From 282a1782cfed7bd7e9bd54380aafa3b2e72751a7 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sat, 24 Sep 2022 13:58:30 +0800 Subject: [PATCH] 20220924 noon --- 工具/模板文件/日常选题讲义模板.tex | 76 ++ 工具/模板文件/题目清单.synctex.gz | Bin 2256 -> 0 bytes 工具/添加关联题目.ipynb | 12 +- 工具/讲义生成.ipynb | 31 +- 工具/题号选题pdf生成.ipynb | 13 +- 题库0.3/Problems.json | 1126 ++++++++++++++++++++++++++-- 6 files changed, 1189 insertions(+), 69 deletions(-) create mode 100644 工具/模板文件/日常选题讲义模板.tex delete mode 100644 工具/模板文件/题目清单.synctex.gz diff --git a/工具/模板文件/日常选题讲义模板.tex b/工具/模板文件/日常选题讲义模板.tex new file mode 100644 index 00000000..1e38f089 --- /dev/null +++ b/工具/模板文件/日常选题讲义模板.tex @@ -0,0 +1,76 @@ +\documentclass[10pt,a4paper,twoside]{article} +\usepackage[UTF8, fontset = none, heading = true]{ctex} +\setCJKmainfont[BoldFont=黑体,ItalicFont=楷体]{华文中宋} +\usepackage{amssymb,amsmath,amsfonts,amsthm,mathrsfs,dsfont,graphicx} +\usepackage{ifthen,indentfirst,enumerate,color,lastpage} +\usepackage{tikz} +\usepackage{multicol} +\usepackage{makecell} +\usepackage{longtable} +\usepackage{diagbox} +\usepackage[top=1in, bottom=1in,left=0.8in,right=0.8in]{geometry} +\usepackage{fancyhdr} +\fancyhf{} +\fancyhead[LO]{学号\blank{50} \ 姓名\blank{80}} +\chead{\notestitle} +\rhead{--\ \thepage\ of \pageref{LastPage} \ --} +\pagestyle{fancy} +\ctexset{section={ +name={}, +number=\chinese{section}, +}} +\CTEXsetup[format={\bfseries\raggedright}]{section} +\usetikzlibrary{arrows,calc,intersections,patterns,decorations.pathreplacing,3d,angles,quotes,positioning,shapes.geometric} + +\renewcommand{\baselinestretch}{1.5} +\newtheorem{defi}{定义~} +\newtheorem{eg}{例~} +\newtheorem{ex}{~} +\newtheorem{rem}{注~} +\newtheorem{thm}{定理~} +\newtheorem{coro}{推论~} +\newtheorem{axiom}{公理~} +\newtheorem{prop}{性质~} +\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}} +\newcommand{\bracket}[1]{(\hbox to #1pt{})} +\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}} +A.~#1\\ +B.~#2\\ +C.~#3\\ +D.~#4 +\end{tabular}} +\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}} +A.~#1& B.~#2\\ +C.~#3& D.~#4 +\end{tabular}} +\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}} +(1)~#1& (2)~#2\\ +(3)~#3& (4)~#4 +\end{tabular}} +\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}} +A.~#1 &B.~#2& C.~#3& D.~#4 +\end{tabular}} +\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}} +(1)~#1 &(2)~#2& (3)~#3& (4)~#4 +\end{tabular}} + + +% 修改标题处 +\newcommand{\notestitle}{标题文字待处理} + +\begin{document} +\begin{center} +{\bf\large \notestitle} +\end{center} + + +%\section{课前练习} + +\begin{enumerate}[1.] +待替换1 +\end{enumerate} + + + + +\end{document} \ No newline at end of file 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 deleted file mode 100644 index a7bb1e5d47bf4360d0f66d61ae4382cc8a74371e..0000000000000000000000000000000000000000 GIT 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0$''的\\bracket{20}.\n\\twoch{充分而不必要条件}{必要而不充分条件}{充要条件}{既不充分又不必要条件}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "选择题", + "ans": "C", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第一章-20220924修改", + "edit": [ + "20220803\t伍杨超, 王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "020081" + ], + "remark": "", + "space": "" + }, + "030032": { + "id": "030032", + "content": "已知$m$是实常数. 命题甲: 关于$x$的方程$x^2+x+2m=0$有两个相异的负根; 命题乙: 关于$x$的方程$4x^2+x+2m=0$无实根, 若这两个命题有且只有一个是真命题, 则实数$m$的取值范围为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "填空题", + "ans": "$(0,\\dfrac 1{32}]\\cup [\\dfrac 18,+\\infty)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "002747" + ], + "remark": "", + "space": "16ex" + }, + "030033": { + "id": "030033", + "content": "判断题: (如果正确请在题目前面的横线上写``\\checkmark'', 错误请在题目前面的横线上写``$\\times$'')\\\\ \n\\blank{30}(1) 若$a>b$, $c\\geq d$, 则$a+c>b+d$;\\\\ \n\\blank{30}(2) 若$a>b$, $c\\geq d$, 则$a+c\\geq b+d$;\\\\ \n\\blank{30}(3) 若$a\\ge b$, $c\\ge d$, 则$a+c\\ge b+d$.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1117-不等式的性质-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001085" + ], + "remark": "", + "space": "" + }, + "030034": { + "id": "030034", + "content": "利用绝对值的三角不等式$|a+b|\\le |a|+|b|$, 证明: 对任意$x,y\\in\\mathbf{R}$, $|x-y|\\ge ||x|-|y||$.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "解答题", + "ans": "证明略", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1119-含有绝对值的不等式基本性质-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001096" + ], + "remark": "", + "space": "12ex" + }, + "030035": { + "id": "030035", + "content": "证明: $|x+2|-|3-x|\\ge -5$, 对所有实数$x$均成立, 并求等号成立时$x$的取值范围.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "解答题", + "ans": "证明略, 等号成立时$x$的取值范围为$(-\\infty,-2]$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第一册习题-20220924修改", + "edit": [ + "20220806\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "011853", + "010104" + ], + "remark": "", + "space": "12ex" + }, + "030036": { + "id": "030036", + "content": "已知关于$x$的不等式$|x-4|+|x+3|0$的解集为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "教材复习题-20220924修改", + "edit": [ + "20220624\t王伟叶, 余利成", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "000035" + ], + "remark": "", + "space": "" + }, + "030039": { + "id": "030039", + "content": "不等式$\\dfrac1{|x-2|}\\ge 3 $的解集为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "填空题", + "ans": "$[\\dfrac 53,2)\\cup (2,\\dfrac 73]$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "赋能练习-20220924修改", + "edit": [ + "20220624\t朱敏慧, 王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "000540" + ], + "remark": "", + "space": "" + }, + "030040": { + "id": "030040", + "content": "已知关于$x$的不等式$ax^2-bx+c>0$的解集是$(-\\dfrac 32,\\dfrac 12)$, 对于$a,b,c$有以下结论: \\textcircled{1} $a>0$; \\textcircled{2} $b>0$; \\textcircled{3} $c>0$; \\textcircled{4} $a+b+c>0$; \\textcircled{5} $a-b+c>0$. 其中正确的序号有\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "填空题", + "ans": "\\textcircled{2}\\textcircled{3}\\textcircled{4}", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "002775" + ], + "remark": "", + "space": "" + }, + "030041": { + "id": "030041", + "content": "已知三个个正数$a,b,c$满足$a^{\\lg bx}=b^{\\lg ax}$, 则$a,b,c$满足的条件为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "$a=b$或$c=1$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "代数精编第三章函数-20220924修改", + "edit": [ + "20220720\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "005650" + ], + "remark": "", + "space": "" + }, + "030042": { + "id": "030042", + "content": "函数$y=\\log_2(x^2+x-2)$的递增区间是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1155-对数函数-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001331", + "001325" + ], + "remark": "", + "space": "" + }, + "030043": { + "id": "030043", + "content": "若函数$f(x)={\\log_a}(x^2-4ax+1)\\ (a>0, \\ a\\ne 1)$没有最小值, 则$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "赋能练习-20220924修改", + "edit": [ + "20220624\t朱敏慧, 王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "000795" + ], + "remark": "", + "space": "" + }, + "030044": { + "id": "030044", + "content": "不等式$\\log_{\\frac{1}{2}}(x^2+x+1)<\\log_{\\frac{1}{2}}(5x-2)$的解集为\\blank{80}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "$(\\dfrac 25,1)\\cup (3,+\\infty)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1155-对数函数-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001328" + ], + "remark": "", + "space": "" + }, + "030045": { + "id": "030045", + "content": "已知函数$y=f(2x+1)$的定义域为$[0,3]$, 则函数$y=f(3x-1)$的定义域为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "$[\\dfrac 23,\\dfrac 83]$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1146-一次函数与分式线性函数-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001262" + ], + "remark": "", + "space": "" + }, + "030046": { + "id": "030046", + "content": "作出函数$y=(x^3-1)^2-1$的大致图像, 写出它的单调区间, 并证明你的结论.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "教材复习题-20220924修改", + "edit": [ + "20220624\t王伟叶, 余利成", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "000092" + ], + "remark": "", + "space": "12ex" + }, + "030047": { + "id": "030047", + "content": "判断函数$y=(\\sqrt{x}+2)(2^x+1)$的单调性, 并证明.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "解答题", + "ans": "证明略", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1140-函数的运算复合与奇偶性单调性的关系-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001218" + ], + "remark": "", + "space": "12ex" + }, + "030048": { + "id": "030048", + "content": "设常数$a\\in \\mathbf{R}$. 若$y=\\log_{\\frac 12}(x^2-2ax+12)$在$[-2,+\\infty)$上是严格减函数, 则$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "002895" + ], + "remark": "", + "space": "" + }, + "030049": { + "id": "030049", + "content": "判断函数$y=\\dfrac{\\sqrt{4x^2+1}+2x+1}{\\sqrt{4x^2+1}+2x-1}$的奇偶性, 并说明理由.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "解答题", + "ans": "(1) 奇函数, 证明略", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1141-更多奇偶性与单调性的练习-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001221" + ], + "remark": "", + "space": "" + }, + "030050": { + "id": "030050", + "content": "已知$f(x)=ax+\\dfrac{1}{x+1}, \\ a\\in \\mathbf{R}$. 若$y=f(x)$在$x\\in [3,4]$时有零点, 则$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海2019年秋季高考试题18-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "003648" + ], + "remark": "", + "space": "" + }, + "030051": { + "id": "030051", + "content": "函数$y=x^3+\\dfrac{27}{x}, \\ x\\in [1,4]$的最大值为\\blank{50}, 最小值为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1142-函数的最值-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001227" + ], + "remark": "", + "space": "" + }, + "030052": { + "id": "030052", + "content": "已知函数$y=-x^2+2ax$, $x\\in [0, 1]$的最大值为$a+1$. 求实数$a$的值.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "解答题", + "ans": "$-1$或$2$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "教材复习题-20220924修改", + "edit": [ + "20220624\t王伟叶, 余利成", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "000087" + ], + "remark": "", + "space": "12ex" + }, + "030053": { + "id": "030053", + "content": "已知$y=f(x)$是定义在$(-2,2)$上的奇函数, 在区间$[0,2)$上是严格增函数, 且$f(1-a)+f(1-a^2)<0$, 则实数$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "$(1,\\sqrt{3})$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "二期课改练习册高一第一学期-20220924修改", + "edit": [ + "20220726\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "007939" + ], + "remark": "", + "space": "" + }, + "030054": { + "id": "030054", + "content": "直角坐标平面内, 终边过点$(1,\\sqrt{2})$的所有角组成的集合可表示成\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "$\\{x|x=2k\\pi+\\arctan \\sqrt{2}, \\ k\\in \\mathbf{Z}\\}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "代数精编第四章三角函数-20220924修改", + "edit": [ + "20220720\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "005902" + ], + "remark": "", + "space": "" + }, + "030055": { + "id": "030055", + "content": "已知角$\\alpha$的终边上一点的坐标为$\\left(\\sin\\dfrac{3\\pi}{7},\\cos\\dfrac{3\\pi}{7}\\right)$, 则角$\\alpha$的最小正值为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "$\\dfrac{\\pi}{14}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016年双基百分百-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "003959" + ], + "remark": "", + "space": "" + }, + "030056": { + "id": "030056", + "content": "四点三十分时, 时针和分针的夹角的弧度数为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t2104-弧度制与任意角[1]-20220912修改-20220924修改", + "edit": [ + "20220912\t王伟叶\t朱敏慧", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001387", + "030015" + ], + "remark": "", + "space": "" + }, + "030057": { + "id": "030057", + "content": "已知$\\theta$是象限角, 化简下列各式.\\\\ \n(1) $\\dfrac{\\cos(-\\theta)\\sin(\\pi-\\theta)}{\\cos(\\theta-3\\pi)}+\\dfrac{\\sin(-2\\pi-\\theta)\\sin(\\theta+\\pi)}{\\sin(4\\pi-\\theta)}=$\\blank{50}.\\\\ \n(2) $\\sin\\left(\\dfrac{\\pi}{2}-\\theta\\right)+\\sin\\left(\\dfrac{5\\pi}{2}+\\theta\\right)\n-\\sin\\left(\\dfrac{3\\pi}{2}-\\theta\\right)+\\sin\\left(\\dfrac{3\\pi}{2}+\\theta\\right)=$\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t2108-诱导公式-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001412" + ], + "remark": "", + "space": "" + }, + "030058": { + "id": "030058", + "content": "已知点$A$的坐标为$(3, 4)$, 将$OA$绕坐标原点$O$逆时针旋转$\\dfrac\\pi 4$至$OA'$. 求点$A'$的坐标.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第二册课堂练习-20220924修改", + "edit": [ + "20220730\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "009561" + ], + "remark": "", + "space": "12ex" + }, + "030059": { + "id": "030059", + "content": "方程$\\sin x+4\\cos x=0$的解集为\\blank{150}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "$\\{x|x=-\\arctan 4+k\\pi, \\ k\\in \\mathbf{Z}\\}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t2125-三角方程-20220924修改", + "edit": [ + "20220625\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "001587", + "001586" + ], + "remark": "", + "space": "" + }, + "030060": { + "id": "030060", + "content": "如图, 用长为$l$的铁丝弯成中间为矩形, 两端为半圆形的空心框架, 若矩形一边长为$2x$, 试用解析式将此框架围成的面积$y$表示为$x$的函数.\n\\begin{center}\n \\begin{tikzpicture}[>=latex]\n \\draw (2,0) -- (2,1.5) arc (0:180:1) -- (0,0) arc (180:360:1) -- cycle;\n \\draw [<->] (0,0.3) -- (2,0.3) node [midway, fill = white] {$2x$};\n \\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "002830" + ], + "remark": "", + "space": "12ex" + }, + "030061": { + "id": "030061", + "content": "下列各式中, 不正确的是\\bracket{20}.\n\\twoch{$\\sin \\alpha +\\sin \\beta =2\\sin \\dfrac{\\beta +\\alpha}2\\cos \\dfrac{\\beta -\\alpha}2$}{$\\sin \\alpha -\\sin \\beta =2\\cos \\dfrac{\\beta +\\alpha}2\\sin \\dfrac{\\alpha -\\beta}2$}{$\\cos \\alpha +\\cos \\beta =2\\cos \\dfrac{\\beta +\\alpha}2\\cos \\dfrac{\\beta -\\alpha}2$}{$\\cos \\alpha -\\cos \\beta =2\\sin \\dfrac{\\beta +\\alpha}2\\sin \\dfrac{\\alpha -\\beta}2$}", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "选择题", + "ans": "D", + "solution": "", + "duration": -1, + "usages": [], + "origin": "代数精编第五章三角恒等式与解三角形-20220924修改", + "edit": [ + "20220720\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "006286" + ], + "remark": "", + "space": "" + }, + "030062": { + "id": "030062", + "content": "在$\\triangle ABC$中, $b=3,c=2$, $B-C=\\dfrac{\\pi}2$, 则$\\tan A=$\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三上期中区统考第12题-20220924修改", + "edit": [ + "20220711\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "004672" + ], + "remark": "", + "space": "" + }, + "030063": { + "id": "030063", + "content": "在$\\triangle ABC$中, 已知$A=60^\\circ$, $b=6$. 若$a=2\\sqrt{7}$, 则$B=$\\blank{50}; 若$a=6$, 则$B=$\\blank{50}; 若$a=9$, 则$B=$\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "教材复习题-20220924修改", + "edit": [ + "20220624\t王伟叶, 余利成", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "000116" + ], + "remark": "", + "space": "" + }, + "030064": { + "id": "030064", + "content": "函数$y=\\sqrt{\\cos x}+\\dfrac 1{\\sqrt{36-x^2}}$的定义域为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "003155" + ], + "remark": "", + "space": "" + }, + "030065": { + "id": "030065", + "content": "求函数$y=\\sin x(\\sin x+\\sqrt{3}\\cos x)$的最大值与最小值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "003156" + ], + "remark": "", + "space": "12ex" + }, + "030066": { + "id": "030066", + "content": "求函数$y=\\dfrac{\\cos^2 x-3}{1-\\sin x}$的最大值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "003163" + ], + "remark": "", + "space": "12ex" + }, + "030067": { + "id": "030067", + "content": "已知函数$f(x)=(2\\sin(x+\\dfrac{\\pi}3)+\\sin x)\\cos x-\\sqrt 3\\sin^2 x$, 求$f(x)$的单调递减区间", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "003175" + ], + "remark": "", + "space": "12ex" + }, + "030068": { + "id": "030068", + "content": "设常数$a\\in \\mathbf{R}$. 若函数$y=\\sin 2x+a\\cos 2x$的图像关于直线$x=\\dfrac{\\pi}3$对称, 则$a=$\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "填空题", + "ans": "$-\\dfrac{\\sqrt{3}}3$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三第一轮复习讲义-20220924修改", + "edit": [ + "20220701\t王伟叶", + "20220924\t王伟叶" + ], + "same": [], + "related": [ + "003181" + ], + "remark": "", + "space": "" } } \ No newline at end of file