\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{bendystraw}
\pdfinfo{
  /Title (pre-calc.pdf)
  /Creator (Cheatography)
  /Author (bendystraw)
  /Subject (Pre Calc 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}{7DA36F}
\definecolor{LightBackground}{HTML}{F6F9F6}
\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{Pre Calc Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{bendystraw} via \textcolor{DarkBackground}{\uline{cheatography.com/38297/cs/11944/}}}
\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}bendystraw \\
  \uline{cheatography.com/bendystraw} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 28th May, 2017.\\
   Updated 29th May, 2017.\\
   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*}{2}

\begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Sequences}}  \tn
% Row 0
\SetRowColor{LightBackground}
Arithmetic Sequence & An = A1 + D(n - 1) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Geometric Sequence & An = A1(r\textasciicircum{}n-1\textasciicircum{}) \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Finite Sum & Sn = A1(1 - r\textasciicircum{}n\textasciicircum{}) / 1 - r \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
Infinite Sum (|r| \textless{} 1) & A1 / 1 - r \tn 
% Row Count 7 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{1.6 cm} x{6.4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Volumes}}  \tn
% Row 0
\SetRowColor{LightBackground}
Sphere & V = (4/3)πr\textasciicircum{}2\textasciicircum{}\{\{nl\}\}A = 4πr\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Cone & V = (1/3)πr\textasciicircum{}2\textasciicircum{}h \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Pyramid & V = (1/3)bh \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\seqsplit{Cylinder} & πr\textasciicircum{}2\textasciicircum{}h \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.08 cm} x{5.92 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Sin/Cos}}  \tn
% Row 0
\SetRowColor{LightBackground}
Law of Cosines & c\textasciicircum{}2\textasciicircum{} = a\textasciicircum{}2\textasciicircum{}+b\textasciicircum{}2\textasciicircum{}-2ab(cos(C)) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Arc Length & L = rθ \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Double angle: & sin2x = 2cosxsinx\{\{nl\}\}cos2x = cos\textasciicircum{}2\textasciicircum{}x - sin\textasciicircum{}2\textasciicircum{}x\{\{nl\}\}cos2x = 2cos\textasciicircum{}2\textasciicircum{}x - 1\{\{nl\}\}cos2x = 1 - 2sin\textasciicircum{}2\textasciicircum{}x\{\{nl\}\}tan2x = 2tanx / 1 - tan\textasciicircum{}2\textasciicircum{}x \tn 
% Row Count 8 (+ 5)
% Row 3
\SetRowColor{white}
Half angle: & sinx/2 = +/- sqrt((1 - cosx) / 2)\{\{nl\}\}cosx/2 = +/- sqrt((1 + cosx) / 2)\{\{nl\}\}tanx/2 = +/- sqrt((1 - cosx) / (1 + cosx))\{\{nl\}\}tanx/2 = (1 - cosx) / sinx \tn 
% Row Count 14 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Vertical line test}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{If a vertical line intersects a supposed function at two different points, it is not a function.% Row Count 2 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2 cm} x{6 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Probability}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Combinations:} & Order doesn't matter\{\{nl\}\}8c5 = 8! / (8-5)!5! \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\seqsplit{Permutations:} & Order matters\{\{nl\}\}8p5 = 8! / 5! \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\seqsplit{Probability:} & P(A and B) = P(A) * P(B)\{\{nl\}\}P(A or B) = P(A) + P(B) - P(A and B)\{\{nl\}\}If A and B are mutually exclusive:\{\{nl\}\}P(A or B) = P(A) + P(B) \tn 
% Row Count 9 (+ 5)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4.08 cm} x{3.92 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Coordinates}}  \tn
% Row 0
\SetRowColor{LightBackground}
Point-slope form & y - y1 = m(x - x1) \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Vertex of parabola: & x = -b/2a \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.44 cm} x{4.56 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Parabola}}  \tn
% Row 0
\SetRowColor{LightBackground}
Vertex & (h, k) \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Focus & (h, k +/- p) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Directrix & y = k - p \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.6 cm} x{4.4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Ellipse}}  \tn
% Row 0
\SetRowColor{LightBackground}
Center & (h, k) \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Vertices & (h, k +/- a) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Foci & (h, k +/- c) \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
Major Axis & 2a \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Minor Axis & 2b \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.64 cm} x{5.36 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Hyperbola}}  \tn
% Row 0
\SetRowColor{LightBackground}
Center & (h, k) \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Vertices & (h, k +/- a) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Foci & (h, k +/- c) \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
Asymptotes & y = k +/- (a/b)(x-h) \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.08 cm} x{5.92 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Sin/Cos/Tangent equations}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Asin(Bx+C)+D} & A = Amplitude\{\{nl\}\}B = Period\{\{nl\}\}C = Phase shift\{\{nl\}\}D = Vertical shift \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
sin or cos(Bx) & Period = 2π/b \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
tan(Bx) & Period = π/b \tn 
% Row Count 6 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Binomial Theorum}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Image could not be loaded.} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{More binomial theorum}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/bendystraw_1496083588_binomial-n-choose-k.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}