0.969", - "20220802\t2023届高三5班\t0.925", - "20220802\t2023届高三6班\t0.950", - "20220802\t2023届高三7班\t1.000", - "20220802\t2023届高三8班\t0.939", - "20220802\t2023届高三9班\t0.906" + "20220802\t2023届高三12班\t0.962" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -230889,18 +232175,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.970", + "20220802\t2023届高三02班\t1.000", + "20220802\t2023届高三03班\t0.968", + "20220802\t2023届高三04班\t1.000", + "20220802\t2023届高三05班\t1.000", + "20220802\t2023届高三06班\t0.725", + "20220802\t2023届高三07班\t0.971", + "20220802\t2023届高三08班\t0.939", + "20220802\t2023届高三09班\t0.988", "20220802\t2023届高三10班\t0.974", "20220802\t2023届高三11班\t0.958", - "20220802\t2023届高三12班\t0.962", - "20220802\t2023届高三1班\t0.970", - "20220802\t2023届高三2班\t1.000", - "20220802\t2023届高三3班\t0.968", - "20220802\t2023届高三4班\t1.000", - "20220802\t2023届高三5班\t1.000", - "20220802\t2023届高三6班\t0.725", - "20220802\t2023届高三7班\t0.971", - "20220802\t2023届高三8班\t0.939", - "20220802\t2023届高三9班\t0.988" + "20220802\t2023届高三12班\t0.962" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -230923,18 +232209,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.940", + "20220802\t2023届高三02班\t0.938", + "20220802\t2023届高三03班\t0.871", + "20220802\t2023届高三04班\t0.844", + "20220802\t2023届高三05班\t0.850", + "20220802\t2023届高三06班\t0.725", + "20220802\t2023届高三07班\t0.765", + "20220802\t2023届高三08班\t0.788", + "20220802\t2023届高三09班\t0.938", "20220802\t2023届高三10班\t0.763", "20220802\t2023届高三11班\t0.792", - "20220802\t2023届高三12班\t0.923", - "20220802\t2023届高三1班\t0.940", - "20220802\t2023届高三2班\t0.938", - "20220802\t2023届高三3班\t0.871", - "20220802\t2023届高三4班\t0.844", - "20220802\t2023届高三5班\t0.850", - "20220802\t2023届高三6班\t0.725", - "20220802\t2023届高三7班\t0.765", - "20220802\t2023届高三8班\t0.788", - "20220802\t2023届高三9班\t0.938" + "20220802\t2023届高三12班\t0.923" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -230957,18 +232243,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t1.000", + "20220802\t2023届高三02班\t1.000", + "20220802\t2023届高三03班\t0.903", + "20220802\t2023届高三04班\t0.938", + "20220802\t2023届高三05班\t0.850", + "20220802\t2023届高三06班\t0.975", + "20220802\t2023届高三07班\t0.941", + "20220802\t2023届高三08班\t0.848", + "20220802\t2023届高三09班\t0.938", "20220802\t2023届高三10班\t0.974", "20220802\t2023届高三11班\t0.917", - "20220802\t2023届高三12班\t1.000", - "20220802\t2023届高三1班\t1.000", - "20220802\t2023届高三2班\t1.000", - "20220802\t2023届高三3班\t0.903", - "20220802\t2023届高三4班\t0.938", - "20220802\t2023届高三5班\t0.850", - "20220802\t2023届高三6班\t0.975", - "20220802\t2023届高三7班\t0.941", - "20220802\t2023届高三8班\t0.848", - "20220802\t2023届高三9班\t0.938" + "20220802\t2023届高三12班\t1.000" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -230991,18 +232277,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t1.000\t0.940", + "20220802\t2023届高三02班\t0.938\t0.875", + "20220802\t2023届高三03班\t0.967\t0.839", + "20220802\t2023届高三04班\t1.000\t0.938", + "20220802\t2023届高三05班\t0.950\t0.800", + "20220802\t2023届高三06班\t0.975\t0.925", + "20220802\t2023届高三07班\t1.000\t0.882", + "20220802\t2023届高三08班\t0.970\t0.848", + "20220802\t2023届高三09班\t0.969\t0.906", "20220802\t2023届高三10班\t0.921\t0.789", "20220802\t2023届高三11班\t0.958\t0.708", - "20220802\t2023届高三12班\t1.000\t0.808", - "20220802\t2023届高三1班\t1.000\t0.940", - "20220802\t2023届高三2班\t0.938\t0.875", - "20220802\t2023届高三3班\t0.967\t0.839", - "20220802\t2023届高三4班\t1.000\t0.938", - "20220802\t2023届高三5班\t0.950\t0.800", - "20220802\t2023届高三6班\t0.975\t0.925", - "20220802\t2023届高三7班\t1.000\t0.882", - "20220802\t2023届高三8班\t0.970\t0.848", - "20220802\t2023届高三9班\t0.969\t0.906" + "20220802\t2023届高三12班\t1.000\t0.808" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -231025,18 +232311,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.910", + "20220802\t2023届高三02班\t0.656", + "20220802\t2023届高三03班\t0.839", + "20220802\t2023届高三04班\t0.750", + "20220802\t2023届高三05班\t0.650", + "20220802\t2023届高三06班\t0.775", + "20220802\t2023届高三07班\t0.696", + "20220802\t2023届高三08班\t0.576", + "20220802\t2023届高三09班\t0.656", "20220802\t2023届高三10班\t0.632", "20220802\t2023届高三11班\t0.458", - "20220802\t2023届高三12班\t0.500", - "20220802\t2023届高三1班\t0.910", - "20220802\t2023届高三2班\t0.656", - "20220802\t2023届高三3班\t0.839", - "20220802\t2023届高三4班\t0.750", - "20220802\t2023届高三5班\t0.650", - "20220802\t2023届高三6班\t0.775", - "20220802\t2023届高三7班\t0.696", - "20220802\t2023届高三8班\t0.576", - "20220802\t2023届高三9班\t0.656" + "20220802\t2023届高三12班\t0.500" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -231059,18 +232345,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.790", + "20220802\t2023届高三02班\t0.969", + "20220802\t2023届高三03班\t0.903", + "20220802\t2023届高三04班\t0.844", + "20220802\t2023届高三05班\t0.700", + "20220802\t2023届高三06班\t0.750", + "20220802\t2023届高三07班\t0.848", + "20220802\t2023届高三08班\t0.788", + "20220802\t2023届高三09班\t0.875", "20220802\t2023届高三10班\t0.684", "20220802\t2023届高三11班\t0.792", - "20220802\t2023届高三12班\t0.846", - "20220802\t2023届高三1班\t0.790", - "20220802\t2023届高三2班\t0.969", - "20220802\t2023届高三3班\t0.903", - "20220802\t2023届高三4班\t0.844", - "20220802\t2023届高三5班\t0.700", - "20220802\t2023届高三6班\t0.750", - "20220802\t2023届高三7班\t0.848", - "20220802\t2023届高三8班\t0.788", - "20220802\t2023届高三9班\t0.875" + "20220802\t2023届高三12班\t0.846" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -231093,18 +232379,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.730", + "20220802\t2023届高三02班\t0.500", + "20220802\t2023届高三03班\t0.645", + "20220802\t2023届高三04班\t0.562", + "20220802\t2023届高三05班\t0.550", + "20220802\t2023届高三06班\t0.400", + "20220802\t2023届高三07班\t0.382", + "20220802\t2023届高三08班\t0.545", + "20220802\t2023届高三09班\t0.562", "20220802\t2023届高三10班\t0.289", "20220802\t2023届高三11班\t0.125", - "20220802\t2023届高三12班\t0.500", - "20220802\t2023届高三1班\t0.730", - "20220802\t2023届高三2班\t0.500", - "20220802\t2023届高三3班\t0.645", - "20220802\t2023届高三4班\t0.562", - "20220802\t2023届高三5班\t0.550", - "20220802\t2023届高三6班\t0.400", - "20220802\t2023届高三7班\t0.382", - "20220802\t2023届高三8班\t0.545", - "20220802\t2023届高三9班\t0.562" + "20220802\t2023届高三12班\t0.500" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -231127,18 +232413,18 @@ "solution": "", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.940", + "20220802\t2023届高三02班\t0.938", + "20220802\t2023届高三03班\t0.806", + "20220802\t2023届高三04班\t0.809", + "20220802\t2023届高三05班\t1.000", + "20220802\t2023届高三06班\t0.843", + "20220802\t2023届高三07班\t0.947", + "20220802\t2023届高三08班\t0.933", + "20220802\t2023届高三09班\t0.953", "20220802\t2023届高三10班\t0.861", "20220802\t2023届高三11班\t0.875", - "20220802\t2023届高三12班\t0.962", - "20220802\t2023届高三1班\t0.940", - "20220802\t2023届高三2班\t0.938", - "20220802\t2023届高三3班\t0.806", - "20220802\t2023届高三4班\t0.809", - "20220802\t2023届高三5班\t1.000", - "20220802\t2023届高三6班\t0.843", - "20220802\t2023届高三7班\t0.947", - "20220802\t2023届高三8班\t0.933", - "20220802\t2023届高三9班\t0.953" + "20220802\t2023届高三12班\t0.962" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -231161,18 +232447,18 @@ "solution": "$p_4\\approx 1-2.55\\times 10^{-7}$, $p_2\\approx 1-1.6\\times 10^{-5}$, $p_4>p_2$.", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t1.000", + "20220802\t2023届高三02班\t0.878", + "20220802\t2023届高三03班\t0.774", + "20220802\t2023届高三04班\t0.863", + "20220802\t2023届高三05班\t0.975", + "20220802\t2023届高三06班\t0.993", + "20220802\t2023届高三07班\t0.824", + "20220802\t2023届高三08班\t0.803", + "20220802\t2023届高三09班\t0.697", "20220802\t2023届高三10班\t0.750", "20220802\t2023届高三11班\t0.708", - "20220802\t2023届高三12班\t0.823", - "20220802\t2023届高三1班\t1.000", - "20220802\t2023届高三2班\t0.878", - "20220802\t2023届高三3班\t0.774", - "20220802\t2023届高三4班\t0.863", - "20220802\t2023届高三5班\t0.975", - "20220802\t2023届高三6班\t0.993", - "20220802\t2023届高三7班\t0.824", - "20220802\t2023届高三8班\t0.803", - "20220802\t2023届高三9班\t0.697" + "20220802\t2023届高三12班\t0.823" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -231195,18 +232481,18 @@ "solution": "(1) $M=\\dfrac 32$, $m=\\dfrac 12$.\\\\\n(2) 设$P(X=0)=p$, $P(X=2)=q$, 则$P(X=1)=1-p-q$, 其中$p\\ge 0$, $q\\ge 0$, $p+q\\le 1$.\\\\\n$E[X]=1\\cdot (1-p-q)+2q=1-p+q$, $E[X^2]=1(1-p-q)+4q=1-p+3q$. 故$D[X]=1-p+3q-(1-p+q)^2=p+q-(p-q)^2\\le 1+0=1$.\\\\\n而当$p=q=\\dfrac 12$时, $D[X]$能取到$1$, 故$D[X]$的最大可能值为$1$.", "duration": -1, "usages": [ + "20220802\t2023届高三01班\t0.990\t0.270", + "20220802\t2023届高三02班\t0.834\t0.038", + "20220802\t2023届高三03班\t0.968\t0.032", + "20220802\t2023届高三04班\t0.781\t0.013", + "20220802\t2023届高三05班\t0.750\t0.037", + "20220802\t2023届高三06班\t0.885\t0.130", + "20220802\t2023届高三07班\t0.571\t0.047", + "20220802\t2023届高三08班\t0.758\t0.091", + "20220802\t2023届高三09班\t0.856\t0.013", "20220802\t2023届高三10班\t0.650\t0.013", "20220802\t2023届高三11班\t0.333\t0.042", - "20220802\t2023届高三12班\t0.769\t0.008", - "20220802\t2023届高三1班\t0.990\t0.270", - "20220802\t2023届高三2班\t0.834\t0.038", - "20220802\t2023届高三3班\t0.968\t0.032", - "20220802\t2023届高三4班\t0.781\t0.013", - "20220802\t2023届高三5班\t0.750\t0.037", - "20220802\t2023届高三6班\t0.885\t0.130", - "20220802\t2023届高三7班\t0.571\t0.047", - "20220802\t2023届高三8班\t0.758\t0.091", - "20220802\t2023届高三9班\t0.856\t0.013" + "20220802\t2023届高三12班\t0.769\t0.008" ], "origin": "2023届高三前暑假概率初步续单元测验", "edit": [ @@ -231323,10 +232609,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t0.788", "20220822\t2023届高三10班\t0.967", - "20220822\t2023届高三2班\t0.788", - "20220823\t2023届高三11班\t1.000", - "20220823\t2023届高三8班\t0.906" + "20220823\t2023届高三08班\t0.906", + "20220823\t2023届高三11班\t1.000" ], "origin": "新教材必修第一册习题", "edit": [ @@ -231449,10 +232735,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t0.758", "20220822\t2023届高三10班\t0.967", - "20220822\t2023届高三2班\t0.758", - "20220823\t2023届高三11班\t0.920", - "20220823\t2023届高三8班\t0.844" + "20220823\t2023届高三08班\t0.844", + "20220823\t2023届高三11班\t0.920" ], "origin": "新教材必修第一册习题", "edit": [ @@ -231480,13 +232766,13 @@ "solution": "", "duration": -1, "usages": [ + "20220821\t2023届高三02班\t0.576", + "20220821\t2023届高三03班\t0.708", + "20220821\t2023届高三09班\t0.323", "20220821\t2023届高三10班\t0.646", "20220821\t2023届高三12班\t0.250", - "20220821\t2023届高三2班\t0.576", - "20220821\t2023届高三3班\t0.708", - "20220821\t2023届高三9班\t0.323", - "20220822\t2023届高三10班\t0.125", - "20220822\t2023届高三8班\t0.323" + "20220822\t2023届高三08班\t0.323", + "20220822\t2023届高三10班\t0.125" ], "origin": "新教材必修第一册习题", "edit": [ @@ -231562,8 +232848,8 @@ "duration": -1, "usages": [ "20220824\t2023届高三10班\t0.936", - "20220825\t2023届高三2班\t0.970\t0.970\t0.970\t0.939\t0.667", - "20220825\t2023届高三8班\t1.000\t1.000\t1.000\t0.871\t0.742" + "20220825\t2023届高三02班\t0.970\t0.970\t0.970\t0.939\t0.667", + "20220825\t2023届高三08班\t1.000\t1.000\t1.000\t0.871\t0.742" ], "origin": "新教材必修第一册习题", "edit": [ @@ -232274,7 +233560,7 @@ "solution": "", "duration": -1, "usages": [ - "20220906\t2023届高三2班\t0.742" + "20220906\t2023届高三02班\t0.742" ], "origin": "新教材必修第一册习题", "edit": [ @@ -233317,12 +234603,12 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略, 等号成立时$x$的取值范围为$(-\\infty,-2]$", "solution": "", "duration": -1, "usages": [ - "20220831\t2023届高三10班\t0.793", - "20220831\t2023届高三2班\t0.688" + "20220831\t2023届高三02班\t0.688", + "20220831\t2023届高三10班\t0.793" ], "origin": "新教材必修第一册习题", "edit": [ @@ -233338,7 +234624,9 @@ "010105": { "id": "010105", "content": "(1) 求$-64$的立方根;\\\\\n(2) 求$256$的$4$次方根.", - "objs": [], + "objs": [ + "K0201002B" + ], "tags": [ "第二单元" ], @@ -233359,7 +234647,9 @@ "010106": { "id": "010106", "content": "求下列各根式的值:\\\\\n(1)$\\sqrt[5]{\\dfrac{243}{32}}$;\\\\\n(2) $-\\sqrt[3]{0.125}$;\\\\\n(3) $\\sqrt[7]{(-2)^7}$;\\\\\n(4) $\\sqrt[6]{(-27)^2}$.", - "objs": [], + "objs": [ + "K0201002B" + ], "tags": [ "第二单元" ], @@ -233380,7 +234670,9 @@ "010107": { "id": "010107", "content": "用有理数指数幂的形式表示下列各式(其中$x>0$, $y>0$):\\\\\n(1) $\\sqrt[3]{x^5}$;\\\\\n(2) $(\\sqrt[5]{x})^3$;\\\\\n(3) $\\sqrt[7]{x^3y^4}$;\\\\\n(4) $\\sqrt[7]{\\dfrac{x^3}{y^4}}$.", - "objs": [], + "objs": [ + "K0202002B" + ], "tags": [ "第二单元" ], @@ -233401,7 +234693,9 @@ "010108": { "id": "010108", "content": "用根式的形式表示下列各式(其中$a>0$):\\\\\n(1) $a^\\frac 23$;\\\\\n(2) $a^\\frac 34$;\\\\\n(3) $a^{-\\frac 25}$;\\\\\n(4) $a^{-\\frac 52}$.", - "objs": [], + "objs": [ + "K0202002B" + ], "tags": [ "第二单元" ], @@ -233423,7 +234717,9 @@ "id": "010109", "content": "求下列各式中$x$的值(其中$x>0$):\n(1) $x^3=27$;\\\\\n(2) $x^4=121$;\\\\\n(3) $x^\\frac 32=1000$;\\\\\n(4) $x^{-\\frac 43}=\\dfrac{16}{625}$.", "objs": [ - "K0324006B" + "K0324006B", + "K0203002B", + "K0201004B" ], "tags": [ "第二单元" @@ -233452,11 +234748,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a^\\frac{7}{12}$; (2) $a^{\\frac 12}$; (3) $a^2b^{-3}$; (4) $ab^{-\\frac 76}$", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t1.000\t1.000\t0.875\t0.906" + "20220907\t2023届高三02班\t1.000\t1.000\t0.875\t0.906" ], "origin": "新教材必修第一册习题", "edit": [ @@ -233470,7 +234766,9 @@ "010111": { "id": "010111", "content": "化简下列各式(其中$a>0$, $b>0$):\\\\\n(1) $\\dfrac{(2a^\\frac 23b^\\frac 12)(-6a^\\frac 12b^\\frac 13)}{3a^\\frac 16b^\\frac 56}$;\\\\\n(2) $(a^{2-\\sqrt 3}b)^{2+\\sqrt 3}\\cdot b^{2-\\sqrt 3}$.", - "objs": [], + "objs": [ + "K0203002B" + ], "tags": [ "第二单元" ], @@ -233491,7 +234789,9 @@ "010112": { "id": "010112", "content": "当$x<0$时, 求$|x|+\\sqrt[6]{x^6}+2\\sqrt[3]{x^3}$的值.", - "objs": [], + "objs": [ + "K0201002B" + ], "tags": [ "第二单元" ], @@ -233512,7 +234812,9 @@ "010113": { "id": "010113", "content": "设$a^{2x}=2$, 且$a>0$. 求$\\dfrac{a^{3x}+a^{-3x}}{a^x+a^{-x}}$的值.", - "objs": [], + "objs": [ + "K0203002B" + ], "tags": [ "第二单元" ], @@ -233543,11 +234845,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t0.844" + "20220907\t2023届高三02班\t0.844" ], "origin": "新教材必修第一册习题", "edit": [ @@ -233561,7 +234863,9 @@ "010115": { "id": "010115", "content": "把下列指数式写成对数式:\\\\\n(1) $3^4=81$;\\\\\n(2) $5^{-\\frac1 2}=x$.", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -233582,7 +234886,9 @@ "010116": { "id": "010116", "content": "将下列对数式写成指数式:\\\\\n(1) $\\log_{\\frac 13}27=-3$;\\\\\n(2) $\\log_2\\dfrac 18=-3$.", - "objs": [], + "objs": [ + "K0204004B" + ], "tags": [ "第二单元" ], @@ -233603,7 +234909,10 @@ "010117": { "id": "010117", "content": "求下列各式的值:\\\\\n(1) $\\log_3 27$;\\\\\n(2) $\\log_{\\frac 12}8$;\\\\\n(3) $\\ln \\dfrac 1{\\mathrm{e}}+\\lg \\sqrt {10}$.", - "objs": [], + "objs": [ + "K0204001B", + "K0204003B" + ], "tags": [ "第二单元" ], @@ -233624,7 +234933,10 @@ "010118": { "id": "010118", "content": "求下列各式中$x$的值:\\\\\n(1) $\\log_2x=5$;\\\\\n(2) $\\log_{\\sqrt 5}\\dfrac1{125}=x$;\\\\\n(3) $\\log_x4=\\dfrac 12$.", - "objs": [], + "objs": [ + "K0204001B", + "K0204004B" + ], "tags": [ "第二单元" ], @@ -233645,7 +234957,10 @@ "010119": { "id": "010119", "content": "求下列各式的值:\\\\\n(1) $\\log_2(2\\times 3\\sqrt 2)$;\\\\\n(2) $\\log_{21}3+\\log_{21}7$;\\\\\n(3) $\\log_5\\sqrt 6-\\dfrac 12\\log_5 150$;\\\\\n(4) $3^{\\log_31}+\\log_248-\\log_23$;\\\\\n(5) $3\\log_3\\dfrac 32-\\log_3\\dfrac 74+\\dfrac 12\\log_34+\\log_37$.", - "objs": [], + "objs": [ + "K0204002B", + "K0205002B" + ], "tags": [ "第二单元" ], @@ -233666,7 +234981,9 @@ "010120": { "id": "010120", "content": "已知$A=\\log_ax$, $B=\\log_ay$, $C=\\log_az$($a>0$且$a\\ne 1)$. 用$A$、$B$及$C$表示下列各式:\\\\\n(1) $\\log_a(xy^2)$;\\\\\n(2) $\\log_a\\dfrac{xy}{\\sqrt z}$;\\\\\n(3) $\\log_a(x^2y^2)+\\log_a(y\\sqrt x)$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -233687,7 +235004,9 @@ "010121": { "id": "010121", "content": "求下列各式的值:\\\\\n(1) $\\log_42\\sqrt 2$;\\\\\n(2) $\\log_23\\times \\log_92$;\\\\\n(3) $\\dfrac 3{\\log_26}+\\dfrac 3{\\log_36}$;\\\\\n(4) $(\\log_43+\\log_83)(\\log_32+\\log_92)+\\log_{\\frac 12}\\sqrt[4]{32}$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -233708,7 +235027,9 @@ "010122": { "id": "010122", "content": "已知$a=\\lg 5$, 用$a$表示$\\lg 2$和$\\lg$ $20$.", - "objs": [], + "objs": [ + "K0205002B" + ], "tags": [ "第二单元" ], @@ -233729,7 +235050,9 @@ "010123": { "id": "010123", "content": "求下列各式中$x$的取值范围:\\\\\n(1) $\\log_2(1-3x)$;\\\\\n(2) $\\log_a(x^2+x)$($a>0$且$a\\ne 1)$.", - "objs": [], + "objs": [ + "K0204001B" + ], "tags": [ "第二单元" ], @@ -233752,7 +235075,9 @@ "010124": { "id": "010124", "content": "求下列各式的值:\\\\\n(1) $\\log_48-\\log_{\\frac 19}3-\\log_{\\sqrt 2}4$;\\\\\n(2) $2^{\\log_65}\\times 3^{\\log_65}$;\\\\\n(3) $(\\lg 50)^2+\\lg 2\\times \\lg 50^2+(\\lg 2)^2$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -233780,11 +235105,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "约等于$22$($10^{1.35}$)", "solution": "", "duration": -1, "usages": [ - "20220907\t2023届高三2班\t0.969" + "20220907\t2023届高三02班\t0.969" ], "origin": "新教材必修第一册习题", "edit": [ @@ -233798,7 +235123,9 @@ "010126": { "id": "010126", "content": "已知$\\lg 2=a$, $\\lg 3=b$. 用$a$及$b$表示$\\log_2 3$及$\\log_{12}25$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -233819,7 +235146,10 @@ "010127": { "id": "010127", "content": "已知$5.4^x=3$, $0.6^y=3$. 求$\\dfrac 1x-\\dfrac 1y$的值.", - "objs": [], + "objs": [ + "K0204004B", + "K0205002B" + ], "tags": [ "第二单元" ], @@ -233842,7 +235172,9 @@ "010128": { "id": "010128", "content": "设$a$、$b$、$c$、$d$均为正数, 且$a$、$c$均不为$1$. 求证:\n$\\log_ab\\cdot \\log_cd=\\log_ad\\cdot \\log_cb$.", - "objs": [], + "objs": [ + "K0206002B" + ], "tags": [ "第二单元" ], @@ -233863,7 +235195,9 @@ "010129": { "id": "010129", "content": "若幂函数$y=x^a$的图像经过点$(\\sqrt[4]{3}, 3)$, 求此幂函数的表达式.", - "objs": [], + "objs": [ + "K0207001B" + ], "tags": [ "第二单元" ], @@ -233886,7 +235220,10 @@ "010130": { "id": "010130", "content": "求下列函数的定义域, 并作出它们的大致图像:\\\\\n(1) $y=x^\\frac 15$;\\\\\n(2) $y=x^{-2}$;\\\\\n(3) $y=x^{-\\frac 34}$.", - "objs": [], + "objs": [ + "K0207001B", + "K0207003B" + ], "tags": [ "第二单元" ], @@ -233909,7 +235246,9 @@ "010131": { "id": "010131", "content": "在固定压力差(压力差为常数)的前提下, 当气体通过圆形管道时, 其速率$v$(单位: $\\text{cm}^3/\\text{s}$)与管道半径$r$(单位: $\\text{cm}$)的四次方成正比. 若在半径为$3\\text{cm}$的管道中, 某气体的速率为$400\\text{cm}^3/\\text{s}$, 求该气体通过半径为$5\\text{cm}$的管道时的速率. (结果精确到$1\\text{cm}^3/\\text{s}$)", - "objs": [], + "objs": [ + "K0207001B" + ], "tags": [ "第二单元" ], @@ -233930,7 +235269,9 @@ "010132": { "id": "010132", "content": "比较下列各题中两个数的大小:\\\\\n(1) $3.1^{-\\frac 12}$与$3.2^{-\\frac 12}$;\\\\\n(2) $(a+2)^{\\frac 13}$与$a^{\\frac 13}$.", - "objs": [], + "objs": [ + "K0208004B" + ], "tags": [ "第二单元" ], @@ -233951,7 +235292,10 @@ "010133": { "id": "010133", "content": "下列幂函数在区间$(0, +\\infty)$上是严格增函数, 且图像关于原点成中心对称的是\\blank{50}(请填入全部正确的序号).\\\\\n\\textcircled{1} $y=x^\\frac 12$; \\textcircled{2} $y=x^\\frac 13$; \\textcircled{3} $y=x^\\frac 23$; \\textcircled{4} $y=x^{-\\frac 13}$.", - "objs": [], + "objs": [ + "K0208002B", + "K0207004B" + ], "tags": [ "第二单元" ], @@ -233972,7 +235316,9 @@ "010134": { "id": "010134", "content": "作出函数$y=\\dfrac{x-1}{x+2}$的大致图像.", - "objs": [], + "objs": [ + "K0208005B" + ], "tags": [ "第二单元" ], @@ -233996,7 +235342,10 @@ "010135": { "id": "010135", "content": "幂函数$y=x^{n(n+1)}$($n$为正整数)的图像一定经过\\blank{50}象限.", - "objs": [], + "objs": [ + "K0208001B", + "K0207003B" + ], "tags": [ "第二单元" ], @@ -234017,7 +235366,9 @@ "010136": { "id": "010136", "content": "若幂函数$y=x^s$在$00$且$a\\ne 1$. 假设无论$a$取何值, 函数$y=a^{2-x}$的图像恒经过一个定点, 求此定点的坐标.", - "objs": [], + "objs": [ + "K0210002B" + ], "tags": [ "第二单元" ], @@ -234217,7 +235585,9 @@ "010145": { "id": "010145", "content": "比较下列各题中两个数的大小:\\\\\n(1) $1.2^{2.6}$和$1.2^{2.61}$;\\\\\n(2) $(\\sqrt 3)^{-\\frac 13}$和$(\\dfrac{\\sqrt 3}3)^\\frac 12$.", - "objs": [], + "objs": [ + "K0210006B" + ], "tags": [ "第二单元" ], @@ -234238,7 +235608,9 @@ "010146": { "id": "010146", "content": "求下列不等式的解集:\\\\\n(1) $3^{x^2-2x+3}<3^{2x}$;\\\\\n(2) $(\\dfrac 13)^{\\sqrt{x}}\\le \\dfrac 1{81}$.", - "objs": [], + "objs": [ + "K0210006B" + ], "tags": [ "第二单元" ], @@ -234259,7 +235631,9 @@ "010147": { "id": "010147", "content": "已知指数函数$y=a^x$($a>0$且$a\\ne 1)$在区间$[1, 2]$上的最大值与最小值之和等于$6$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0211001B" + ], "tags": [ "第二单元" ], @@ -234280,7 +235654,9 @@ "010148": { "id": "010148", "content": "某公司去年购置平板电脑$50$台, 并计划从今年起, 新购置的平板电脑数将按每年$5\\%$的比例增长. 求从今年起的第$10$年新购置的平板电脑数. (结果精确到$1$台)", - "objs": [], + "objs": [ + "K0211002B" + ], "tags": [ "第二单元" ], @@ -234301,7 +235677,9 @@ "010149": { "id": "010149", "content": "在同一平面直角坐标系中, 指数函数$y=a^x$($a>0$且$a\\ne 1$)和一次函数$y=a(x+1)$的图像关系可能是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex,scale=0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2:1.3] plot (-\\x,{pow(2,\\x)});\n\\draw (-1.5,-1) -- (0.25,2.5);\n\\draw (0.2,1) -- (0,1) node [below left] {$1$};\n\\draw (-1,0.2) -- (-1,0) node [above left] {$-1$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale=0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2:1.3] plot (-\\x,{pow(2,\\x)});\n\\draw (-1,-1) -- (2,0.5);\n\\draw (0.2,1) -- (0,1) node [below left] {$1$};\n\\draw (1,0.2) -- (1,0) node [below] {$1$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale=0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2:1.3] plot (\\x,{pow(2,\\x)});\n\\draw (-1.5,-1) -- (0.25,2.5);\n\\draw (0.2,1) -- (0,1) node [below right] {$1$};\n\\draw (-1,0.2) -- (-1,0) node [below left] {$-1$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale=0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2:1.3] plot (\\x,{pow(2,\\x)});\n\\draw (-2,-0.5) -- (2,1.5);\n\\draw (0.2,1) -- (0,1) node [above left] {$1$};\n\\draw (-1,0.2) -- (-1,0) node [below] {$-1$};\n\\end{tikzpicture}}", - "objs": [], + "objs": [ + "K0210005B" + ], "tags": [ "第二单元" ], @@ -234322,7 +235700,9 @@ "010150": { "id": "010150", "content": "如图所示的是某池塘中的浮萍蔓延的面积$y$(单位: $\\text{m}^2$)与时间$t$(单位: 月)的关系: $y=a^t$($a>0$且$a\\ne 1)$. \n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (0,0) -- (4,0) node [below] {$t/\\text{月}$};\n\\draw [->] (0,0) -- (0,9) node [left] {$y/\\text{m}^2$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:3.1] plot (\\x,{pow(2,\\x)});\n\\foreach \\i in {1,2,3}{\\draw [dashed] (\\i,0) -- (\\i,{pow(2,\\i)}) -- (0,{pow(2,\\i)}); \\draw (\\i,0) node [below] {$\\i$};};\n\\foreach \\i in {2,4,8}{\\draw (0,\\i) node [left] {$\\i$};};\n\\end{tikzpicture}\n\\end{center}\n以下结论:\n\\textcircled{1} 这个指数函数的底数是$2$; \n\\textcircled{2} 第$5$个月时, 浮萍的面积就会超过$30\\text{m}^2$;\n\\textcircled{3} 浮萍面积从$4\\text{m}^2$到$12\\text{m}^2$需要经过$1.5$个月;\n\\textcircled{4} 浮萍每个月增加的面积都相等. 其中, 正确结论的序号是\\bracket{20}.\n\\fourch{\\textcircled{1}\\textcircled{2}\\textcircled{3}}{\\textcircled{1}\\textcircled{2}\\textcircled{3}\\textcircled{4}}{\\textcircled{2}\\textcircled{3}\\textcircled{4}}{\\textcircled{1}\\textcircled{2}}", - "objs": [], + "objs": [ + "K0210005B" + ], "tags": [ "第二单元" ], @@ -234343,7 +235723,9 @@ "010151": { "id": "010151", "content": "若$x>0$时, 指数函数$y=(a^2-1)^x$的值总大于$1$, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0211001B" + ], "tags": [ "第二单元" ], @@ -234364,7 +235746,9 @@ "010152": { "id": "010152", "content": "若$-11$, 若$a^{x^2+2x+1}0$且$a\\ne 1$);\\\\\n(2) $y=\\log_2\\dfrac1{x^2-2x+5}$.", - "objs": [], + "objs": [ + "K0212002B" + ], "tags": [ "第二单元" ], @@ -234448,7 +235839,10 @@ "010156": { "id": "010156", "content": "已知对数函数$y=\\log_ax$($a>0$且$a\\ne 1)$的图像经过点$(3, 2)$. 若点$P(b, 4)$为此函数图像上的点, 求实数$b$的值.", - "objs": [], + "objs": [ + "K0212001B", + "K0204004B" + ], "tags": [ "第二单元" ], @@ -234469,7 +235863,10 @@ "010157": { "id": "010157", "content": "在同一平面直角坐标系中画出下列函数的图像, 并指出这些函数图像之间的关系.\\\\\n(1) $y=\\log_3x$;\\\\\n(2) $y=\\log_{\\frac 13}x$;\\\\\n(3) $y=(\\dfrac 13)^x$.", - "objs": [], + "objs": [ + "K0213005B", + "K0213001B" + ], "tags": [ "第二单元" ], @@ -234490,7 +235887,9 @@ "010158": { "id": "010158", "content": "已知常数$a>0$且$a\\ne 1$, 假设无论$a$取何值, 函数$y=\\log_ax-1$的图像恒经过一个定点. 求此点的坐标.", - "objs": [], + "objs": [ + "K0213002B" + ], "tags": [ "第二单元" ], @@ -234513,7 +235912,10 @@ "010159": { "id": "010159", "content": "根据下列不等式, 确定底数$a$的取值范围:\\\\\n(1) $\\log_a 0.2<\\log_a 0.1$;\\\\\n(2) $\\log_a\\pi >\\log_a\\mathrm{e}$.", - "objs": [], + "objs": [ + "K0213008B", + "K0214002B" + ], "tags": [ "第二单元" ], @@ -234534,7 +235936,9 @@ "010160": { "id": "010160", "content": "已知$y=\\log_{a^2-1}x$在区间$(0, +\\infty)$上是严格减函数, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0213007B" + ], "tags": [ "第二单元" ], @@ -234555,7 +235959,9 @@ "010161": { "id": "010161", "content": "已知对数函数$y=\\log_ax$($a>1$)在区间$[1, 2]$上的最大值比最小值大$1$, 求$a$的值.", - "objs": [], + "objs": [ + "K0214002B" + ], "tags": [ "第二单元" ], @@ -234601,7 +236007,10 @@ "010163": { "id": "010163", "content": "设常数$a>0$且$a\\ne 1$, 求函数$y=\\log_a(a-a^x)$的定义域.", - "objs": [], + "objs": [ + "K0212002B", + "K0211001B" + ], "tags": [ "第二单元" ], @@ -234622,7 +236031,9 @@ "010164": { "id": "010164", "content": "根据下列不等式, 比较正数$m$及$n$的大小:\\\\\n(1) $\\log_3m<\\log_3n$;\\\\\n(2) $\\log_am<\\log_an$($a>0$且$a\\ne 1$);\\\\\n(3) $\\log_mN<\\log_nN$($0=latex,scale = 0.6]\n \\draw [->] (-1,0) -- (4,0) node [below] {$x$};\n \\draw [->] (0,-1) -- (0,4) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\foreach \\i in {1,2,3}\n {\n \\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};\n \\draw (0.1,\\i) -- (0,\\i) node [left] {$\\i$}; \n };\n \\draw (0,0) -- (1,1) -- (2,1) (2,2) -- (3,2);\n \\draw [dashed] (0,1) -- (1,1) -- (1,0) (0,2) -- (2,2) (2,0) -- (2,2) (3,0) -- (3,2);\n \\filldraw [fill = white, draw = black] (2,1) circle (0.05) (2,2) circle (0.05) (3,2) circle (0.05);\n \\draw (1.5,-1) node [below] {(1)};\n \\end{tikzpicture}\n \\begin{tikzpicture}[>=latex,scale = 0.6]\n \\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n \\draw [->] (0,-1) -- (0,4) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\foreach \\i in {1,2}\n {\n \\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};\n \\draw (0.1,\\i) -- (0,\\i) node [left] {$\\i$}; \n };\n \\foreach \\i in {-1,-2}\n {\n \\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};\n };\n \\draw (-2,2) -- (-1,2) -- (0,0) -- (1,2) -- (2,2);\n \\draw [dashed] (-2,0) -- (-2,2) (2,0) -- (2,2) (-1,2) -- (1,2);\n \\filldraw [fill = white, draw = black] (-2,2) circle (0.05) (2,2) circle (0.05);\n \\draw (0,-1) node [below] {(2)};\n \\end{tikzpicture}\n \\begin{tikzpicture}[>=latex,scale = 0.6]\n \\draw [->] (-2.5,0) -- (5.5,0) node [below] {$x$};\n \\draw [->] (0,-1) -- (0,4) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\foreach \\i in {-2,-1,1,2,3,4,5}\n {\n \\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};\n \n };\n \\foreach \\i in {-1,1,2,3}\n {\n \\draw (0.1,\\i) -- (0,\\i) node [left] {$\\i$}; \n };\n \\draw [domain = -2:5] plot (\\x,{2/49*(3+2*sqrt(2))*\\x*\\x+4/49*(-1-3*sqrt(2))*\\x+(17-40*sqrt(2))/49});\n \\draw [dashed] (0,-1) -- ({7*sqrt(2)-9},-1) (5,0) -- (5,3) -- (0,3) (-2,0) -- (-2,1) -- (0,1);\n \\filldraw [fill = white, draw = black] (-2,1) circle (0.05) (5,3) circle (0.05);\n \\draw (1.5,-1) node [below] {(3)};\n \\end{tikzpicture}\n\\end{center}", - "objs": [], + "objs": [ + "K0216002B", + "KNONE" + ], "tags": [ "第二单元" ], @@ -234773,7 +236197,9 @@ "010171": { "id": "010171", "content": "设$a$是常数, 求下列函数的定义域\\\\\n(1) $y=\\dfrac1{|x|-a}$;\\\\\n(2) $y=\\sqrt{x(x-a)}$.", - "objs": [], + "objs": [ + "K0215003B" + ], "tags": [ "第二单元" ], @@ -234794,7 +236220,9 @@ "010172": { "id": "010172", "content": "已知函数$y=f(x)$的表达式为$f(x)= \\begin{cases} 2x(3+x), & x\\ge 0,\\\\ 2x(3-x), & x<0.\\end{cases}$ 求$f(2)$, $f(-4)$及$f(-a)$, 其中$a$为实数.", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -234815,7 +236243,9 @@ "010173": { "id": "010173", "content": "若函数$y=f(x)$的定义域为$\\mathbf{R}$, 则$y=f(x)$为奇函数的一个充要条件为\\bracket{20}.\n\\twoch{$f(0)=0$}{对任意$x\\in \\mathbf{R}$, $f(x)=0$都成立}{存在某个$x_0\\in \\mathbf{R}$, 使得$f(x_0)+f(-x_0)=0$}{对任意给定的$x\\in \\mathbf{R}$, $f(x)+f(-x)=0$都成立}", - "objs": [], + "objs": [ + "KNONE" + ], "tags": [ "第二单元" ], @@ -234838,7 +236268,9 @@ "010174": { "id": "010174", "content": "证明下列函数$y=f(x)$为偶函数:\\\\\n(1) $f(x)=x^2+x^{-2}$;\\\\\n(2) $f(x)=\\dfrac{x(2^x-1)}{2^x+1}$.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -234859,7 +236291,9 @@ "010175": { "id": "010175", "content": "证明下列函数$y=f(x)$为奇函数:\\\\\n(1) $f(x)=x^{-3}$;\\\\\n(2) $f(x)=\\dfrac{\\mathrm{e}^x-\\mathrm{e}^{-x}}2$", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -234880,7 +236314,9 @@ "010176": { "id": "010176", "content": "判断下列函数$y=f(x)$的奇偶性, 并说明理由:\\\\\n(1) $f(x)=2x+\\sqrt[3]x$;\\\\\n(2) $f(x)=2x^4-x^2$;\\\\\n(3) $f(x)=x^2-x$;\\\\\n(4) $f(x)=\\dfrac{1-x}{1+x}$;\\\\\n(5) $f(x)=\\lg\\dfrac {1-x}{1+x}$.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -234901,7 +236337,9 @@ "010177": { "id": "010177", "content": "证明:函数$y=x-\\dfrac 1x$, $x\\in (-\\infty, 0)$是严格增函数.", - "objs": [], + "objs": [ + "K0219003B" + ], "tags": [ "第二单元" ], @@ -234929,11 +236367,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ - "20220914\t2023届高三2班\t0.813" + "20220914\t2023届高三02班\t0.813" ], "origin": "新教材必修第一册习题", "edit": [ @@ -234947,7 +236385,9 @@ "010179": { "id": "010179", "content": "求下列函数的最大值与最小值, 并写出取最值时相应自变量的值:\\\\\n(1) $y=x^2-4x-2$;\\\\\n(2) $y=6x-3x^2$;\\\\\n(3) $y=-x^2-4x-3$, $x\\in [-3, 1]$;\\\\\n(4) $y=x^2-2x-3$, $x\\in [-2, 0]$.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -234968,7 +236408,9 @@ "010180": { "id": "010180", "content": "求函数$y=\\log_{\\frac 12}(x+2)$, $x\\in [2, 6]$的最大值与最小值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -234991,7 +236433,9 @@ "010181": { "id": "010181", "content": "已知$y=x^2+px+q$和$y=x+\\dfrac 4x$都是定义在$[1, 4]$上的函数, 且在$x_0$处同时取到相同的最小值. 求$y=x^2+px+q$的最大值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -235012,7 +236456,9 @@ "010182": { "id": "010182", "content": "已知实数$b<2$, 而函数$y=x^2+ax+1$, $x\\in [b, 2]$是偶函数. 求实数$a$、$b$的值.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -235033,7 +236479,9 @@ "010183": { "id": "010183", "content": "判断下列函数$y=f(x)$的奇偶性, 并说明理由:\\\\\n(1) $f(x)=\\dfrac{10^x-10^{-x}}{10^x+10^{-x}}$;\\\\\n(2) $f(x)=x(\\dfrac 1{2^x-1}+\\dfrac 12)$.", - "objs": [], + "objs": [ + "K0218001B" + ], "tags": [ "第二单元" ], @@ -235054,7 +236502,10 @@ "010184": { "id": "010184", "content": "当表达式$f(x)=$\\blank{50}时, 函数$y=f(x)$同时满足以下条件:\\\\\n\\textcircled{1} 不是偶函数;\\\\\n\\textcircled{2} 在区间$(-\\infty, -1)$上是严格减函数;\\\\\n\\textcircled{3} 在区间$(0, 1)$上是严格增函数.", - "objs": [], + "objs": [ + "K0219001B", + "K0217004B" + ], "tags": [ "第二单元" ], @@ -235075,7 +236526,14 @@ "010185": { "id": "010185", "content": "作出函数$y=x^2-2|x|$的大致图像, 并分别写出它的定义域、奇偶性、单调区间及最小值.", - "objs": [], + "objs": [ + "K0215003B", + "K0217004B", + "K0219002B", + "K0220003B", + "K0221002B", + "KNONE" + ], "tags": [ "第二单元" ], @@ -235098,7 +236556,12 @@ "010186": { "id": "010186", "content": "研究函数$y=\\dfrac1{1+x^2}$的定义域、奇偶性、单调性及最大值.", - "objs": [], + "objs": [ + "K0221002B", + "K0219003B", + "K0218001B", + "K0215003B" + ], "tags": [ "第二单元" ], @@ -235128,11 +236591,11 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[2,+\\infty)$", "solution": "", "duration": -1, "usages": [ - "20220914\t2023届高三2班\t1.000" + "20220914\t2023届高三02班\t1.000" ], "origin": "新教材必修第一册习题", "edit": [ @@ -235148,7 +236611,9 @@ "010188": { "id": "010188", "content": "设$t$是实数, 且$t<4$. 求函数$y=|2^{x+1}-8|$, $x\\in [t, 4]$的最小值.", - "objs": [], + "objs": [ + "K0221002B" + ], "tags": [ "第二单元" ], @@ -235248,11 +236713,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略, 近似值为$0.5$", "solution": "", "duration": -1, "usages": [ - "20220913\t2023届高三2班\t0.097" + "20220913\t2023届高三02班\t0.097" ], "origin": "新教材必修第一册习题", "edit": [ @@ -235344,11 +236809,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ - "20220913\t2023届高三2班\t0.774" + "20220913\t2023届高三02班\t0.774" ], "origin": "新教材必修第一册习题", "edit": [ @@ -235369,11 +236834,11 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,0)\\cup (0,1)$", "solution": "", "duration": -1, "usages": [ - "20220913\t2023届高三2班\t0.484" + "20220913\t2023届高三02班\t0.484" ], "origin": "新教材必修第一册习题", "edit": [ @@ -235387,7 +236852,9 @@ "010198": { "id": "010198", "content": "已知函数$y=x^2-4x-5$, $x\\in [1, 3]$, 判断其是否存在反函数. 若存在, 求出反函数; 若不存在, 说明理由.", - "objs": [], + "objs": [ + "K0225002B" + ], "tags": [ "第二单元" ], @@ -235410,7 +236877,9 @@ "010199": { "id": "010199", "content": "求下列函数的反函数:\\\\\n(1) $y=-x^3$;\\\\\n(2) $y=\\dfrac x{x+2}$;\\\\\n(3) $y=x^2+1$, $x\\in (-\\infty, 0)$.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -235431,7 +236900,9 @@ "010200": { "id": "010200", "content": "求下列函数的反函数:\\\\\n(1) $y=10^x+1$;\\\\\n(2) $y=\\log_2(x+1)$;\\\\\n(3) $y=\\log_2(2x)$.", - "objs": [], + "objs": [ + "K0225005B" + ], "tags": [ "第二单元" ], @@ -235452,7 +236923,9 @@ "010201": { "id": "010201", "content": "已知$f(x)=1-\\log_2x$, 设$y=f^{-1}(x)$是$y=f(x)$的反函数. 求$f^{-1}(-3)$的值.", - "objs": [], + "objs": [ + "K0225004B" + ], "tags": [ "第二单元" ], @@ -235473,7 +236946,9 @@ "010202": { "id": "010202", "content": "已知函数$y=\\dfrac a{x+1}$的反函数的图像经过点$(\\dfrac 12, 1)$, 求实数$a$的值.", - "objs": [], + "objs": [ + "K0226004B" + ], "tags": [ "第二单元" ], @@ -248038,7 +249513,13 @@ "010789": { "id": "010789", "content": "自由落体运动的位移$d$(单位: $\\text{m}$)与时间$t$(单位: $\\text{s}$)满足函数关系$d=\\dfrac 12gt^2$($g$为重力加速度).\\\\\n(1) 分别求$[4,4.1]$、$[4,4.01]$、$[4,4.001]$这些时间段内自由落体的平均速度;\\\\\n(2) 求$t=4$时的瞬时速度;\\\\\n(3) 求$t=a$($a>0$)时的瞬时速度;\\\\\n(4) 借助(3)的结果, 求$t=\\dfrac 52$时的瞬时速度.", - "objs": [], + "objs": [ + "K0227001X", + "K0227002X", + "K0227003X", + "K0227004X", + "K0227005X" + ], "tags": [ "第二单元" ], @@ -248059,7 +249540,13 @@ "010790": { "id": "010790", "content": "竖直向上发射的火箭熄火时上升速度达到$100\\text{m}/\\text{s}$, 此后其位移$H$(单位: $\\text{m}$)与时间$t$(单位: $\\text{s}$)近似满足函数关系$H=100t-5t^2$.\\\\\n(1) 分别求火箭在$[0, 2]$、$[2, 4]$这些时间段内的平均速度;\\\\\n(2) 求火箭在$t=2$时的瞬时速度;\\\\\n(3) 熄火后多长时间火箭上升速度为$0$?", - "objs": [], + "objs": [ + "K0227001X", + "K0227002X", + "K0227003X", + "K0227004X", + "K0227005X" + ], "tags": [ "第二单元" ], @@ -248080,7 +249567,13 @@ "010791": { "id": "010791", "content": "某水管的流水量$y$(单位: $\\text{m}^3$)与时间$t$(单位: $\\text{s}$)满足函数关系$y=f(t)$, 其中$f(t)=3t$.\\\\\n(1) 求$f(t)$在$t=a$处的导数$f'(a)$;\\\\\n(2) $f'(a)$的实际意义是什么?\\\\\n(3) 随着$a$的取值变化, $f'(a)$是否发生变化? 为什么?", - "objs": [], + "objs": [ + "K0227001X", + "K0227002X", + "K0227003X", + "K0227004X", + "K0227005X" + ], "tags": [ "第二单元" ], @@ -248101,7 +249594,13 @@ "010792": { "id": "010792", "content": "将石子投入水中, 水面产生的圆形波纹不断扩散. 计算:\\\\\n(1) 当半径$r$从$a$增加到$a+h$($h>0$)时, 圆面积相对于半径的平均变化率;\\\\\n(2) 当半径$r=a$时, 圆面积相对于半径的瞬时变化率.", - "objs": [], + "objs": [ + "K0227001X", + "K0227002X", + "K0227003X", + "K0227004X", + "K0227005X" + ], "tags": [ "第二单元" ], @@ -248124,7 +249623,9 @@ "010793": { "id": "010793", "content": "函数$y=f(x)$的图像如图所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-1,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed] (5,0) -- (5,4) coordinate (S) node [above] {$Q$} -- (0,4) (1,0) -- (1,1) coordinate (T) node [right] {$P$} -- (0,1);\n\\draw (1,0) node [below] {$1$} (5,0) node [below] {$5$} (0,1) node [left] {$1$} (0,4) node [left] {$4$};\n\\draw ($(S)!-0.2!(T)$) -- ($(T)!-0.2!(S)$);\n\\draw [domain = 0.5:5.5] plot (\\x,{-(1/2)+(33*\\x)/20-3*pow(\\x,2)/20}) node [right] {$y=f(x)$};\n\\end{tikzpicture}\n\\end{center}\n(1) 求割线$PQ$的斜率;\\\\\n(2) 当点$Q$沿曲线向点$P$运动时, 割线$PQ$的斜率会变大还是变小?", - "objs": [], + "objs": [ + "K0228001X" + ], "tags": [ "第二单元" ], @@ -248145,7 +249646,10 @@ "010794": { "id": "010794", "content": "已知$f(x)=-x^2$, 求曲线$y=f(x)$在下列各点处的切线斜率, 并说明这些斜率的值是如何随着自变量的变化而变化的:\n(1) $x=-2$;\\\\\n(2) $x=-1$;\\\\\n(3) $x=0$;\\\\\n(4) $x=1$;\\\\\n(5) $x=2$.", - "objs": [], + "objs": [ + "K0228003X", + "K0228004X" + ], "tags": [ "第二单元" ], @@ -248166,7 +249670,9 @@ "010795": { "id": "010795", "content": "借助函数图像, 判断下列导数的正负:\\\\\n(1) $f'(-\\dfrac \\pi 4)$, 其中$f(x)=\\cos x$;\\\\\n(2) $f'(3)$, 其中$f(x)=\\ln x$.", - "objs": [], + "objs": [ + "K0229004X" + ], "tags": [ "第二单元" ], @@ -248189,7 +249695,13 @@ "010796": { "id": "010796", "content": "已知车辆启动后的一段时间内, 车轮旋转的角度和时间(单位: 秒)的平方成正比, 且车辆启动后车轮转动第一圈需要$1$秒.\\\\\n(1) 求车轮转动前$2$秒的平均角速度;\\\\\n(2) 求车轮在转动开始后第$3$秒的瞬时角速度.", - "objs": [], + "objs": [ + "K0227001X", + "K0227002X", + "K0227003X", + "K0227004X", + "K0227005X" + ], "tags": [ "第二单元" ], @@ -248210,7 +249722,10 @@ "010797": { "id": "010797", "content": "根据导数的几何意义, 求函数$y=\\sqrt{4-x^2}$在下列各点处的导数:\\\\\n(1) $x=-1$;\\\\\n(2) $x=0$;\\\\\n(3) $x=1$.", - "objs": [], + "objs": [ + "K0229003X", + "K0229002X" + ], "tags": [ "第二单元" ], @@ -248231,7 +249746,9 @@ "010798": { "id": "010798", "content": "已知函数$y=f(x)$在$x=1$处的切线方程为$y=4x-3$, 求$f(1)$和$f'(1)$.", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元" ], @@ -248252,7 +249769,9 @@ "010799": { "id": "010799", "content": "如图, 已知直线$l$是曲线$y=f(x)$在$x=3$处的切线, 求$f'(3)$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (-5,-1) .. controls (0,4) and (0,-1) .. (3,-2);\n\\draw (3,-2) .. controls (3.9,-2.3) and (4,-1).. (5,-1) node [right] {$y=f(x)$};\n\\filldraw (0,-1) circle (0.05) node [below left] {$-1$} coordinate (Q);\n\\filldraw (3,-2) circle (0.05) node [below] {$P$} coordinate (P);\n\\draw ($(P)!-1!(Q)$) node [right] {$l$} -- ($(P)!2.5!(Q)$);\n\\draw [dashed] (3,0) node [below right] {$3$} -- (3,-2) -- (0,-2) node [left] {$-2$};\n\\end{tikzpicture}\n\\end{center}", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元" ], @@ -248273,7 +249792,9 @@ "010800": { "id": "010800", "content": "求下列函数$y=f(x)$的导数:\\\\\n(1) $f(x)=\\pi$;\\\\\n(2) $f(x)=\\sqrt[3]{x^5}$;\\\\\n(3) $f(x)=\\dfrac1{x^3}$.", - "objs": [], + "objs": [ + "K0229002X" + ], "tags": [ "第二单元" ], @@ -248294,7 +249815,10 @@ "010801": { "id": "010801", "content": "求曲线$y=\\cos x$在$x=\\pi 2$处的切线方程.", - "objs": [], + "objs": [ + "K0229004X", + "K0228003X" + ], "tags": [ "第二单元" ], @@ -248315,7 +249839,10 @@ "010802": { "id": "010802", "content": "已知曲线$y=x^3$在原点以外某点$P$处切线的斜率为$a$.\\\\\n(1) 求点$P$的坐标;\\\\\n(2) 判断$a$的正负.", - "objs": [], + "objs": [ + "K0229002X", + "K0228003X" + ], "tags": [ "第二单元" ], @@ -248336,7 +249863,9 @@ "010803": { "id": "010803", "content": "求曲线$y=x^3-3x+5$平行于$x$轴的切线及其切点坐标.", - "objs": [], + "objs": [ + "K0233003X" + ], "tags": [ "第二单元" ], @@ -248357,7 +249886,10 @@ "010804": { "id": "010804", "content": "求曲线$y=\\dfrac 1x$平行于直线$y=-x$的切线及其切点坐标.", - "objs": [], + "objs": [ + "K0229002X", + "K0228003X" + ], "tags": [ "第二单元" ], @@ -248378,7 +249910,9 @@ "010805": { "id": "010805", "content": "求下列函数$y=f(x)$的导数:\\\\\n(1) $f(x)=2x^{\\mathrm{e}}-\\mathrm{e}^2$;\\\\\n(2) $f(x)=\\mathrm{e}^x\\cos x$;\\\\\n(3) $f(x)=\\dfrac{x-1}{x-2}$;\\\\\n(4) $f(x)=\\dfrac{\\ln x}{\\sin x}$.", - "objs": [], + "objs": [ + "K0230004X" + ], "tags": [ "第二单元" ], @@ -248399,7 +249933,12 @@ "010806": { "id": "010806", "content": "用两种方法求函数$y=(x-2)(3-4x)$的导数.", - "objs": [], + "objs": [ + "K0230002X", + "K0229002X", + "K0230001X", + "K0230003X" + ], "tags": [ "第二单元" ], @@ -248420,7 +249959,11 @@ "010807": { "id": "010807", "content": "已知函数$y=f(x)$与$y=g(x)$满足条件$f(1)=2$, $f'(1)=3$, $g(1)=4$与$g'(1)=5$.对于下列函数$y=h(x)$, 求$h(1)$和$h'(1)$:\\\\\n(1) $h(x)=2g(x)-\\dfrac 13f(x)$;\\\\\n(2) $h(x)=2g(x)f(x)-\\dfrac 13$;\\\\\n(3) $h(x)=\\dfrac{2g(x)-1}{3f(x)}$.", - "objs": [], + "objs": [ + "K0230001X", + "K0230002X", + "K0230003X" + ], "tags": [ "第二单元" ], @@ -248441,7 +249984,9 @@ "010808": { "id": "010808", "content": "利用$y=f(ax+b)$型复合函数的求导法则, 求下列函数的导数:\\\\\n(1) $y= \\sqrt{2x-5}$;\\\\\n(2) $y=\\cos \\dfrac x2$;\\\\\n(3) $y= \\dfrac 1{\\mathrm{e}^{x+1}}$.", - "objs": [], + "objs": [ + "K0231003X" + ], "tags": [ "第二单元" ], @@ -248462,7 +250007,11 @@ "010809": { "id": "010809", "content": "用两种方法求函数$y= \\dfrac 2{x-1}$的导数.", - "objs": [], + "objs": [ + "K0230002X", + "K0229002X", + "K0231003X" + ], "tags": [ "第二单元" ], @@ -248483,7 +250032,12 @@ "010810": { "id": "010810", "content": "某种动物的体温犜(单位: $^\\circ\\text{C}$)与太阳落山后经过的时间$t$(单位: $\\text{min}$)满足函数关系$T=\\dfrac{120}{t+5}+15$.\\\\\n(1) 当$t=5$时, 求该动物体温的瞬时变化率;\\\\\n(2) 在哪一时刻该动物体温的瞬时变化率是$-2^\\circ\\text{C}/\\text{min}$? (结果精确到$0.1\\text{min}$)", - "objs": [], + "objs": [ + "K0230002X", + "K0229002X", + "K0231003X", + "K0227004X" + ], "tags": [ "第二单元" ], @@ -250912,21 +252466,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$\\{1,2,3,4,6\\}$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.967", + "20220913\t2023届高三02班\t0.967", + "20220913\t2023届高三04班\t0.897", + "20220913\t2023届高三05班\t0.973", + "20220913\t2023届高三06班\t0.950", + "20220913\t2023届高三07班\t0.903", "20220913\t2023届高三10班\t0.971", "20220913\t2023届高三11班\t0.957", - "20220913\t2023届高三1班\t0.967", - "20220913\t2023届高三2班\t0.967", - "20220913\t2023届高三4班\t0.897", - "20220913\t2023届高三5班\t0.973", - "20220913\t2023届高三6班\t0.950", - "20220913\t2023届高三7班\t0.903", - "20220914\t2023届高三12班\t1.000", - "20220914\t2023届高三8班\t0.906", - "20220914\t2023届高三9班\t0.938" + "20220914\t2023届高三08班\t0.906", + "20220914\t2023届高三09班\t0.938", + "20220914\t2023届高三12班\t1.000" ], "origin": "2022届高三上学期周末卷1试题1", "edit": [ @@ -250950,21 +252504,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$(-1,2)$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t1.000", + "20220913\t2023届高三02班\t0.967", + "20220913\t2023届高三04班\t0.931", + "20220913\t2023届高三05班\t0.919", + "20220913\t2023届高三06班\t0.975", + "20220913\t2023届高三07班\t1.000", "20220913\t2023届高三10班\t1.000", "20220913\t2023届高三11班\t1.000", - "20220913\t2023届高三1班\t1.000", - "20220913\t2023届高三2班\t0.967", - "20220913\t2023届高三4班\t0.931", - "20220913\t2023届高三5班\t0.919", - "20220913\t2023届高三6班\t0.975", - "20220913\t2023届高三7班\t1.000", - "20220914\t2023届高三12班\t1.000", - "20220914\t2023届高三8班\t1.000", - "20220914\t2023届高三9班\t1.000" + "20220914\t2023届高三08班\t1.000", + "20220914\t2023届高三09班\t1.000", + "20220914\t2023届高三12班\t1.000" ], "origin": "2022届高三上学期周末卷1试题2", "edit": [ @@ -250990,21 +252544,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$(1,2)$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.967", + "20220913\t2023届高三02班\t0.933", + "20220913\t2023届高三04班\t0.966", + "20220913\t2023届高三05班\t0.973", + "20220913\t2023届高三06班\t0.975", + "20220913\t2023届高三07班\t0.935", "20220913\t2023届高三10班\t0.914", "20220913\t2023届高三11班\t0.913", - "20220913\t2023届高三1班\t0.967", - "20220913\t2023届高三2班\t0.933", - "20220913\t2023届高三4班\t0.966", - "20220913\t2023届高三5班\t0.973", - "20220913\t2023届高三6班\t0.975", - "20220913\t2023届高三7班\t0.935", - "20220914\t2023届高三12班\t1.000", - "20220914\t2023届高三8班\t0.969", - "20220914\t2023届高三9班\t0.969" + "20220914\t2023届高三08班\t0.969", + "20220914\t2023届高三09班\t0.969", + "20220914\t2023届高三12班\t1.000" ], "origin": "2022届高三上学期周末卷1试题3", "edit": [ @@ -251026,21 +252580,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.967", + "20220913\t2023届高三02班\t0.933", + "20220913\t2023届高三04班\t0.931", + "20220913\t2023届高三05班\t0.973", + "20220913\t2023届高三06班\t0.975", + "20220913\t2023届高三07班\t0.968", "20220913\t2023届高三10班\t0.914", "20220913\t2023届高三11班\t0.957", - "20220913\t2023届高三1班\t0.967", - "20220913\t2023届高三2班\t0.933", - "20220913\t2023届高三4班\t0.931", - "20220913\t2023届高三5班\t0.973", - "20220913\t2023届高三6班\t0.975", - "20220913\t2023届高三7班\t0.968", - "20220914\t2023届高三12班\t0.909", - "20220914\t2023届高三8班\t0.969", - "20220914\t2023届高三9班\t0.969" + "20220914\t2023届高三08班\t0.969", + "20220914\t2023届高三09班\t0.969", + "20220914\t2023届高三12班\t0.909" ], "origin": "2022届高三上学期周末卷1试题4", "edit": [ @@ -251086,21 +252640,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$(0,+\\infty)$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.967", + "20220913\t2023届高三02班\t0.967", + "20220913\t2023届高三04班\t0.897", + "20220913\t2023届高三05班\t1.000", + "20220913\t2023届高三06班\t0.925", + "20220913\t2023届高三07班\t0.903", "20220913\t2023届高三10班\t1.000", "20220913\t2023届高三11班\t0.957", - "20220913\t2023届高三1班\t0.967", - "20220913\t2023届高三2班\t0.967", - "20220913\t2023届高三4班\t0.897", - "20220913\t2023届高三5班\t1.000", - "20220913\t2023届高三6班\t0.925", - "20220913\t2023届高三7班\t0.903", - "20220914\t2023届高三12班\t1.000", - "20220914\t2023届高三8班\t0.875", - "20220914\t2023届高三9班\t0.969" + "20220914\t2023届高三08班\t0.875", + "20220914\t2023届高三09班\t0.969", + "20220914\t2023届高三12班\t1.000" ], "origin": "2022届高三上学期周末卷1试题6", "edit": [ @@ -251119,21 +252673,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$60$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.933", + "20220913\t2023届高三02班\t0.733", + "20220913\t2023届高三04班\t0.793", + "20220913\t2023届高三05班\t0.892", + "20220913\t2023届高三06班\t0.850", + "20220913\t2023届高三07班\t0.710", "20220913\t2023届高三10班\t0.857", "20220913\t2023届高三11班\t0.826", - "20220913\t2023届高三1班\t0.933", - "20220913\t2023届高三2班\t0.733", - "20220913\t2023届高三4班\t0.793", - "20220913\t2023届高三5班\t0.892", - "20220913\t2023届高三6班\t0.850", - "20220913\t2023届高三7班\t0.710", - "20220914\t2023届高三12班\t0.773", - "20220914\t2023届高三8班\t0.719", - "20220914\t2023届高三9班\t0.938" + "20220914\t2023届高三08班\t0.719", + "20220914\t2023届高三09班\t0.938", + "20220914\t2023届高三12班\t0.773" ], "origin": "2022届高三上学期周末卷1试题7", "edit": [ @@ -251154,21 +252708,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$[-1,1]$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.967", + "20220913\t2023届高三02班\t0.933", + "20220913\t2023届高三04班\t1.000", + "20220913\t2023届高三05班\t1.000", + "20220913\t2023届高三06班\t0.975", + "20220913\t2023届高三07班\t0.968", "20220913\t2023届高三10班\t1.000", "20220913\t2023届高三11班\t1.000", - "20220913\t2023届高三1班\t0.967", - "20220913\t2023届高三2班\t0.933", - "20220913\t2023届高三4班\t1.000", - "20220913\t2023届高三5班\t1.000", - "20220913\t2023届高三6班\t0.975", - "20220913\t2023届高三7班\t0.968", - "20220914\t2023届高三12班\t0.955", - "20220914\t2023届高三8班\t1.000", - "20220914\t2023届高三9班\t1.000" + "20220914\t2023届高三08班\t1.000", + "20220914\t2023届高三09班\t1.000", + "20220914\t2023届高三12班\t0.955" ], "origin": "2022届高三上学期周末卷1试题8", "edit": [ @@ -251208,21 +252762,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{5\\sqrt{6}}2$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.967", + "20220913\t2023届高三02班\t0.900", + "20220913\t2023届高三04班\t0.862", + "20220913\t2023届高三05班\t0.865", + "20220913\t2023届高三06班\t0.925", + "20220913\t2023届高三07班\t0.903", "20220913\t2023届高三10班\t0.971", "20220913\t2023届高三11班\t1.000", - "20220913\t2023届高三1班\t0.967", - "20220913\t2023届高三2班\t0.900", - "20220913\t2023届高三4班\t0.862", - "20220913\t2023届高三5班\t0.865", - "20220913\t2023届高三6班\t0.925", - "20220913\t2023届高三7班\t0.903", - "20220914\t2023届高三12班\t0.955", - "20220914\t2023届高三8班\t0.906", - "20220914\t2023届高三9班\t0.969" + "20220914\t2023届高三08班\t0.906", + "20220914\t2023届高三09班\t0.969", + "20220914\t2023届高三12班\t0.955" ], "origin": "2022届高三上学期周末卷1试题10", "edit": [ @@ -251241,21 +252795,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$[1,\\dfrac 54)$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.667", + "20220913\t2023届高三02班\t0.333", + "20220913\t2023届高三04班\t0.276", + "20220913\t2023届高三05班\t0.351", + "20220913\t2023届高三06班\t0.375", + "20220913\t2023届高三07班\t0.065", "20220913\t2023届高三10班\t0.371", "20220913\t2023届高三11班\t0.217", - "20220913\t2023届高三1班\t0.667", - "20220913\t2023届高三2班\t0.333", - "20220913\t2023届高三4班\t0.276", - "20220913\t2023届高三5班\t0.351", - "20220913\t2023届高三6班\t0.375", - "20220913\t2023届高三7班\t0.065", - "20220914\t2023届高三12班\t0.318", - "20220914\t2023届高三8班\t0.312", - "20220914\t2023届高三9班\t0.156" + "20220914\t2023届高三08班\t0.312", + "20220914\t2023届高三09班\t0.156", + "20220914\t2023届高三12班\t0.318" ], "origin": "2022届高三上学期周末卷1试题11", "edit": [ @@ -251274,21 +252828,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$13$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.967", + "20220913\t2023届高三02班\t0.967", + "20220913\t2023届高三04班\t0.966", + "20220913\t2023届高三05班\t0.865", + "20220913\t2023届高三06班\t0.950", + "20220913\t2023届高三07班\t0.742", "20220913\t2023届高三10班\t0.829", "20220913\t2023届高三11班\t0.652", - "20220913\t2023届高三1班\t0.967", - "20220913\t2023届高三2班\t0.967", - "20220913\t2023届高三4班\t0.966", - "20220913\t2023届高三5班\t0.865", - "20220913\t2023届高三6班\t0.950", - "20220913\t2023届高三7班\t0.742", - "20220914\t2023届高三12班\t0.727", - "20220914\t2023届高三8班\t0.844", - "20220914\t2023届高三9班\t0.812" + "20220914\t2023届高三08班\t0.844", + "20220914\t2023届高三09班\t0.812", + "20220914\t2023届高三12班\t0.727" ], "origin": "2022届高三上学期周末卷1试题12", "edit": [ @@ -251307,21 +252861,21 @@ "" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.800", + "20220913\t2023届高三02班\t0.900", + "20220913\t2023届高三04班\t0.759", + "20220913\t2023届高三05班\t0.865", + "20220913\t2023届高三06班\t0.875", + "20220913\t2023届高三07班\t0.839", "20220913\t2023届高三10班\t0.800", "20220913\t2023届高三11班\t0.870", - "20220913\t2023届高三1班\t0.800", - "20220913\t2023届高三2班\t0.900", - "20220913\t2023届高三4班\t0.759", - "20220913\t2023届高三5班\t0.865", - "20220913\t2023届高三6班\t0.875", - "20220913\t2023届高三7班\t0.839", - "20220914\t2023届高三12班\t0.864", - "20220914\t2023届高三8班\t0.906", - "20220914\t2023届高三9班\t0.938" + "20220914\t2023届高三08班\t0.906", + "20220914\t2023届高三09班\t0.938", + "20220914\t2023届高三12班\t0.864" ], "origin": "2022届高三上学期周末卷1试题13", "edit": [ @@ -251340,21 +252894,21 @@ "" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.933", + "20220913\t2023届高三02班\t0.833", + "20220913\t2023届高三04班\t0.862", + "20220913\t2023届高三05班\t0.838", + "20220913\t2023届高三06班\t0.875", + "20220913\t2023届高三07班\t0.806", "20220913\t2023届高三10班\t0.800", "20220913\t2023届高三11班\t0.826", - "20220913\t2023届高三1班\t0.933", - "20220913\t2023届高三2班\t0.833", - "20220913\t2023届高三4班\t0.862", - "20220913\t2023届高三5班\t0.838", - "20220913\t2023届高三6班\t0.875", - "20220913\t2023届高三7班\t0.806", - "20220914\t2023届高三12班\t0.909", - "20220914\t2023届高三8班\t0.812", - "20220914\t2023届高三9班\t0.781" + "20220914\t2023届高三08班\t0.812", + "20220914\t2023届高三09班\t0.781", + "20220914\t2023届高三12班\t0.909" ], "origin": "2022届高三上学期周末卷1试题14", "edit": [ @@ -251373,21 +252927,21 @@ "" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.900", + "20220913\t2023届高三02班\t0.900", + "20220913\t2023届高三04班\t0.931", + "20220913\t2023届高三05班\t0.919", + "20220913\t2023届高三06班\t0.900", + "20220913\t2023届高三07班\t1.000", "20220913\t2023届高三10班\t0.943", "20220913\t2023届高三11班\t0.957", - "20220913\t2023届高三1班\t0.900", - "20220913\t2023届高三2班\t0.900", - "20220913\t2023届高三4班\t0.931", - "20220913\t2023届高三5班\t0.919", - "20220913\t2023届高三6班\t0.900", - "20220913\t2023届高三7班\t1.000", - "20220914\t2023届高三12班\t1.000", - "20220914\t2023届高三8班\t0.875", - "20220914\t2023届高三9班\t0.969" + "20220914\t2023届高三08班\t0.875", + "20220914\t2023届高三09班\t0.969", + "20220914\t2023届高三12班\t1.000" ], "origin": "2022届高三上学期周末卷1试题15", "edit": [ @@ -251406,21 +252960,21 @@ "" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.700", + "20220913\t2023届高三02班\t0.600", + "20220913\t2023届高三04班\t0.690", + "20220913\t2023届高三05班\t0.486", + "20220913\t2023届高三06班\t0.625", + "20220913\t2023届高三07班\t0.613", "20220913\t2023届高三10班\t0.657", "20220913\t2023届高三11班\t0.478", - "20220913\t2023届高三1班\t0.700", - "20220913\t2023届高三2班\t0.600", - "20220913\t2023届高三4班\t0.690", - "20220913\t2023届高三5班\t0.486", - "20220913\t2023届高三6班\t0.625", - "20220913\t2023届高三7班\t0.613", - "20220914\t2023届高三12班\t0.591", - "20220914\t2023届高三8班\t0.562", - "20220914\t2023届高三9班\t0.562" + "20220914\t2023届高三08班\t0.562", + "20220914\t2023届高三09班\t0.562", + "20220914\t2023届高三12班\t0.591" ], "origin": "2022届高三上学期周末卷1试题16", "edit": [ @@ -251439,21 +252993,21 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{4\\sqrt{2}}3$; (2) $\\arccos\\dfrac{\\sqrt{3}}6$.", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.844\t0.733", + "20220913\t2023届高三02班\t0.906\t0.742", + "20220913\t2023届高三04班\t0.793\t0.759", + "20220913\t2023届高三05班\t0.919\t0.676", + "20220913\t2023届高三06班\t0.950\t0.800", + "20220913\t2023届高三07班\t0.903\t0.742", "20220913\t2023届高三10班\t0.981\t0.779", "20220913\t2023届高三11班\t0.920\t0.870", - "20220913\t2023届高三1班\t0.844\t0.733", - "20220913\t2023届高三2班\t0.906\t0.742", - "20220913\t2023届高三4班\t0.793\t0.759", - "20220913\t2023届高三5班\t0.919\t0.676", - "20220913\t2023届高三6班\t0.950\t0.800", - "20220913\t2023届高三7班\t0.903\t0.742", - "20220914\t2023届高三12班\t0.939\t0.903", - "20220914\t2023届高三8班\t0.688\t0.617", - "20220914\t2023届高三9班\t0.865\t0.668" + "20220914\t2023届高三08班\t0.688\t0.617", + "20220914\t2023届高三09班\t0.865\t0.668", + "20220914\t2023届高三12班\t0.939\t0.903" ], "origin": "2022届高三上学期周末卷1试题17", "edit": [ @@ -251472,21 +253026,21 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{x|x=k\\pi-\\dfrac\\pi 6, \\ k\\in \\mathbf{Z}\\}$; (2) $\\dfrac{3\\sqrt{3}}4$.", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.861\t0.879", + "20220913\t2023届高三02班\t0.856\t0.700", + "20220913\t2023届高三04班\t0.678\t0.711", + "20220913\t2023届高三05班\t0.432\t0.216", + "20220913\t2023届高三06班\t0.912\t0.900", + "20220913\t2023届高三07班\t0.930\t0.645", "20220913\t2023届高三10班\t0.919\t0.879", "20220913\t2023届高三11班\t1.000\t0.832", - "20220913\t2023届高三1班\t0.861\t0.879", - "20220913\t2023届高三2班\t0.856\t0.700", - "20220913\t2023届高三4班\t0.678\t0.711", - "20220913\t2023届高三5班\t0.432\t0.216", - "20220913\t2023届高三6班\t0.912\t0.900", - "20220913\t2023届高三7班\t0.930\t0.645", - "20220914\t2023届高三12班\t0.742\t0.784", - "20220914\t2023届高三8班\t0.901\t0.769", - "20220914\t2023届高三9班\t0.844\t0.863" + "20220914\t2023届高三08班\t0.901\t0.769", + "20220914\t2023届高三09班\t0.844\t0.863", + "20220914\t2023届高三12班\t0.742\t0.784" ], "origin": "2022届高三上学期周末卷1试题18", "edit": [ @@ -251505,21 +253059,21 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) 不符合要求, 证明略; (2) $S=\\dfrac{12}{1+\\sin(2\\theta+\\dfrac \\pi 4)}, \\ \\theta\\in [0,\\arctan\\dfrac 34]$, $S$的最小值为$12\\sqrt{2}-12$.", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t1.000\t0.812", + "20220913\t2023届高三02班\t0.944\t0.642", + "20220913\t2023届高三04班\t0.931\t0.629", + "20220913\t2023届高三05班\t0.973\t0.486", + "20220913\t2023届高三06班\t1.000\t0.581", + "20220913\t2023届高三07班\t1.000\t0.685", "20220913\t2023届高三10班\t0.943\t0.643", "20220913\t2023届高三11班\t1.000\t0.505", - "20220913\t2023届高三1班\t1.000\t0.812", - "20220913\t2023届高三2班\t0.944\t0.642", - "20220913\t2023届高三4班\t0.931\t0.629", - "20220913\t2023届高三5班\t0.973\t0.486", - "20220913\t2023届高三6班\t1.000\t0.581", - "20220913\t2023届高三7班\t1.000\t0.685", - "20220914\t2023届高三12班\t0.932\t0.790", - "20220914\t2023届高三8班\t0.969\t0.648", - "20220914\t2023届高三9班\t0.901\t0.609" + "20220914\t2023届高三08班\t0.969\t0.648", + "20220914\t2023届高三09班\t0.901\t0.609", + "20220914\t2023届高三12班\t0.932\t0.790" ], "origin": "2022届高三上学期周末卷1试题19", "edit": [ @@ -251538,21 +253092,21 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) $3$; (2) 证明略.", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t1.000\t0.678", + "20220913\t2023届高三02班\t1.000\t0.717", + "20220913\t2023届高三04班\t0.914\t0.557", + "20220913\t2023届高三05班\t0.919\t0.432", + "20220913\t2023届高三06班\t0.900\t0.512", + "20220913\t2023届高三07班\t0.968\t0.511", "20220913\t2023届高三10班\t1.000\t0.700", "20220913\t2023届高三11班\t1.000\t0.406", - "20220913\t2023届高三1班\t1.000\t0.678", - "20220913\t2023届高三2班\t1.000\t0.717", - "20220913\t2023届高三4班\t0.914\t0.557", - "20220913\t2023届高三5班\t0.919\t0.432", - "20220913\t2023届高三6班\t0.900\t0.512", - "20220913\t2023届高三7班\t0.968\t0.511", - "20220914\t2023届高三12班\t0.966\t0.667", - "20220914\t2023届高三8班\t0.969\t0.620", - "20220914\t2023届高三9班\t0.938\t0.495" + "20220914\t2023届高三08班\t0.969\t0.620", + "20220914\t2023届高三09班\t0.938\t0.495", + "20220914\t2023届高三12班\t0.966\t0.667" ], "origin": "2022届高三上学期周末卷1试题20", "edit": [ @@ -251571,21 +253125,21 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) 当$k=1$时, $y=f(x)$是偶函数; 当$k=-1$时, $y=f(x)$是奇函数; 当$k\\ne 1$且$k \\ne -1$时, $y=f(x)$既不是奇函数, 又不是偶函数; (2) $m=\\log_4 k$; (3) $\\{-3\\}\\cup (1,+\\infty)$.", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.900\t0.956\t0.783", + "20220913\t2023届高三02班\t0.883\t0.733\t0.588", + "20220913\t2023届高三04班\t0.750\t0.649\t0.698", + "20220913\t2023届高三05班\t0.703\t0.946\t0.730", + "20220913\t2023届高三06班\t0.912\t0.571\t0.416", + "20220913\t2023届高三07班\t0.492\t0.591\t0.387", "20220913\t2023届高三10班\t0.421\t0.295\t0.207", "20220913\t2023届高三11班\t0.533\t0.116\t0.033", - "20220913\t2023届高三1班\t0.900\t0.956\t0.783", - "20220913\t2023届高三2班\t0.883\t0.733\t0.588", - "20220913\t2023届高三4班\t0.750\t0.649\t0.698", - "20220913\t2023届高三5班\t0.703\t0.946\t0.730", - "20220913\t2023届高三6班\t0.912\t0.571\t0.416", - "20220913\t2023届高三7班\t0.492\t0.591\t0.387", - "20220914\t2023届高三12班\t0.898\t0.636\t0.295", - "20220914\t2023届高三8班\t0.477\t0.328\t0.371", - "20220914\t2023届高三9班\t0.641\t0.448\t0.125" + "20220914\t2023届高三08班\t0.477\t0.328\t0.371", + "20220914\t2023届高三09班\t0.641\t0.448\t0.125", + "20220914\t2023届高三12班\t0.898\t0.636\t0.295" ], "origin": "2022届高三上学期周末卷1试题21", "edit": [ @@ -255709,22 +257263,22 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(1-\\sqrt{2},1+\\sqrt{2})$; (2) $[-\\dfrac 12,+\\infty)$; (3) $1$", "solution": "", "duration": -1, "usages": [ + "20220914\t2023届高三01班\t0.950\t0.932\t0.827", + "20220914\t2023届高三02班\t0.909\t0.754\t0.784", + "20220914\t2023届高三03班\t0.979\t0.613\t0.703", + "20220914\t2023届高三04班\t0.969\t0.785\t0.600", + "20220914\t2023届高三05班\t0.949\t0.744\t0.585", + "20220914\t2023届高三06班\t0.882\t0.631\t0.573", + "20220914\t2023届高三07班\t0.889\t0.542\t0.394", + "20220914\t2023届高三08班\t0.932\t0.695\t0.578", + "20220914\t2023届高三09班\t0.926\t0.607\t0.368", "20220914\t2023届高三10班\t0.946\t0.324\t0.600", "20220914\t2023届高三11班\t0.884\t0.353\t0.270", - "20220914\t2023届高三12班\t0.827\t0.721\t0.358", - "20220914\t2023届高三1班\t0.950\t0.932\t0.827", - "20220914\t2023届高三2班\t0.909\t0.754\t0.784", - "20220914\t2023届高三3班\t0.979\t0.613\t0.703", - "20220914\t2023届高三4班\t0.969\t0.785\t0.600", - "20220914\t2023届高三5班\t0.949\t0.744\t0.585", - "20220914\t2023届高三6班\t0.882\t0.631\t0.573", - "20220914\t2023届高三7班\t0.889\t0.542\t0.394", - "20220914\t2023届高三8班\t0.932\t0.695\t0.578", - "20220914\t2023届高三9班\t0.926\t0.607\t0.368" + "20220914\t2023届高三12班\t0.827\t0.721\t0.358" ], "origin": "2022届高三上学期周末卷8试题20", "edit": [ @@ -275024,10 +276578,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t0.455", "20220822\t2023届高三10班\t0.533", - "20220822\t2023届高三2班\t0.455", - "20220823\t2023届高三11班\t0.680\t0.520", - "20220823\t2023届高三8班\t0.438" + "20220823\t2023届高三08班\t0.438", + "20220823\t2023届高三11班\t0.680\t0.520" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -275075,13 +276629,13 @@ "solution": "", "duration": -1, "usages": [ + "20220821\t2023届高三02班\t0.182", + "20220821\t2023届高三03班\t0.500", + "20220821\t2023届高三09班\t0.000", "20220821\t2023届高三10班\t0.715", "20220821\t2023届高三12班\t0.000", - "20220821\t2023届高三2班\t0.182", - "20220821\t2023届高三3班\t0.500", - "20220821\t2023届高三9班\t0.000", - "20220822\t2023届高三10班\t0.917\t0.083", - "20220822\t2023届高三8班\t0.194" + "20220822\t2023届高三08班\t0.194", + "20220822\t2023届高三10班\t0.917\t0.083" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -275181,10 +276735,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t0.788", "20220822\t2023届高三10班\t0.757", - "20220822\t2023届高三2班\t0.788", - "20220823\t2023届高三11班\t0.640", - "20220823\t2023届高三8班\t0.844" + "20220823\t2023届高三08班\t0.844", + "20220823\t2023届高三11班\t0.640" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -275212,13 +276766,13 @@ "solution": "", "duration": -1, "usages": [ + "20220821\t2023届高三02班\t0.606", + "20220821\t2023届高三03班\t0.792", + "20220821\t2023届高三09班\t0.387", "20220821\t2023届高三10班\t0.604", "20220821\t2023届高三12班\t0.333", - "20220821\t2023届高三2班\t0.606", - "20220821\t2023届高三3班\t0.792", - "20220821\t2023届高三9班\t0.387", - "20220822\t2023届高三10班\t0.125", - "20220822\t2023届高三8班\t0.355" + "20220822\t2023届高三08班\t0.355", + "20220822\t2023届高三10班\t0.125" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -275340,10 +276894,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t0.697", "20220822\t2023届高三10班\t0.773", - "20220822\t2023届高三2班\t0.697", - "20220823\t2023届高三11班\t0.840", - "20220823\t2023届高三8班\t0.688" + "20220823\t2023届高三08班\t0.688", + "20220823\t2023届高三11班\t0.840" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -275368,10 +276922,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t0.727", "20220822\t2023届高三10班\t0.750", - "20220822\t2023届高三2班\t0.727", - "20220823\t2023届高三11班\t0.600", - "20220823\t2023届高三8班\t0.562" + "20220823\t2023届高三08班\t0.562", + "20220823\t2023届高三11班\t0.600" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -275959,10 +277513,10 @@ "solution": "", "duration": -1, "usages": [ + "20220822\t2023届高三02班\t1.000\t1.000\t0.848", "20220822\t2023届高三10班\t0.811", - "20220822\t2023届高三2班\t1.000\t1.000\t0.848", - "20220823\t2023届高三11班\t1.000\t1.000\t0.920", - "20220823\t2023届高三8班\t0.938" + "20220823\t2023届高三08班\t0.938", + "20220823\t2023届高三11班\t1.000\t1.000\t0.920" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -276039,22 +277593,22 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{(0,0)\\}$", "solution": "", "duration": -1, "usages": [ + "20220914\t2023届高三01班\t0.939", + "20220914\t2023届高三02班\t0.871", + "20220914\t2023届高三03班\t0.935", + "20220914\t2023届高三04班\t0.750", + "20220914\t2023届高三05班\t0.846", + "20220914\t2023届高三06班\t0.878", + "20220914\t2023届高三07班\t0.818", + "20220914\t2023届高三08班\t0.844", + "20220914\t2023届高三09班\t0.735", "20220914\t2023届高三10班\t0.676", "20220914\t2023届高三11班\t0.522", - "20220914\t2023届高三12班\t0.808", - "20220914\t2023届高三1班\t0.939", - "20220914\t2023届高三2班\t0.871", - "20220914\t2023届高三3班\t0.935", - "20220914\t2023届高三4班\t0.750", - "20220914\t2023届高三5班\t0.846", - "20220914\t2023届高三6班\t0.878", - "20220914\t2023届高三7班\t0.818", - "20220914\t2023届高三8班\t0.844", - "20220914\t2023届高三9班\t0.735" + "20220914\t2023届高三12班\t0.808" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -276151,8 +277705,8 @@ "duration": -1, "usages": [ "20220824\t2023届高三10班\t0.852", - "20220825\t2023届高三2班\t1.000\t1.000\t1.000\t0.788\t0.970\t0.909\t0.939", - "20220825\t2023届高三8班\t1.000\t0.968\t0.968\t0.742\t0.935\t0.968\t0.935" + "20220825\t2023届高三02班\t1.000\t1.000\t1.000\t0.788\t0.970\t0.909\t0.939", + "20220825\t2023届高三08班\t1.000\t0.968\t0.968\t0.742\t0.935\t0.968\t0.935" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -276327,9 +277881,9 @@ "solution": "", "duration": -1, "usages": [ - "20220824\t2023届高三10班\t1.000", - "20220824\t2023届高三2班\t0.970", - "20220824\t2023届高三8班\t0.970" + "20220824\t2023届高三02班\t0.970", + "20220824\t2023届高三08班\t0.970", + "20220824\t2023届高三10班\t1.000" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -276378,21 +277932,21 @@ "solution": "", "duration": -1, "usages": [ + "20220824\t2023届高三02班\t0.636", + "20220824\t2023届高三08班\t0.515", "20220824\t2023届高三10班\t0.518", - "20220824\t2023届高三2班\t0.636", - "20220824\t2023届高三8班\t0.515", + "20220914\t2023届高三01班\t0.970", + "20220914\t2023届高三02班\t0.806", + "20220914\t2023届高三03班\t0.935", + "20220914\t2023届高三04班\t0.844", + "20220914\t2023届高三05班\t0.846", + "20220914\t2023届高三06班\t0.902", + "20220914\t2023届高三07班\t0.758", + "20220914\t2023届高三08班\t0.750", + "20220914\t2023届高三09班\t0.618", "20220914\t2023届高三10班\t0.919", "20220914\t2023届高三11班\t0.739", - "20220914\t2023届高三12班\t0.692", - "20220914\t2023届高三1班\t0.970", - "20220914\t2023届高三2班\t0.806", - "20220914\t2023届高三3班\t0.935", - "20220914\t2023届高三4班\t0.844", - "20220914\t2023届高三5班\t0.846", - "20220914\t2023届高三6班\t0.902", - "20220914\t2023届高三7班\t0.758", - "20220914\t2023届高三8班\t0.750", - "20220914\t2023届高三9班\t0.618" + "20220914\t2023届高三12班\t0.692" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -276588,8 +278142,8 @@ "solution": "", "duration": -1, "usages": [ - "20220824\t2023届高三10班\t0.681", - "20220824\t2023届高三2班\t0.758\t0.909\t0.727\t0.515\t0.788" + "20220824\t2023届高三02班\t0.758\t0.909\t0.727\t0.515\t0.788", + "20220824\t2023届高三10班\t0.681" ], "origin": "2025届高一校本作业必修第一章", "edit": [ @@ -279752,7 +281306,7 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) $M=10+mx-x-10\\sqrt{x}, \\ x\\in \\{1,2,3,\\cdots,16\\}$; (2) $[\\dfrac 72,\\dfrac{19}4]$.", "solution": "", "duration": -1, "usages": [], @@ -279842,7 +281396,7 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(0,80]$; (2) 车流量的最大值约为$3250\\text{辆}/\\text{小时}$, 此时车流密度约为$87\\text{辆}/\\text{千米}$.", "solution": "", "duration": -1, "usages": [], @@ -279884,21 +281438,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.967", + "20220913\t2023届高三02班\t1.000", + "20220913\t2023届高三04班\t1.000", + "20220913\t2023届高三05班\t1.000", + "20220913\t2023届高三06班\t1.000", + "20220913\t2023届高三07班\t1.000", "20220913\t2023届高三10班\t1.000", "20220913\t2023届高三11班\t0.957", - "20220913\t2023届高三1班\t0.967", - "20220913\t2023届高三2班\t1.000", - "20220913\t2023届高三4班\t1.000", - "20220913\t2023届高三5班\t1.000", - "20220913\t2023届高三6班\t1.000", - "20220913\t2023届高三7班\t1.000", - "20220914\t2023届高三12班\t1.000", - "20220914\t2023届高三8班\t0.969", - "20220914\t2023届高三9班\t1.000" + "20220914\t2023届高三08班\t0.969", + "20220914\t2023届高三09班\t1.000", + "20220914\t2023届高三12班\t1.000" ], "origin": "2022届高三上学期周末卷1试题5修改", "edit": [ @@ -279919,21 +281473,21 @@ "" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\pi}3$", "solution": "", "duration": -1, "usages": [ + "20220913\t2023届高三01班\t0.767", + "20220913\t2023届高三02班\t0.800", + "20220913\t2023届高三04班\t0.448", + "20220913\t2023届高三05班\t0.757", + "20220913\t2023届高三06班\t0.700", + "20220913\t2023届高三07班\t0.419", "20220913\t2023届高三10班\t0.600", "20220913\t2023届高三11班\t0.522", - "20220913\t2023届高三1班\t0.767", - "20220913\t2023届高三2班\t0.800", - "20220913\t2023届高三4班\t0.448", - "20220913\t2023届高三5班\t0.757", - "20220913\t2023届高三6班\t0.700", - "20220913\t2023届高三7班\t0.419", - "20220914\t2023届高三12班\t0.727", - "20220914\t2023届高三8班\t0.625", - "20220914\t2023届高三9班\t0.719" + "20220914\t2023届高三08班\t0.625", + "20220914\t2023届高三09班\t0.719", + "20220914\t2023届高三12班\t0.727" ], "origin": "2022届高三上学期周末卷1试题9修改", "edit": [ @@ -280054,7 +281608,7 @@ }, "030019": { "id": "030019", - "content": "把$5\\sin \\alpha +12\\cos \\alpha$化成$A\\sin (\\alpha +\\varphi)$($A>0$, $\\varphi\\in (0,2\\pi)$)的形式, 则其中常数$\\varphi$的值为\\blank{50}.", + "content": "把$5\\sin \\alpha +12\\cos \\alpha$化成$A\\sin (\\alpha +\\varphi)$($A>0$, $\\varphi\\in (0,2\\pi)$)的形式, 则常数$\\varphi$的值为\\blank{50}.", "objs": [ "K0311002B" ], @@ -280101,5 +281655,56 @@ ], "remark": "", "space": "" + }, + "030021": { + "id": "030021", + "content": "若函数$f(x)=\\log_2\\dfrac{x-a}{x+1}$的图像过点$(3,-2)$, 则$a=$\\blank{50}.", + "objs": [ + "K0216002B" + ], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "$2$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "赋能练习-20220918修改", + "edit": [ + "20220624\t朱敏慧, 王伟叶", + "20220918\t王伟叶" + ], + "same": [], + "related": [ + "000330" + ], + "remark": "", + "space": "" + }, + "030022": { + "id": "030022", + "content": "设常数$a>0$, $(x+\\dfrac{a}{\\sqrt{x}})^9$展开式中$x^6$的系数为$4$, 则$a+a^2+\\cdots+a^{100}=$\\blank{50}.", + "objs": [], + "tags": [ + "第四单元", + "第八单元" + ], + "genre": "填空题", + "ans": "$\\dfrac 12 (1 - (\\dfrac 13)^{100})$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "赋能练习-20220918修改", + "edit": [ + "20220624\t朱敏慧, 王伟叶", + "20220918\t王伟叶" + ], + "same": [], + "related": [ + "000333" + ], + "remark": "", + "space": "" } } \ No newline at end of file