19/12/2025
Good morning!...
តណភ្ជាប់ link : https://t.me/lysarith168/5195
#ឡាតិច
\documentclass[12pt,a4paper]{article}
%%%::::::::::::::::::::::::::::::::::::::: គែមក្រដាស
\usepackage[left=1.5cm,right=1.5cm,top=2.2cm,bottom=1.5cm]{geometry}
%%%::::::::::::::::::::::::::::::::::::::: គណិត
\usepackage{euler}
\everymath{\displaystyle}
\usepackage{pifont,mathtools,amsmath,amssymb,fontawesome }
%%::::::::::::::::::::::::::::::::::::::: រូបខាងក្រោមកិច្ចការ
\usepackage{pgfornament}
%%%::::::::::::::::::::::::::::::::::::::: ប្រអប់
\usepackage[most]{tcolorbox}
\usepackage{tikz,multicol,tkz-tab}
%%%::::::::::::::::::::::::::::::::::::::: រចនា
\usetikzlibrary{calc,shapes,shadows.blur}
%%%::::::::::::::::::::::::::::::::::::::: គម្លាតចុះ
\usepackage{setspace}
\setstretch{.8}
%%%::::::::::::::::::::::::::::::::::::::: អក្សរខ្មែរ
\usepackage{fontspec}
\setmainfont[Scale =.83,Script=Khmer,AutoFakeBold=2.5]{Kh Preyveng}
%%%::::::::::::::::::::::::::::::::::::::: តាងពុម្ពអក្សរ
\newcommand{\kml}{\fontspec[Scale=.83, Script=Khmer]{Khmer OS Muol Light}\selectfont}
\newcommand{\kbk}{\fontspec[Scale=.83, Script=Khmer]{Khmer OS Bokor}\selectfont}
\newcommand{\en}{\fontspec{Times New Roman}\selectfont}
%%%::::::::::::::::::::::::::::::::::::::: អក្សរខ្មែរកំណត់តាម geometry
\XeTeXlinebreaklocale "kh"
\XeTeXlinebreakskip=0pt plus 1pt minus .5pt
%%%::::::::::::::::::::::::::::::::::::::: លេខរៀង
\usepackage{enumerate}
\usepackage{enumitem}
%%%::::::::::::::::::::::::::::::::::::::: លេខរៀង--លេខខ្មែរ--និង អក្សរខ្មែរ
\makeatletter
\def\ #1{\expandafter\@\number #1\}
\def\@ #1{
\ifx #1\
\else
\char\numexpr #1+"17E0\relax
\expandafter\@\fi
}
\def\knum #1{\expandafter\\csname c@ #1\endcsname}
\def\khmernumeral #1{\@ #1\}
\AddEnumerateCounter{\knum}{\}{}
\makeatother
\makeatletter
\newcommand*{\kalph}[1]{
\expandafter\\csname c@ #1\endcsname
}
\newcommand*{\}[1]{
\ifcase #1\or ក\or ខ\or គ\or ឃ\or ង\or ច\or ឆ\or ជ\or ឈ\or ញ\or
ដ\or ឋ\or ឌ\or ឍ\or ណ\or ត\or ថ\or ទ\or ធ\or ន\or ប\or ផ\or ព\or
ភ\or ម\or យ\or រ\or ល\or វ\or ស\or ហ\or ឡ\or អ
\else\\fi
}
\AddEnumerateCounter{\kalph}{\}{}
\makeatother
%%%::::::::::::::::::::::::::::::::::::::: លេខរៀងរង្វង់
\newcommand{\ly}[1]{\tikz[overlay,xshift=-10pt,baseline=-6pt]\node[circle,draw=blue,inner sep=1.5pt]{ #1};}
%%%::::::::::::::::::::::::::::::::::::::: លេខរៀងរង្វង់មានផ្ទៃ
\newcommand{\sa}[1]{\tikz[overlay,xshift=-10pt,baseline=-6pt]\node[circle,draw=blue,inner sep=1.5pt,fill=col1]{\color{white} #1};}
%%%::::::::::::::::::::::::::::::::::::::: លេខរៀងការេមានស្រមោល
\newcommand{\rith}[1]{\tikz[overlay,xshift=-11pt,baseline=-4pt]\node[
drop shadow={fill=col1,opacity=2,shadow xshift=.5mm,shadow yshift=.5mm},fill=col1,rectangle,draw=black,line width=1pt,inner sep=1.5pt]{\color{white} #1};}
%%%::::::::::::::::::::::::::::::::::::::: ពុះអត្ថបទ ( multicols )
\SetEnumitemKey{2}{before=\raggedcolumns\setlength{\multicolsep}{\topsep}\begin{multicols}{2},after=\end{multicols}}
\SetEnumitemKey{3}{before=\raggedcolumns\setlength{\multicolsep}{\topsep}\begin{multicols}{3},after=\end{multicols}}
\SetEnumitemKey{4}{before=\raggedcolumns\setlength{\multicolsep}{\topsep}\begin{multicols}{4},after=\end{multicols}}
%%%::::::::::::::::::::::::::::::::::::::: ទំព័រទទេ
\pagestyle{empty}
%%%::::::::::::::::::::::::::::::::::::::: បាតលើក្រោម
\newcommand{\LySarith}[1][]{}
\AddToHook{shipout/foreground}{\begin{tikzpicture}[remember picture,overlay]
\fill[col1!50] (current page.north east)--(current page.north west)-- ([yshift=-20mm]current page.north west) [out=0,in=180]to ([yshift=-6mm]current page.north east)--cycle;%::::ស្រមោលបាតលើ
\fill[col1] (current page.north east)--(current page.north west)--([yshift=-19mm]current page.north west) [out=2,in=180]to ([yshift=-2mm]current page.north east)--cycle;%::::បាតលើ
\fill[rounded corners=5mm,col1] (current page.south west)--($(current page.south west)+(0.5cm,0.5)$)--($(current page.south east)+(-.5cm,.5)$) node[fill=col1,draw=col1,text=white,trapezium stretches,rounded corners=11pt,minimum height=.8cm,minimum width=2.5cm,sloped,pos=.15] at (0,2){{\kbk ទំព័រទី}~~$\thepage$}--(current page.south east);%::::បាតក្រោម
\node[font=\large,right,white] at ($(current page.north west)+(.9,-.8)$){\LySarith};
\ifnum\value{page}=1
\else\fi
\end{tikzpicture}}
\renewcommand\LySarith{\includegraphics[scale=.39]{Logo math 4 you .png} $Math ~4~ You$}
%%%::::::::::::::::::::::::::::::::::::::: ប្រអប់ប្រធានលំហាត់
\definecolor{col1}{HTML}{008ca5}
\newtcolorbox{lysarith}[1][]{drop shadow=blue,toprule=1pt,
colback=white,breakable,enhanced,title=\kbk{ភាពជោគជ័យគ្មានដានជើងមនុស្សខ្ជិលទេ},
attach boxed title to top right={yshift=-4mm},top=5mm,colframe=col1,arc=0mm,sharp corners,boxed title style={interior hidden, frame code={\fill[col1] ([yshift=-5mm] frame.south east) [out=10,in=270]to
([xshift=3mm,yshift=-3mm]frame.east)--([xshift=3mm,yshift=0mm]frame.east) [out=90,in=0]to (frame.north east) --(frame.north west)--([xshift=-4mm]frame.west)--(frame.south west)--(frame.south east) [out=350,in=0]to cycle;
}},overlay unbroken and first={\def\wid{6cm}
\ifthenelse{\equal{ #1}{}}{}{
\node[text width=\wid,anchor=west,minimum height=7mm,font=\kbk,text=white] (framee) at (interior.north west){\kbk{ #1}};
\fill[col1]([yshift=-5mm]framee.south west) [out=170,in=270]to
([xshift=-3mm,yshift=-3mm]framee.west)--([xshift=-3mm,yshift=0mm]framee.west) [out=90,in=180]to (framee.north west)--(framee.north east)--([xshift=-4mm]framee.east)--(framee.south east)-- (framee.south west) [out=190,in=170]to cycle;
\node[text width=\wid,anchor=west,minimum height=7mm,font=\kbk,text=white] at (interior.north west){\kbk{ #1}};
}}}
%%%::::::::::::::::::::::::::::::::::::::: ប្រអប់ដំណោះស្រាយ
\newtcolorbox{LYSARITH}[1][]{drop shadow=blue,colback=white,enhanced,title={\color{white}\Large\faPencilSquareO
},attach boxed title to top right={yshift=-3mm},breakable,top=5mm,colframe=col1,arc=0mm,sharp corners,
,overlay unbroken and first={\def\wid{3cm}
\ifthenelse{\equal{ #1}{}}{}{
\node[text width=\wid,anchor=west,minimum height=.7mm,font=\kbk,text=white] (framee) at (interior.north west){\kbk{ #1}};
\fill[col1]([yshift=-5mm]framee.south west) [out=170,in=270]to
([xshift=-3mm,yshift=-3mm]framee.west)--([xshift=-3mm,yshift=0mm]framee.west) [out=90,in=180]to (framee.north west)--(framee.north east)--([xshift=-4mm]framee.east)--(framee.south east)--(framee.south west) [out=190,in=170]to cycle;
\node[text width=\wid,anchor=west,minimum height=7mm,font=\kbk,text=white] at (interior.north west){\kbk{ #1}};}}}
%%%::::::::::::::::::::::::::::::::::::::: បន្ទាត់ក្នុងចម្លើយ
\usepackage{pgffor,ifthen}
\newcommand{\Rith}[3][\empty]{
\noindent\vspace{10pt}\\
\foreach \n in {1,..., #2}{
\ifthenelse{\equal{ #1}{\empty}}
{\rule{ #3}{0.5pt}\\}
{\rule{ #3}{0.5pt}\vspace{ #1}\\}}}
\begin{document}
\begin{center}
\tcbox[enhanced,size=fbox,colback=col1,colframe=green,drop lifted shadow,arc=17pt,outer arc=13pt]{~~\Large\kml \color{white} ប្រឡងប្រចាំខែធ្នូ~~}
\end{center}
\begin{lysarith}[{~\color{yellow}$I.$}\quad\kml កុំផ្លិច \hspace*{2.5cm}២០ពិន្ទុ]
ចូរគណនាផលបូកនិងផលដកនៃចំនួនកុំផ្លិចខាងក្រោម៖
\begin{enumerate}[label=\protect\sa{$\arabic*$}.,2]
\item$ \left(\dfrac{10}{7}+\dfrac{1}{3}i\right)+\dfrac{5}{7}i $
\item$ \left(\dfrac{1}{7}+i\right)-\left(-2-\dfrac{3}{5}i\right) $
\item $\left(\dfrac{1}{2}+i\right)+\left(\dfrac{3}{4}+\dfrac{1}{2} i\right)$
\item$ -\left(\dfrac{9}{4}-\dfrac{9}{4} i\right)+\left(\dfrac{3}{7}-\dfrac{1}{5} i\right) $
\item$ \sqrt{2}i-\left(-\dfrac{1}{\sqrt{2}}+\dfrac{\sqrt{2}}{2}i\right) $
\item$ \dfrac{5}{\sqrt{5}}-\dfrac{\sqrt{2}}{4}i\left(1+\sqrt{5}i\right) $
\item$ (2+2i)-\dfrac{2}{\sqrt{2}}\left(\sqrt{2}-68i\right) $
\item$ \left(\sqrt{3}-\sqrt{5}i\right)+ \left(\sqrt{3}+\sqrt{5}i\right) $
\end{enumerate}
\end{lysarith}
\begin{lysarith}[{~\color{yellow}$II.$}\quad\kml ធរណីមាត្រ \hspace*{1cm}១៥ពិន្ទុ]
នៅក្នុងតម្រុយអរតូណរម៉ាល់ $\left(O,\overrightarrow{i},\overrightarrow{j},\overrightarrow{k}\right)$ ដែលមានទិសដៅវិជ្ជមាន។ គេឲ្យចំណុច $A(1,1,3)\;;\;B(3,3,3)$ និង $C(-1,0,-2)$\;។
\begin{enumerate}[label=\kbk\protect\sa{\kalph*}.]
\item សរសេរកូអរដោនេនៃវ៉ិចទ័រ $\overrightarrow{AB}\;;\;\overrightarrow{AC}\;;\;\overrightarrow{BC}$ ជាទម្រង់វ៉ិចទ័រឯកតា\;។
\item រកទំហំនៃវ៉ិចទ័រ $\overrightarrow{AB}\;;\;\overrightarrow{AC}\;;\;\overrightarrow{BC}$ ខ្នាតគិតជា $(dm)$\;។
\item រកកូអរដោនេចំណុចកណ្ដាលនៃវ៉ិចទ័រ $\overrightarrow{AB}\;;\;\overrightarrow{AC}\;;\;\overrightarrow{BC}$\;។
\end{enumerate}
\end{lysarith}
\begin{lysarith}[{~\color{yellow}$III.$}\quad\kml អនុគមន៍ \hspace*{1cm}៣៥ពិន្ទុ]
គេមានអនុគមន៍ $f $ កំណត់ដោយ $f(x)=\dfrac{2x-4}{x^2-4x-5}$\;។ យើងតាងដោយ $(C)$ ជាក្រាបរបស់វាលើតម្រុយអរតូណរម៉ាល់ $\left(0,\overrightarrow{i},\overrightarrow{j}\right)$\;។
\begin{enumerate}[label=\kbk\protect\sa{\knum*}.]
\item រកដែនកំណត់ $D$ នៃអនុគមន៍ $f$\;។
\item សិក្សាលីមីត $\lim_{x\to\;-2} f(x)\;,\;\lim_{x\to\;5} f(x)$ \;,\; $\lim_{x\to-\infty} f(x)$ និង $\lim_{x\to+\infty}f(x)$ \;។
\item ទាញបញ្ជាក់សមីការអាស៊ីមតូតឈរ និងអាស៊ីមតូតដេកនៃក្រាប $(C)$\;។
\item ចូរស្រាយបញ្ជាក់ថា $\forall x\in D : f'(x)= -\dfrac{2(x^2-4x+13)}{(x^2-4x-5)^2}$\;។
\item សិក្សាអថេរភាពនៃអនុគមន៍ $f$ និងសង់តារាងអថេរភាពនៃអនុគមន៍ $f$\;។
\item សង់ក្រាប $(C)$ នៃអនុគមន៍ $f$\;។
\end{enumerate}
\end{lysarith}
\begin{LYSARITH}[\color{white}\kml ដំណោះស្រាយ]
\Rith[10pt]{155}{\textwidth}
\end{LYSARITH}\vskip2.5cm
\begin{center}
{\color{blue}\pgfornament[scale=1]{97}}
\color{col1}\large{\kml សូមសំណាងល្អណា!...}
{\color{blue}\pgfornament[scale=1]{98}}\\
\pgfornament[scale=.25]{85}
\end{center}
\end{document}
%%%::::::::::::::::::::::::::::::::::: លេខរៀង
label=\arabic* : លេខរៀង 1 2 3...
label=\knum* : លេខរៀង ១ ២ ៣...
label=\kalph* : លេខរៀង ក ខ គ...
label=\alph* : លេខរៀង a b c ...
label=\Alph* : លេខរៀង A B C...
label=\Roman* : លេខរៀង I II III...
label=\roman* : លេខរៀង i ii iii...
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