diff options
author | Karl Berry <karl@freefriends.org> | 2022-12-04 21:07:43 +0000 |
---|---|---|
committer | Karl Berry <karl@freefriends.org> | 2022-12-04 21:07:43 +0000 |
commit | fc934166e6db327e06b3e089fc1f64aeb8692260 (patch) | |
tree | 3cf3abc9bd992fa16fcf24c23b3234805510bec6 /Master | |
parent | 3ad82ab49bb65a75be1ad82b86076f2783713bea (diff) |
hfutexam (4dec22)
git-svn-id: svn://tug.org/texlive/trunk@65192 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master')
17 files changed, 1632 insertions, 1 deletions
diff --git a/Master/texmf-dist/doc/latex/hfutexam/CHANGELOG.md b/Master/texmf-dist/doc/latex/hfutexam/CHANGELOG.md new file mode 100644 index 00000000000..c0174e3a9e4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/CHANGELOG.md @@ -0,0 +1,18 @@ +# 更新日志 + +## [1.5] - 2022/12/04 ++ 现在`\XiZhuRenQianMing`不设置或设置为空时即可不显示签名. + +## [1.4] - 2022/12/04 ++ 修复了有时选择题选项未能正确计算行数的问题. ++ 修复了有时填空题答案会被横线截断的问题. + +## [1.3] - 2022/11/27 ++ 移除了简易模式下学期的下划线. ++ 打分框的宽度减少了`10%`. + +## [1.2] - 2022/10/31 ++ 选择题选项后增加了`5pt`的垂直间距. + +## [1.1] - 2022/10/30 ++ 首次提交. diff --git a/Master/texmf-dist/doc/latex/hfutexam/LICENSE b/Master/texmf-dist/doc/latex/hfutexam/LICENSE new file mode 100644 index 00000000000..22443139013 --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/LICENSE @@ -0,0 +1,416 @@ +The LaTeX Project Public License +=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- + +LPPL Version 1.3c 2008-05-04 + +Copyright 1999 2002-2008 LaTeX3 Project + Everyone is allowed to distribute verbatim copies of this + license document, but modification of it is not allowed. + + +PREAMBLE +======== + +The LaTeX Project Public License (LPPL) is the primary license under +which the LaTeX kernel and the base LaTeX packages are distributed. + +You may use this license for any work of which you hold the copyright +and which you wish to distribute. 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--- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam.pdf diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam.tex b/Master/texmf-dist/doc/latex/hfutexam/hfutexam.tex new file mode 100644 index 00000000000..ffadfa29594 --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam.tex @@ -0,0 +1,270 @@ +\documentclass{hfutexam} + +%% 示例所需的自定义命令 +\newcommand{\diff}{\,\mathrm{d}} +\usetikzlibrary{arrows.meta, overlay-beamer-styles} +\newfontfamily\couriernew{Courier New} +\usepackage{enumitem} +\usepackage{tcolorbox} +\usepackage{listings} +\makeatletter +\definecolor{winered}{rgb}{0.5,0,0} +\definecolor{lightgrey}{rgb}{0.9,0.9,0.9} +\definecolor{frenchplum}{RGB}{190,20,83} +\lstset{language=[LaTeX]TeX, + basicstyle=\couriernew, + texcsstyle=*\color{winered}, + mathescape, + breaklines=true, + keywordstyle=\color{winered}, + commentstyle=\color{green!70!black}, + stringstyle=\color{green!50!blue}, + frame=single, + tabsize=3, + framerule=0.5pt, + columns=flexible, + backgroundcolor=\color{black!5}, + morekeywords={\diff, \maketitle, \titlesep, \BiaoTi, \XueNian, \XueQi, \KeChengDaiMa, \KeChengMingCheng, \XueFen, \KeChengXingZhi, \KaoShiXingShi, \ZhuanYeBanJi, \KaoShiRiQi, \MingTiJiaoShi, \XiZhuRenQianMing, \tigan, \scorebox, \score, \Score, \fillblank, \xx, \notice, \xuanzeti, \yihang, \erhang, \sihang, XeLaTeX}, + keywordstyle=\color{winered}, + morekeywords=[2]{hfutexam, shijuan, datizhi, cankaodaan, simple, nofangzheng, flalign, 5cm, enumerate, align}, + keywordstyle=[2]\color{blue}, +} +\tcbset{ + colback=white, + colframe=blue, + boxrule=0.5pt, + arc=0pt, +} +\makeatother + +\begin{document} +\BiaoTi{合肥工业大学试卷(A)} +\XueNian{2021}{2022} +\XueQi{二} +\KeChengDaiMa{034Y01} +\KeChengMingCheng{数学(下)} +\XueFen{5} +\KeChengXingZhi{必修} +\KaoShiXingShi{闭卷} +\ZhuanYeBanJi{少数民族预科班} +\KaoShiRiQi{2022年6月18日8:00-10:00} +\MingTiJiaoShi{集体} +\XiZhuRenQianMing{} + + +\tigan{一、模板选项} + +\indent +本模板 (2022/12/04 v1.5) 旨在为将合肥工业大学试卷的 word 格式转为\LaTeX{}格式. +使用时, 只需在文档开头写上 +\begin{lstlisting} +\documentclass[shijuan]{hfutexam} +\end{lstlisting} +即可使用. +需要使用~{\color{blue}{\lstinline|UTF-8|}} 编码, 并使用 \lstinline|XeLaTeX| 至少编译两次, 以正确生成页码. + +\indent +可使用的选项为: \lstinline|shijuan| (试卷), \lstinline|datizhi| (答题纸), \lstinline|cankaodaan| (参考答案) 和 \lstinline|simple| (简易模式). 如果留空则为默认值 \lstinline|shijuan| (试卷). +\begin{enumerate} +\item 试卷/答题纸/参考答案三个选项下页面会设置为 A3 大小, 三种情形的页眉页脚显示的内容以及标题的文字间隔有所不同. +\item 简易模式选项下页面会设置为 A4 大小, 页眉页脚也较为简单. 此时需要使用命令 \lstinline|\maketitle| 来生成标题. +一般用于保存(多张)试卷的内容,或者便于打印使用. +\item 标题默认使用方正字体, 因此请在使用前先安装字体: {\bfseries\titlesongti 方正小标宋}和{\bfseries\titlefangsong 方正仿宋}(右键选择为所有用户安装), 否则请使用选项 \lstinline|nofangzheng| (采用新宋体和仿宋代替). +\end{enumerate} + +\tigan{二、试卷信息} + +\indent +通过下述命令来设置试卷信息. + +\textit{\color{blue}{试卷信息示例:}} +\begin{lstlisting} +\BiaoTi{合肥工业大学试卷(A)} % 试卷标题, 一般为: 合肥工业大学试卷(A)或(B) +\XueNian{2021}{2022} % 学年起始和结束, 一般为相差 1 的 4 位数字 +\XueQi{二} % 学期, 一般为: 一, 二 +\KeChengDaiMa{034Y01} % 课程代码 +\KeChengMingCheng{数学(下)} % 课程名称 +\XueFen{5} % 学分 +\KeChengXingZhi{必修} % 课程性质, 只能为: 必修, 选修, 限修 +\KaoShiXingShi{闭卷} % 考试形式, 只能为: 开卷, 闭卷 +\ZhuanYeBanJi{少数民族预科班} % 专业班级, 一般不需要填写 +\KaoShiRiQi{2022年6月18日8:00-10:00} % 考试日期 +\MingTiJiaoShi{集体} % 命题教师 +\XiZhuRenQianMing{dengbing.png} % 系主任签名 +\end{lstlisting} +其中系主任签名处需要填写相应的图片名, 若不设置或设置为空则不显示. + +其它选项默认均为空, 可根据需要只填部分内容. + +\newpage +\tigan{三、命令} +\begin{enumerate} +\item \lstinline|\tigan{三、命令}| 用于生成题干, 字体相对较大, 且为黑体. 小题建议使用~{\color{blue}\lstinline|enumerate|} 环境来生成. +\item \hspace{-8mm}\scorebox\hspace{8mm}\lstinline|\scorebox| 用于生成打分框, 请放置在答题纸一行的开头使用. +\vspace{-2mm} +\item \lstinline|\notice| 用于生成答题纸提示信息, 请放置在答题纸的正文开始处. +\item 答题纸中可能需要设置一定高度的空白, 使用命令 \lstinline|\hspace{5cm}| 之类的命令即可. 也可以使用 \lstinline|\newpage| 换到新的一页(或分栏). +\end{enumerate} + +\tigan{填空题相关} +\begin{enumerate}[resume] +\item \lstinline|\fillblank[长度][最低高度]{内容}| 用于生成填空题的空白, 内容可以为空. 其中长度默认值是~{\color{blue}{\lstinline|3.5cm|}}, 最低高度默认值是~{\color{blue}{\lstinline|1cm|}} (答题纸和参考答案)或~{\color{blue}{\lstinline|0.5cm|}} (其它). +\end{enumerate} + +\textit{\color{blue}{填空题示例:}} +\begin{lstlisting} +\textbf{请将你的答案对应填在横线上:} + +\textbf{1.} \fillblank{}, +\textbf{2.} \fillblank[5cm]{}, +\textbf{3.} \fillblank{}. +\end{lstlisting} + +\begin{tcolorbox} +\textbf{请将你的答案对应填在横线上:} + +\textbf{1.} \fillblank[3.5cm][1cm]{}, +\textbf{2.} \fillblank[5cm][1cm]{}, +\textbf{3.} \fillblank[3.5cm][1cm]{}. +\end{tcolorbox} + +\tigan{选择题相关} +\begin{enumerate}[resume] +\item \lstinline|\xx{选项}{选项}{选项}{选项}| 用于生成选择题的选项, 直接在选择题题干后使用即可. 该命令会自动根据选项长度设置行数. 只支持四个选项, 选项会自动带上 ABCD. +\item 如果想要手动改变每行显示的选项数, 可使用命令 \lstinline|\xx[每行显示的选项数]{选项}{选项}{选项}{选项}|, 每行只能显示 1, 2 或 4 个选项. +\item \lstinline|\xuanzeti{题号}{答案}| 用于生成答题纸选择题的答题区域, 或参考答案选择题的答案区域. +\end{enumerate} + +\textit{\color{blue}{选择题示例:}} +\begin{lstlisting} +\begin{enumerate} +\item 柳宗元的《江雪》包含下面哪一句? (~~~~) +\xx[2]{一山鸟飞绝}{百山鸟飞绝}{千山鸟飞绝}{亿山鸟飞绝} +\item 张志和的《渔歌子》是(~~~~). +\xx{东塞山前白鹭飞,桃花流水鳜鱼肥。青箬笠,绿蓑衣,斜风细雨不须归。} +{南塞山前白鹭飞,桃花流水鳜鱼肥。青箬笠,绿蓑衣,斜风细雨不须归。} +{西塞山前白鹭飞,桃花流水鳜鱼肥。青箬笠,绿蓑衣,斜风细雨不须归。} +{北塞山前白鹭飞,桃花流水鳜鱼肥。青箬笠,绿蓑衣,斜风细雨不须归。} +\end{enumerate} +\end{lstlisting} + +\begin{tcolorbox} +\begin{enumerate} +\item 柳宗元的《江雪》包含下面哪一句? (~~~~). +\xx[2]{一山鸟飞绝}{百山鸟飞绝}{千山鸟飞绝}{亿山鸟飞绝} +\item 张志和的《渔歌子》是(~~~~). +\xx{东塞山前白鹭飞,桃花流水鳜鱼肥。青箬笠,绿蓑衣,斜风细雨不须归。} +{南塞山前白鹭飞,桃花流水鳜鱼肥。青箬笠,绿蓑衣,斜风细雨不须归。} +{西塞山前白鹭飞,桃花流水鳜鱼肥。青箬笠,绿蓑衣,斜风细雨不须归。} +{北塞山前白鹭飞,桃花流水鳜鱼肥。青箬笠,绿蓑衣,斜风细雨不须归。} +\end{enumerate} +\end{tcolorbox} + +%\newpage +\textit{\color{blue}{选择题示例:}} +\begin{lstlisting} +\textbf{请将你所选择的字母 A, B, C, D 之一对应填在下列表格里:} + +\xuanzeti{\textbf{题号}}{\textbf{答案}}% +\xuanzeti{1}{}\xuanzeti{2}{}\xuanzeti{3}{}\xuanzeti{4}{} +\end{lstlisting} + +\begin{tcolorbox} +\textbf{请将你所选择的字母 A, B, C, D 之一对应填在下列表格里:} + +\xuanzeti{\textbf{题号}}{\textbf{答案}}% +\xuanzeti{1}{}\xuanzeti{2}{}\xuanzeti{3}{}\xuanzeti{4}{} +\end{tcolorbox} + +\newpage +\tigan{得分点相关} +\begin{enumerate}[resume] +\item \lstinline|\score{数值}| 用于在参考答案一行结尾处生成得分点的虚线.\score2 +\item \lstinline|\Score{(2分, 缺少常数得1分)}| 用于自定义得分说明.\Score{(2分, 缺少常数得1分)} +\item 在公式中也可使用, 但是需要编译两次才会正常计算出虚线长度. +\end{enumerate} +\textit{\color{blue}{得分点示例:}} +\begin{lstlisting} +\[\int e^x\diff x=e^x+C. \Score{(4分, 缺少常数得2分)}\] +\begin{align*} +\int\sin x\diff x&=-\cos x+C, \Score{(4分, 缺少常数得2分)}\\ +\int_0^\pi(1+\sin x)\diff x&=\pi+2. \score5 +\end{align*} +\end{lstlisting} + +\begin{tcolorbox} +\[\int e^x\diff x=e^x+C. \Score{(4分, 缺少常数得2分)}\] +\begin{align*} +\int\sin x\diff x&=-\cos x+C, \Score{(4分, 缺少常数得2分)}\\ +\int_0^\pi(1+\sin x)\diff x&=\pi+2. \score5 +\end{align*} +\end{tcolorbox} + +\textbf{如有疑问或建议, 欢迎联系我: {\color{red}{zhangshenxing@hfut.edu.cn}} 或 {\color{blue}{QQ362037052}}.} + +\textbf{CTAN: \color{blue}https://www.ctan.org/pkg/hfutexam} + +\newpage +\tigan{一、填空题(每题3分,共18分)} +\begin{enumerate} +\item 如果 $f(x)>0$ 且 $\displaystyle\lim_{x\to\infty}f(x)=0$, 则 $\displaystyle\lim_{x\to\infty}\bigl[1+f(x)\bigr]^{1/f(x)}=$\fillblank{}. +\item 设 $y=\sin(x^2+1)$, 则 $\diff y=$\fillblank{}. +\item 极限 $\displaystyle\lim_{n\to\infty}\left(\frac1{n^2-1}+\frac2{n^2-2}+\cdots+\frac n{n^2-n}\right)=$\fillblank{}. +\item 曲线 $y=2\ln(x+1)$ 在点 $(1,2\ln2)$ 处的切线方程为\fillblank{}. +\item 若 $e^{y-1}=1+xy$, 则 $\dfrac{\diff y}{\diff x}\bigg|_{x=0}=$\fillblank{}. +\item 如果函数 $f(x)$ 的定义域是 $(0,+\infty)$, 且 $x=0$ 是曲线 $y=f(x)$ 的垂直渐近线, 那么 $\displaystyle\lim_{x\to0^+}\frac1{f(x)}=$\fillblank{}. +\end{enumerate} + +\tigan{二、选择题(每题3分,共18分)} +\begin{enumerate} +\item 当 $x\to+\infty$ 时, $\dfrac1x$ 和(~~~~)是等价无穷小. +% 自动根据选项长度设置行数 +\xx{$\sin\dfrac1x$}{$\sin x$}{$e^{-x}$}{$e^{1/x}$} +\item 若当 $x\to0$ 时, $\arctan(e^x-1)\cdot(\cos x-1)$ 和 $x^n$ 是同阶无穷小, 则 $n=$(~~~~). +\xx{$0$}{$1$}{$2$}{$3$} +\item 设 $f(x)=\arctan\dfrac1{x(x-1)^2}$, 则 $x=0$ 是 $f(x)$ 的(~~~~). +\xx{可去间断点}{跳跃间断点}{第二类间断点}{连续点} +\item +\begin{tikzpicture}[overlay,xshift=12.5cm,yshift=-3cm] +\draw[-Stealth,thick](-3,0)--(3,0); +\draw[-Stealth,thick](0,-0.8)--(0,2.5); +\draw[very thick,smooth,domain=-55:55] plot ({\x/50-1.3}, {tan(\x)*tan(\x)}); +\draw[very thick,smooth,domain=0.15:2] plot ({\x}, {-ln(\x)}); +\draw + (-0.3,-0.3) node {$O$} + (2.8,-0.3) node {$x$} + (-0.3,2.3) node {$y$}; +\end{tikzpicture} +设 $f(x)$ 是定义在 $(-\infty,+\infty)$ 上的连续函数, 且 $f'(x)$ 的图像如下图所示, 则 $f(x)$ 有(~~~~). +% 手动设置为每行1个 +\xx[1]{一个极大值点,没有极小值点}{没有极大值点,一个极小值点}{一个极大值点和一个极小值点}{一个极大值点和两个极小值点} +\newpage +\item 设函数 $f(x)$ 在点 $x=0$ 处可导, 且 $f(0)=0$, 则 $\displaystyle\lim_{x\to0}\frac{f(x^{2022})+x^{2021}f(x)}{x^{2022}}=$(~~~~). +\xx{$0$}{$f'(0)$}{$2f'(0)$}{$2022f'(0)$} +\item 如果点 $(x_0,y_0)$ 是曲线 $y=f(x)$ 的拐点, 则 $f''(x_0)=$(~~~~). +\xx{$0$}{$\infty$}{不存在}{$0$ 或不存在} +\end{enumerate} + +\tigan{三、解答题(每题8分,共64分)} +\begin{enumerate} +\item 求极限 $\displaystyle\lim_{x\to-1}\frac{x^2-1}{x^2+3x+2}$. +\item 求极限 $\displaystyle\lim_{x\to0}\frac{e^x-1-x}{\arcsin x^2}$. +\item 设 $\begin{cases}x=t^2+t&\\y=t^3+t&\end{cases}$, 求 $\dfrac{\diff y}{\diff x}$ 和 $\dfrac{\diff^2 y}{\diff x^2}$. +\item 设 $f(x)=\begin{cases}x\arctan\dfrac1x,&x<0,\\x^2+ax+b,&x\ge0.\end{cases}$ +求常数 $a,b$ 使得函数 $f(x)$ 在 $(-\infty,+\infty)$ 内可导, 并求出此时曲线 $y=f(x)$ 的渐近线. +\item 求函数 $f(x)=x^3-x^2-x$ 在区间 $[-2,2]$ 上的最大值和最小值. +\item 证明: 当 $-\dfrac\pi2<x_1<x_2<\dfrac\pi2$ 时, $\tan x_2-\tan x_1\ge x_2-x_1$. +\item 设函数 $f(x)$ 在 $(-\infty,+\infty)$ 内可导, 且 $f(1)=0$. +证明: 存在 $\xi\in(0,1)$ 使得 $\xi f'(\xi)+2022f(\xi)=0$. +\item 设函数 $f(x)=\ln x+\dfrac2{x^2}, x\in(0,+\infty)$. 求 +\begin{enumerate} +\item[(1)] 函数 $f(x)$ 的增减区间及极值; +\item[(2)] 曲线 $y=f(x)$ 的凹凸区间及拐点. +\end{enumerate} +\end{enumerate} + +\end{document} + + + + diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam_cankaodaan.pdf b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_cankaodaan.pdf Binary files differnew file mode 100644 index 00000000000..3776c11ac84 --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_cankaodaan.pdf diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam_cankaodaan.tex b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_cankaodaan.tex new file mode 100644 index 00000000000..f9f20890d59 --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_cankaodaan.tex @@ -0,0 +1,158 @@ +\documentclass[cankaodaan]{hfutexam} +\usepackage{extarrows} +\newcommand{\diff}{\,\mathrm{d}} + +\begin{document} +\BiaoTi{合肥工业大学试卷参考答案(A)} +\XueNian{2021}{2022} +\XueQi{二} +\KeChengDaiMa{034Y01} +\KeChengMingCheng{数学(下)} +\XueFen{5} +\KeChengXingZhi{必修} +\KaoShiXingShi{闭卷} +\ZhuanYeBanJi{少数民族预科班} +\KaoShiRiQi{2022年6月18日8:00-10:00} +\MingTiJiaoShi{集体} +%\XiZhuRenQianMing{dengbing.png} + +\tigan{一、填空题(每小题3分,共18分)} + +\textbf{请将你的答案对应填在横线上:} + +\textbf{1.} \fillblank{$e$}, +\textbf{2.} \fillblank{$2x\cos(x^2+1)\diff x$}, +\textbf{3.} \fillblank{$\dfrac12$}, + +\textbf{4.} \fillblank{$y=x-1+2\ln 2$}, +\textbf{5.} \fillblank{$1$}, +\textbf{6.} \fillblank{$0$}. + +\tigan{二、选择题(每小题3分,共18分)} + +\textbf{请将你所选择的字母 A, B, C, D 之一对应填在下列表格里:} + +\xuanzeti{\textbf{题号}}{\textbf{答案}}% +\xuanzeti{1}{A}% +\xuanzeti{2}{D}% +\xuanzeti{3}{B}% +\xuanzeti{4}{A}% +\xuanzeti{5}{C}% +\xuanzeti{6}{D} + +\tigan{三、解答题(每小题8分,共64分)} +% 得分点命令 \score1, 得分点长度是自动的 +% \Score{(2分, 缺少常数得1分)} 用于自定义得分说明 + +\textbf{1. (8分)【解】} +\begin{align*} +\lim_{x\to-1}\frac{x^2-1}{x^2+3x+2}&=\lim_{x\to-1}\frac{(x-1)(x+1)}{(x+2)(x+1)} \score3\\ +&=\lim_{x\to-1}\frac{x-1}{x+2} \score3\\ +&=\frac{-2}1=-2. \score2 +\end{align*} + +\textbf{2. (8分)【解】} +\begin{align*} +\lim_{x\to0}\frac{e^x-1-x}{\arcsin x^2}&=\lim_{x\to0}\frac{e^x-1-x}{x^2} \score3\\ +&\xlongequal{\text{洛必达}}\lim_{x\to0}\frac{e^x-1}{2x} \score3\\ +&=\lim_{x\to0}\frac{x}{2x}=\frac12. \score2 +\end{align*} + +\newpage + +\textbf{3. (8分)【解】} +\begin{align*} +\frac{\diff y}{\diff x}&=\frac{\diff y/\diff t}{\diff x/\diff t} \score2\\ +&=\frac{3t^2+1}{2t+1}, \score2\\ +\frac{\diff^2 y}{\diff x^2}&=\frac{\diff y'/\diff t}{\diff x/\diff t} \score2\\ +&=\frac{6t(2t+1)-(3t^2+1)2}{(2t+1)^3}=\frac{6t^2+6t-2}{(2t+1)^3}. \score2 +\end{align*} + +\textbf{4. (8分)【解】} + +\indent 由于 $f(x)$ 在 $x=0$ 处连续, 因此 +\begin{align*} +f(0)&=f(0^+) \score1\\ + &=b=\lim_{x\to0^-}x\arctan\frac1x=0\times\left(-\frac\pi2\right)=0. \score1 +\end{align*} + +\indent 由于 $f(x)$ 在 $x=0$ 处可导, 因此 +\begin{align*} +f'_-(0)&=f'_+(0), \score1\\ +f'_-(0)&=\lim_{x\to0^-}\frac{x\arctan\frac1x}x=\lim_{x\to0^-}\arctan\frac1x=-\frac\pi2 \score1\\ +f'_+(0)&=(2x+a)|_{x=0}=a, \score1 +\end{align*} +因此 $a=-\dfrac\pi2$. \score1 + +\indent 由于 +\begin{align*} +\lim_{x\to+\infty}\frac yx&=\lim_{x\to+\infty}\left(x-\frac\pi2\right)=+\infty, \score1\\ +\lim_{x\to-\infty}\frac yx&=\lim_{x\to-\infty}\arctan\frac1x=0,\\ +\lim_{x\to-\infty}y&=\lim_{x\to-\infty}x\arctan\frac1x=\lim_{t\to0^-}\frac{\arctan t}t=1, +\end{align*} +因此曲线 $y=f(x)$ 的渐近线只有 $y=1$. \score1 + +\newpage + +\textbf{5. (8分)【解】} + +\indent 由 +\[f'(x)=3x^2-2x-1=(3x+1)(x-1)=0 \score2\] +可得驻点 $x=-\dfrac13,1$. \score2 + +\indent 由于 +\[f(-2)=-10,\quad f(2)=2,\quad f\left(-\frac13\right)=\frac5{27},\quad f(1)=-1, \score2\] +因此最大值为 $2$, 最小值为 $-10$. \score2 + +\textbf{6. (8分)【证明】} + +\textbf{证法一}: 设 $f(x)=\tan x-x$, 则 \score2 +\begin{align*} +f'(x)=\frac1{\cos^2x}-1=\tan^2x\ge0. \score2 +\end{align*} +因此 $f(x)$ 在 $\left(-\dfrac\pi2,\dfrac\pi2\right)$ 上单调递增, 从而 \score2 +\begin{align*} +f(x_2)\ge f(x_1),\quad\tan x_2-\tan x_1\ge x_2-x_1. \score2 +\end{align*} + +\textbf{证法二}: 设 $f(x)=\tan x$, 则 $f(x)$ 在 $[x_1,x_2]$ 上连续, $(x_1,x_2)$ 内可导. \score2 + +\indent 由拉格朗日中值定理, 存在 $\xi\in(x_1,x_2)$ 使得 +\begin{align*} +\frac{f(x_2)-f(x_1)}{x_2-x_1}=f'(\xi), \score2 +\end{align*} +即 +\begin{align*} +\frac{\tan x_2-\tan x_1}{x_2-x_1}=\frac1{\cos^2\xi}\ge1. \score2 +\end{align*} +所以 $\tan x_2-\tan x_1\ge x_2-x_1$. \score2 +\newpage + +\textbf{7. (8分)【证明】} + +\indent 设 $F(x)=x^{2022}f(x)$, \score2\\ +则 $F(x)$ 在 $[0,1]$ 上连续, $(0,1)$ 内可导, \score1\\ +且 $F(0)=0,F(1)=f(1)=0$. \score1 + +\indent 由罗尔中值定理, 存在 $\xi\in(0,1)$ 使得 $F'(\xi)=0$. \score2\\ +由于 $F'(x)=x^{2022}f'(x)+2022x^{2021}f(x)$ 且 $\xi\neq0$, \score1\\ +所以 $\xi f'(\xi)+2022f(\xi)=1$. \score1 + + +\textbf{8. (8分)【解】} + +(1) +\[f'(x)=\frac1x-\frac4{x^3}=\frac{x^2-4}{x^3}=\frac{(x+2)(x-2)}{x^3}. \score1\] +当 $0<x<2$ 时, $f'(x)<0$. 当 $x>2$ 时, $f'(x)>0$. \score1\\ +因此 $(0,2]$ 是 $f(x)$ 的单减区间, $[2,+\infty)$ 是 $f(x)$ 的单增区间. \Score{(1分, 写成开区间不扣分)}\\ +所以 $f(x)$ 只有唯一的极小值 $f(2)=\ln2+\dfrac12$. \score1 + +(2) +\[f''(x)=-\frac1{x^2}+\frac{12}{x^4}=-\frac{x^2-12}{x^4}=-\frac{(x-2\sqrt3)(x+2\sqrt3)}{x^4}. \score1\] +当 $0<x<2\sqrt3$ 时, $f''(x)>0$. 当 $x>2\sqrt3$ 时, $f''(x)<0$. \score1\\ +因此 $(0,2\sqrt3]$ 是曲线 $y=f(x)$ 的凹区间, \\ +$[2\sqrt3,+\infty)$ 是曲线 $y=f(x)$ 的凸区间, \Score{(1分, 写成开区间不扣分)}\\ +拐点为 $\left(2\sqrt3,\ln(2\sqrt3)+\dfrac16\right)$. \score1 + +\end{document} + diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam_datizhi.pdf b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_datizhi.pdf Binary files differnew file mode 100644 index 00000000000..ad9dc41adef --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_datizhi.pdf diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam_datizhi.tex b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_datizhi.tex new file mode 100644 index 00000000000..d5ad8907e45 --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_datizhi.tex @@ -0,0 +1,73 @@ +\documentclass[datizhi]{hfutexam} +\newcommand{\diff}{\,\mathrm{d}} + +\begin{document} +\BiaoTi{合肥工业大学考试专用答卷纸(A)} +\XueNian{2021}{2022} +\XueQi{二} +\KeChengDaiMa{034Y01} +\KeChengMingCheng{数学(下)} +\XueFen{5} +\KeChengXingZhi{必修} +\KaoShiXingShi{闭卷} +\ZhuanYeBanJi{少数民族预科班} +\KaoShiRiQi{2022年6月18日8:00-10:00} +\MingTiJiaoShi{集体} +%\XiZhuRenQianMing{dengbing.png} + + +\notice + +%\scorebox 为打分框, 必须放在行首 +\scorebox\tigan{一、填空题(每小题3分,共18分)} + +\textbf{请将你的答案对应填在横线上:} + +\textbf{1.} \fillblank{}, +\textbf{2.} \fillblank{}, +\textbf{3.} \fillblank{}, + +\textbf{4.} \fillblank{}, +\textbf{5.} \fillblank{}, +\textbf{6.} \fillblank{}. + +\scorebox\tigan{二、选择题(每小题3分,共18分)} + +\textbf{请将你所选择的字母 A, B, C, D 之一对应填在下列表格里:} + +\xuanzeti{\textbf{题号}}{\textbf{答案}}% +\xuanzeti{1}{}% +\xuanzeti{2}{}% +\xuanzeti{3}{}% +\xuanzeti{4}{}% +\xuanzeti{5}{}% +\xuanzeti{6}{} + +\tigan{三、解答题(每小题8分,共64分)} + +\scorebox\textbf{1. (8分)【解】} +% \vspace 用于生成一定高度的空白, \newpage 直接换页 +\vspace{3cm} + +\scorebox\textbf{2. (8分)【解】} +\newpage + +\scorebox\textbf{3. (8分)【解】} +\vspace{7cm} + +\scorebox\textbf{4. (8分)【解】} +\newpage + +\scorebox\textbf{5. (8分)【解】} +\vspace{7cm} + +\scorebox\textbf{6. (8分)【证明】} +\newpage + +\scorebox\textbf{7. (8分)【证明】} +\vspace{7cm} + +\scorebox\textbf{8. (8分)【解】} + +\end{document} + diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam_shijuan.pdf b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_shijuan.pdf Binary files differnew file mode 100644 index 00000000000..97f57ce4027 --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_shijuan.pdf diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam_shijuan.tex b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_shijuan.tex new file mode 100644 index 00000000000..e4a5617329f --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_shijuan.tex @@ -0,0 +1,82 @@ +\documentclass{hfutexam} +\newcommand{\diff}{\,\mathrm{d}} +\usetikzlibrary{arrows.meta, overlay-beamer-styles} + +\begin{document} +\BiaoTi{合肥工业大学试卷(A)} +\XueNian{2021}{2022} +\XueQi{二} +\KeChengDaiMa{034Y01} +\KeChengMingCheng{数学(下)} +\XueFen{5} +\KeChengXingZhi{必修} +\KaoShiXingShi{闭卷} +\ZhuanYeBanJi{少数民族预科班} +\KaoShiRiQi{2022年6月18日8:00-10:00} +\MingTiJiaoShi{集体} +\XiZhuRenQianMing{} +% \XiZhuRenQianMing{dengbing.png} + +\tigan{一、填空题(每题3分,共18分)} +\begin{enumerate} +\item 如果 $f(x)>0$ 且 $\displaystyle\lim_{x\to\infty}f(x)=0$, 则 $\displaystyle\lim_{x\to\infty}\bigl[1+f(x)\bigr]^{1/f(x)}=$\fillblank{}. +\item 设 $y=\sin(x^2+1)$, 则 $\diff y=$\fillblank{}. +\item 极限 $\displaystyle\lim_{n\to\infty}\left(\frac1{n^2-1}+\frac2{n^2-2}+\cdots+\frac n{n^2-n}\right)=$\fillblank{}. +\item 曲线 $y=2\ln(x+1)$ 在点 $(1,2\ln2)$ 处的切线方程为\fillblank{}. +\item 若 $e^{y-1}=1+xy$, 则 $\dfrac{\diff y}{\diff x}\bigg|_{x=0}=$\fillblank{}. +\item 如果函数 $f(x)$ 的定义域是 $(0,+\infty)$, 且 $x=0$ 是曲线 $y=f(x)$ 的垂直渐近线, 那么 $\displaystyle\lim_{x\to0^+}\frac1{f(x)}=$\fillblank{}. +\end{enumerate} + +\tigan{二、选择题(每题3分,共18分)} +\begin{enumerate} +\item 当 $x\to+\infty$ 时, $\dfrac1x$ 和(~~~~)是等价无穷小. +% 自动根据选项长度设置行数 +\xx{$\sin\dfrac1x$}{$\sin x$}{$e^{-x}$}{$e^{1/x}$} +\item 若当 $x\to0$ 时, $\arctan(e^x-1)\cdot(\cos x-1)$ 和 $x^n$ 是同阶无穷小, 则 $n=$(~~~~). +\xx{$0$}{$1$}{$2$}{$3$} +\item 设 $f(x)=\arctan\dfrac1{x(x-1)^2}$, 则 $x=0$ 是 $f(x)$ 的(~~~~). +\xx{可去间断点}{跳跃间断点}{第二类间断点}{连续点} +\item +\begin{tikzpicture}[overlay,xshift=13cm,yshift=-3.5cm] +\draw[-Stealth,thick](-3,0)--(3,0); +\draw[-Stealth,thick](0,-1)--(0,3); +\draw[very thick,smooth,domain=-55:55] plot ({\x/50-1.3}, {tan(\x)*tan(\x)}); +\draw[very thick,smooth,domain=0.15:2] plot ({\x}, {-ln(\x)}); +\draw + (-0.3,-0.3) node {$O$} + (2.8,-0.3) node {$x$} + (-0.3,2.8) node {$y$}; +\end{tikzpicture} +设 $f(x)$ 是定义在 $(-\infty,+\infty)$ 上的连续函数, 且 $f'(x)$ 的图像如下图所示, 则 $f(x)$ 有(~~~~). +% 手动设置为每行1个 +\xx[1]{一个极大值点,没有极小值点}{没有极大值点,一个极小值点}{一个极大值点和一个极小值点}{一个极大值点和两个极小值点} +\newpage +\item 设函数 $f(x)$ 在点 $x=0$ 处可导, 且 $f(0)=0$, 则 $\displaystyle\lim_{x\to0}\frac{f(x^{2022})+x^{2021}f(x)}{x^{2022}}=$(~~~~). +\xx{$0$}{$f'(0)$}{$2f'(0)$}{$2022f'(0)$} +\item 如果点 $(x_0,y_0)$ 是曲线 $y=f(x)$ 的拐点, 则 $f''(x_0)=$(~~~~). +\xx{$0$}{$\infty$}{不存在}{$0$ 或不存在} +\end{enumerate} + +\tigan{三、解答题(每题8分,共64分)} +\begin{enumerate} +\item 求极限 $\displaystyle\lim_{x\to-1}\frac{x^2-1}{x^2+3x+2}$. +\item 求极限 $\displaystyle\lim_{x\to0}\frac{e^x-1-x}{\arcsin x^2}$. +\item 设 $\begin{cases}x=t^2+t&\\y=t^3+t&\end{cases}$, 求 $\dfrac{\diff y}{\diff x}$ 和 $\dfrac{\diff^2 y}{\diff x^2}$. +\item 设 $f(x)=\begin{cases}x\arctan\dfrac1x,&x<0,\\x^2+ax+b,&x\ge0.\end{cases}$ +求常数 $a,b$ 使得函数 $f(x)$ 在 $(-\infty,+\infty)$ 内可导, 并求出此时曲线 $y=f(x)$ 的渐近线. +\item 求函数 $f(x)=x^3-x^2-x$ 在区间 $[-2,2]$ 上的最大值和最小值. +\item 证明: 当 $-\dfrac\pi2<x_1<x_2<\dfrac\pi2$ 时, $\tan x_2-\tan x_1\ge x_2-x_1$. +\item 设函数 $f(x)$ 在 $(-\infty,+\infty)$ 内可导, 且 $f(1)=0$. +证明: 存在 $\xi\in(0,1)$ 使得 $\xi f'(\xi)+2022f(\xi)=0$. +\item 设函数 $f(x)=\ln x+\dfrac2{x^2}, x\in(0,+\infty)$. +\begin{enumerate} +\item[(1)] 函数 $f(x)$ 的增减区间及极值; +\item[(2)] 曲线 $y=f(x)$ 的凹凸区间及拐点. +\end{enumerate} +\end{enumerate} + +\end{document} + + + + diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam_simple.pdf b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_simple.pdf Binary files differnew file mode 100644 index 00000000000..18b857b946c --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_simple.pdf diff --git a/Master/texmf-dist/doc/latex/hfutexam/hfutexam_simple.tex b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_simple.tex new file mode 100644 index 00000000000..54175ece65f --- /dev/null +++ b/Master/texmf-dist/doc/latex/hfutexam/hfutexam_simple.tex @@ -0,0 +1,260 @@ +\documentclass[simple]{hfutexam} +\newcommand{\diff}{\,\mathrm{d}} +\usetikzlibrary{arrows.meta, overlay-beamer-styles} +\RequirePackage{extarrows} + +\begin{document} +\BiaoTi{合肥工业大学期中试卷} +\XueNian{2021}{2022} +\XueQi{二} +\KeChengDaiMa{034Y01} +\KeChengMingCheng{数学(下)} +\XueFen{5} +\KeChengXingZhi{必修} +\KaoShiXingShi{闭卷} +\ZhuanYeBanJi{少数民族预科班} +\KaoShiRiQi{2022年5月13日8:00-10:00} +\MingTiJiaoShi{集体} +\maketitle + +\begin{enumerate} +\item \textbf{(10分)} 求函数 $\displaystyle f(x)=\ln\frac1{\sqrt{x^2-1}}+\arctan\frac1x$ 的定义域. +\item \textbf{(5分)} 求函数 $\displaystyle y=\begin{cases} +1/x,&x<0,\\1,&x=0,\\1+e^{-x},&x>0\end{cases}$ 的反函数. +\item \textbf{(10分)} 求极限 $\displaystyle\lim_{x\to0^-}(1-x)^{1/x}$. +\item \textbf{(5分)} 求极限 $\displaystyle\lim_{x\to-2}\frac{x^2-4}{x^3+8}$. +\item \textbf{(5分)} 求极限 $\displaystyle\lim_{x\to0}\frac{\sin(e^{-x}-1)}{\arctan(1-\cos x)}$. +\item \textbf{(5分)} 求极限 $\displaystyle\lim_{x\to0}\frac{\sqrt{1+2x-x^2}-\sqrt{1-2x+x^2}}x$. +\item \textbf{(5分)} 求极限 $\displaystyle\lim_{x\to\infty}\left(\cos\frac1x\right)^{\frac1{\ln(1+x^2)-2\ln x}}$. +\item \textbf{(5分)} 求极限 $\displaystyle\lim_{x\to\infty}\left(\frac\pi{e^x-1}-\arctan\frac x2\right)$. +\item \textbf{(5分)} 求极限 $\displaystyle\lim_{n\to\infty}\left(\frac1{n^2+2}+\frac2{n^2+4}+\cdots+\frac n{n^2+2n}\right)$. +\item \textbf{(5分)} 设 $a_1=4,a_{n+1}=\sqrt{a_n+6}$, 证明 $\displaystyle\lim_{n\to\infty}a_n$ 存在并求之. +\item \textbf{(10分)} 证明 $e^x+x=4$ 在 $(0,+\infty)$ 内有零点. +\item \textbf{(5分)} 设函数 $f(x)$ 在 $[-1,1]$ 上连续, 且 $f(-1)\le1\le f(1)$. 证明存在 $\xi\in[-1,1]$, 使得 $f(\xi)=\xi^2$. +\item \textbf{(10分)} 求 $y=e^{x+1}\sin x-e^2\sin1$ 的导数. +\item \textbf{(5分)} 求 $y=\arctan e^x$ 的导数. +\item \textbf{(5分)} 求曲线 $y=\tan x$ 在点 $\left(-\dfrac\pi4,-1\right)$ 处的切线方程和法线方程. +\item \textbf{(5分)} 设 +$\displaystyle f(x)=\begin{cases}\dfrac{e^{3x}-1}{\arctan x},&x<0,\\2x+a,&x\ge0\end{cases}$ +在 $x=0$ 处连续, 求常数 $a$. +\end{enumerate} +\newpage + +\BiaoTi{合肥工业大学试卷(A)} +\XueNian{2021}{2022} +\XueQi{二} +\KeChengDaiMa{034Y01} +\KeChengMingCheng{数学(下)} +\XueFen{5} +\KeChengXingZhi{必修} +\KaoShiXingShi{闭卷} +\ZhuanYeBanJi{少数民族预科班} +\KaoShiRiQi{2022年6月18日8:00-10:00} +\MingTiJiaoShi{集体} +\maketitle + +\tigan{一、填空题(每题3分,共18分)} +\begin{enumerate} +\item 如果 $f(x)>0$ 且 $\displaystyle\lim_{x\to\infty}f(x)=0$, 则 $\displaystyle\lim_{x\to\infty}\bigl[1+f(x)\bigr]^{1/f(x)}=$\fillblank{}. +\item 设 $y=\sin(x^2+1)$, 则 $\diff y=$\fillblank{}. +\item 极限 $\displaystyle\lim_{n\to\infty}\left(\frac1{n^2-1}+\frac2{n^2-2}+\cdots+\frac n{n^2-n}\right)=$\fillblank{}. +\item 曲线 $y=2\ln(x+1)$ 在点 $(1,2\ln2)$ 处的切线方程为\fillblank{}. +\item 若 $e^{y-1}=1+xy$, 则 $\dfrac{\diff y}{\diff x}\bigg|_{x=0}=$\fillblank{}. +\item 如果函数 $f(x)$ 的定义域是 $(0,+\infty)$, 且 $x=0$ 是曲线 $y=f(x)$ 的垂直渐近线, 那么 $\displaystyle\lim_{x\to0^+}\frac1{f(x)}=$\fillblank{}. +\end{enumerate} + +\tigan{二、选择题(每题3分,共18分)} +\begin{enumerate} +\item 当 $x\to+\infty$ 时, $\dfrac1x$ 和(~~~~)是等价无穷小. +\xx{$\sin\dfrac1x$}{$\sin x$}{$e^{-x}$}{$e^{1/x}$} +\item 若当 $x\to0$ 时, $\arctan(e^x-1)\cdot(\cos x-1)$ 和 $x^n$ 是同阶无穷小, 则 $n=$(~~~~). +\xx{$0$}{$1$}{$2$}{$3$} +\item 设 $f(x)=\arctan\dfrac1{x(x-1)^2}$, 则 $x=0$ 是 $f(x)$ 的(~~~~). +\xx{可去间断点}{跳跃间断点}{第二类间断点}{连续点} +\item +\begin{tikzpicture}[overlay,xshift=12cm,yshift=-3cm] +\draw[-Stealth,thick](-3,0)--(3,0); +\draw[-Stealth,thick](0,-0.8)--(0,2.5); +\draw[very thick,smooth,domain=-55:55] plot ({\x/50-1.3}, {tan(\x)*tan(\x)}); +\draw[very thick,smooth,domain=0.15:2] plot ({\x}, {-ln(\x)}); +\draw + (-0.3,-0.3) node {$O$} + (2.8,-0.3) node {$x$} + (-0.3,2.3) node {$y$}; +\end{tikzpicture} +设 $f(x)$ 是定义在 $(-\infty,+\infty)$ 上的连续函数, 且 $f'(x)$ 的图像如下图所示, 则 $f(x)$ 有(~~~~). +\xx[1]{一个极大值点,没有极小值点}{没有极大值点,一个极小值点}{一个极大值点和一个极小值点}{一个极大值点和两个极小值点} +\item 设 $f(x)$ 在点 $x=0$ 处可导, 且 $f(0)=0$, 则 $\displaystyle\lim_{x\to0}\frac{f(x^{2022})+x^{2021}f(x)}{x^{2022}}=$(~~~~). +\xx{$0$}{$f'(0)$}{$2f'(0)$}{$2022f'(0)$} +\item 如果点 $(x_0,y_0)$ 是曲线 $y=f(x)$ 的拐点, 则 $f''(x_0)=$(~~~~). +\xx{$0$}{$\infty$}{不存在}{$0$ 或不存在} +\end{enumerate} + +\tigan{三、解答题(每题8分,共64分)} +\begin{enumerate} +\item 求极限 $\displaystyle\lim_{x\to-1}\frac{x^2-1}{x^2+3x+2}$. +\item 求极限 $\displaystyle\lim_{x\to0}\frac{e^x-1-x}{\arcsin x^2}$. +\item 设 $\begin{cases}x=t^2+t&\\y=t^3+t&\end{cases}$, 求 $\dfrac{\diff y}{\diff x}$ 和 $\dfrac{\diff^2 y}{\diff x^2}$. +\item 设 $f(x)=\begin{cases}x\arctan\dfrac1x,&x<0,\\x^2+ax+b,&x\ge0.\end{cases}$ +求常数 $a,b$ 使得函数 $f(x)$ 在 $(-\infty,+\infty)$ 内可导, 并求出此时曲线 $y=f(x)$ 的渐近线. +\item 求函数 $f(x)=x^3-x^2-x$ 在区间 $[-2,2]$ 上的最大值和最小值. +\item 证明: 当 $-\dfrac\pi2<x_1<x_2<\dfrac\pi2$ 时, $\tan x_2-\tan x_1\ge x_2-x_1$. +\item 设函数 $f(x)$ 在 $(-\infty,+\infty)$ 内可导, 且 $f(1)=0$. +证明: 存在 $\xi\in(0,1)$ 使得 $\xi f'(\xi)+2022f(\xi)=0$. +\item 设函数 $f(x)=\ln x+\dfrac2{x^2}, x\in(0,+\infty)$. 求 +\begin{enumerate} +\item[(1)] 函数 $f(x)$ 的增减区间及极值; +\item[(2)] 曲线 $y=f(x)$ 的凹凸区间及拐点. +\end{enumerate} +\end{enumerate} + +\newpage +\BiaoTi{合肥工业大学试卷参考答案(A)} +\XueNian{2021}{2022} +\XueQi{二} +\KeChengDaiMa{034Y01} +\KeChengMingCheng{数学(下)} +\XueFen{5} +\KeChengXingZhi{必修} +\KaoShiXingShi{闭卷} +\ZhuanYeBanJi{少数民族预科班} +\KaoShiRiQi{2022年6月18日8:00-10:00} +\MingTiJiaoShi{集体} +\maketitle + +\tigan{一、填空题(每小题3分,共18分)} + +\textbf{请将你的答案对应填在横线上:} + +\textbf{1.} \fillblank{$e$}, +\textbf{2.} \fillblank{$2x\cos(x^2+1)\diff x$}, +\textbf{3.} \fillblank{$\dfrac12$}, \\ +\textbf{4.} \fillblank{$y=x-1+2\ln 2$}, +\textbf{5.} \fillblank{$1$}, +\textbf{6.} \fillblank{$0$}. + +\tigan{二、选择题(每小题3分,共18分)} + +\textbf{请将你所选择的字母 A, B, C, D 之一对应填在下列表格里:} + +\xuanzeti{\textbf{题号}}{\textbf{答案}}% +\xuanzeti{1}{A}% +\xuanzeti{2}{D}% +\xuanzeti{3}{B}% +\xuanzeti{4}{A}% +\xuanzeti{5}{C}% +\xuanzeti{6}{D} + +\tigan{三、解答题(每小题8分,共64分)} + +\textbf{1. (8分)【解】} +\vspace{-\baselineskip} + +\begin{align*} +\lim_{x\to-1}\frac{x^2-1}{x^2+3x+2}&=\lim_{x\to-1}\frac{(x-1)(x+1)}{(x+2)(x+1)} \score3\\ +&=\lim_{x\to-1}\frac{x-1}{x+2} \score3\\ +&=\frac{-2}1=-2. \score2 +\end{align*} + +\textbf{2. (8分)【解】} +\vspace{-\baselineskip} + +\begin{align*} +\lim_{x\to0}\frac{e^x-1-x}{\arcsin x^2}&=\lim_{x\to0}\frac{e^x-1-x}{x^2} \score3\\ +&\xlongequal[]{\text{洛必达}}\lim_{x\to0}\frac{e^x-1}{2x} \score3\\ +&=\lim_{x\to0}\frac{x}{2x}=\frac12. \score2 +\end{align*} + +\textbf{3. (8分)【解】} +\vspace{-\baselineskip} + +\begin{align*} +\frac{\diff y}{\diff x}&=\frac{\diff y/\diff t}{\diff x/\diff t} \score2\\ +&=\frac{3t^2+1}{2t+1}, \score2\\ +\frac{\diff^2 y}{\diff x^2}&=\frac{\diff y'/\diff t}{\diff x/\diff t} \score2\\ +&=\frac{6t(2t+1)-(3t^2+1)2}{(2t+1)^3}=\frac{6t^2+6t-2}{(2t+1)^3}. \score2 +\end{align*} + +\newpage +\textbf{4. (8分)【解】} + +\indent 由于 $f(x)$ 在 $x=0$ 处连续, 因此 +\begin{align*} +f(0)&=f(0^+) \score1\\ +&=b=\lim_{x\to0^-}x\arctan\frac1x=0\times\left(-\frac\pi2\right)=0. \score1 +\end{align*} + +\indent 由于 $f(x)$ 在 $x=0$ 处可导, 因此 +\begin{align*} +f'_-(0)&=f'_+(0), \score1\\ +f'_-(0)&=\lim_{x\to0^-}\frac{x\arctan\frac1x}x=\lim_{x\to0^-}\arctan\frac1x=-\frac\pi2 \score1\\ +f'_+(0)&=(2x+a)|_{x=0}=a, \score1 +\end{align*} +因此 $a=-\dfrac\pi2$. \score1 + +\indent 由于 +\begin{align*} +\lim_{x\to+\infty}\frac yx&=\lim_{x\to+\infty}\left(x-\frac\pi2\right)=+\infty, \score1\\ +\lim_{x\to-\infty}\frac yx&=\lim_{x\to-\infty}\arctan\frac1x=0,\\ +\lim_{x\to-\infty}y&=\lim_{x\to-\infty}x\arctan\frac1x=\lim_{t\to0^-}\frac{\arctan t}t=1, +\end{align*} +因此曲线 $y=f(x)$ 的渐近线只有 $y=1$. \score1 + +\textbf{5. (8分)【解】} + +\indent 由 +\[f'(x)=3x^2-2x-1=(3x+1)(x-1)=0 \score2\] +可得驻点 $x=-\dfrac13,1$. \score2 + +\indent 由于 +\[f(-2)=-10,\quad f(2)=2,\quad f\left(-\frac13\right)=\frac5{27},\quad f(1)=-1, \score2\] +因此最大值为 $2$, 最小值为 $-10$. \score2 + +\textbf{6. (8分)【证明】} + +\textbf{证法一}: 设 $f(x)=\tan x-x$, 则 \score2 +\[f'(x)=\frac1{\cos^2x}-1=\tan^2x\ge0. \score2\] +因此 $f(x)$ 在 $\left(-\dfrac\pi2,\dfrac\pi2\right)$ 上单调递增, 从而 \score2 +\[f(x_2)\ge f(x_1),\quad\tan x_2-\tan x_1\ge x_2-x_1. \score2\] + +\newpage +\textbf{证法二}: 设 $f(x)=\tan x$, 则 $f(x)$ 在 $[x_1,x_2]$ 上连续, $(x_1,x_2)$ 内可导. \score2 + +\indent 由拉格朗日中值定理, 存在 $\xi\in(x_1,x_2)$ 使得 +\[\frac{f(x_2)-f(x_1)}{x_2-x_1}=f'(\xi), \score2\] +即 +\[\frac{\tan x_2-\tan x_1}{x_2-x_1}=\frac1{\cos^2\xi}\ge1. \score2\] +所以 $\tan x_2-\tan x_1\ge x_2-x_1$. \score2 + +\textbf{7. (8分)【证明】} + +\indent 设 $F(x)=x^{2022}f(x)$, \score2\\ +则 $F(x)$ 在 $[0,1]$ 上连续, $(0,1)$ 内可导, \score1\\ +且 $F(0)=0,F(1)=f(1)=0$. \score1 + +\indent 由罗尔中值定理, 存在 $\xi\in(0,1)$ 使得 $F'(\xi)=0$. \score2\\ +由于 $F'(x)=x^{2022}f'(x)+2022x^{2021}f(x)$ 且 $\xi\neq0$, \score1\\ +所以 $\xi f'(\xi)+2022f(\xi)=1$. \score1 + + +\textbf{8. (8分)【解】} + +(1) +\[f'(x)=\frac1x-\frac4{x^3}=\frac{x^2-4}{x^3}=\frac{(x+2)(x-2)}{x^3}. \score1\] +当 $0<x<2$ 时, $f'(x)<0$. 当 $x>2$ 时, $f'(x)>0$. \score1\\ +因此 $(0,2]$ 是 $f(x)$ 的单减区间,\\ +$[2,+\infty)$ 是 $f(x)$ 的单增区间. \Score{(1分, 写成开区间不扣分)}\\ +所以 $f(x)$ 只有唯一的极小值 $f(2)=\ln2+\dfrac12$. \score1 + +(2) +\[f''(x)=-\frac1{x^2}+\frac{12}{x^4}=-\frac{x^2-12}{x^4}=-\frac{(x-2\sqrt3)(x+2\sqrt3)}{x^4}. \score1\] +当 $0<x<2\sqrt3$ 时, $f''(x)>0$. 当 $x>2\sqrt3$ 时, $f''(x)<0$. \score1\\ +因此 $(0,2\sqrt3]$ 是曲线 $y=f(x)$ 的凹区间,\\ +$[2\sqrt3,+\infty)$ 是曲线 $y=f(x)$ 的凸区间,\Score{(1分, 写成开区间不扣分)}\\ +拐点为 $\left(2\sqrt3,\ln(2\sqrt3)+\dfrac16\right)$. \score1 + +\end{document} + + + + diff --git a/Master/texmf-dist/tex/latex/hfutexam/hfutexam.cls b/Master/texmf-dist/tex/latex/hfutexam/hfutexam.cls new file mode 100644 index 00000000000..4d560ba7b4b --- /dev/null +++ b/Master/texmf-dist/tex/latex/hfutexam/hfutexam.cls @@ -0,0 +1,346 @@ +% 文件 `hfutexam.cls' +% !TEX TS-program = xelatex +% !TEX encoding = UTF-8 Unicode +% 合肥工业大学试卷模板 +% 作者: 张神星 +% 使用前请先安装字体: 方正小标宋、方正仿宋, 否则请使用选项 nofangzheng (采用新宋体和仿宋代替) +% 编译模式: XeLaTeX +% 你可以任意修改或再次分发该文件 +\NeedsTeXFormat{LaTeX2e} +\ProvidesClass{hfutexam}[2022/12/04 v1.5 HFUTExam document class by Zhang Shenxing] +% 文档选项 shijuan, datizhi, cankaodaan, simple +\newif\ifHFUT@ShiJuan\HFUT@ShiJuantrue +\newif\ifHFUT@DaTiZhi\HFUT@DaTiZhifalse +\newif\ifHFUT@CanKaoDaAn\HFUT@CanKaoDaAnfalse +\newif\ifHFUT@Simple\HFUT@Simplefalse +\DeclareOption{datizhi}{\HFUT@ShiJuanfalse\HFUT@DaTiZhitrue} +\DeclareOption{cankaodaan}{\HFUT@ShiJuanfalse\HFUT@CanKaoDaAntrue} +\DeclareOption{simple}{\HFUT@ShiJuanfalse\HFUT@Simpletrue} +% 文档选项 nofangzheng +\newif\ifHFUT@Fandol\HFUT@Fandoltrue +\DeclareOption{nofangzheng}{\HFUT@Fandolfalse} +% 基于 ctexart 文档类 +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{ctexart}} +\ProcessOptions\relax +\ifHFUT@Simple\else\PassOptionsToClass{twocolumn}{ctexart}\fi +\ProcessOptions\relax +\LoadClass[12pt,oneside]{ctexart} +% 页面设置 +\RequirePackage{amsmath,amssymb,amsthm} +\RequirePackage{graphicx} +\RequirePackage{enumitem} +\RequirePackage{geometry} +\ifHFUT@Simple + \geometry{a4paper,scale=0.8} +\else + \geometry{ + paperheight=29.7cm, + paperwidth=42cm, + left=3.17cm, + right=3.17cm, + voffset=2.2cm, + headheight=77pt, + headsep=12pt, + footskip=1cm + } +\fi +% 试卷信息 +\newcommand{\BiaoTi}[1]{\gdef\HFUT@BiaoTi{#1}} +\newcommand{\XueNian}[2]{\gdef\HFUT@XueNians{#1}\gdef\HFUT@XueNiane{#2}} +\newcommand{\XueQi}[1]{\gdef\HFUT@XueQi{#1}} +\newcommand{\KeChengDaiMa}[1]{\gdef\HFUT@KeChengDaiMa{#1}} +\newcommand{\KeChengMingCheng}[1]{\gdef\HFUT@KeChengMingCheng{#1}} +\newcommand{\XueFen}[1]{\gdef\HFUT@XueFen{#1}} +\newcommand{\KeChengXingZhi}[1]{\gdef\HFUT@KeChengXingZhi{#1}} +\newcommand{\KaoShiXingShi}[1]{\gdef\HFUT@KaoShiXingShi{#1}} +\newcommand{\ZhuanYeBanJi}[1]{\gdef\HFUT@ZhuanYeBanJi{#1}} +\newcommand{\KaoShiRiQi}[1]{\gdef\HFUT@KaoShiRiQi{#1}} +\newcommand{\MingTiJiaoShi}[1]{\gdef\HFUT@MingTiJiaoShi{#1}} +\newcommand{\XiZhuRenQianMing}[1]{\gdef\HFUT@XiZhuRenQianMing{#1}} +\BiaoTi{} +\XueNian{}{} +\XueQi{} +\KeChengDaiMa{} +\KeChengMingCheng{} +\XueFen{} +\KeChengXingZhi{} +\KaoShiXingShi{} +\ZhuanYeBanJi{} +\KaoShiRiQi{} +\MingTiJiaoShi{} +\XiZhuRenQianMing{} +% 粗字体设定 +\newfontfamily\timesnewroman[AutoFakeBold={1.5}]{Times New Roman} % 粗罗马 +\ifHFUT@Fandol + \setCJKfamilyfont{titlesongti}[AutoFakeBold={1.5}]{FZXiaoBiaoSong-B05S} % 粗方正小标宋 + \newfontfamily\entitlesongti[AutoFakeBold={1.5}]{FZXiaoBiaoSong-B05S} + \setCJKfamilyfont{titlefangsong}[AutoFakeBold={1.5}]{FZFangSong-Z02S} % 粗方正仿宋 + \newfontfamily\entitlefangsong[AutoFakeBold={1.5}]{FZFangSong-Z02S} +\else + \setCJKfamilyfont{titlesongti}[AutoFakeBold={4}]{NSimSun} % 粗新宋体 + \newfontfamily\entitlesongti[AutoFakeBold={4}]{NSimSun} + \setCJKfamilyfont{titlefangsong}[AutoFakeBold={1.5}]{FangSong} % 粗仿宋 + \newfontfamily\entitlefangsong[AutoFakeBold={1.5}]{FangSong} +\fi +\newcommand{\titlesongti}{\entitlesongti\CJKfamily{titlesongti}} +\newcommand{\titlefangsong}{\entitlefangsong\CJKfamily{titlefangsong}} +\setCJKfamilyfont{xinsongti}[AutoFakeBold={1.5}]{NSimSun} % 粗新宋体 +\newfontfamily\enxinsongti[AutoFakeBold={1.5}]{NSimSun} +\newcommand{\xinsongti}{\enxinsongti\CJKfamily{xinsongti}} +\setCJKfamilyfont{cusongti}[AutoFakeBold={1.5}]{SimSun} % 粗宋体 +\newcommand{\cusongti}{\CJKfamily{cusongti}} +% 重新设定字体大小 +\renewcommand{\LARGE}{\fontsize{21}{21}} +\renewcommand{\large}{\fontsize{14}{14}} +\renewcommand{\normalsize}{\fontsize{12}{12}} +\renewcommand{\small}{\fontsize{10.5}{10.5}} +% 缩进 +\setlength{\parindent}{0em} +\renewcommand{\indent}{\hspace*{2em}} +% 分栏 +\setlength\columnsep{0.8cm} % 分栏间距 +\columnseprule=0.5pt % 分栏线宽度 +% 填空题 +\newlength{\ltemp} +\RequirePackage[normalem]{ulem} +\ifHFUT@ShiJuan% + \NewDocumentCommand\fillblank{O{3.5cm} O{0.5cm} m}{\uline{\makebox[#1]{\rule{0pt}{#2}#3}}}% + \else\ifHFUT@DaTiZhi% + \NewDocumentCommand\fillblank{O{3.5cm} O{1cm} m}{\uline{\makebox[#1]{\rule{0pt}{#2}#3}}}% + \else% + \NewDocumentCommand\fillblank{O{3.5cm} O{1cm} m}{% + \settodepth{\ltemp}{#3}% + \uline{\makebox[#1]{\rule{0pt}{#2}\raisebox{\ltemp}{#3}}}% + }% +\fi\fi +% 页眉页脚 +\RequirePackage{fancyhdr} +\RequirePackage{lastpage} +\RequirePackage{etoolbox} +\renewcommand\headrulewidth{0.5pt} % 页眉线宽度 +\renewcommand\footrulewidth{0.5pt} % 页脚线宽度 +\pagestyle{fancy} +\fancyhf{} +\newcommand{\boxyes}{{\raisebox{-0.5mm}{\LARGE$\checkmark\hspace{-1.2em}\square$}}} +\newcommand{\boxno}{{\raisebox{-0.5mm}{\LARGE$\square$}}} +\newcommand{\filltitle}[2]{\uline{\makebox[#1]{#2}}} +\newlength{\ltitle} +\settowidth{\ltitle}{\HFUT@BiaoTi} +\ifHFUT@ShiJuan%试卷页眉页脚 + \fancyhead[C]{% + \hfill\bfseries\LARGE\titlesongti\ifdimcomp\ltitle>{0.5\linewidth}{\HFUT@BiaoTi}{\makebox[0.5\linewidth][s]{\HFUT@BiaoTi}}\hfill% + \large\cusongti 共\filltitle{1.5em}{\timesnewroman\pageref{LastPage}}页第\filltitle{1.5em}{\timesnewroman\thepage}页\\\vspace{5pt}% + \timesnewroman\HFUT@XueNians\titlefangsong~\timesnewroman\HFUT@XueNiane\titlefangsong 学年第\filltitle{2em}{\HFUT@XueQi}学期\hfill% + 课程代码\filltitle{5em}{\HFUT@KeChengDaiMa}\hfill% + 课程名称\filltitle{12em}{\HFUT@KeChengMingCheng}\hfill% + 学分\filltitle{2.5em}{\HFUT@XueFen}\hfill% + 课程性质: 必修\ifdefstring{\HFUT@KeChengXingZhi}{必修}{\boxyes}{\boxno}% + 选修\ifdefstring{\HFUT@KeChengXingZhi}{选修}{\boxyes}{\boxno}% + 限修\ifdefstring{\HFUT@KeChengXingZhi}{限修}{\boxyes}{\boxno}\hfill% + 考试形式: 开卷\ifdefstring{\HFUT@KaoShiXingShi}{开卷}{\boxyes}{\boxno}% + 闭卷\ifdefstring{\HFUT@KaoShiXingShi}{闭卷}{\boxyes}{\boxno}\\\vspace{2pt}% + 专业班级(教学班)\filltitle{11em}{\HFUT@ZhuanYeBanJi}\hfill% + 考试日期\filltitle{16em}{\HFUT@KaoShiRiQi}\hfill% + 命题教师\fillblank[5.5em][0.6cm]{\HFUT@MingTiJiaoShi}\hfill% + 系(所或教研室)主任审批签名% + \begin{tikzpicture}[overlay,xshift=3.25em,yshift=0.15cm]% + \node at (0,0) {\ifx\HFUT@XiZhuRenQianMing\@empty\else\includegraphics[height=0.9cm]{\HFUT@XiZhuRenQianMing}\fi};% + \end{tikzpicture}% + \filltitle{6.5em}{}\vspace{4pt}% + } + \fancyfoot[C]{\small\vspace{0.5\baselineskip}命题教师注意事项: + 1. 主考教师必须于考试一周前将“试卷A”、“试卷B”经教研室主任审批签字后送教务科印刷。\hspace{1em}% + 2. 请命题教师用黑色水笔工整地书写题目或用A4纸横式打印贴在试卷版芯中。 + } +\fi +\ifHFUT@DaTiZhi%答题纸页眉页脚 + \fancyhead[C]{% + \bfseries\LARGE\xinsongti\scalebox{2.0}[1.0]{% + \ifdimcomp\ltitle>{0.35\linewidth}{\HFUT@BiaoTi}{\makebox[0.35\linewidth][s]{\HFUT@BiaoTi}}% + }\\\vspace{8pt}% + \large\timesnewroman\HFUT@XueNians\titlefangsong~\timesnewroman\HFUT@XueNiane\titlefangsong 学年第\filltitle{2em}{\HFUT@XueQi}学期\hfill% + 课程代码\filltitle{6.5em}{\HFUT@KeChengDaiMa}\hfill% + 课程名称\filltitle{13em}{\HFUT@KeChengMingCheng}\hfill% + 命题教师\filltitle{7em}{\HFUT@MingTiJiaoShi}\hfill% + 系主任审批% + \begin{tikzpicture}[overlay,xshift=3.5em,yshift=0.2cm]% + \node at (0,0) {\ifx\HFUT@XiZhuRenQianMing\@empty\else\includegraphics[height=0.9cm]{\HFUT@XiZhuRenQianMing}\fi};% + \end{tikzpicture}% + \filltitle{7em}{}\\\vspace{2pt}% + 教学班级\filltitle{10.5em}{}\hfill% + 学生姓名\fillblank[8em][0.6cm]{}\hfill% + 学号\filltitle{8em}{}\hfill% + 考试日期\filltitle{16em}{\HFUT@KaoShiRiQi}\hfill% + 成绩\filltitle{6.3em}{}\vspace{4pt}% + } + \fancyfoot[C]{\small\vspace{0.5\baselineskip} + 第 \timesnewroman\thepage 页~共 \timesnewroman\pageref{LastPage} 页 + } +\fi +\ifHFUT@CanKaoDaAn%参考答案页眉页脚 + \fancyhead[C]{% + \bfseries\LARGE\titlesongti\ifdimcomp\ltitle>{0.6\linewidth}{\HFUT@BiaoTi}{\makebox[0.6\linewidth][s]{\HFUT@BiaoTi}}\\\vspace{5pt}% + \large\timesnewroman\HFUT@XueNians\titlefangsong~\timesnewroman\HFUT@XueNiane\titlefangsong 学年第\filltitle{2em}{\HFUT@XueQi}学期\hfill% + 课程代码\filltitle{6.5em}{\HFUT@KeChengDaiMa}\hfill% + 课程名称\filltitle{13em}{\HFUT@KeChengMingCheng}\hfill% + 命题教师\filltitle{7em}{\HFUT@MingTiJiaoShi}\hfill% + 系主任审批% + \begin{tikzpicture}[overlay,xshift=3.5em,yshift=0.2cm]% + \node at (0,0) {\ifx\HFUT@XiZhuRenQianMing\@empty\else\includegraphics[height=0.9cm]{\HFUT@XiZhuRenQianMing}\fi};% + \end{tikzpicture}% + \filltitle{7em}{}\\\vspace{2pt}% + 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+\newcommand\tigan[1]{\noindent{\large\textbf{#1}}} +% 打分栏 +\RequirePackage{tikz} +\usetikzlibrary{overlay-beamer-styles} +\newcommand\scorebox{% + \vspace{0.5\baselineskip}\noindent% + \begin{tikzpicture}[overlay,xshift=13.8cm,yshift=-1.6cm]% + \draw (0,0) rectangle (3.6,2);% + \draw (1.8,0)--(1.8,2);% + \draw (0,1)--(3.6,1);% + \draw (0.9,1.5) node {\textbf{\normalsize 得分}};% + \draw (2.7,1.5) node {\textbf{\normalsize 阅卷人}};% + \end{tikzpicture}% +} +% 答题纸提示信息 +\newcommand\notice{% + \noindent\textbf{\small 考生注意事项:\\% + \indent 1. 本试卷分试题与答卷两部分;\\% + \indent 2. 所有试题的解答(包括选择、填空)必须写在专用答卷纸上,在试题上直接作答一律无效;\\% + \indent 3. 考试结束后,必须将试题、答卷整理上交,不得将试题带离考场;\\% + \indent 4. 考生务必认真填写班级、姓名、学号等信息。}\par% + {\leavevmode\xleaders\hbox{\rule[4pt]{8pt}{0.5pt}\,}\hfill\null}% +} +% 选择题, 根据选项内容长度自动排版 +\newlength{\lxxmax} +\newlength{\lquar} +\newlength{\lhalf} +\newlength{\lfull} +\newcounter{lxxtype} +\NewDocumentCommand\xx{O{0} m m m m}{% + \setlength{\lfull}{\columnwidth}% + \addtolength{\lfull}{-\leftmargin}% + \setlength{\lhalf}{0.5\lfull}% + \setlength{\lquar}{0.25\lfull}% + \setcounter{lxxtype}{0}% + \ifnum#1=1\setcounter{lxxtype}{1}\fi% + \ifnum#1=2\setcounter{lxxtype}{2}\fi% + \ifnum#1=4\setcounter{lxxtype}{4}\fi% + \settowidth{\lxxmax}{A.~#2~}% 获取最长选项长度 + \settowidth{\ltemp}{B.~#3~}% + \ifdimcomp\ltemp>\lxxmax{\setlength{\lxxmax}{\ltemp}}{}% + \settowidth{\ltemp}{C.~#4~}% + \ifdimcomp\ltemp>\lxxmax{\setlength{\lxxmax}{\ltemp}}{}% + \settowidth{\ltemp}{D.~#5~}% + \ifdimcomp\ltemp>\lxxmax{\setlength{\lxxmax}{\ltemp}}{}% + \ifnum\value{lxxtype}=0% + \setcounter{lxxtype}{4}% + \ifdimcomp\lxxmax>\lquar{\setcounter{lxxtype}{2}}{}% + \ifnum\value{lxxtype}=2% + \ifdimcomp\lxxmax>\lhalf{\setcounter{lxxtype}{1}}{}% + \fi% + \fi% + \vspace{5pt}% + \ifnum\value{lxxtype}=1% + \\\makebox[\lfull][l]{A.~#2}% + \\\makebox[\lfull][l]{B.~#3}% + \\\makebox[\lfull][l]{C.~#4}% + \\\makebox[\lfull][l]{D.~#5}% + \fi% + \ifnum\value{lxxtype}=2% + \\\makebox[\lhalf][l]{A.~#2}% + \makebox[\lhalf][l]{B.~#3}% + \\\makebox[\lhalf][l]{C.~#4}% + \makebox[\lhalf][l]{D.~#5}% + \fi% + \ifnum\value{lxxtype}=4% + \\\makebox[\lquar][l]{A.~#2}% + \makebox[\lquar][l]{B.~#3}% + \makebox[\lquar][l]{C.~#4}% + \makebox[\lquar][l]{D.~#5}% + \fi% +} +% 选择题答题框 +\newcommand\xuanzeti[2]{% + \begin{tikzpicture}% + \draw (0,0) rectangle (1.8,2);% + \draw (0,1)--(1.8,1);% + \draw (0.9,0.5) node {#2} (0.9,1.5) node {\textbf{#1}};% + \end{tikzpicture}% +} +% 得分点命令 +% https://ask.latexstudio.net/ask/question/7557.html +\RequirePackage{zref-savepos} +\makeatletter +\ExplSyntaxOn +\zref@require@unique +\NewDocumentCommand{\examscore}{O{} m}{ + \mode_if_math:TF + { \@@_math_cdotfill:n {\text{#2}} } + { \__examzh_cdotfill: #2 } + \mode_if_math:F{ + \ignorespaces + } +} +\cs_new:Npn \__examzh_cdotfill: +{ + \mode_leave_vertical: + \cleaders \hb@xt@ .44em {\hss $\cdot$ \hss} \hfill + \kern\z@ +} +\cs_new_protected:Npn \@@_math_cdotfill:n #1 +{ + \stepcounter { zref@unique } + \hbox_overlap_right:n + { + \zsaveposx { \thezref@unique L } + \zref@ifrefundefined { \thezref@unique R } + { } + { + \cleaders + \hbox_to_wd:nn { .44em } { \hss $\cdot$ \hss } + \skip_horizontal:n + { + \zposx { \thezref@unique R } sp + - \zposx { \thezref@unique L } sp + } + } + } + \tag * { \zsaveposx { \thezref@unique R } #1 } +} +\ExplSyntaxOff +\makeatother +\newcommand\Score[1]{~~~\examscore{#1}} +\newcommand\score[1]{~~~\examscore{(#1分)}} +\renewcommand\le{\leqslant} +\renewcommand\ge{\geqslant} + diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check index a85dbe3b6d3..92cd36d19c2 100755 --- a/Master/tlpkg/bin/tlpkg-ctan-check +++ b/Master/tlpkg/bin/tlpkg-ctan-check @@ -396,7 +396,7 @@ my @TLP_working = qw( hep-math hep-math-font hep-paper hep-reference hep-text hep-title hepnames hepparticles hepthesis hepunits here hereapplies heros-otf hershey-mp heuristica hexboard hexgame - hf-tikz hfbright hfoldsty hfutthesis + hf-tikz hfbright hfoldsty hfutexam hfutthesis hhtensor hideanswer highlightlatex hindawi-latex-template hindmadurai histogr historische-zeitschrift hitec hitreport hitszthesis hitszbeamer hithesis diff --git a/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc b/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc index fb211a273d5..3d7d50809b4 100644 --- a/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc +++ b/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc @@ -89,6 +89,7 @@ depend hagenberg-thesis depend har2nat depend hecthese depend hep-paper +depend hfutexam depend hfutthesis depend hithesis depend hitszthesis diff --git a/Master/tlpkg/tlpsrc/hfutexam.tlpsrc b/Master/tlpkg/tlpsrc/hfutexam.tlpsrc new file mode 100644 index 00000000000..e69de29bb2d --- /dev/null +++ b/Master/tlpkg/tlpsrc/hfutexam.tlpsrc |