\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{Aurora}
\pdfinfo{
  /Title (matte-s1-22.pdf)
  /Creator (Cheatography)
  /Author (Aurora)
  /Subject (Matte S1,22 Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{84BDD9}
\definecolor{LightBackground}{HTML}{EFF6FA}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Matte S1,22 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Aurora} via \textcolor{DarkBackground}{\uline{cheatography.com/143081/cs/31687/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Aurora \\
  \uline{cheatography.com/aurora} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 20th May, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Potenser og Logaritmer}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{1.1  -  Potenser}} \newline % Row Count 1 (+ 1)
{\emph{Regneregel}} \newline % Row Count 2 (+ 1)
Potenser er når et tall er opphøyd i et annet. Det kan for eksempel være 5\textasciicircum{}3\textasciicircum{}. I eksempelet er 3 eksponenten og 5 er grunntallet. Eksponenten viser hvor mange ganger grunntallet skal gange med seg selv. 5\textasciicircum{}3\textasciicircum{}= 5 5 5 = 125. Man bruker multiplikasjons med potenser når de er to potenser er ganget sammen, men om to potenser er delt på hverandre bruker vi divisjon. Med divisjon kan man stryke over det samme tallet både under og over. Når det kommer til brøk med potenser så kan man også ta å subtrahere eksponentene med hverandre, eks 5\textasciicircum{}3-2\textasciicircum{}= 5. Svaret vil bli det samme. \newline % Row Count 14 (+ 12)
{\emph{Regnerekkefølge:}} \newline % Row Count 15 (+ 1)
(-4)\textasciicircum{}2\textasciicircum{}= 16 -{}-\textgreater{} -4 ganger -4 = 16 (minus + minus = pluss) \newline % Row Count 17 (+ 2)
-4\textasciicircum{}2\textasciicircum{}= -16 -{}-\textgreater{} -4 ganger 4 = -16 (minus + pluss = minus) \newline % Row Count 19 (+ 2)
{\emph{Potenser med produkt, brøk eller potens som grunntall}} \newline % Row Count 21 (+ 2)
Produkt som grunntall: (a * b) = a\textasciicircum{}n\textasciicircum{} * b\textasciicircum{}n\textasciicircum{} \newline % Row Count 22 (+ 1)
Brøk som grunntall: (a/b)\textasciicircum{}n\textasciicircum{} = a\textasciicircum{}n\textasciicircum{}/b\textasciicircum{}n\textasciicircum{} \newline % Row Count 23 (+ 1)
Potens som grunntall: (a\textasciicircum{}m\textasciicircum{})\textasciicircum{}n\textasciicircum{} = a\textasciicircum{}m*n\textasciicircum{} \newline % Row Count 24 (+ 1)
{\emph{Når eksponenten er null eller negativ}} \newline % Row Count 25 (+ 1)
Når eksponenten er null, ved for eksempel a\textasciicircum{}2\textasciicircum{}/a\textasciicircum{}2\textasciicircum{} = a\textasciicircum{}2-2\textasciicircum{}= a\textasciicircum{}0\textasciicircum{}, så når eksponenten blir null, betyr det at svaret vil bli 1, vi definerer at eksponenten, som er null, blir 1. \newline % Row Count 29 (+ 4)
{\emph{a\textasciicircum{}0\textasciicircum{} = 1}} \newline % Row Count 30 (+ 1)
} \tn 
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Potenser og Logaritmer (cont)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Når eksponenten er minus, ved for eksempel a\textasciicircum{}2\textasciicircum{}/a\textasciicircum{}5\textasciicircum{} = a\textasciicircum{}2-5\textasciicircum{} = a\textasciicircum{}-3\textasciicircum{}, så for at a\textasciicircum{}-3\textasciicircum{} skal ha samme verdi som1/a\textasciicircum{}3\textasciicircum{}, definerer vi at a\textasciicircum{}-n\textasciicircum{} = 1/a\textasciicircum{}n\textasciicircum{} \newline % Row Count 4 (+ 4)
{\emph{Tall på standarform}} \newline % Row Count 5 (+ 1)
10\textasciicircum{}2\textasciicircum{} = 100 \newline % Row Count 6 (+ 1)
10\textasciicircum{}1\textasciicircum{} = 10 \newline % Row Count 7 (+ 1)
10\textasciicircum{}0\textasciicircum{} = 1 \newline % Row Count 8 (+ 1)
10\textasciicircum{}-1\textasciicircum{} = 0,1 \newline % Row Count 9 (+ 1)
10\textasciicircum{}-2\textasciicircum{} = 0.01 \newline % Row Count 10 (+ 1)
eks: 5,4 * 10\textasciicircum{}3\textasciicircum{} = 5,4 * 1000 = 5400.% Row Count 11 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Funksjonsdrøfting og optimalisering}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 0 (+ 0)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Funksjoner}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 0 (+ 0)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Sannsynlighet}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 0 (+ 0)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Derivasjon}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 0 (+ 0)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}