\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{Jianmin Feng (taotao)}
\pdfinfo{
  /Title (psat-math-ch11-adv-principles.pdf)
  /Creator (Cheatography)
  /Author (Jianmin Feng (taotao))
  /Subject (PSAT MATH Ch11 Adv Principles 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}{076921}
\definecolor{LightBackground}{HTML}{F7FAF8}
\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{PSAT MATH Ch11 Adv Principles Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Jianmin Feng (taotao)} via \textcolor{DarkBackground}{\uline{cheatography.com/79308/cs/20436/}}}
\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}Jianmin Feng (taotao) \\
  \uline{cheatography.com/taotao} \\
  \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 1st September, 2019.\\
   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{2.09034 cm} x{2.88666 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Function}}  \tn
% Row 0
\SetRowColor{LightBackground}
function f(x) & solve the equation x-{}-\textgreater{}y \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
 & PITA \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
 & f(g(x)) \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
 & problem =\textgreater{}write function \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Roots of a Function (x) & x intercept (graph cross x-axis) \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
 & x =\textgreater{} f(x)=0 \tn 
% Row Count 9 (+ 1)
% Row 6
\SetRowColor{LightBackground}
 & factor of a question \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.69218 cm} x{3.28482 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Quadratic Equations}}  \tn
% Row 0
\SetRowColor{LightBackground}
expanding & FOIL: First Outer Inner Last \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
factoring & factor constant/multiply, calc coefficent/add \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
 & PITA \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
solving & f(x)=zero=\textgreater{}factoring=\textgreater{}zero factor \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
 & PITA \tn 
% Row Count 8 (+ 1)
% Row 5
\SetRowColor{white}
 & ( -b +/ sqrt(b\textasciicircum{}2\textasciicircum{} -4ac)) / 2a \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
 & graph the equation \tn 
% Row Count 11 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{other quadratics problems} \tn 
% Row Count 12 (+ 1)
% Row 8
\SetRowColor{LightBackground}
 & word question \tn 
% Row Count 13 (+ 1)
% Row 9
\SetRowColor{white}
 & charts question (build equation, plug in point) \tn 
% Row Count 15 (+ 2)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{forms of quadratic} \tn 
% Row Count 16 (+ 1)
% Row 11
\SetRowColor{white}
std form & y = ax\textasciicircum{}2\textasciicircum{} + bx + c \tn 
% Row Count 17 (+ 1)
% Row 12
\SetRowColor{LightBackground}
vertex (h,k), min/max & y = a(x − h)\textasciicircum{}2 \textasciicircum{}+ k \tn 
% Row Count 19 (+ 2)
% Row 13
\SetRowColor{white}
a & parabola opening up for positive a \tn 
% Row Count 21 (+ 2)
% Row 14
\SetRowColor{LightBackground}
std\textless{}=\textgreater{}vertex & y = x\textasciicircum{}2\textasciicircum{} – 4x – 12 \tn 
% Row Count 22 (+ 1)
% Row 15
\SetRowColor{white}
1) zero, move & 0 =  x\textasciicircum{}2\textasciicircum{} – 4x – 12 =\textgreater{}  12=  x\textasciicircum{}2\textasciicircum{} – 4x \tn 
% Row Count 24 (+ 2)
% Row 16
\SetRowColor{LightBackground}
2)add half sq & 12+4=  x\textasciicircum{}2\textasciicircum{} – 4x +4 \tn 
% Row Count 25 (+ 1)
% Row 17
\SetRowColor{white}
3)sq form & 16=  (x-2)\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 26 (+ 1)
% Row 18
\SetRowColor{LightBackground}
4)vextex & y=  (x-2)\textasciicircum{}2\textasciicircum{} -16 \tn 
% Row Count 27 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Anaysis in Science: question in scientific context}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{world problem: identify the variable} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{chart/graph/table related} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{scientific situation ==\textgreater{} conclusion, POE strategy} \tn 
% Row Count 3 (+ 1)
\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}{Meaning in context}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Plugin number to see} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{POE} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{math concept: intercept, slope, and coefficients} \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{SUMMARY}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{1 Given a function, you put an x value in and get an f(x) or y value out. \newline % Row Count 2 (+ 2)
2 Look for ways to use Plugging In and PITA on function questions. \newline % Row Count 4 (+ 2)
3 For questions about the graphs of functions, remember that f(x) = y. \newline % Row Count 6 (+ 2)
4 If the graph contains a labeled point or the question gives you a point, plug it into the equations in the answers and eliminate any that aren't true. \newline % Row Count 10 (+ 4)
5 To find a point of intersection, set the equations equal, plug a given point into both equations to see if it works, or graph the equations on your calculator when it is allowed.% Row Count 14 (+ 4)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{SUMMARY - quadratic equation}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{6 When solving quadratic equations, you may need to FOIL or factor to get the equation into the easiest form for the question task. \newline % Row Count 3 (+ 3)
7 To solve for the roots of a quadratic equation, set it equal to zero by moving all the terms to the left side of the equation, or use the quadratic formula: \newline % Row Count 7 (+ 4)
8 The vertex form of a parabola equation is y = a(x – h)2 + k, where (h, k) is the vertex. To get a parabola in the standard form into vertex form, complete the square. \newline % Row Count 11 (+ 4)
9 Plugging In can also be used on Meaning In Context questions. If a question asks you to identify a part of an equation, plug your own amounts into the equation so you can start to see what is going on. \newline % Row Count 16 (+ 5)
10 Analysis in Science questions may seem weird, but they can usually be handled with the same strategies as those used for other math questions. Plug In or translate, read the chart or text carefully, and always use Process of Elimination to get rid of answers that don't match the data or don't make sense. \newline % Row Count 23 (+ 7)
11 If you come across a hard Meaning in Context question or Science question, see if you can eliminate anything and make a guess. If not, find another question to do!% Row Count 27 (+ 4)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}